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The Interaction Among Financial Intermediaries In The Money And Capital Markets: A Theoretical And Empirical Study

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The Interaction Among Financial Intermediaries In The Money And Capital Markets: A Theoretical And Empirical Study

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Content This dissertation has been microfilmed exactly as received 69-650 WATSON, William Roger, 1934- THE INTERACTION AMONG FINANCIAL INTER MEDIARIES IN THE MONEY AND CAPITAL MARKETS: A THEORETICAL AND EMPIRICAL STUDY. University of Southern California, Ph.D., 1968 Economics, theory University Microfilms, Inc,, Ann Arbor, Michigan THE INTERACTION AMONG FINANCIAL INTERMEDIARIES IN THE MONEY AND CAPITAL MARKETS: A THEORETICAL AND EMPIRICAL STUDY by William Roger Watson A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Economics) June 1968 UNIVERSITY O F SO U T H E R N CALIFORNIA TH E GRADUATE SCHOO L UNIVERSITY PARK LOS ANGELES. CA LIFO RN IA 9 0 0 0 7 This dissertation, written by ...... under the direction of / z . i s . . . Dissertation Com mittee, and approved by all its members, has been presented to and accepted by the Graduate School, in partial fulfillment of requirements for the degree of D O C T O R OF P H IL O S O P H Y Dean D ate . ^ . > . . 1 1 ^ 1.... DISSERTATION COMMITTEE TABLE OF CONTENTS CHAPTER PAGE ! I. INTRODUCTION.................................. 1 Scope and Purpose......................... 1 j The Portfolio Effect ....................... 5 A Preview of the Analysis................. 11 Methodological Questions ................... 18 [ The Organization of This Study............. 25 II. THE BACKGROUND............................... 29 j General Equilibrium ....................... 31 The Basic Model— The Consumer.......... 33 The homogeneity of the system........ 36 The Basic Model— Production ............. 37 The homogeneity of the system........ 39 The Complete System..................... 40 I The Introduction of Money into the System 45 Say's L a w ............................... 49 Conclusion................... 51 The Wealth Effect......................... 51 The Keynesian Critique of the Neoclassical Employment Theory ..................... 53 The Wealth Effect....................... 58 The Patinkin Controversy ................... 68 CHAPTER 1 PAGE The micro system....................... 76 The macro system....................... 83 The explicit and implicit money functions......................... 84 Invalidity I ......................... 87 Invalidity I I ....................... 87 The Pat inkin System..................... 91 The Critique of the Patinkin System . . . 101 The definition of consistency ........ 102 The interpretation of the money equations 103 The correct interpretation of the neoclassical system . 106 The Outcome of the Controversy.......... 118 Stock versus Flow Analysis................. 121 The Relation of Stocks to F l o w s........ 125 The Controversy over Stocks or Flows . . . 126 The New Stock-Flow Analysis............. 131 The interpretation of the "desired stock"............................... 135 The basic model— the consumer........ 137 The homogeneity of the system .... 141 The basic model— production.......... 141 The homogeneity of the system .... 144 The complete system................... 145 Walras1 Law and stock-flow analysis . 148 iii CHAPTER ( PAGE Later Developments in the Stock versus Plow Debate........................... 149 Patinkin's views on stock analysis versus flow analysis in monetary theory . . . 151 The argument against the equivalence of stock analysis and flow analysis . . . 154 A Digression on the Implications of Stock-Flow Analysis ................... 155 The Patinkin controversy ............... 155 The LP-LF debate.................... 155 Conclusion............................ 157 The Structure of Financial Markets and the Economically Relevant Components of Net Wealth............................ 160 What is Economically Relevant Wealth? . . 160 The Development of the Concept of Net Financial Wealth ....................... 163 The Gurley-Shaw m o d e l ............. 166 The process of intermediation ........ 167 The process of deposit creation .... 172 Inside versus outside money .......... 177 The implications of inside-outside money to the wealth effect, the dichotomy, and neutrality................... 179 iv CHAPTER PAGE Net money versus gross money doctrine . 183 A Different Conception of Net Financial Wealth............ 186 The Pesek-Saving thesis ............... 187 Commodity and fiat money . . '.... 187 Private money production ............... 189 Pure competition........... ,......... 189 Monopolistic competition ....... 190 Do non-monetary financial intermediaries create net wealth?................ 192 Conclusion............................ 194 The Approach............................ 196 Considerations of Portfolio Balance . . . 199 The optimum portfolio............. 199 The portfolio approach ................. 201 From an Operationally Meaningful to an Operationally Feasible Hypothesis . . . 201 : The problem............................ 203 III. THE THEORY................................ 209 The Mathematical Method Used........... 212 ! | The M o d e l .................................. 216 The Adjustment Process ................... 219 The Consumer Sector........ ° .......... 222 The utility function ................... 226 | The budget constraint ................. 234 CHAPTER PAGE Consumer equilibrium ................... 235 The Non-Financial Production Sector . . . 239 The decision function ................. 242 The quasi-profit function ............ 246 Non-financial producer equilibrium . . . 252 The Financial Production Sector ........ 255 The non-monetary intermediary sub-sector 257 The decision function ............... 258 The quasi-profit function .......... 258 NMI producer equilibrium......... 263 The monetary intermediary sub-sector . . 266 The decision function ............... 270 The quasi-profit function .......... 272 MI producer equilibrium......... 278 The Complete System..................... 284 The market functions ................... 289 Market equilibrium ..................... 293 Short run (weekly) equilibrium .... 294 Long run (full) equilibrium..... 296 Conclusion............................ 301 Appendix I Glossary of Symbols .......... 311 IV. AN APPLICATION OF THE THEORY............. 317 A Macro Model ..... ................... 318 The Goods and Services Market....... 322 vi CHAPTER PAGE The Labor Market...................... 325 The Money Market...................... 327 Solutions and Conclusion ................. 331 A Micro Model ............................. 339 The Equations ■ . . 341 Alternative Measures of Substitutability . 345 Conclusion............................ 359 V. ESTIMATION AND RESULTS.................... 362 Data Used and Definition of Variables . . . 364 Method of Estimation ....................... 367 Results and Interpretations ............... 373 Single Equation, Pooled Estimate— Demand Deposits............................ 376 Single Equation, Pooled Estimate— Time Deposits.................. 381 Single Equation, Pooled Estimate— Saving and Loan Association Shares....... 384 Conclusions............................ 387 The Portfolio Approach— The Evidence . . . 392 The Gurley-Shaw Hypothesis— The Evidence . 393 Appendix I Single Equation Ordinary Least Squares Estimates "Portfolio Approach" Stock Demand Functions Cross-Sectional Sample....................... 395 vii CHAPTER PAGE Appendix II Single Equation Ordinary- Least Squares Estimates "Normal" Stock Demand Functions Pooled Sample ............ 403 VI. CONCLUSION.................................... 404 Suggestions for Future Research ............ 407 BIBLIOGRAPHY ........................................ 413 viii LIST OP FIGURES FIGURE PAGE 1. The Income, Wealth, and Substitution Effects 9 2. Deposit Creation Process— Initial Deposit . . 173 3. Deposit Creation Process— Lending ........... 173 4. Inside versus Outside Money . . ........... 178 5. Money and Net Wealth.................... 192 6. The "Portfolio Effect"................. 350 7. The Implications of Dummy Variables..... 365 ix CHAPTER I INTRODUCTION ! I | I. SCOPE AND PURPOSE j i It is possible to view adjustments due to disequi- libria in the financial markets as problems in portfolio j readjustments. Although several scholars in the field of monetary economics have given an extensive verbal treatment j to the ’ ’portfolio approach," no attempt has been made to j develop a portfolio model within the confines of the neo- ■ classical or modern tradition. The major purpose of this j dissertation, therefore, is to remedy this situation and, i in so doing, to provide a simple and consistent framework j i from which financial phenomena and their interaction with real variables may be studied both on the theoretical and i j empirical levels. For empirical applications this frame- j work is much too general to be of much use without signifi- j cant modification— i.e., the theoretical model must be made "operationally feasible"^ before it can be used in empiri- ^■We are using this phrase in the Samuelsonian sense.; ;An operationally feasible hypothesis is one that can in fact be tested; this is to be contrasted with an operation ally meaningful hypothesis which is a hypothesis that can | be tested in principle. See Paul A. -Samuelson, Foundations I of Economic- Ana1ysis (Cambridge; Harvard University Press, ; 1947), pp. 4-5. 1 2 cal applications. A subsidiary purpose of this study is, then, to suggest possible modifications to the basic model so that the analysis will focus directly on the question that is being addressed. This study emphasizes the method of analysis rather than any specific question that the method is capable of handling. As an illustration of the application of the theoretical construct to a specific question, the degree and type of interdependence in demand between various short term financial instruments— what has become known as the "Gurley-Shaw hypothesis"— will be investigated empirically. The answers to questions concerning the interdependence in demand between financial instruments, and between financial and physical stocks, have a great deal of significance for economic theory in general, and particularly for monetary economics. Historically speaking, money has been a subject of investigation as long as there have been economists; its importance has changed from time to time in the eyes of economists from being a "veil" and therefore of no impor tance in the determination of "real" magnitudes,"^ to ^The charge of considering money as a "veil" can only be levied against certain of the Classical economists, and particularly J. B. Say and his followers. See J. A. Schumpeter, History of Economic Analysis (New York: Oxford University Press, 1954), p. 282. For Say's view on the function of money, see J. B. Say, A Treatise on Political 3 ' I I i having importance for dynamic adjustments but having no effect on the equilibrium values of the "real" magnitudes,3! to, finally, the view that money does influence both the j a i adjustment process and the equilibrium values. All this time, however, non-monetary financial assets and liabili ties have been treated as a poor cousin; no one was quite sure what to do with them or where to put them. As a re- i suit, non-monetary financial instruments were either ig nored or briefly mentioned and then dismissed.3 More recently, monetary theorists— as exemplified I by Don Patinkin— have attempted to follow Hicks1 early j j suggestion that, "What is wanted is a 'marginal revolu- j ! Economy, trans. C. R. Prinsep (Boston, 1924), reprinted in j Philips C. Newman, Arthur D. Gayer, and Milton H. Spencer j (eds.), Source Readings in Economic Thought (New York: j W. W. Norton & Company, Inc., 1954), pp. 158-164. j j ^This statement is more accurate when considering changes in the quantity of money. For the view of one of j the best neoclassical economists on this point see Irving Fisher, Purchasing Power of Money (New York: The Macmillan Company, 1911), chap. 5. ^The best known example is the Keynesian theory. John M. Keynes, The General Theory of Employment, Interest,j and Money (New York: Harcourt, Brace & World, Inc., 1936).I 3This is not strictly correct. For example, see Leon Walras, Elements of Pure Economics, trans. William Jaffe (Homewood, Illinois: Richard D. Irwin, Inc., 1954), Lessons XXIII-XXX. tion'i". ^ To this end, monetary theory has, in Harry Johnson's words, f been worked over with the apparatus of general equilibrium analysis developed by J. R. Hicks, . . . and Keynes' emphasis on treating money as an asset has been followed by subsequent theorists as a means of bringing money within the general framework of the theory of choice.7 Incorporating monetary and non-monetary financial assets and liabilities into the general theory of choice j does appear to be the most promising, and surely the most consistent, approach to the study of financial phenomena. This is the general approach that will be followed in this i study. ! Within these few opening paragraphs, however, sev- | eral terms have been used that are frequently understood to I I have a somewhat different connotation than that used here. To facilitate the interpretation of what has been said and of the analysis that comprises the remainder of this study,I the following definitions are given: j I 1. Financial market— any market that deals exclu- | sively in financial goods. j J. R. Hicks, "A Suggestion for Simplifying the Theory of Money,” Economica, II, New Series (1935) , re printed in Friedrich A. Lutz and Lloyd W. Mints (eds.), Readings in Monetary Theory (Homewood, Illinois: Richard D. Irwin, Inc., 1951), p. 14. ^H. G. Johnson, "Monetary Theory and Policy," The American Economic Review, LII (June, 1962), 335-336. 2. Portfolio— a statement of an individual's assets and liabilities.-'-!. e.'v a balance sheet. : For purposes, of this study,, .the. aggregate port folio is defined as a statement of all assets held by all individuals in the economy. (This is not a general definition of the aggregate * ' j portfolio? for a discussion of its limitations j j see Chapter III; and, for a discussion of al- j ternative views on this subject see Chapter II l 3. Flow good— a good whose quantity is measured in units "per unit of time." j I 4. Stock good— a good whose quantity is measured j at various instants of time— i.e., it bears no time dimension. i 5. Stock-flow good— a good that exhibits the char-j i acteristies of both a stock good and a flow good. ; 6. Stock-flow economy— an economy that contains j one or more stock-flow goods. | I I II. THE PORTFOLIO EFFECT j It appears plausible that when investigating the behavior of financial variables in response to changes in various market outcomes, the peculiar properties, that dif- : ferentiate financial from real variables pose problems that 6 are not encountered in the traditional economic theory. Specifically, financial assets and liabilities have the following properties: their stock is generally very large relative to the level of current production; they are non depreciating in the sense that they do not lose value with use or with the passage of time; they yield (in most cases) j i two forms of income, spendable income and income in the form of the services of "liquidity"; the services that flow from financial instruments are a function of their prices I relative to the general price level; and, the cost of pro- I duction of most financial instruments is almost zero. , These characteristics suggest that there are stock influ ences, as well as the flow influences usually considered, affecting price and quantity determination in such a cir cumstance, and that these stock influences are potentially :important enough to be explicitly considered. In particular, it is the contention of this study that, in a stock-flow economy, these stock effects signifi cantly influence quantity demanded and supplied, especially in the financial markets. Considerations of this type have led some writers in the money field to imply that there is a new effect— in addition to the substitution, income, and | wealth effects— that should be recognized; this new effect i is what has been called the portfolio effect. Unfortu- ! nately, to our knowledge the portfolio effect has never 7 been unambiguously defined. For. example,: Milton Friedman and Anna Schwartz, in a preliminary draft of a forthcoming book, mention the portfolio effect in the. context of mone tary expansion, and imply that Its. definition should be in terras of changes in the desired ratios in. which stocks are g held. However, any changes, in the desired ratios are pre sumably brought about by a change In relative prices (or, perhaps, some other parameter.) , which makes it very diffi cult to distinguish the portfolio effect from the substitu tion effect. What Friedman and Schwartz seem to be driving at is that the portfolio effect is the change in quantity de manded after a change in relative prices due to the influ- : ence of the presence of other stocks, which is predicated : on the notion that there is some functional form that de scribes the desired ratio in which stocks are held. This definition, however, appears to be describing what is ■ normally referred to as the substituion effect as it ap plied to pure stock good. To illustrate this point, consider an individual whose portfolio consists of two financial goods: good 1 ®Milton Friedman and Anna J. Schwartz, "Trends in ; Money, Income,, and Prices” .(preliminary draft of a work to be published by the National Bureau of Economic Research, Inc., New York, .November, .1966) , chap. 2. and good 2. As we shall discuss at some length later in this study, it is with the real values of stocks that a i rational individual is concerned which, in the case of financial goods, is equivalent to price times quantity de flated by the price level. However, as will become evident later— see Figure 5— it is impossible to isolate the vari ous effects consequent upon a price change graphically when the real values of financial goods are the measure used on j the axes of an indifference map; thus, we shall consider here an indifference map of a given individual for goods 1 and 2 in the quantity-quantity plane, which would appear as| | follows {Figure 1) , where Q-^ and Q2 are the respective ; quantities in terms of some standardized face value (say $1) . | i Assume initially that the individual is in equilib- | i rium at point A with a wealth constraint as indicated by j j wealth line aa. Suppose now that the price of good 2 de creases (i.e., the interest rate of good 2 increases) so that there is a shift in the wealth constraint line to ab; in the absence of any other considerations, the individual j j would now be in equilibrium at point B. However, the de- ; crease in price of one of the stocks held by this individ- 1 ual leads to a decrease in the individual's real wealth, which causes a (non-parallel) shift in the wealth line to cd. This individual is now in equilibrium at point C, and Q. FIGURE 1 THE INCOME, WEALTH, AND SUBSTITUTION EFFECTS the wealth effect is measured as the movement from B to C. We may also isolate the income effect by taking away any gain in real income experienced by the individual due to the price change and observing his new. equilibrium collection of stocks. Using the Hicksian definition of real income, this may be done by shifting the wealth con straint line parallel to cd to ef; the income effect may then be measured by the movement from C to D. The inter- ; pretation of the income effect in the case of a pure stock good is not as straightforward as it would be in the case of a pure flow or stock-flow good. In this case, it may be i interpreted as the increase in real income experienced by | the individual due to the lower price paid for any planned : additions to this particular stock. Since the slopes of the lines OX and OY are a measure of the desired ratio in which the stocks are held j before and after the price change, the Friedman-Schwartz ! definition of the portfolio effect is the movement from A j to E. The substitution effect would then be the movement from E to D. However, the entire movement from A to D is due to the change in relative prices, and it is due to the existence of other stocks in the same sense that a similar movement in the case of pure flow goods is due to existing patterns of consumption. Hence, it seems preferable to consider the movement from A to D as being caused by a 11 single effect; whether this is called a portfolio effect or a substitution effect is immaterial as long as the ter minology does not lead to any confusion. We shall, however, have occasion in Chapters IV and V to discuss a phenomenon which is referred to as a port folio effect. This will have reference to a conceptual experiment in which the initial stocks of an individual are varied in such a way so as to keep his real wealth and prices constant, and his market befravior under varying con ditions with respect to his desired stocks will then be observed. This "portfolio effect" has nothing to do with changes in relative prices, and is an attempt to arrive at a measure of the degree of substitutability or complemen tarity between two financial goods. III. A PREVIEW OF THE ANALYSIS At this point it might be informative to consider the implications to the traditional (i.e., neoclassical) general equilibrium system as stocks of various goods are introduced as endogenous variables. It will be informative in the sense that it will give some indication as to the rationale behind the theoretical stock-flow system that will be developed in Chapter III of this study. The traditional neoclassical general equilibrium model explained only pure flow prices and quantities; stocks were subsumed under the heading of data and were assumed not to be traded. Their presence, however, was re-; I fleeted in the size (and perhaps sign) of the coefficients, ! but the analysis was unable to differentiate the effects due to the presence of these stocks from the pure flow effects. The analysis did recognize that the services of these stocks (a flow) were traded and provided a mechanism for the price and quantity determination of the flow of these services. The only stock that explicitly appeared in I the analysis was the quantity of money, but this only ap- j peared in the Cambridge equation in the form of an exoge- ! nous variable.^ | Now, consider an individual consumer in an ideal ized pure flow economy— an economy where there are no ; stocks in existence and no one desires to accumulate any j stocks--and assume that the price of a commodity decreases, j j On the individual level, this price decrease will have two j j effects. The individual's real income will have increased, ; and hp will attempt to consume more of all (non-inferior) j t ;goods; this is the so-called income effect. After the price decrease, the good in question will appear less ex pensive relative to all other commodities; hence, the indi- j vidual will attempt to substitute the relatively less ^However, see supra, n. 5. ; 13 : expensive, commodity, for. those (substitute), commodities, that; now appear more expensive: in relative terms. : This is the i substitution effect. In. a pure flow economy, these two: j effects completely describe the: reactions of a consumer to j a price change. j Once we aggregate over all individuals we can no j longer vary the price of one commodity independent of the prices of all other commodities. We must, instead, speak j about a change in an exogenous variable and then consider the reaction to this change and its influence on equilib rium prices and quantities."*-® Following through with the | example used in the case of the individual, let us assume ! I that the price decrease observed by the consumer was brought about by an improvement in the techniques of pro- I duction of the commodity in question. Ignoring distribu- | tional effects of the change in real income, each individ- j I i ual will experience a rise in real income, and will attempt; i to substitute, the commodity in question for all those (sub-| stitute) commodities that now appear relatively more expen-! sive. The new equilibrium position will be such that— assuming the normal signs of the relevant derivatives'---the j \price of the commodity in question will be lower and the l®This refers to Patinkin's distinction between an ! "individual experiment" and a "market experiment.1 1 See | Don Patinkin, Money, Interest, and Prices (2d ed.; New York:: Harper & Row, Publishers, 1965) , pp. 11-12; 387-394. quantity consumed higher. The signs of the changes in j prices and quantities of all other goods that are non- inferior and substitutes, or inferior and complements, are | j ambiguous and cannot be determined on a priori grounds; the I ! relevant considerations are the signs and magnitudes of the j income and substitution effects. Those other goods that j are non-inferior and complementary to the good in question j will experience an increase in both price and quantity de- I manded; those that are inferior and substitutes will ex perience a drop in price and quantity demanded. Once again,! the changes in the equilibrium values can be completely explained in terms of the income and substitution effects j j provided, of course, that there are no stocks in existence.! ■ Now consider an economy in which there are both stock and flow goods. Assume that the price of a commodity that is both consumed and held as a stock decreases as j j viewed by the average consumer. As before, there is an income effect and a substitution effect; the only differ- j ence in these two effects from the case of a pure flow economy is that there are now stocks to be considered. Thus, questions concerning the real income elasticity of I portfolio size and composition and questions concerning portfolio size and composition as a function of relative i prices become important. It is one of the major hypotheses! of this study that these influences significantly affect |market outcomes in the financial markets. The introduction of stocks into the analysis brings with it a new effect— the wealth effect. Consider a typi cal consumer after the price decrease; if he holds any of the good in question as a stock, he will be made worse off ' ' i to the extent that his (non-human) wealth will decrease in market value. On the other hand, the general price level | will have decreased by reason of the fact that one of its ! i components has decreased in price and, therefore, the con sumer's real wealth will have increased. The net effect on j ; ' ! :real wealth will depend upon the proportion of the individ- | ual's wealth held in the form of the commodity in question j and the importance of the commodity in determining the gen- i I eral price level; however, under certain assumptions an un- j j i ambiguous answer can be given. Let j I i yi = number of units of commodity i held as a stock. p^ = price per unit of commodity i. j n P = £ ajJPi* the general price level, where the i=l a^ are given weights, m W = E p-jy-i, nominal wealth, where m<n. i i=l ! ' | R = W/P, real wealth. | Differentiate R partially with respect to the price of the ; i i " * - * 1 stock, (1.3.1) 9R/3Pi = (aw/apiJ/p - [(aP/3Pi)/p] ( w/p) ; The first term on the right is the effect on real wealth of I a change in p-^ holding the price level constant,, the second ; term is the effect on real wealth of a percentage change in ip^ holding nominal wealth constant. Performing the indi cated operations and simplifying, we have (1.3.2) aR/aPi = P-jYi/P - aiPiW/P2 = ,Pi(Yi/P - a±W/P2) ; Assuming that y^ and a^ are constants , and that a^ is very small relative to all the other magnitudes in the expres- n I sion— this is justified by the fact that aj e 1 by definition— so that a^W-^O, real wealth is a positive func tion of the price of the i*-*1 stock (i = 1,2,... ,m) . No- ; tice that if the commodity in question is not held as a ; stock the first term on the right is identically equal to zero and any change in price would effect real wealth in the opposite direction. This is, of course, exactly what : we would expect to happen. Thus, in the. case under consideration, the individ- ; ual would be made worse off by reason of his decrease in real wealth if he held any of the commodity as a stock. On the basis of theory, we would expect the individual to re arrange his portfolio and to cut down on his consumption I , i ' 17 ! : expenditures in such a circumstance; however.,, behavior with respect to changes, in wealth is an empirical question. The : ' i available evidence, at least as it pertains to aggregate behavior, appears to point to a positive, relation. ; When aggregation over all individuals is performed,j we must, as before,, take our derivatives with respect to some exogenous variable to investigate the behavior of wealth and its. effect on the behavior of the economy. Once again, assume that a technological improvement has taken place in the methods of production of the good in question j in such a way that the equilibrium price decreases. Some individuals will be made better off (those that do not holdj any of this commodity as a stock) and others will be made j worse off (probably those that do hold a stock of the com modity) , the net effect will depend, in addition to those factors analyzed in the discussion of the individual, upon I : j the proportion of real wealth held in the form of the good j i ! that experienced the price decrease. However, interpretingj the discussion of (1. 3.1) - (1.3.2) as pertaining to aggre gates, we may say that it is probable that the real wealth : of the economy (provided that there dre no offsetting li abilities) has decreased. As was pointed out before, the j -*-^See,: for example,. A. Ando and F. Modigliani, "The 'Life Cycle' Hypothesis of Saving," The: American Economic Review, LIII (March, 1963), 55-84. S 18 i available evidence suggests that aggregate consumption and investment will decrease. Thus, in a stock-flow economy we have seen that a price change will elicit responses that are somewhat dif ferent than in a pure flow economy due to the presence of ; wealth in the form of stock goods. However, it will be ; argued in this study that a wealth effect is only one por tion of the difference between a flow and a stock-flow economy; it will be argued that the presence of stocks im plies that the level and composition of an individual's (or the aggregate) portfolio significantly influences market outcomes. The "portfolio approach" as it is developed in this study is designed to take into consideration these influences. The neoclassical analysis, on the other hand, placed the stock influences in the background; their ef fects showed up in the functions only in the signs and mag nitudes of the coefficients. As long as only pure flows are being considered, this does little harm; however, if it is stock quantities that are being investigated, a neo classical type analysis hides more than it shows. IV. METHODOLOGICAL QUESTIONS The methodology of science has been the subject of investigation from before the time of the ancient Greeks; a majority of this work has been done, however, in the con text of the natural sciences, and a discussion of the meth odology of the social sciences— and economics in particular — is of a relatively recent vintage. It would be wise, therefore, to consult the natural scientists to see how they approach their problems. Karl Popper sums up the role of the scientist vis- ik-vis theory when he wrote: A scientist, whether theorist or experimenter, puts forward statements, or systems of statements, and tests them step by step. In the field of the empir ical sciences, more particularly, he constructs hy potheses, or systems of theories, and tests them against experience by observation and experiment. : Popper then goes on to say, According to the view that will be put forward here, the method of critically testing theories, and. selecting them according to the results of tests, always proceeds on the following lines. From a new idea, put up tentatively, and not yet justified in any way . . . conclusions are drawn by means of logical deduction. These conclusions are then com pared with one another and with other relevant statements, so as to find what logical relations . . . exist between them. We may if we like distinguish four different lines along which the testing of a theory could be carried out. First there is the logical comparison of the conclusions among themselves, by which the internal consistency of the system is tested. Secondly, there is the investigation of the logical form of the theory, with the object of determining whether it has the character of an empirical or scientific l^Karl R. Popper, The Logic of Scientific Discovery (2d ed.; New York: Basic Books, 1960), p. 27. 20 theory, or whether it is, for example, tautological. Thirdly, there is the comparison with other theo ries, chiefly with the aim of determining whether the theory would constitute a scientific advance should it survive our various tests. And finally, there is the testing of the theory by way of empir ical applications of the conclusions [emphasis added] which can be derived from it.13 Thus, according to Popper's view, a theory once it is formulated must undergo tests before it can gain the stature of "acceptance"; this requirement, however, places certain restrictions on the form that a theory may take. In other words, there is no such thing as induction. Thus inference to theories, from singular statements which are "verified by experience," . . . is logically in admissible. Theories are, therefore, never empiri cally verifiable. . . . But I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation. In other words: I shall not require of a scientific system that it shall be capable of being singled out, onc6 and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.14 Milton Friedman agrees with the "refutability doctrine,."' and, further, agrees with Popper on the level that the test 13ibid., pp. 32-33. l^ibid., pp. 40-41. 21 should be performed (see Popper's earlier quote) when he. . wrote., The only relevant test of the. validity, of a hypoth esis is. comparison of its predictions with experi ence: [emphasis added]. . .The hypothesis is rejected if its predictions are contradicted; . . . it is accepted if its predictions are not contradicted; great confidence is attached to it if it has sur vived many opportunities for contradiction. Fac tual evidence can never "prove" a hypothesis; it can only fail to. disprove .it, which is what we generally mean when we say, somewhat inexactly, that the hypothesis has been "confirmed" by experience.15 Friedman1s contention that a theory should be tested at the level of the conclusion implies— and is ar- i gued by Friedman-.-that the relevant test of a theory cannot I be performed on the premises and, in fact,, one normally finds that there is a negative, correlation between the "worth" of a theory and the realism of the assumptions. Friedman's position, however, is not universally held by all economists. For example, Paul Samuelson takes the position that "the empirical validity or fruitfulness of the theorems, of course, cannot surpass that of the original! hypothesis."16 | • I Another respected source in the field of economics i takes a more middle of the road approach,. Andreas ' 15 Mi1ton Friedman, "The Methodology of Positive Economics.," Essays in Positive Economics (Chicago: The University, of Chicago Press, 1953), pp. 8-9. 16Samuelson, 0£. cit., p. 5. Papandreau contends that a theory can be .tested at any level from its assumptions to. its. conclusions; what is im portant for a theory is that It "adequately characterize . the relevant social space." Most economic theories, ac cording to- Papandreau, are basic theories in the sense that they have been given an incomplete interpretation, there fore it is important that the ". . . class of admissible interpretations be adequately characterized by the theo rist."-*-^ In other words, what Papandreau is arguing is that if a theory adequately characterizes the relevant so cial space it can be validly tested at any level; however, most economic theories do not possess this characteristic. To remedy this situation, he contends that economic theo rists should completely specify the data, assumptions, and the variables so that the theory may be tested unambigu ously. With regard to the present study, the refutability criterion will be accepted; however, with regard to the appropriate level to perform the test, the position will be taken here, which is not an uncommon one in economics, that it all depends on the circumstances. Perhaps an example will: clarify, this point. The position was taken earlier in 1^Andreas papandreau, Economics as a Science (Chicago: J. B.. Lippincott Co., 1958), p. 10. this, chapter that when studying an economy that deals in financial instruments as well as other goods and services, the explicit recognition of stocks becomes important. Sup posing that the purpose of this study was to predict the demand for money (however defined) over some relatively short time horizon, it would not make much difference to the study whether a vector of prices and quantities of al ternative financial instruments was included in the analy sis or not, provided that the movements in at least one of the endogenous variables paralleled the movements in the portfolio variables— which is entirely possible. In other words, it is possible that the predictive power of a (pseudo) demand for money function would not be signifi cantly improved by adding a vector of prices and quantities of alternative financial instruments as an argument. Now, assume that the purpose of the study is to determine the effect on the demand function for money of the existence of highly liquid financial instruments. It how becomes cru cial to. the success of the study whether or not the port folio variables are explicitly introduced into the analysis — the assumption, i.e., the recognition of the existence of alternatives to holding money in a portfolio, are now more realistic.IS As far as the physical means of testing are con cerned, the social scientist is at a great disadvantage. The natural scientist, in most cases, is able to perform controlled experiments in which he is able to hold all things constant except the variables that he is directly concerned with. The social scientist, and particularly the economist, on the other hand, has no laboratory in which, for example, he can vary the price of a commodity and ob serve the variations in quantity demanded, ceteris paribus. Consequently, the economist must devise other methods of testing his theories; he has taken a hint from the astron omers (who face some very similar problems) and borrowed from the fields of mathematics and statistics, and has de veloped a new branch of economics called econometrics. Econometric research is the most recent, but not the only attempt by economists to. test their theories; for example, an economist schooled in the institutional approach would 18 This is analogous to the identification problem found in empirical work in economics. It is well known that if prediction is the only consideration in a study, there is no need to consider the. identification of the equation in question; however, if the study is concerned with explanation, it is important to insure unbiased and consistent estimates of the coefficients— this is where the identification problem becomes important. On this point, see Mordecia Ezekiel and Karl A. Fox, Methods of Correla tion and Regression Analysis (3d ed.; New York: John Wiley & Sons, Inc., 1959), p. 421. test his theories in terms of their explanatory and predic tive power with respect to the behavior of existing insti tutions and the evolution of new institutions. It is not claimed here that econometrics is the best method of test ing all economic theories; the best method of testing any particular theory would, once again, depend on the purpose for which the theory is developed. It is claimed, however, that the type of theory developed in this study lends it self well to econometric research in the sense that the data and variables are easily quantifiable and the rela tions are easily stated in mathematical form. Hence, it is a short step to the estimation and significance testing that is so typical of econometric research. A more power ful philosophic reason for advocating econometric tech niques for testing this theory is that the type of experi ence that could be expected to refute the theory would come in quantitative form. V. THE ORGANIZATION OF THIS STUDY The remainder of this study is subdivided into, five ;basic parts: a review of the relevant literature, the de- ;velopment of a general equilibrium model based on the port folio approach, suggestions for simplifying the general equilibrium model into an operationally feasible system, an empirical investigation of the Gurley-Shaw thesis, and 26 I i I conclusions . Chapter. II will be devoted to a review of the pre- : cedent studies in the literature that are concerned with ■ the same type of problems that we are concerned with in :this work. Since the stepping off point of most modern ; general equilibrium theory is, at least in the essential details,: the Walrasian system, we shall open the chapter with a review of traditional static general equilibrium theory. From there we shall trace briefly the modifica tions that have been suggested for a monetary economy; spe-. cifically, the development of the Pigou and wealth effects and the whole debate that has become known as the "P.atinkin controversy will be considered. Once this has been accom plished, the contributions to stock-flow analysis and the :later contributions to the theory of the wealth effect will |be reviewed. The chapter will close with a review of the literature on the portfolio approach and a review of the :works of those contributors who have attempted to simplify a relatively complex system into an operationally feasible system. In Chapter III a general equilibrium model is de- veloped using the "temporary equilibrium" method of J. R. Hicks.^ This chapter draws heavily from the works of J. R. Hicks, Value and Capital (2d ed.; London: Oxford University Press, 1946), chaps. IX-X. 27 Patinkin, Bushaw and Clower, Gurley and Shaw, Pesek and 9 0 Saving, and J. R. Hicks, u but differs from the contribu tions of these authors— taken severally or collectively— in several important respects. The model is built up from the assumptions of Hicksian general equilibrium analysis, but recognizes that each economic entity enters each "week1 1 with a portfolio inherited from the past, and that he (whether he be a consumer or producer) may wish to alter the size and composition of his portfolio in response to changing market conditions. Questions concerning the equi librium rate of adjustment of actual to desired stocks are also addressed in this chapter. Once this very general model has been formulated, it is necessary to simplify it for testing purposes. There are an infinite number of possible simplifications; the ex act form of the simplification would depend on the particu lar question that is being addressed. In Chapter IV two possible simplifications are considered: a "macro" model developed along Keynesian lines and a "micro" model that would be capable of investigating the "validity" of the Gurley-Shaw hypothesis are presented. In relation to the micro model, the portfolio approach leads to a measure of the degree of substitutability or complementarity, a con- 20 For the appropriate references, see the relevant sections of Chapter II. 28 cept that is crucial for an empirical evaluation of the Gurley-Shaw hypothesis. In Chapter. V we shall bring empirical evidence to bear on the Gurley-Shaw hypothesis in the form of estimated interest rate and portfolio balance coefficients. As it turns out, the structure of the theoretical micro model developed in Chapter IV allows certain empirical tests to be performed that give an indication of the efficacy of the portfolio approach as an explanatory framework. Although there is evidence that the estimates are subject to various biases and distortions, the estimates indicate that neither the Gurley-Shaw hypothesis nor the portfolio approach hy pothesis can be rejected on the evidence presented in this study. After these tasks have been completed, it only re mains to sum up the results of this study and to give sug gestions as to the direction that future research in the area of the portfolio approach might take. This is done in Chapter VI. CHAPTER II ! THE BACKGROUND Before proceeding with our own analysis, it will be instructive to consider in some detail the developments in economic theory as it relates to monetary and non-monetary !financial variables. Unfortunately from our point of view, ithe great majority of the work in this area has been con cerned with monetary theory; but, as we shall see, the problems encountered in the subjects covered by traditional monetary theory are not substantially different from those encountered when non-monetary financial instruments are introduced. The purpose of this chapter is rather narrow in ;relation to the literature in the field of financial asset itheory. Specifically, the intent of this chapter is to itrace the development of static general equilibrium theory !from its first formal presentation by Walras^ to the pres- ent time, concentrating on the subtleties introduced when ■'■Leon Walras, Elements of Pure Economics, trans. William Jaffe (Homewood, minors: Richard D. Irwin, Inc., ;1954). The other classic works in this field are due to I Gustav Cassel, The Theory of Social Economy, trans. S. L. Barron (new rev. ed.; New York: Harcourt, Brace and Co., 1932); V. Pareto, Manuel d'Economie Politique (2d ed.; Paris: Marcel Giard, 1927")"; and P. Divisia, Economique Rationelle (Paris: Gaston Doin et Cie, 1928). 29 30 stocks (primarily financial) are added to the traditional pure flow analysis. With this in mind we shall proceed by first consid ering a typical version of the neoclassical static general equilibrium model; next the modifications to the basic model introduced by Haberler,^ pigou,^ and others in response to the Keynesian challenge^ will be considered; the next task will be to review the entire inconsistency charge initiated by Lange's classic article.^ The last section of this chap ter will be devoted to more recent developments; the com plications introduced when both stock and flow quantities are considered simultaneously, the correct components of economically relevant wealth, and the relevant contributions to the theory of the portfolio approach will be considered. It is anticipated that his review will form a sound basis for the theoretical system that will be con structed in Chapter III. ^Gottfried Haberler, Prosperity and Depression (Geneva: League of Nations, 1939), 3A. c. Pigou, Employment and Equilibrium (2d ed.; London: Macmillan & Company, Ltd., 1952). ^John M. Keynes, The General Theory of Employment, Interest, and Money (New York: Harcourt, Brace & World, 1936). ^Oscar Lange, "Say's Law: A Restatement and Criti cism," Studies in Mathematical Economics and Econometrics, ed. Oscar Lange, Francis McIntyre, and Theodore O. Yntema (Chicago: University of Chicago Press, 1942), pp. 49-68). I. GENERAL EQUILIBRIUM Since this work is not a treatise on the history of : doctrine we shall not be concerned here with the historical I development of static neoclassical general equilibrium ; analysis; rather, we shall discuss what might be called a typical version of the analysis as presented by Hicks and Allen.^ The following model very closely follows the presentation of Henderson and Quandt which, as will become evident as the analysis unfolds, has certain desirable properties for our analysis.' The neoclassical system is a closed system in the ; sense that all variables are determined within the system; : however, we must make, certain behavior and institutional assumptions and possess certain data before the system can be solved for the equilibrium values of the variables. The usual institutional assumption is that pure competition prevails in all markets in the sense that no single buyer ; or seller can influence market prices through his own ac- i tions and that there are no barriers to entry to, or exit 6j. Hicks, Value and Capital (2d ed.; London: I Oxford University Press, 1946), chaps. IV-VIII; and R. G. D. Allen, Mathematical Economics (2d ed.; New York: St. Mar kin's Press, 1959), chap. 10. ■ 7 • James H. Henderson and Richard E. Quandt, Micro- ; economic Theory (New York: McGraw-Hill Book Company, j1958), chap. 5. 32 Q from, an industry. Now, consider an individual consumer. The behavior assumption is his desire to maximize utility; the data are his utility function, and the market prices of all commodi ties and factors; the variables are the amounts purchased and consumed of commodities and the amount of factor ser vices sold. For the individual producer the basic behavior assumption is his desire to maximize profit; the data are his production function and the market prices of all com modities and factors; and, the variables are the quantities of inputs that he purchases and uses and the quantity of commodities he produces and sells. Market prices appear as parameters to the individ ual economic entities; it is only when the actions of all economic units are considered together can the equilibrium market prices be determined. This system, however, deter mines only a subset of all possible prices that are of in terest to the economist. Specifically, it determines only those prices (and quantities) that are included in the sub set of all prices (and quantities), that have the property of being non-financial, flow, and newly created (except, in some instances, circulating money). Among other things, ^Free entry and exit is not a necessary, nor indeed the normal, assumption in general equilibrium analysis. See Allen, op. cit., p. 314. this system rules out price and quantity determination of financial assets, an explanation of capital accumulation, 9 and relegates all stocks to the category of data. A good part of the remaining portion of this work will be devoted to an attempt to remedy these deficiencies. The Basic Model— The Consumer Consider a market in which there are n consumers (i=l, 2,..., n) and m goods (j=lf 2,..., m) of which z are factor services (j=l, 2,..., z) and m-z are commodities (j=z+l, z+2,..., m). The ith consumer possesses an initial endowment of factors and he may sell the services of these factors (x*.q , x*i2,..., x*^z) at the given market prices (p^/-P2» » Pz) Per period of time. This is the i^*1 con sumer's income. The consumer will spend his income on com modities (x. ,, x. «,..., x. ) that he desires to con- 1 f ZtX 1; ZtZ J.UL sume per period of time. The excess demand for the ith consumer is defined as the quantity that he. consumes if it is a commodity ®If doctrinal accuracy is what we are striving for, this is not completely correct. However, most of the earlier attempts to introduce stocks into, the analysis were analytically unsatisfying. See, for example-, William Jaffe, "Leon Walras* Theory of Capital Accumulation," Studies in Mathematical Economics and Econometrics, ed. Oscar Lange, et al. (Chicago: The. University of Chicago Press, 1942), pp. 37-48. 34 (2.1.1) E = x.. (j=z+l, z+2,..., m) ij 13 and the quantity that he consumes less his initial endow ment if it is a factor (2.1.2) E^j = xij - (j=l, 2,..., z) A consumer's excess demand for a commodity will either be zero or positive? his excess demand for a factor may be negative, positive, or zero. The income of the i*-*1 consumer is (2.1.3) y± = £ p j=l 3 3 and, if we assume that the consumer spends his entire in come, his expenditures, are m (2.1.4) Yi = s P-jxii j=l. Combining (2.1.1) to (2.1.4), the budget restraint of the i ^ consumer is m (2.1.5) 2 pjEj • sO 3=1 3 3 The. consumer derives utility from the goods and services that he consumes, i.e., the initial endowment of factors that he retains and the commodities that he pur chases. The i^*1 consumer's utility function is 35 (2.1.6) x^2/•••j x£m) We may state the utility function in an alternative manner by substituting from (2.1.1) and (2.1.2) (2 .1.7) ^ = ui ^Eil+X*il' Ei2+X*i2'---- Eiz+X*iz' Ei,z+1'''•*' Eim^ The consumer wishes to maximize his utility (2.1.7) subject to the budget restraint (2.1.5). Form the new function m (2.1.8) z. = u.( ) - X( 2 p.E.■) where X is a Lagrangian multiplier. The first order condi tion for a maximum is that the first partial derivative of (2.1.8) with respect to each of the variables (the E^j and X) vanish.^ We shall assume that the second order conditions for a maximum are satisfied throughout this work. Addi tionally, the questions of existence, uniqueness, and sta bility will be ignored except where explicitly mentioned. We shall further assume that equality of the number of (independent) equations and unknowns is a necessary and sufficient condition for consistency and determinancy. For ia more complete statement on these questions see Allen, loc. cit., and Hicks, op. cit., chaps. IV-VIII and Appendices. Using one of the m+1 equations (arbitrarily chosen) to eliminate the X, we then have m equations in m unknowns (the j 1 s) , and the Ej_j may be expressed in terms of the exogenous Pj (2.1.10) Efj ^ij (Pj' &2r 'm m' (0— / 2, • • • , m) which are the excess demand functions for commodities and factors of the it^ 1 consumer. The homogeneity of the system. The system (2.1.10) is homogeneous of degree zero in prices; i.e., the excess demands of the individual consumer are not effected by an equipropDrtionate change in all prices. To see this con sider (2.1.8), and assume that prices change by the factor t (t^O). m (2.1.11) z± = u.( ) - X[ 2 (tp.)E..] j=l Differentiating partially with respect to the vari ables Ej_j and X, and setting them equal to zero, we have 37 3zi 3ui (2.1.12) = - Xtp-i = 0 (j=l, 2,..., m) 9Ei j 3Eij dZ ■ m m (2.1.13) = - S tp^Ej • = -t S P-iEj-; = 0 j=i 3 13 j=i 3 3 Consider (2.1.13); since t ^ 0, then m PjEij - 0 Next, consider (2.1.12); if the xis eliminated from the system by arbitrarily choosing one equation and dividing the other m-1 equations through by it, we have ui / ui = p - i/p„ (j^g) 3Eij / 3Eij 3 9 which are the maximum conditions before the equipropor- tionate price change. Hence, the excess demands of the iU11 consumer are dependent on relative prices-— not on the ab solute price level. The Basic Model— Production Within the same markets that the consumers operate in, there are production units that combine factors (x^, xz)— purchased from the n consumers— and primary and intermediate products (xz+1, xz+2,..., x^)— produced by the firm in question or purchased from other firms— to produce quantities of products (xz+i, xz+2- # • ••/ xm) per unit of 1 1 time. There are m^-zindustries (k=z+l, z+2,..., m), Nk firms within each industry (h=l, 2,,.., Nk) , and m-z goods (j=z+l, z+2,.,.., m) in our model. The hth firm's profit function is m (2.1.14) 7rh = s PjXhkj where xhkj is the quantity of the jth input (if it is nega tive) or the quantity of the output (if it is positive) of the h ^ firm in the k*'*1 industry. The firm is assumed to desire to maximize its profit subject to the technical relation between inputs and outputs— the production or transformation function— which we shall state in implicit form (2.1.15) f(Khkl' xhk2'**'' xhkm^ " ® Using the familiar maximum rule, we form the new function -^The reader will notice that there is no differen tiation between primary products, intermediate products, and final products. This does not do the analysis any ham; some primary and intermediate products will also be used as final products in the sense that consumers will have a positive excess demand for them, others will not. In the case of the latter, variety, the excess demand of the consumer sector will be zero. If our analysis were ori ented more towards the production side of the market, it would be wise to differentiate— at least as far as the notation— between the three different types of products. 39 m (2.1.16) . Vhl_ = 2 p.x_ . - yf< ) hk j=i 3 hk3 where y is a Lagrangian multiplier. Differentiating (2.1.16) partially with respect to the xhkj and y and set ting them equal to zero, we have 3Vhk 3f = p ■ y = 0 (J=1 * 2, • •., m) 9Xhkj ^ 3Xhkj (2.1.17) ^ - = f( , -.0 3y Using one of the m+ 1 equations to eliminate the y, we have m equations to solve for the m xhkj = Ehkj as functions of the exogenous pj (j=l, 2,..., m) (2.1.18) Ehkj = Ehkj ^pl' p2' ’ ' *r pm^ * 2,..., m) If the k1 " * 1 industry has Nk identical firms, the ex cess demands of the k ^ industry for products and factors are (2.1.19) Efc;. = NkEhkj(pl' p2'' ’ ' ' pmJ “ - Ekj*Pl' p2/,**f pm/ (j=if 2,..., m) The homogeneity of the system. The excess demand functions of the individual firm are also homogeneous of degree zero in prices. The proof is completely analogous 40 to the case of the consumer; assume that all prices experi ence an eguiproportionate change by the factor t (t^O). Now, consider (2.1.16) after the equiproportionate change in the pj m vhk = .2 (tPj^hkj " > -)=1 Again, differentiating partially with respect to the and \i, and setting the first partial derivatives equal to zero, we have 3Vhk af (2.1.20) = tPj - = 0 (J-l, 2 m) 2 2 * - , = o Arbitrarily choosing one of the m+1 equations to ieliminate the y, we have ^ / ^ = Pj/Pg (j?is> Hence, the equilibrium conditions are, once again, independent of the absolute price and are dependent only on relative prices. The Complete System j _ r _ The market excess demand for the j commodity or factor is the summation of the excess demands of the n con sumers and the m-s industries. 41 n (2..1.21) Ej “ . ^ 2 ^*i j ^P'l* P2 *m m • f Pm^ m , s._ Ekj(pl' p2 . P m» Nk} k=z+l J (j=l/ .2 f.» • , ni) Hence, the market excess demands are functions of the Pj (j=l, 2,..., m) and the Nj^ (k=z+l, z+2,..., m) . (2.1.22) = Ej(plf p2,...,pm; Nz+1, Nz+2/ v » ’ Nm) (j=lt 2, • • •, m) In equilibrium, actual behavior will correspond to desired behavior in the sense that, with given market :prices, each consumer consumes exactly what he had planned to and each firm produces and sells exactly what it had planned to (both utility and profits are maximized). In other words, each market just clears. (2.1.23) Ej(p-^, P2/***f Pm7 ^z+i' ^z+2/***' Nn l = ^ (j—1, 2 r , m) Our definition of pure competition as including ;free entry and exit implies another equilibrium condition; namely, that in long run equilibrium all profits will be competed away. 42 (2.1.24) P2 t - • • 1 Pj^) = ^ (k=z+1/ z+2,,.., in) One often hears the allegation that if the produc tion function is homogeneous of degree one in inputs, the zero profit condition will be fulfilled without the addi tional equilibrium condition (2.1.24). However, as Samuel- son has pointed out, if the production function contains only "measurable quantitative economic goods and services . . ." (as ours does) it need not be homogeneous of degree one. Further, if it were homogeneous of degree one in in puts, stable equilibrium for a purely competitive firm would be impossible. Samuelson concludes that "it is only through the competition of new firms that the demand curve of the firm may so shift downward as to make the position of maximum profit one at which total gross revenue equals total expenditure. " - * - 2 Hence, to insure a zero long run profit position, it is necessary to. explicitly include (2.1.24) in the long run equilibrium conditions^. Further, notice that the profit functions are homo geneous of degree one in prices. To see this refer to (2.1.14); if prices experience an equiproportionate change by the factor t (t^O), (2.1.14) becomes ■^Paul A. Samuelson, Foundations of Economic Anal ysis (Cambridge, Mass: Harvard University Press, 1947), p. 85. ! 43 I m m ■ * (tPj)xhkj 5 t Z PjXhkj 5 tiThk D~1 3=1 The system (2.1.23) and (2.1.24) contains 2m-z jequations and 2m-z (pj and Nk) unknowns, and is seemingly a I consistent and determinant system. However, one of the ex cess demand functions is linearly dependent upon the re maining m-1; therefore, we have only 2m-z-l independent equations to determine 2m-z unknowns— our system is under determined. To show that one of the m excess demand functions is dependent on the other m-1, we may have recourse to what has been termed Walras1 Law. Simply stated, Walras1 Law asserts the logical impossibility of oversupply of goods in a barter economy, or m (2.1.25) Z p.E. = 0 j=i 3 3 ;In other words, if an individual has a positive excess de mand for one good he must necessarily have a negative ex cess demand (positive supply) of another good of equal mag nitude in terms of market values— i.e., if an individual :has a demand for a good he must be willing to trade some other good of equal value for it. It follows directly that if any m-1 markets are in equilibrium, the mt* 1 market must also be in equilibrium, that is, m-1 If Z PjEj =0, then pmEm = 0 j=l 44 i This conclusion may be easily extended to a monetary econ omy by interpreting (say) the m ^ good as the medium of exchange. An alternative way of arriving at the same conclu sion is to consider the nature of the individual excess demand functions. As was shown earlier, the individual excess demand functions of the consumers and producers are homogeneous of degree zero in prices; hence, the market functions are also homogeneous of degree zero in the same :variables because they are linear combinations of the indi vidual functions. Now, it is a well known mathematical theorem that if a system of equations is homogeneous of degree zero in all of the variables, if one solution exists any multiple of that solution will also satisfy the system 1— i.e., there are an infinite number of solutions. Thus, one equation in the system is not independent. Therefore, we have only 2m-z-l independent equa tions and 2m-z unknowns; this means that we can only deter- imine the price ratios. Choosing to eliminate p^— the deci sion as to what price to eliminate is completely arbitrary — our system becomes (2.1.26) Ej(l, P2/P1/..Pm/Plr wz+l' Nz+2' • • •' ■ Nm) 5=0 (] = l f 2 f m m • j I t l ) 45 (2.1.27) Tr^(l, P2/ P — ^ (k=z+l, z+2,.. ., m) This system of 2m-z-l independent equations can be solved for the m-1 price ratios and the m-z firm numbers. Once the price ratios have been determined, they can be substituted back into the individual excess demand func tions— which are also functions of relative prices— to ob tain each individual's (consumer's and producer's) excess demand for commodities and factors. The Introduction of Money into the System So far we have developed a static general equilib rium system without ever explicitly mentioning money. Var ious types of money can be introduced into the analysis; we have already implicitly included a type of money— whose sole purpose is to serve as a unit of account— by arbitrar ily choosing to express all the prices in terms of p^. This is the Walrasian numeraire. 1 • By setting the price of the numeraire identically equal to some constant, we could give money the additional function of serving as a standard of value. However, prices are rarely expressed in terms of other commodities or factors; accounting money is injected into the system by specifying the value of a unit of numeraire in terms of the 46 monetary unit— be it dollars, pesos, etc. Money that possess the above properties is not cir culating money as we know it; factors and commodities still exchange for factors and commodities. Money does not serve as a store of value nor a medium of exchange. In a static system it is rather hard to rationalize the holding of a stock of circulating money unless there is some utility im puted to it— i.e.., unless money appears in the utility function or some outside restraint is placed on money bal ances held. However, most neoclassical writers got around this by assuming that individuals would wish to hold some quantity of money because of the non-synchronous nature of 13 expenditures and receipts. Each individual receives periodic income payments from his sale of factor services and is required to make periodic payments to purchase com modities and factor services, and there is no reason to think that the receipts and expenditures will occur simul taneously. Hence, to avoid the inconvenience and embar rassment of not being able to meet an obligation an indi vidual will keep on hand a stock of (utilityless) money. Disregarding the problems involved— these will be covered later in this chapter— we may proceed as follows. ■^See,. for example, Irving Fisher, Purchasing Power of Money (New York: The Macmillan Company, 1911), chap. 5. The consumer's excess demand for money is the quantity he desires to hold less his initial endowment^ (2.1.28) E. = x. * — x*. . j i,m+l i,m+l i,m+l where m+1 indicates that the commodity in question is money. The budget restraint must now be redefined m+1 (2.1.29) 2 p.E,. s 0 j=l 3 13 where pm+i = 1. Since money does not enter the utility function, the excess demand for money must be derived by means other than utility maximization; the usual assumption is that the desired stock of money is proportional to the level of the consumer1s transactions m (2.1.30) xi,m+l = ai Pjxij where a >_0 and a constant. Substituting (2.1.30) into (2.1.28) we have m (2.1.31) Ei Tn.i = a. 2 p.x. . - x*. i,m+l i x,m+l J “ The aggregate demand for money is the summation of (2.1.31) over all n consumers ■^The demand for money of the production sector is usually implicitly assumed to be zero. If it is assumed to be positive, questions arise that this type of analysis is not equipped to answer. This is nothing more than the familiar Cambridge equation M = kPT, and in equilibrium must equal zero— i.e., desired balances must equal actual balances. The system, consisting of (2.1.26), (2.1.27), and (2.1.32), has 2m-z independent equations and 2m-z variables (the p. and the N,)— the absolute prices are no longer in- D K determinant. The pricing process is completely dichoto mized; relative prices are determined in the "real" sphere > [the Ej (j=l, 2,..., m)] and the price level is determined in the monetary sphere. It should be emphasized that the excess demand function for money is not homogeneous of any degree in prices, but is homogeneous of degree zero in money prices 1 R and initial money holdings. To see this, consider (2.1.32). The last term on the right does not contain any Pj (it is a constant) and therefore the function cannot be homogeneous of any degree in prices. However, assume an ■^Henderson and Quandt, 0£. cit., p. 144, state that "The excess demand for commodities [emphasis added] and money are not homogeneous of degree zero in commodity prices . . . [but they) are homogeneous of degree zero in commodity prices and initial money stocks." As will become evident in the discussion of Section 3 of this chapter, the introduction of money into the budget restraint by; itself has no effect on the homogeneity of the excess demand functions. equiproportionate change in prices and initial money hold ings by the factor t (t^O), (2.1.32) becomes n m n E .- i = a Z Z (tp.)x. . - Z (tx*. ,- 1) m+l . n • n n in • i i,m+l 1=1 n=l J J i=l To investigate the influence on Em+^ of a small variation in t, differentiate the above function partially with re spect to t. 3Em+l n m n aZ Z p.x..- Z x*. i=l i=l ^ i=l ^ m+1 3t i=J_ y which is equal to zero if the money market was in equilib rium before the equiproportionate change in the Pj and x*i,m+l* Say1s Law There is a good deal of argument and confusion over what the classical and neoclassical writers meant when they talked about Say's Law. Sometime^ they appeared to be making the very strong statement that "people hold the amount of money in existence in the form of cash balances and never want to alter these balances by financing a pur chase out of them or by using the proceeds from a sale to add to them." 16 This is Say's Identity which implies 16M. Blaug, Economic Theory in Retrospect (Homewood, Illinois: Richard D~ Irwin, Inc., 1962), p. 132. For a more detailed discussion of the classical and neoclassical literature on this subject, see Don Patinkin, Money, In- In other places the classical and neoclassical ; writers seemed to be making amuch weaker statement--that an excess supply of commodities or factors tended to be self correcting. This is Say's Equality and it implies m (2.1.34) Z pjEj = Em+1 - 0 in equilibrium. It makes some difference to the determinacy of the system what interpretation Say's Law is given. If Say's Identity (2.1.33) holds, the money market is always in equilibrium— i.e., people will desire to hold! the existing : stock of money no matter what the price level— and the ab solute prices become indeterminant. Say's Identity is in consistent with the behavior assumed by the Cambridge equa tion (2.1.32), and it would imply that a is a variable that insured the equality between the desired and actual stock of money no matter what the price level. ^ However, if Say's Equality (2.1.34) holds no damage is done to the system. Say's Equality is just a broader terest, and Prices (2d ed.; New York: Harper & Row, Pub lishers, 1965), pp. 527-666; and, by the same author, "Dichotomies of the Pricing Process in Economic Theory," Economica, XXI, New Series (May, 1954), 113-128. ^However, see infra. Section III. 51 statement of our equilibrium condition that, in equilib- 18 rium, all markets must clear. Conclusion The purpose of this section has been to state, in a rather abbreviated form, what we have termed a "typical version of a neoclassical static general equilibrium model." No attempt has been made to clear up any of the short comings or inconsistencies of the model; this is the task of the remaining sections of this chapter and, indeed, the remaining chapters of this work. II. THE WEALTH EFFECT The system presented in the preceding section is a full employment system in the sense that in equilibrium all factors are employed that desire to be employed at the pre vailing (equilibrium) prices. It was well recognized that there were periods of unemployment; the reasons for these "business cycles" were extensively explored in the neo- 18This is the contention of Gary S. Becker and William J. Baumol, "The Classical Monetary Theory: The Outcome of the Discussion," Economica, XIX, New Series (November, 1952), 360-362. However, Say's Equality does not.guarantee that the system is free of Patinkin's Inval idity I and Invalidity II if the excess demand functions are postulated as being homogeneous of degree zero in prices alone (the Casselian' system). On this point see infra, Section III, and especially n. 42. 19 classical literature. The fact remained, however, that any deviation from full employment was believed to set in j motion automatic mechanisms within the price system so that: the system had a tendency to return to the full employment j j position. Say's Law— using the Say's Equality interpreta- ! tion— coupled with flexible wages and prices insured this j tendency; but, no serious consideration of the exact mecha-; nism occurred until the neoclassical system was effectively! challenged on the theoretical level. i This challenge was supplied by J. M. Keynes in his | | General Theory» Keynes1 contention was that a purely com- i petitive system could reach a stable position where factors! that were ready, willing, and able to work at the prevail ing market price were unable to do so— this is the so- ( i j called less than full employment equilibrium. The Keynes- j ian system is not an equilibrium system as the word is normally understood; it is a situation in which the goods j market and the money market are in equilibrium but where the labor market is not in equilibrium. The crucial point ; is, however, that there are conditions under which there are no forces set in motion to correct the disequilibrium j i in the labor market— in other words, the system is in l^The neoclassical literature on business cycles is; very extensive; for a good review of the various theories : see Joseph A. Schumpeter, History of Economic Analysis (New: York: Oxford University Press, 1954), pp. 1117-1135. 53 equilibrium in the sense that once it attains this position there is no tendency for any of the values of the variables to change even though one of the markets does not satisfy the normal equilibrium condition that supply equal demand. The Keynesian Critique of. the Neoclassical Employment Theory A model that would be equally acceptable to either a neoclassical economist or to Keynes could be stated as follows 9Md 3Ma (2.2.1) = kPy + PL(r), where > 0, > 0, and 9Md — _ < 0 3r (2.2.2) Md = Ms 3Y (2.2.3) y = y(N), where — - > • 0 3N 3Nd (2.2.4) Nj = (D/P) , where — — — - < 0 a u 3(D/P) ^This is essentially the model, with a few modifi cations, presented by Gardner Ackley, Macroeconomic Theory (New York: The Macmillan Company, 1961) , p. 403. However, it is not universally agreed that (2.2.1) is a valid repre sentation of a new-classical or classical demand for money function. For example, E. J. Mishan considers the major difference between the neoclassical and Keynesian model to be whether or not the rate of interest is included as an argument in the demand for money function. E. J. Mishan, "A Fallacy in the Interpretation of the Cash Balance Ef fect," Economica, XXV, New Series (May, 1958), 111. 54 3NS (2.2.5) Ns = N (D/P) , where ■ > 0 s s 3(D/P) (2.2.6) N , = N a s (2.2.7) S = S(y,r), where .i®. > 0, and l£ > 0 3Y. 3r (2.2.8) I = I(r), where iH. < 0 3r (2.2.9) S = I where = demand for nominal balances. Ms = nominal stock of money k = desired proportion of nominal income held in the form of nominal balances. y = real income. = demand for labor. Ns = supply of labor. P = price level. D = nominal wages. S = real saving. I = real investment, r = "the” rate of interest. The above system of nine equations can, under cer tain conditions, be solved for the nine endogenous variables' Md, P, y, r, Nd, Ng, D, S, and I. Ms and K are exogenous variables to the system. Assume that the system is in disequilibrium such that there is unemployed resources and, consequently, a less than full employment level of income. The question is: Is there any mechanism within this system to insure that a full employment equilibrium will be established? A neoclassical economist would say that there is such a mech anism; the existence and efficiency of the adjustment mech anism, however, would depend upon the existence and degree of wage and price flexibility. A typical adjustment process might proceed as fol lows: As workers found themselves unemployed they would compete among themselves for employment, thus driving the nominal wage rate (D) down. Simultaneously, producers would find unsold commodities on their shelves and would begin to lower prices in order to reduce their unplanned inventory accumulations. As nominal wages and prices fell, the demand for money would fall relative to the stock of money (see (2.2.1) and (2.2.2)); interest rates would fall making it less attractive to save (see (2.2.7))— i.e., an increase in consumption— and more attractive to invest (see (2.2.8)). Meanwhile, nominal wages are falling faster than prices (the real wage rate is decreasing) and, therefore, employment and output are increasing— both aggregate demand and aggregate supply are increasing. Thus, the system is driven towards the full employment equilibrium. 56 Keynes, however, pointed out that there are circum stances in which these automatic forces, could be stymied. The most obvious case is a situation in which nominal wages and prices are rigid; there was no disagreement, how ever, between Keynes and the neoclassicals on this point, both agreed that rigid wages and prices are apt to lead to involuntary unemployment— a situation which the wealth ef fect is powerless to overcome. The substantive issues raised by Keynes boils down to postulating certain shapes to the functions involved that would lead a purely competi tive system to come to rest at a less than full employment position; the main bone of contention, then between Keynes and the neoclassicals was an empirical question regarding the signs and magnitudes of various elasticities and co- 91 efficients. To be more specific, if any one of the fol lowing four conditions prevail the above system is pre vented from moving toward the full employment equilibrium position: 1. If the investment function (2.2.8) is perfectly inelastic with respect to the rate of interest, at least at relatively low interest rates, 2 - * - As Keynes said: "Our criticism of the accepted classical theory of economics has consisted not so much in finding logical flaws in its analysis as in pointing out that its tacit assumptions are seldom or never satisfied, with the result that it cannot solve the economic problems of the actual world." Keynes, o£. cit. , • p. 378. 57 aggregate demand could be deficient at the full employment level of income even if nominal wages and prices fall to. zero. 2. If the investment function (2.2.8) is situated such that the full employment level of invest ment can only be attained with a negative rate of interest, aggregate demand will be deficient at the full employment level of income no mat ter how far nominal wages and prices fall. 3. If the money demand function (2.2.1) becomes infinitely elastic with respect to the rate of interest at a level above the full employment rate, once again aggregate demand will be in sufficient to maintain the full employment level of income. 4. If the nominal wage rate elasticities of sup ply (marginal cost) are such that prices fall roughly in proportion to nominal wages— i.e., so that the real wage rate remains relatively constant— there is no automatic tendency for the system to move towards full employment once 99 xt deviates from this position. ^ 22in terms of the Hicks-Hansen IS-LM analysis, the above four conditions mean, respectively: (1) the IS curve will be perfectly inelastic within the range of the perfect inelasticity of the investment functions; (2.) the IS curve will intersect the income axis at a less than full employ- ! 58 An additional implication of the Keynesian analysis is that if any one of the above four conditions prevails, monetary policy will do no good. What is needed, according to the analysis, is some policy that has a direct effect on aggregate demand and does not rely on an indirect mechanism via the rate of interest. The obvious conclusion, of course, is that fiscal policy is the correct action to take to bring an economy out of a less than full employment "equilibrium." Note, however, that fiscal policy will be effective only if the proportionality of nominal wage and price changes does not hold (condition four above); in the case of perfectly inflexible wages and prices, the only way in which a full employment equilibrium position can be reached is through autonomous shifts in the production function (2.2.3) or in the supply of labor function (2.2.5). The Wealth Effect The neoclassical economists were not long in pro viding an answer to the Keynesian challenge. Gottfried Haberler was the first to come up with the answer in terms of what has since become known as the real balance effect. ment level; (3) the LM function will be infinitely elastic within the range of the infinite elasticity of the demand for money function; and (4) the IS function will be per fectly interest inelastic within the relevant range. | Haberler wrote, I | With the continuance of contraction . . . banks and individual firms become more and more liquid. Money hoards grow, both in terms of money and— since prices fall— .still more in purchasing power. Now, it is clear that this process will be accelerated if wages are reduced and prices fall more than they would ' without a fall in wages. In other words, the fall in money wages and prices reduces the volume of work which money has to perform in mediating the exchange, of goods and services in the different stages of production. Money is set free in this line of its employment, and becomes available for .hoarding. Pari passu with the fall in prices, existing money hoards (M2) rise in real value and, sooner or later, the point will be reached where even the most cau tious individuals will find an irresistible tempta tion to stop hoarding and to dishoard.23 The impact of the real balance effect was to rescue i the neoclassical system from the Keynesian challenge on the theoretical level. For now, even if the conditions set out earlier prevail, there is an automatic response that is ! capable of pushing aggregate demand up to the full employ ment level— that is, of course, the effect on the saving ; (and perhaps investment) function of an increase in real money balances held as a result of a decrease in the price ^ H a b e r l e r , qjd. cit., p. 403. However., it was ]Pigou who supplied the rationale that the later Keynesians ! have used in ignoring the real balance effect on the empir ical level when he wrote: "Thus the puzzles we have been considering . . . are academic exercises, of some slight i use perhaps for clarifying thought, but with very little I chance of ever being posed on the chequer board of actual life." A. C. Pigou, "Economic Progress in a Stable Envi ronment," Economica, XIV, New Series (1947), reprinted in ; Friedrich A. Lutz and Lloyd W. Mints. :(eds.), Readings in Monetary Theory (Homewood, Illinois: Richard D. Irwin, Inc., 1951), p. 251. 60 | level. Once again, however, notice that if condition four prevails, the real balance effect is powerless in the sense ; that it cannot force an increased level of employment and real income. A. C. Pigou took up the banner from Haberler to :argue that the real balance effect— or, in the context of Pigou1s writings, the wealth effect— rescued a purely com petitive economy from the possibility of a less than full employment "stationary equilibrium." To Pigou the possi bility of the investment function being defined at a nega tive rate of interest was not in the realm of reality; he was concerned, however, with the possibility that the sav ing function would be so situated that nil saving— to correspond to the nil investment of the stationary state— could only occur at a negative rate of interest— or, to put the matter a little differently, he was concerned with the possibility that desired saving would be larger than de sired investment in the stationary state. As Pigou put 'it, People desire additions to accumulated wealth, not merely for the income they will presently yield, but also for the amenity, in sense of power, sense of security and so on, which the possession of them carries. In these conditions the rate of interest at which they would be prepared to supply exactly a nil flow of new investment would be equal, not to the representative man's rate of time preference proper, but to this rate corrected by subtracting something to allow for that amenity; that is to say, . . . to (q-v), where v is positive. If, then, v is sufficiently large, it may happen, for all pos sible amounts of capital accumulation, that the 61 rate, of interest at which exactly nil new investment will be supplied is negative. He then rescues his system by means of the wealth effect: Since money income is continuously contracting, and prices, therefore, falling, the existing stock of money— as also the stock of land and of some other sorts of property, such as Old Masters, which are especially suitable as embodiments of, or recepta cles for, saving— is continually becoming more and more valuable in terms of consumption goods. Hence, . . . the amenity utility of a marginal unit of investment . . . grows continually smaller. But, since investment in capital instruments is no longer going on, the representative man's real income is no longer growing. Hence the utility of the marginal unit oif real income consumed . . . is unchanged. It follows that the element . . . [v] progressively con tracts, approaching nearer and nearer to nothing, as money income falls. Consequently, since our element * q is always positive, . . . (q-v) . . . must, when j money income has contracted sufficiently, not merely become positive, but approach to q. The conditions which prevented a high-level stationary state from being established are thus destroyed.24 Following Pigou1s lead, we may now state our saving function as^5 (2.2.9) S = S(y, r, M/P), where aS/a(M/P) < 0 This is only part of the picture, however. A price change not only effects the value of monetary balances but it also effects the real value of all assets that are fixed C. Pigou, Employment and Equilibrium (2d. rev. ed.; London: Macmillan & Co., Ltd., 1949), pp. 130-133. *^A. C. Pigou, "The Classical Stationary State," The Economic Journal, LIII (December., 1943) , 343-351 62 in nominal terms— the net effect has become known as the Pigou or wealth effect; or, in Harry Johnson's words. The Pigou effect in modern usage is the effect on the demand for goods of a change in private real wealth resulting from the effect of the price level on the real value of net private financial assets, . . . it is the real balance effect corrected for the presence of government debt and money issued against private debt.26 Further, what we have been discussing is what Pesek and Saving call the "price induced" wealth effect; another effect on wealth that is potentially as important as the price induced wealth effect is what they call the "interest induced" wealth effect. In Lloyd A. Metzler's words, We may say that the real value of the given common stock [in Metzler's terminology all real nonhuman wealth is measured by the quantity of "common stock"] is inversely related to the prevailing rate of interest. The higher the rate of interest, the lower the real value of common-stock holdings and conversely.27 Thus, if the interest rate decreases at all— i.e., if the demand for money function has any interest elasticity— 2 f i H. G. Johnson, "Monetary Theory and Policy," The ;American Economic Review, LII (June, 1962), 341, n. 5. The original observation that all money is not necessarily net wealth to the private sector is probably due to M. Kalecki; see his "Professor Pigou on 'The Classical Sta tionary State1: A Comment," The Economic Journal, LIV (April, 1944), 131-132. ^Lloyd Metzler, "Wealth, Saving, and the Rate >of Interest," The Journal of Political Economy, LIX (April, 1951), 101, as quoted-TrT"Boris P. Pesek and Thomas R. Saving, Money, Wealth, and Economic Theory (New York: The ■Macmillan Company, 1967), p. 13. 63 during a period of less than full employment, the economy's real wealth will be increased and the Keynesian propensity to save function will fall. The neoclassical system now ;has another device to pull itself out of a period of less than full employment income. We have to revise our saving function once again; it may now be stated in the form (2.2.10) S = S(y, r, M/P + Wn) where Wn is the stock of real non-monetary, non-human wealth, and is a function of the rate of interest such that 3Wn/9r < 0, Equation (2.2.10) contains two effects; the real balance term (M/P) and the real wealth term (M/P + Wn). The interpretation of these two quantities on the aggregate level is not completely straightforward; it is the net ef fect of changes in the wealth term that influences aggre gate economic behavior, and it is the concept of net wealth in the private sector that is in question. We shall not dwell here on this distinction; a discussion of the correct components of net wealth will be deferred to a later sec tion of this chapter. However, E; J. Mishan has brought up a point that does deserve some consideration at this time. As mentioned earlier, he differentiates between the neoclassical and \ j 64 :Keynesian system on the basis of the interest elasticity of the demand for money function. The neoclassical function is (2.2.11) Md = kPy and the Keynesian function is (2.2.12) Md = MD(Py, r) and, in equilibrium in either system (2.2.13) Mp = Mg The systems characterized by (2.2.11) are called "interest-flexible monetary systems," and those character ized by (2.2.12) are called "interest-stabilized monetary systems"; the "flexible" or "stabilized" character depends on whether or not the M0 function has any interest elas ticity. Mishan’s point is that, assuming wage and price flexibility, what he calls the "cash balance effect"— the effect of a divergence of actual from desired nominal bal ances on nominal saving and nominal investment and denoted by (MS-MD)— is operative on nominal income in either, type of system, while what he calls the "asset-expenditure ef fect" (i.e., the Pigou effect)— the effect of a change in real wealth on nominal saving and nominal investment and denoted by Mg/p— is only operative on nominal income in an OQ interest-stabilized monetary system. ° His reasoning is as follows: state the saving and investment functions (2.2.14) S = S (Py, r, [Mg-MD] , • Mg/P) (2.2.15) I = I (Py, .r, [Mg-MD] , Mg/P) where S and I are now to be interpreted as nominal values. Consider an interest-flexible system, so that (2.2.11) is the relevant money demand function. In this type of system money income is uniquely determined once k and Mg are determined— this is the crucial point of Mishan's analysis. Turning first of all to the cash-balance effect, Mishan analyzes its effect in an interest-flexible system in terms of an increase in Ms; if Mg increased autonomously, (Ms-Md)>0, and, therefore, expenditures would increase until the price level was driven up to the point where (Mg-MD)=0, and equilibrium was restored (the same result Iwould be obtained in an interest-stabilized monetary sys tem) . Consider now the asset-expenditure effect in an in terest-flexible system; assume that, for some reason, the price level falls and, consequently, Mg/P increases. This 28if wage rigidities are introduced, the. cash- balance effect is unaffected, but the asset-expenditure effect becomes inoperative. See Mishan, o£. cit., pp. 115- 118. 66 in turn shifts both the S and I functions to the right which, in general, will alter, the equilibrium levels of r and nominal saving and investment. The point is, however, that since nominal income is uniquely determined by Mg and k in an interest-flexible system, the shift in the saving and investment functions has no effect on money income. Hence, as Mishan said, If we are introduced to a disequilibrium situation in which aggregate money income and the level of prices are failing there is nothing in the operation of the asset expenditure effect by itself to inhibit this movement. In the absence of the cash balance effect, involuntary underemployment would remain and the level of money income and prices would fall in definitely. Put otherwise, the asset-expenditure relation cannot determine the level of money income in an interest-flexible system; this is a role which is reserved for the "money market" alone— for . . . [k] and . . . [Mg].29 If, on the other hand, the cash-balance effect is explicitly introduced into the saving and investment func tions, forces are automatically set in motion to cure fall ing prices and money income. Assuming that k is constant, a situation where prices and real income were falling would cause MD to fall relative to Mg; people would attempt to get rid of their unwanted stocks of nominal balances by ^spending more, and prices and money income would be driven Ibid., p. 115. However, in an interest-stabil ized economy money income is no longer, uniquely determined by k and Mg— rather it is determined in a truly general equilibrium fashion, see (2.2.12)— and, therefore, any shift in S and/or I will have an effect on money income. upwards. Mishan's. analysis, however, appears to be belabor ing a point that is well understood and that has been im puted to the real balance term since its inception. Any stock term that appears as an argument in a demand (or sup ply) function is normally interpreted to have two effects: an effect due to it being a component of wealth (Mishan*s asset-expenditure effect), and an effect due to the rela tion that the actual level bears to the desired level (Mishan*s cash-balance effect). Thus, the real balance 30 effect could be written ( [J%/P - Md/P] Ms/P) !The theoretical system developed in Chapter III of this work will take the conventional view with regard to the in terpretation of stock terms, and not the modification sug gested by Mishan. One additional point should be made concerning Mishan's work— one that will become important in Section III ^Opatinkin would not agree with this point on the grounds that the desired level of. real balances (Md/P) is itself an endogenous variable and therefore has no place as an argument in a demand function. On the individual level we agree with him; however, it is not the level of desired balances that appears in this expression, but the deviation of the desired level from the actual level. See Patinkin, Money, Interest, and Prices, op. cit., pp. 435-436. of this chapter in connection with the Archibald and Lipsey critique of Patinkin. This is that Mishan points out that, in equilibrium, the cash-balance term drops out of the equations— i.e., (Mg-Mp)=0— while, although the asset- expenditure effect is not operative in equilibrium, the asset-expenditure term is a determinant of the equilibrium level of S and I and, therefore, does not drop out of the equations in equilibrium. 3- ! - This ends our review of the wealth effect and the function that it performed in economic theory when it was first introduced. The next section will examine the role that it has come to play in monetary theory, a subject that is much more germane to the main stream of this work. III. THE PATINKIN CONTROVERSY What has become known as the Patinkin controversy is essentially concerned with the construction of a consis tent and determinant model of a monetary economy. The con text in which the controversy has taken place is a discus sion of the validity or invalidity of the classical dichot 31 These and the reasons outlined in footnote 30 above persuaded Patinkin that the asset-expenditure term is the appropriate one.to include in the demand functions. Ibid., p. 438, n. 24. 69 omy,32 whereby relative prices are determined by the real sphere supply and demand equations and the absolute prices are determined by the quantity, of money in circulation rel ative to the velocity of circulation. The controversy, in Harry Johnson's words, has become a protracted, often confused, and usually intensely mathematical investigation of the "consistency" or "validity" of the classical dichotomy, the require ments of a consistent theory of value in a monetary economy, and the conditions under which money will or will not be "neutral." . . . In the course of the controversy at least as much has been learned about the difficulty of extracting theoretical conclusions from systems of equations as has been contributed to usable monetary theory.33 This does not mean-, however, that the controversy is a sterile debate that has no relevance for monetary 32^e shan define the "dichotomy" as a situation in which the real variables (relative prices and the rate of interest) are independent of both the supply and demand for money, in both a schedule and quantity sense. An alterna tive definition is that, if the dichotomy prevails, the real sphere equations may be solved independently of the monetary equations; the converse need not be true. On the other hand, money is said to be "neutral" if the real sphere equations are independent of the supply of money; again, in both a schedule and quantity sense. No tice that the dichotomy implies neutrality, but not vice versa. See Franco Modigliani, "The Monetary Mechanism and Its Interactions with Real Phenomena," The Review of Eco nomics and Statistics, XLV, Supplement (February, 1963), 83-84. 33johnson, d£. cit., p. 337. 70 ; theory; on the contrary, as Patinkin put it, Our ultimate interest is the developing of models to explain the. real economic world. It is the contention of this paper that such models should be internally consistent and should provide a determinate solution for the economic variables they attempt to explain. Models which do not meet these requirements should not be given any further consideration— not because they are "mathematically inelegant," but because their ability to represent the real world is doubted. On the other hand, models which do meet these require ments should then be subjected to empirical testing, and accepted or rejected on this basis.34 Thus, we shall examine the major contributions to this debate in some detail in the hope that it will shed considerable light on the structure of a consistent and determinate model of a monetary economy. Consistency, Determinacy, Dependence, and Validity A good deal of the confusion that has entered into this controversy is due to the failure of the contributors, in most instances, to make clear the sense in which they were using the words consistency, determinacy, dependence, and validity.. Consider the following system of simultaneous equa- : tions (2.3.1) Xj(p^, P2 Pjft) = .0 (j-=3 * . / . 2 m) ■^Don patinkin, "The Invalidity of Classical Mone tary Theory," Econometrica, XliX (April, 1951), 136. 71 Mathematical consistency implies that there exists at least one set of values of the variables such that all equations of (2.3.1) are satisfied— i.e., Xj (j=l, 2,..., m) vanish. Generally, determinacy implies that the number of consis tent solutions be finite.^5 Mathematical consistency, as defined above, must be carefully distinguished from logical consistency. A set of propositions is said to. be logically inconsistent if "it 36 simultaneously implies a propositon and its negative." This distinction is quite important in that a good deal of the latter stages of the Patinkin controversy hinge on a confusion of these two types of inconsistencies. Dependence can apply to either functional depen dence or equational dependence. The system Xj (j=l, 2, .. ., m) is said to be functionally dependent if there is a functional relationship, f(Xlf X2,..., = 0, that con nects them. As Patinkin has shown, there is no relation ship between functional dependence and consistency. On the other hand, equational dependence occurs if "a solution of [m-1] of . . . [the Xj] is necessarily a solution of the ■^In economics two additional requirements are usu ally put on the solutions: (1) the solutions must be in the positive, real number domain; and (2. ) the solutions are unique. Patinkin, Money, Interest, and Prices, op. cit., p. 177. . . . [mt h ] . " 37 Both the neoclassical and modern general equilib rium theorists have been careful to insure that the number of unknowns exactly equaled the number of interdependent equations— if the system were underdetermined (i.e., more unknowns than equations) the system would be indeterminate; if the system were overdetermined (i.e., more equations than unknowns) the system would be inconsistent. However, the equality of the number of equations and unknowns is neither a necessary nor sufficient condition for determi nacy or consistency. Nevertheless, the Patinkin contro versy has proceeded on the assumption that equality of equations and unknowns is a necessary, though not suffi cient, condition for both determinacy and consistency. Finally, the term "validity," as used in the con text of this controversy, generally applies to a system that is both consistent and determinate. In certain as pects of the debate, however, a little "casual empiricism" has crept into the analysis; in these cases, a "valid" system would, additionally, be required to correspond to what is felt to be actual market behavior. 37W . . . Braddock Hickman, "The Determinacy of Absolute Prices in Classical Economic Theory," Econometrica, XVIII (January, 1950)., p. 12, n. 5. 73 j The Patinkin Controversy The origin of the controversy can probably be traced back to the General Theory, where Keynes observed that so long as economists are concerned with what is called the Theory of Value, they have been accus tomed to teach that prices are governed by the con ditions of supply and demand; and, in particular, changes in marginal cost and the. elasticity of short-period supply have played a prominent part. But when they pass in volume II, or more often in a separate treatise, to the Theory of Money and Prices, we hear no more of these homely but intel ligible concepts and move into a world where prices are governed by the quantity of money, by its income- velocity, by the velocity of circulation relatively to the volume of transactions, by hoarding, by forced saving, by inflation and deflation et hoc genus omne; and little or no attempt is made to relate these vaguer phrases to our former notions of the elasticities of supply and demand. . . . The division of Economics between the Theory of Value and Distribution on the one hand and the The ory of Money on the other hand is, I think, a false division.38 Oscar Lange took up the charge from here, claiming 'that: "Say's Law [Identity] precludes any monetary the ory."3^ Consider an economy where there are m-1 goods and services and money (the m^*1 commodity). Let Dj (j=l, 2, ..., m) be the market demand function for the j commodity land Sj (j.=lf 2,..., m) be the market supply function of the 33Keynes, 0£. cit., pp. 292-293. 3 9 ^Lange, op>. cit., p. 6 6. 74 same commodity. The equilibrium prices are determined by (2.3.2) Dj(p-^f $2' * ' ’r = ^j^l' ^2' * * *' ^m^ (j=l^ 2f , m) However, by Walras 1 Law m m (2.3.3) £ p.D. = £ piSi j=l JJ j=i J J we know that one equation of (2.3.2) is not independent; hence, the solution of (2.3.2) yields the m-1 equilibrium prices of the m-1 goods and services; the Dm and Sm can, since pm s 1 by definition, be deduced from this informa tion. Now, add Say's Law which, in this context, is in terpreted as Say's Identity m-1 m-1 (2.3.4) I p.D. = £ p.S. j=l - J J j=i 3 3 which, by referring to (2.3.3), we can immediately see implies (2.3.5) D - S ~ 0 m m Further, the introduction of Say's Identity means that one of the commodity Dj and Sj (j=l, 2,..., m-1) is now not independent; we have m-1 pj's but only m-2 independent Dj and Sj. We can now only solve for the m-2 relative prices, and (choosing pm_^ arbitrarily) system (2.3.2) becomes Sjtel/pm-l' p2/pm-l'••*' pm“2^pm-l^ (j=l/ 2, . . . . , m) There is nothing in (2.3.6) to determine the abso lute prices; this was accomplished by introducing the Cam bridge equation, which can be written m-1 (2.3.7) kpm_-L 2 (Pj/Pra-^S. - M = .0 (= %-S^ j=l J where M is the nominal stock of money in circulation. If this equality does not hold, this implies that Dm - Sm ^ 0 — i.e., there is an excess demand in the goods and services market. Hence, in a Say’s Identity economy, (2.3.7) must be written m-1 (2.3.8) kp x £ s * 3=1 J J For this identity to hold k must be a variable that adjusts itself to any value of the identity cannot serve to determine the value of k or pm_i— the absolute price level is indeterminate (i.e., there is an infinite combination of k and Pm_2_ that would satisfy (2.3.8)). Nearly sixteen years after the publication of Lange's article, Jose Encarnacion proved that Lange's math- ematical proof of the indeterminacy of absolute prices in the classical system was in error. We may look at Lange's proof as a syllogism; (2.3.5) is the major premise, (2.3.7) is the minor premise, and (2.3.8) is the conclusion. Encarnacion pointed out that (2.3.8) is a stronger state ment than (2.3.7); hence, the inference is not valid.^ Patinkin took up Lange's charge shifting the empha sis from Say's Law to the "homogeneity postulate," by which is meant that the excess demands for goods and services are independent of the absolute prices and only dependent on relative prices.^ Patinkin attacked the classical system on two levels, the micro level (what he called the Walras ian system) and the macro level (what he called the Cassel- ian system). The micro system. The neoclassical general equi librium analysis assumed that individuals derived no direct utility from money balances; therefore money did not enter ^Jose Encarnacion, Jr., "Consistency Between Say's Identity and the Cambridge Equation," The Economic Journal, LXVIII (December, 1958), 827-830. This error is known in formal logic as the fallacy of the "Illicit Process of the Minor"; see F. C. S. Schiller, Formal Logic (2d ed.; Lon don; Macmillan and Co., Limited, 1931), p. 182. 4-^In a barter economy Walras' Law insures that the excess demand functions are homogeneous of degree zero in prices. However, when circulating money is introduced in a "consistent" manner into the analysis the homogeneity disappears— any homogeneity must be introduced into the system either by postulating Say's Identity or by directly postulating homogeneity of the market functions. 77 the utility function. However, for the sake of argument assume that individuals do plan to hold a positive stock of money; the budget constraint of the it*1 individual may then be written E p . X . . S E P - ; X * . . j=l *3 ^3 j=i 13 where the m^h good is circulating money, and the notation is identical as that used in Section I of this chapter. The individual then wishes to maximize the function m m (2.3.9) (2.3.10) m m A( E " 2 Pix*±i) j=l 3 ^ j=l 3 13 where A is a Lagrangian multiplier. The maximization yields 3uj (2.3.11) Ap. = 0 (j=l, 2,...,m-1) “ ij 3 (2.3.12) - Apm = 0 m m (2.3.13) -( e P^Xijj - E p.x*..) = 0 j=l 3 j=l 3 13 Consider (2.3.12); since pm = 1, this implies that A =0. (2.3.11) can then be written 3u. (2.3.14) — 1 = 0 (j=l, 2,..., m-1) If we assume that the marginal utility of a finite amount of any good is positive, (2.3.14) implies that the individual will consume an infinite amount of each good, i.e. , (2.3.15) . (j=l/ 2,..., m-1) Substituting this result into the budget constraint (2.3.9), we have (2.3.16) xim = - » / It is clear, however, that (2.3.16) cannot be a meaningful solution, the x^_. must satisfy (2.3.17) xij > _ 0 (j=l, 2,. . ., m) This is violated for i=m; equivalently, write (2.3.17) for i=m as (2.3.18) Kim = .yim2 where y^m is a real variable. The individual now wishes to maximize his utility subject to (2.3.9) and (2.3.18), i.e., m m (2.3.19) v. = ui( ) - A( 2 p-iXji - 2 p^x*. •) - j=1 J j=1 J J ^<xim " ^im2) where A and y are Lagrangian multipliers. The maximization procedure yields the following 79 (2.3.21) -Ap-y=0 m (2.3.22) 2viyim = 0 m m (2.3.23) E p^x.. - l P-ix*ii = 0 j=l ^ j=i 3 (2.3.24) xim - ^im ~ ® ' Consider (2.3.22); there are three possibilities: (1); |1=0, y^^O; (2) y^O, yim=0.; (3) ii=yim=0. If alterna tives (1) or (3) is true than y=0, and we are back to the situation (2.3.16). Since this is not an admissible solu tion, alternative (2) must be true. Substituting this into (2.3.18) we have (2.3.25) Xim = 0 i.e., people will desire to hold a zero stock of money bal ances no matter what the prices. If we define excess de mand as the desired level minus the initial endowment, (2.3.26) xi;. = (x— - x* — ) (j=l;,. .2,..., m) and (remembering that excess supply is negative excess de mand) substitute (2.3.25) into (2.3.26), we have (2.3.27) Xim = (0 - x*. ) = - x*. im ' im un i.e., each individual will wish to supply his entire ini tial endowment of money no matter what the prices are. The 80 implication of the above analysis is that for the system (2.3.20)-(2.3.24) to be consistent it is necessary for the initial stocks of circulating money to be zero. When this condition is met, the budget constraint (2.3.9) has the form m-1 m-1 (2.3.28) S p-ix-. = 2 p-x*. • j=l J j=i 3 ID This led Patinkin to conclude, If money does not enter the utility function, people will certainly not hold money. Hence we could not possibly have any realistic monetary economy. In fact, . . . the classical discussion of a "monetary economy" is involved in a contradiction unless there are no stocks of moneyI Thus the classical theory deals with money only as a counting unit. There is no treatment of its far more important functions as a medium of exchange or store of value.42 ^Don Patinkin, "Relative Prices, Say's Law, and the Demand for Money," Econometrics, XVI (April, 1948), 135i In this same article Patinkin came to several other conclu sions that bear directly on our analysis: (1.) Say's Law for the individual (SLI) holds if and only if xj_j - x*ij50; and Say's Law for the market (SLM) holds if and only if Xj - x*j=0. Ibid., p. 147. (2) SLI is a sufficient condition for SLM, Under most con ditions , SLI is also a necessary condition for SLM. Ibid., pp. 147-148. (3) If money does not enter the utility function, a neces sary condition for consistency is that the Xij (j — 1, 2f ..., m-1; x=l, 2,..., n) be homogeneous of degree zero in prices. This homogeneity property is a necessary condition for SLI to hold. Ibid., p. 149. (4.) A necessary and sufficient condition for the x^j (j=l, 2,..., m-1; i=l, 2,..., n) to be homogenous of degree zero in prices is that SLI be true. Ibid., p. 153. 81 There has been no dispute about Patinkin's conclu sion that, in the above system, absolute prices and the velocity of circulation would both be infinite. However, Karl Brunner, following the lead of Jacob Marschak, pointed out that money need not appear in the individual1s utility function to keep velocity at a finite level.^3 Specifi cally, assume that there is some other relation, besides the budget constraint, that relates money to variables that do enter the utility function; utility will then be maxi mized subject to two constraints. Assume that the monetary constraint takes the form (2.3.29) xim = k± I Pj(xi:j - x*^) where s<m-l. The summation on the right is the total value ^Karl Brunner, "Inconsistency and Indeterminacy in Classical Economics," Econometrica, XIX (April, 1951), 152- 173; and Jacob Marschak, "The Rationale of Money Demand and of Money Illusion," Metroeconomica, II (August, 1950), 71- 100.. Marschak's presentation differs from that in the text (which follows Brunner's work) in that Marschak traps ve locity at a finite level by introducing (1) price expecta tions into a multiperiod analysis, or by introducing (2) the idea of transaction costs. Additionally, Patinkin's micro system has been cri ticized as being contradictory in the sense that if money has no utility it follows that its price must be zero (Cecil G. Phipps, "A Note on Patinkin's 'Relative Prices,'" Econometrica, XVIII (January, 1950), 25-26). Subsequently, Patinkin has pointed out that under these circumstances money acts only as a pure unit of account and, therefore, no contradiction is involved in assigning it an arbitrary value. See Patinkin, "The Invalidity of Classical Monetary Theory," op. cit., p. 135. 82 iof all goods and services that the individual's excess demand for is non-zero. The k^ is a constant that is de termined "outside the economic nexus." The individual wishes to maximize his utility subject to (2.3.9) and (2.3.29). Form the new function m m (2.3.30) W. = u±( ) - X ( E p.x.. - E Pix*ii) j=l J J j=l J J - y ^xim - ki where X and y are Lagrangian multipliers. The maximization yields 3Uj_ (2.3.31) - Xp. + yk-p. = 0 (j=lf 2,..., s) 9x.. 0 1 J 13 9ui (2.2.32) — - Ap.i = 0 (j=s+l, s+2,..., m-1) i j J (2.3.33) - Apm - ] i = 0 where pm = 1 m m (2.3.34) E d-Xj ■ - E p.x*.. = 0 where p_ = 1 j=l 3 13 j=l ^ 13 (2.3.35) xim - k± s 3 i * Pj(Xij “ X*ij) = ° The above system contains m+2 equations in m+2 variables— the xi;. (j=l, 2,..., m), X, and y. By inspec tion it is obvious that there is no mathematical reason why 83 ' individuals would not wish to hold a positive stock of money; the problem arises in the economic interpretation of the monetary constraint (2.3.29). Don Patinkin, com menting on both Marschak's and Brunner's work, observed that Jacob Marschak's model . . . explains the holding of money for speculative motives, even though money does not enter the utility function. In principle it seems that a similar result can be achieved for the transactions motive. Nevertheless, I still feel that that part of monetary theory which deals with the precautionary motive is best approached by placing money into the utility function. This would represent "the satisfaction derived by individuals from holding money as a means of dealing with un certainty." Brunner's model . . . is an attempt to provide a microeconomic explanation of the holding of money for the transactions motive, on the assumption that money does not enter the utility function. Unfortu nately, I do not believe that he succeeds. . . . He merely confronts us with "some restriction with respect to the rate of utilization of given stocks of money," without giving any indication as to the origin or economic meaning of this restriction. Until this information is forthcoming, Brunner's "additional restriction" can be considered only as a mechanical device— without economic content— which assures that the results of his maximization will yield nonzero holdings of money.44 The macro system. Once we move from the micro to ;the macro level the homogeneity of the supply and demand ; functions becomes a postulate rather than a theorem (unless, 44Patinkin, "The Invalidity of Classical Monetary Theory," op. cit., p. 148, n. 28. of course, the macro functions are built up from micro functions that assume the presence of Say's Law for the individual). This "homogeneity postulate" of the neoclas sical macro economists, according to Patinkin and others, lead them to commit certain logical errors in the construc tion of their theory of a monetary economy; in particular, Patinkin found the neoclassical system deficient in two respects. The explicit and implicit money functions.— Before going on to consider the logical errors, it is first neces sary to investigate the type of money functions that occur in the neoclassical system. Assume, once again, that there are m commodities— the m1 - * 1 being circulating money. If we wish, the market functions can be written (2.3.36), Dj(p^, p2 , •. • , Pm_^ = (P]_, P2 ’ * * * ' ^m-1^ (j 1, 2,•.•, m) where the Dj and Sj are market demand and supply functions, respectively, for the jth commodity and the Pj (j=l, 2,..., m-1) are the corresponding prices. By Walras1 Law we know that m-1 (2.3.37) Djfl = Dm (Pi/ P2 / • • • f Pm-1^ ~ S P-i^T^Pi' j=l J J p2; , ‘ "' Pm-l1 and I 85 | | (2.3.38) Sjq - ' ' ’ * ' Pm-l^ ~ m-1 S PjDjfp-L, p2,..., pm_x) 3=1 J (2.3.37) and (2.3.38) are the so-called "implicit” money relations, and they consider the supply and demand for money in flow terms. However, the neoclassical econo mists were more apt to consider money in stock terms, spec ifying that in equilibrium the desired stock of money would equal the actual stock. This is the so-called "explicit" money relation; the usual form of which is the well known Cambridge equation. It is intuitively obvious that the implicit and explicit money relations cannot be independent of each other. To see this relation, divide the economy into two sectors: the private (P) sector and the government-bank (B) sector. Assume that the B sector has no demand for money balances, so that (2.3.39) = Md where MQ is the desired level of money balances considered as a stock, and the superscript refers to the sector in volved. Assume further that the planned stock demand (MD) and the planned supply (Mg)— which is under the control of the B sector— are functions of the prices | 86 ' (2.3.40) Mq = P 2 P m —i) (2.3.41) Mg = Mg (pj/ P2 r • »• / ^m—1^ Let M° be the initial stock of money balances at •3 the beginning of some relatively short period of time, and Mg the planned stock at the end of this period. Then (2.3.42) MD - M§ 2 - s£ i.e., the planned change in the money stock by the P sector must be identically equal to their excess demand for other commodities; and (2.3.43) Ms - M° ■ S* - D® i.e., the planned change in the money stock by the B sector must be identically equal to their excess demand for com modities other than money. Rearranging and subtracting (2.3.43) from (2.3.42), we have (2.3.44) 1 ^ - Mg 5 (d£ + D*) - (S* + S*) I Letting Mx = Mq - Mg (the excess stock demand) and ! ! ^m = °m “ sm (where Dj-^ h Dm + Dm Sm - Sm + Sm) t (2.3.44) j becomes i (2.3.45) Mx = 5^ 1 This means that the statement Mx = 0 is equivalent to the ! statement Xm = .0. 87 Invalidity I.— It can be shown that if the [Sj (D ■) ] ( [ j ] —1.,. .., [m] - 1) are homoge neous of degree 0 in all the variables, then [Dm (S )] is homogeneous of degree 1 in the same variabl.es. More generally, if the [Sj {D.) 3 ([j]=l, ..•, [m3 -1) are homogeneous of degree t in all the variables, then [Dm (S_)] is homogeneous of degree t+1 in the same variables.45 This means that the (2.3.46) ^(pi t P2*• • * » Pm-i^ — ® Is homogeneous of degree one in the p^ (j=l, 2,..., m-1) if the m-1 commodity equations are homogeneous of degree zero in the same variables. However, the M^. function is usually stated in the Cambridge form (2.3.8), which, since k and M are constants, cannot be homogeneous of any degree in the prices alone. But, by (2.3.45), must be identically equal to ^ — hence, "The classical homogeneity assumption is logically inconsistent with the classical monetary equation.1,46 Invalidity II.— Consider the following system of equations: ^Don patinkin, "The Indeterminacy of Absolute Prices in Calssical Economic Theory," Econometrica, XVII (January, 1949), 14. The quotation has been changed only to make Patinkin's notation consistent with ours. The term "Invalidity I," however, comes from Patinkin, "In validity . . . ," o£. cit., p. 138. ^^Patinkin, "Indeterminacy . . . ," ££. cit., p. 16. 88 (2.3.47) xj(Pl/Pm-l' p2//pm-l' * * ‘' pm-2/pm-l^ = 0 ( j=1, 2 , / ... r m— 1) m-1 (2.3.48) z p.x.( ) = 0 j=i ^ j which has been stated in terms of excess demand functions and takes explicit account of the homogeneity postulate. Notice that the system (2. 3.47)-(2.3.48) is free of Inva lidity I since (2.3.48) is homogeneous of degree one in the prices. The question is: Is this system consistent and determinate? By Walras' Law we know that any solution that sat isfies (2.3.47) must, if the system is consistent, also satisfy (2.3.48). This means, however, that if (2.3.47) has multiple solutions (2.3.48) cannot be used to eliminate any of them. Now, the system (2.3.47) has m-1 equations in the m-2 price ratios; there are, in Patinkin's words, a total of three mutually exclusive possible alter natives: (a) There may be no subset of . . . [m]-2 equations with a solution. . . . (b) There may be a subset of [m]-2 equations with, a solution, but one that does not satisfy the remaining equation. . . . (c) There may be a subset of [m]-2 equations with a solution that does satisfy the remaining equation.47 j 47patinkin, "Invalidity . . . ," op. cit., p. 141. The following proof is independent of the equation that is eliminated by Walras' Law. Patinkin has shown that "no matter what equation is disregarded, we always end up with the same system that we would have obtained by disregarding the excess-demand equation for money." Ibid., p. 140. For an alternative proof, see Brunner, "Inconsistency . . . ," :op. cit., pp. 152-167 and pp. 171-173. | If alternatives (a) or (b) prevail the system is I inconsistent. However, if the system is consistent— i.e., !alternative (c) prevails— (2.3.47), by reason of the homo geneity postulate, only determines the m-2 price ratios and ; any multiple of these price ratios will satisfy (2.3.48). jTherefore, even in the absence of Invalidity I, the neo classical system as presented above is either inconsistent ;or indeterminate in the absolute (money) prices. Say's Law cannot save the system. When Say's Law :is introduced we lose another degree of freedom? the excess demand function for the (m-2)n<^ commodity then has the form m-2 c (2.3.49) Z Pi^( ; ) | j=l J J iwhich is identically equal to zero when the other m-2 ex- ;cess demand functions are satisfied. This implies that the jmoney market is always in equilibrium; alternative (b) is i j eliminated, but (a) and (c.) are still very real alterna tives and Invalidity II still holds.48 Another system considered by Patinkin, and one 48wassily Leontief ("The Consistency of the Clas- |sical Theory of Money and Prices," Econometrica, XVIII i(January, 1950),21-24) argues that Say's Identity removes I the inconsistency from the neoclassical system. Ignoring |alternative (a) of the text, Leontief is correct; however, ISay's Identity does not remove the indeterminacy of the ab- isolute price level (i.e., Invalidity II). See Patinkin, "Invalidity . . . ," op. cit., p. 142, n. 18. 90 j | which is of some interest to us, is one where there are two t : non-homogeneous equations in the system. Let Xj (j=l, 2,..., m-2) be homogeneous of degree zero in pj (j=l, 2,..., m-2) , and non-homogeneous in the same variables— Xm_ - j _ can be interpreted as the excess demand function for bonds, and, if this is so, p , would be a function of the * ■ m-i rate of interest. Now, if is non-homogeneous the theorem quoted in connection with Invalidity I can no longer be applied, so that Xn will also be non-homogeneous— the implicit and explicit money demand functions are no longer contradictory and Invalidity I is absent. With regard to Invalidity II, Walras1 Law makes one equation not independent; if we elim- : inate we have m-2 equations Xj (j=l, 2,..., m-2) to :determine the price ratios and a non-homogeneous function ;— Xm— that is equationally independent of the others and is, therefore, able to determine the absolute prices (i.e., Pm_i); hence, Invalidity II is also absent. Patinkin rejects this "modified Lange" system on ithe grounds [that there is no] justification . . . for singling out one particular equation and assuming it to be nonhomogeneous. . . . A satisfying solution to our problem cannot be achieved by such ad hoc and arbitrary assumptions.^ As Patinkin has subsequently pointed out, however, Karl Brunner has shown that under certain assumptions as to the operation of the banking system there may be good reasons for assuming nonhomogeneity in the bond equation.50 Patinkin's critique of the neoclassical macro sys tem has not enjoyed the general acceptance that his cri tique of the micro system has. In fact, it has triggered the long and involved debate that was alluded to earlier in this section. Before proceeding on to review the other contributions to this controversy, we shall first consider Patinkin's solution to the problems that are due to the classical dichotomization of the pricing process. Patinkin System Patinkin's critique of the neoclassical general equilibrium theory (at least at this stage of the analysis) i is this: The Walrasian and Casselian systems are really an attempt to explain the workings of a barter economy; the 49Patinkin, "Indeterminacy . . . ," 0£. cit., p. 23. ;The original system referred to by Patinkin is in Oscar Lange, Price Flexibility and Employment (San Antonio: Principia Press, 1945), pp. 99-103. 5°Patinkin, "invalidity . . . ,1 1 o£. cit., p. 144, n. 24. The reference to Brunner refers to "Inconsistency . . . ," 0£. cit., p. 164. 92 | only money in such a system is one that performs but one ; function— namely, it acts as a pure unit of account with no objective existence, it is not sufficient to merely tack on an additional equation to this system to explain the be havior of a monetary economy— this violates the spirit of simultaneity that pervades the neoclassical model of a bar ter economy. To this end, Patinkin suggests that stocks as well as flows should appear in every equation in the system; and further, that it is the real value of the stocks that con cern the individual and not their nominal value. In other words, the price level should appear in each and every equation. Consider a closed economy in which there are n in dividuals (i=l, 2,..., n), each of which has an initial endowment of m-2 capital goods which are non-depreciating and non-transferable. However, the services— (j=l, 2,..., m-2)— of these capital goods are salable to other consumers. Assume further that no production activities are carried on in this economy. Let the (m-l)st and the ■^The following presentation follows that of Don Patinkin, "Further Considerations of the General Equilib rium Theory of Money,” The Review of Economic Studies, XIX, No. 45, 186-195. It should be noted, however, that the Patinkin system is based on the suggestion to include money in the utility function made earlier by Paul Samuelson. See Samuelson, o£. cit., pp. 117-122. | 93 |mth commodities be the number of bonds {perpetuities paying ;$1 per period) and circulating (specifically, paper) money, respectively, and denote the individual's initial endowment of these by x*£ and x*-m, respectively. Both bonds and money are transferable assets; and, notice that x*- can be either positive (if the individual is a creditor) or negative (if the individual is a debtor). Even though it is possible to construct a model that allows for finite money balances without including money in the utility function, assume that individuals do derive utility from holding money balances, not because of the utility of the goods and services that the money can be used to purchase, but because of the sense of security, etc. that flow from a stock of money. We can, however, !identify two reasons for holding bonds: (1) to redistrib ute consumption over time, and . (2) to satisfy the "precau tionary motive." This latter motive imputes direct utility ;to bonds; hence, both bonds and money appear in the indi- j ;vidual's utility function. ! I This discussion indicates that this model differs jfrom our earlier (Section I) model in two respects. In the first place, money and bonds now appear in the individual's jutility function (bonds were not considered in the analysis of Section I); and, in the second place, we must now take an intertemporal approach to adequately take into consider- ation the individual's desire to redistribute consumption over time.^2 Consider an individual with a two period time hori zon and who has a unitary elasticity of price expectations in the sense that he expects prices next period to be the C O same as those that prevailed this period. His utility function may be written (2.3.50) ui<xil' xi, rn-2' 'pm-lxi,m-:i/p* ' xir/p' x'il' x’i2 x'i,m-2' <Pm-lxi,m-l/p>' xir/p> where the primed quantities are the planned flows and •stocks at the end of the second period, Pm_i is the recip rocal of the rate of interest, and P is the price level 52in an earlier version of this model (Don Patinkin, "A Reconsideration of the General Equilibrium Theory of Money," The Review of Economic Studies, XVIII, No. 45, 42- 61), Patinkin based his analysis on one period only. As :F. H. Hahn later pointed out, in the absence of a multi period analysis or some other means of rationalizing the jrate of interest (e.g., price uncertainty), the rate of in terest will not appear in the market functions. "Hence, | [in Patinkin1s earlier model] the rate of interest can be lanything at all, and . . . [the model is] indeterminate in ithe ra’ te of interest." F. H. Hahn, "The General Equilib rium Theory of Money— A Comment," The Review of Economic I studies, XIX, No. 50, 182. 53gtrictly speaking, unitary elasticity, of expecta tions means that any "changes in price are expected to be permanent." Hicks, op. cit., p. 205. 95 defined as m-2 (2.3.51) P = E w.p. j=l 3 3 where the Wj are given weights. The individual's budget restraints for the first and second periods, respectively, are m-2 (2.3.52) E p.(x..-x*,.) + p (x. -x* ) + j_2_ j 13 13 m-1 i ,m-l i,m-l <xinTx*im> - x*i,m-l s 0 m-2 (2.3.53) + Pm-l<x'i,m-l-Xi,ia-l> + ^x'im-xim^ " xi,m-l E 0 i.e., for the individual, the sum of the excess of consump tion expenditures over sales of consumption goods plus the change in holdings of bonds— assuming that trading in bonds takes place only on the last day of the period and remem bering that Pm_^ is the reciprocal of the rate of interest i — and money minus the interest receipts (payments) must jequal zero in each period. The individual wishes to maxi mize (2.3.50) subject to (2.3.52) and (2.3.53); to this end, [form the new function I ! I (2 .3.54) Z± = u±( ) - A(2.3.52) - y(2.3.53) i iwhere the X and y are Lagrangian multipliers. Differen- tiating the partially with respect to the Xf j, x'ij (j=l, 2,..., m) and A and n, we have 3u^ (2.3.55) Apj = 0 (j=l, 2,... m-2) 9u- l (2.3.56) Pm-1 - l ,pm_1 + u = 0 3ui (2.3.57) - x + u = 0 (2.3.58) 3xV[j " ypj = 0 Cj=lr 2 m-2) Pm-l av1. (2.3.59) - ~ - PPm-X - .0 8U. (2.3.60) 3x'im — ---- - u = 0 which, together with (2.3.52) and (2.3.53), gives us 2m+2 equations in 2m+2 unknowns. Eliminating the A and u, and rewriting the budget restraints in a more convenient form, we have 97 9ui 3u± 3x'im ( 2 . 3 . 6 2 ) -------------- ■ + = 0 9xi,m-l 9xim Pm-1 3u^ 3X ij Pj (2.3.63) =. (j=l, 2,.. ., m-2) 3 U*5 s 3X' 1m 3llj_ 3Uj_ (2.3.64) = ----- = 0 9X i,m-l 9X im m-2 + (1/P) “ (x*i,m-l^^ ~ ® (2.3.65) ^ (Pj/P) (Xij-K*i:j) + (Po-l/P) m-2 (2.3.66) s. (Pj/P) + (P^/P) (x'i;m_1-xijm_1) 3 ~ + (1/P) (x “ (1/P) (Pm-ixi ,m—1^ d/Pm-!-) = .0 (2.3.61)-(2.3.66) may be solved for the 2m depen dent (endogenous) variables x^j* x'ij 2,..., m-2), Pm-lxi,m-l/E< Pm-lx'i,m-l/p' xiit/p' and x’in/p in terms of the independent (exogenous) variables pj (j=l, 2,..., m-2), Pm-1' p r x*ij 2,..., m-2), x*irin_i' anc^ x*im to yield, for the first period under consideration, (2.3.67) X^j — xj i _ j tP]_/P/ P2/P* • • • f &m-2^' ^m— 1' m-2 < 4 Pjx*ij/p) + <Pm-lx‘i,m-l/P) + '98 + (x*. /P) + (x*. _ i/P)] - x*.. (j=l, 2,... , m-2) (2.3.68) = (p/Pm-l^xi,m-l tP i/p' P2/p'***' pm-2/p/ m-2 Pm-1' Pjx*ij/p^ + (Pm-lx*i,m-l/'E^ 3=1 J + <x‘in/P> + - x*i,m-l m-2 (2.3.69) Xj_m = - pjXij “ pm-lXi,m-l This system contains m-1 independent equations and m unknowns— the X^j (j=l, 2,..., m-2), X^fin-ir and xim* Once the X^j (j=lf 2,..., m-1) have been determined from (2.3.67) and (2.3.68), however, the X^m is automatically determined from (2.3.69). By inspection, it is obvious that (2.3.67) is homogeneous of degree zero in the Pj (j=l, i | 2,..., m-2), P, and x*^mf but not homogeneous in I the pj (j=l, 2,..., m-2) alone. On the other hand, (2.3.68) and (2.3.69) are homogeneous of degree one in the same, variables. Aggregating over all individuals (i=l, 2,..., n), we arrive at the market excess demand functions 99 (2.3.70) Xj — Xj [p-^/P, P2/P,..., Pm—2/^>f Pm—lf m-2 ( 2 p.x*./P) + (x*/P) ] - x*. = 0 j=l 3 3 3 (j=l, 2,...., m-2) (2.3.71) ^m—1 = t^/Pm-1^^m-l i-Pi/P/ P2/^'***' Pm—2 ^ ’ m-2 Pm-1- • < * Pjx*j/P)+6c*m/E' l 1 = 0 3 - r m-2 (2.3.72) ^ = - L pjXj - = 0 3=1 which exhibit the same homogeneity properties as the sys tem (2..3.67) —(2..3.69) . The system contains m-1 independent equations in m variables— the pj (j=l, 2,..., m-2), Pm_j_/ and P. However, P is a function of the pj as defined by (2.3.51); therefore our system (2.3.51), and (2.3.70)- (2.3.72) contains m independent equations in m variables, and is, by our counting rules, consistent and determinate. It can be readily verified that, because of the indicated homogeneity properties, this system is free of both Invalidity I and Invalidity II. This is what Patinkin meant when he said, "A money economy without a 'money 100 C A illusion' is an impossibility." Money illusion, up to this time, had been defined as a situation in which indi viduals were influenced by absolute, rather than relative, prices. In view of Patinkin's reformulation and integra tion of monetary and value theory, the above definition must be changed: An individual is free of money illusion if the amount he demands of any real good (commodities, real bond holdings, and real money holdings) remains invariant under any change which does not affect relative prices, the rate of interest, the time stream of real incomes, and the real value of initial bond and money holdings.55 The market functions exhibit the classical property that a change in the nominal quantity of money changes the money prices proportionally, but leaves the rate of inter est unchanged. Notice, however, that in (2. 3.70) - (2 .3.72) the bond term disappears. Remembering that in a closed ; economy .2. pm-lx*i,m-l = i=l the disappearance of the bond term implies that the dis- ; tribution of bonds does not affect economic behavior— i.e., the reactions of debtors and creditors to economic stimuli are identical. If we assume that there are distributional ^Patinkin, "Indeterminacy . . . ," oj>. cit., p. 2. Italics in the original are omitted. 55 . • ^ Patinkin, Money, Interest, and Prices, op. cit., p. 72. 101 effects the market functions would contain a series of ■ terms reflecting this fact, and the invariance of the rate : of interest to changes in the nominal quantity of money ! would no longer apply. The purpose of this rather abbreviated review of Patinkin1s work has been to indicate the main features of the system that has been proposed as an improvement over the traditional neoclassical model presented in Section I of this chapter. To review briefly, the main feature of the Patinkin model is that real wealth (defined, in this icase, as real income plus real bond holdings plus real money balances) appears in each and every equation of the system; the implications of this have been subjected to a great deal of analysis by Patinkin in other works.^6 It now only remains for us to review the contributions of the critics of the above system; this.is the last topic of this |section. | |The Critique of the IPatinkin System Although it is seldom satisfactory to divide the contributions to any concept into compartments, it will be j instructive to consider the contributors to this critique [ ■ j _ _ _ I ^ P r i m a r i l y in Money, Interest, and Prices. 102 as falling roughly into one of three categories: (1) Those I that take exception to the definition of consistency as used by Patinkin, (2) those that differ as to the interpre- tion of the money equations, and (3) those that differ in the interpretation as to what the neoclassical system is supposed to show. The definition of consistency. One of the corner- ! stones of Patinkin's criticism of the neoclassical system, and the claimed superiority of his own system, is the in consistency between the explicit and implicit monetary functions. Assume that the implicit function is homogene ous of degree one in the prices and that the explicit func tion is non-homogeneous in the same variables. Now, assume that all prices are changed by the factor t (t^O); since all commodity equations (j~1, 2,..., m-1) are homogeneous of degree zero in the prices, all equations of the system | are satisfied at the new price level except the non-homo- j geneous explicit money function. Hence, the form of the Xm function is inconsistent with the form of the Mjj function. This, according to Jose Encarnacion, is a strange use of the word consistency. It would be more proper to say that if (tpj) (j=l, 2,..., m-1) did not satisfy the explicit money function then it is not a solution of the system. The confusion arises in not recognizing the dif ference between dependent and independent variables. 103 Normally, the pj (j=l, 2,..., m-1) are the dependent vari- :ables and the M and k are the independent variables; if a value for the p 's is preselected, then either M or k must 3 now be the dependent variable— i.e., if the value of the ;price level is specified either M or k must vary in order 1 cn for the explicit function to be satisfied. ' It will be remembered that Oscar Lange made a simi- :lar observation, but concluded that the claimed inconsis tency between the 5^ and Mx functions caused the system to be indeterminate in the absolute prices. Encarnacion does not agree with this. His contention, in essence, is that the neoclassical system is not capable of explaining dis equilibrium behavior; the system is capable of yielding equilibrium values of the dependent variables once the value of the independent (exogenous) variables are. known. ! But, once the value of any of the variables are. changed the system is not equipped to explain the process as the system moves toward or away from a new equilibrium situation. Many of the later critics of Patinkin have emphasized this point. The interpretation of the money equations. Con sider, once again, the system of excess demand equations 57 > -"Encarnacion, o£. cit., p. 830. typical of the neoclassical model r I (2.3.73) Xj = xj(Pl/Pm-i' P2/pm-l/* " r pm-2'/pm-l) (j=lI 2,..., m) where the mt* 1 commodity is paper money. The system con- ! tains m equations in m-2 unknowns (the p./P r (j=lf 3 Rl-1 2,..., m-2)), and is, therefore, inconsistent (i.e., over determined) . However, "such a system . . . can neverthe less be.consistent in the mathematical sense if for each 'surplus1 equation there exists an identity connecting the C Q equations that make up the system.1 Two such identities are present in the neoclassical system: they are Walras' I Law, which we may write m-1 i (2.3.74) X = - £ p.X., j=l 3 3 and Say's Identity. System (2.3.73) is now consistent? we may add a new equation (the Cambridge equation) i m-1 (2.3.75) M = k E P-jD. j=i 3 3 which adds one new unknown to our system— Pm_i- However, Isince (2.3.75) is linear in the unknown it does not affect ^Stefan valavanis, "A Denial of Patinkin's Contra diction," Kyklos, VIII (1955), 354. | the mathematical consistency of (2.3.73); we have m inde- I pendent equations in m unknowns. Patinkin would disagree with this on the grounds i that the implict money equation is not consistent with | (2.3.75). But, as Valavanis has pointed out, the condition ; that Xm = 0 is merely a reflection of Say's Identity, and the Cambridge equation fixes the rate at which bar ter can occur with the help of a monetary medium, a strictly technological matter. Why should Say's Law [Identity] have anything to do with "train schedules" and other determinants of velocity? These are two different things and cannot conflict. Valavanis goes on to say that Patinkin's error lies in believing that both the Cambridge restric tion and the excess demand function for money are economic statements. The error consists in his elevating the mirror-image [implicit money func tion] concept into a statement about behavior. * . . . Money is considered as another commodity with its own demand and supply like any other commodity, and both mirror-image [implicit] and the Cambridge [explicit] equations are interpreted as expressing the market for money . . . this is not [italics added] the case in the Classical system. Neither equation explains market behavior in the sense.in which such equations apply to commodities [italics added]. The mirror-image [implicit] equation is nothing but a reflection of the fact that barter operates through a monetary medium. The Cambridge [explicit! equation is nothing but a technological restriction on the rate at which money can" move. There is no contact between the two.59 59Ibid., pp. 356-357. 106 What Valavanis has done is give a strictly tech- I Inological interpretation to the Cambridge k; any behavioral ;characteristics imputed to k under this interpretation are I not valid. However, as Valavanis himself pointed out, "Monetary theory becomes interesting only when Say's Law :[Identity] is denied."^® To anticipate the conclusion of ;this section, we might tentatively state that, although the ;neoclassical system is consistent and determinate in a mathematical sense, it is not capable of adequately ex plaining monetary phenomena. The correct interpretation of the neoclassical system. Archibald and Lipsey have carried the conclusion implicit in Valavanis' critique one step further. They state that the real-balance effect is a transitory phenomenon, which is operative only in some disequilibrium situations. Its role is to. provide a possible dynamic explanation of how the economy moves from one position of static equilibrium to another. Thus, if we are interested in those well-known propositions of the quantity theory which are ^ Ibid., p. 356. Valavanis is not the only one to point out this interpretation of the neoclassical system; Hickman concurs when he said that the Cambridge equation "is a constraint (an equation of condition) and not an identity in the . . . [pj]." Hickman, 0£. cit., p. 15. The Brunner model ("Inconsistency . . . ," o£. cit., pp. 169-171) was constructed using this interpretation; however, as Valavanis pointed out, the price level when viewed from the market is a variable and is dependent on the relative prices and the stock of money and, therefore, should not be included as an argument in the market functions. 107 proposition in comparative statics, the real- balance effect is irrelevant.61 To understand Archibald and Lipsey1s reasoning it is necessary to differentiate between weekly or temporary equilibrium and full or stationary equilibrium, weekly equilibrium prevails when market demand equals market sup ply for each commodity at the current prices; full equilib rium prevails, on the other hand, when market demands equal market supplies and when the same prices prevail at all ! future dates.62 In full equilibrium the individual1s behavior will be constant over time. This means that his rate of consumption will be constant and, assuming there are no bonds in this economy (i.e., the individual's entire income must be used j either to purchase goods or change his nominal balances), 61g. G. Archibald and R. G. Lipsey, "Monetary and Value Theory: A Critique of Lange and Patinkin," The Re view of Economic Studies, XXVI (October, 1958), p. 9. ^This is the Hicksian definition. Hicks, ojj. cit., p. 132. To make the distinction clearer, however, consider a second order difference equation y(t)=Ay(t-l) + By(t—2) We know that the general solution will be in the form y(t)=a(x1)t + b(x2)t + z Assuming that both x^ and X2 are less than unity, y(t)-»-z as t->“? however, for all practical purposes, y(t)=z at some finite t. The values of y(t) at all t such that y(t)=^z is comparable to "weekly equilibrium"; where y(t)=z might be compared to "full equilibrium." 108 his nominal (and, since prices are constant, real) bal ances will also remain constant. In other words, in full equilibrium the individual spends his entire income on consumption goods. But, if this is true, the full equilib rium level of consumption is independent of real balances and only dependent on tastes and real income (which is also constant)— hence, the real balance effect is a "transitory phenomenon." Now in full equilibrium Say's Identity holds, as does Walras' Law. Howver, assume that the money supply is altered by the factor t (t^O); the implicit money equation is automatically satisfied, but the Cambridge equation is not necessarily satisfied at the new price level; i.e., % * “x Thus, the neoclassical dichotomy precludes Walras' Law when the system is not in equilibrium. To paraphrase Archibald and Lipsey, the neoclassical system makes no sense in a disequilibrium situation; but, once equilibrium is attained, Walras' Law holds and the system is perfectly consistent and determinate. Clower and Burstein carry the analysis a little further; they intorduce bonds into the analysis and, there fore, the possibility of permanently changing the distribu tion of real income by means of purchasing income earning ! 109 I I assets . Their analysis also applies to a situation where j |windfall changes in the distribution of monetary assets are capable of permanently changing the distribution of real income.®3 The Clower.-Burstein model is dynamic; the equilib rium level of real consumption expenditures, real bond in come, and real money balances at time T are functions of real "operating income" (i.e., income derived from the initial endowment of goods), relative prices, the rate of interest, and initial real bond and real money holdings, all at time T. It is then shown that, under the assump tions of this model, the full equilibrium values of the relative prices, the rate of interest, and real asset hold ings are invariant to changes in the nominal stock of money and the number of bonds— i.e., the neoclassical dichotomy holds in the Archibald-Lipsey sense. If one were willing to grant the underlying assump tions of this model— namely, that all interest income re ceived plus all windfall profits were spent on consumption — ? — • W. Clower and M. L. Burstein, "On the Invari ance of Demand for Cash and Other Assets," The Review of ;Economic Studies, XXVIII (October, I960)., 32-36. Earlier I Archibald and Lipsey had shown that, assuming each individ ual has a linear expansion path (Engle curve), a non-pro portional change in each individual's nominal stock of money will leave the full equilibrium real values unchanged; however, this conclusion is not certain when the distribu tion of real income is permanently changed. See Archibald and Lipsey, op. cit. 110 goods— the conclusions follow directly. However, it does not seem too realistic to assume that all "non-operating" income is used for consumption purposes; on the contrary, as Patinkin said, Under fairly reasonable assumptions about consumers1 behavior . . . the individual will make use of his interest earnings on savings to generate continuous growth in his levels of wealth, income, and con sumption. Correspondingly, he will generally not consume all of the windfall gain represented by the real-balance-effeet, but will devote part of it to increase his savings and thereby generate a perma nent upward shift in the planned growth-path of his wealth holdings— including wealth in the form of money,64.' Thus, according to Patinkin, the Clower-Burnstein model is deficient on the empirical level— the demand func tion for consumption goods, real bond income, and real balances should not, in comparative static terms, be in variant to changes in nominal balances and the number of bonds. Another degree of complication can be added if we consider an exchange economy that, besides money, contains a depreciating asset. R. J. Ball and Ronald Bodkin con sider such a system;®^ denote the quantity of the asset by ^Patinkin, Money, Interest, and Prices, op. cit., p. 59. “ §^R. Ball and Ronald Bodkin, "The Real Balance Effect and Orthodox Demand Theory: A Critique of Archibald and Lipsey," The Review of Economic Studies, XXVIII {Octo ber, 1960), 44-49. Ill A, and its rate of depreciation per period by. v. The budget constraint for an individual can now be written m-1 (2.3.80) B 2 (p./P)x*i. + (PA/P) [A - A*(1-v)] j=l * * + xim//p " x*im/^ where A* is the beginning stock of the asset A. Remember ing that in full equilibrium the level of stocks and the prices are constant from one period to the next, we may rewrite (2.3.80) in full equilibrium as m-1 (2.3.81) y^ = 2 (p./P)x*. . + v(px/P)A' j_l J 13 ■ a where A1 is the full equilibrium level of the asset A. The level of A 1 is of considerable importance since the higher the ratio of A' to y^, the smaller the proportion of y^ that can be spent on consumption goods. Assume that there is an autonomous shift in an individual's utility function. In the Archibald-Lipsey model this would change the composition of full equilibrium consumption expenditures, but not the level; when, however, there is a depreciating asset, (2.3.81) makes it obvious that the individual's full equilibrium consumption level will be altered. Hence, according to Ball and Bodkin, the Archibald-Lipsey model is for a special case of little interest. 112 A more fundamental criticism of Archibald and j Lipsey made by Ball and Bodkin has to do with the defini tion of equilibrium and disequilibrium. Earlier, Archibald I and Lipsey claimed that the real balance term should be ; written (2.3.82) X*im/P - B where B is the "desired stock of real balances," and the expression (2.3.82) will be recognized as Mishan's cash- balance term. In full equilibrium desired real balances . are equal to actual real balances and, therefore, the term would equal zero and drop out of the demand equations, i However, people hold the "desired" level of real balances . when they are in short run (weekly) equilibrium as well as when they are in full equilibrium? therefore, if the real balance term appeared in the form of (2.3.82) it would I disappear in all equilibrium situations, and (2.3.82) is , greater than (or less than) zero only in situations of complete disequilibrium. But, Archibald and Lipsey would be the first to admit that the real balance term plays an important role in determining the individual's weekly equi- ; librium consumption levels. ! The solution of this seeming paradox probably lies | in the definition of B. Although Archibald and Lipsey : never make it explicit, they seem to interpret B as the 113 full equilibrium desired stock of real balances.On the other hand, Ball and Bodkin appear, to be using a much looser definition— i.e., they seem to be defining B as the desired stock of real balances at any equilibrium position. Even in the event that we use the definition of B that is attributed to Archibald and Lipsey, it is not clear that the real balance term should drop out in full equilib rium. Cliff Lloyd, for example, considered an economy con sisting of individuals with a weekly horizon, and assumed that real balances appeared in their utility functions.*^ The i*-*1 consumer would maximize ui “ ui(xil' xi2'***' Xin/P* subject to m-1 m (Pj)x*lj + x*im * £ (Pj)xij The real balance effect can arise from two sources real balances may change by a direct injection of real bal ances— the "defined real balance effect"— or through a This is also true of their second article; the ;only defense they give is that ex ante - B = 0 |only in full equilibrium. See G. C. Archibald and R. C. ILipsey, "Monetary and Value Theory: Further Comment," The j Review of Economic Studies, XXVIII (June, 1964) , 50-56. . 67Cliff Lloyd, "The Real-Balance Effect and the Slutsky Equation," The Journal of Political Economy, LXXII 1(June, 1964), 295-299. 114 change in P = P(p^/ P 2 Pm-i^— t^ie "derived real bal ance effect." In weekly equilibrium the defined real balance effect is 9X: where A = ‘is _ 1 9x*im/P “ A s 0 PX Pi uxl (s=l, 2,..., m-1) Pm-1 P ul,m-l ulm ^ 1 um,m-l umm and Ag is the co-factor of the (s+l)st column. The ua f c) are the cross partial derivatives of u^ with respect to the a^h an(j bth arguments. The derived real balance effect is 9xis gp 3p_^ = ^ ^""xir^s ~ ^rs + 9pr (”xim-ks J (r,s=l, 2,. .., m-1) where Ars is the co-factor of the (r+l)st row and (s+l)st column. i The interpretation of the terms is as follows: the first term on the right is the Hicksian income effect; the second is the Hicksian substitution effect; and the last is derived real balance effect which is, in turn, composed of an income and substitution effect. 115 In full equilibrium the term x*j_m becomes a vari able; but it is dependent on the values assumed by the x — (j=l, 2,..., m-1) and A. Hence, we can eliminate x*^m so that the defined real balance effect disappears in full equilibrium. However, the derived real balance effect is now 3xs 1 gp 8pr “ b ^”xirBs ”• *Brs + gpr ^"ABms^ (r,s=l, 2,..., m-1) where B is the same as the A determinant except P in the first row and (m+1)st column is replaced by zero. The point is that in full equilibrium the substitu- ition component of the. derived real balance effect does not :vanish. On the basis of this Lloyd concludes that the !Archibald-Lipsey invariance principle--i.e., that the full :equilibrium values are invariant to a change in x*^m— is valid; but nevertheless the real balance term cannot val idly be removed from the full equilibrium equations without making some difference to the comparative static solutions6 . 8 Although Lloyd's point is well taken, he does commit a logical error. In full equilibrium he claims 6^Thus, Lloyd's conclusions coincide with those of IMishan— i.e., the "asset-expenditure" term is a determinant ! of the equilibrium levels and should not be left out of the comparative static system. See supra, Section II of this chapter. 116 that becomes a variable; this is true provided that the individual's horizon extends over a multiweek period. However, Lloyd continues to consider one week horizon indi viduals which is clearly inconsistent with his assumptions concerning the behavior of in full equilibrium. Another criticism of the Archibald-Lipsey model is due to F. H. Hahn, who pointed out that the controversy has been clouded by a failure to distinguish between two rather elementary points. Specifically, consistency can be defined in two ways: {i) A set of equations in some unknowns is said to be consistent if there exists some value of these unknowns which satisfy all equations simultaneously. (ii) An equation or set of equations describing economic behavior are consistent if they can be derived from or do not contradict underlying theory of such behaviour.69 With regard to (i), write a system of equations as n X • = 2 a. . z 1 (j=l r 2,... ., m) j=l. 13 where z = Pj/P (j=l, 2,..., m), a = [a^j], an n x m matrix, and a'z = (z^, %2f•*•' zm)* wish to solve {2.3.83) az = 0 A necessary and sufficient condition for (2.3.83) to 69F. H. Hahn, "The Patinkin Controversy," The Re view of Economic Studies, XXVIII (October, 1960), 42. 117 possess a solution is that |a| = 0. The z's obtained from (2.3.83), can then be used in conjunction with the Cambridge ■ equation to solve for the P. The system is consistent and I i determinant in the mathematical sense as long as the con- ■ dition mentioned earlier is fulfilled. However, according ■ to Hahn, no one has ever disputed this fact. i When (ii) is considered a different picture emerges. ■ Assume that at some Pj (j=l, 2,..., m-1) that is stable over time the Xj = o (j=l, 2,..., m-1) but that > 0.. Since, in this system, the market can only redistribute existing cash balances the Xj^ will not be satisfied in the succeeding periods. Therefore, a necessary and sufficient condition for the pj1s to be the full equilibrium prices is that Xj = 0 (j=l, 2,..., m-1) and Xm = 0. Hence, what | the Archibald-Lipsey model comes down to is that all excess demand functions for goods are independent of money prices (real balances), if everyone always has the real balances he desires.71 The obvious answer to this charge, in Archibald and Lipsey's words, is: j. Baumol makes this same point; see his ! "Monetary and Value Theory: Comments," The Review of Eco- nomic Studies, XXVIII (October, I960)., 30-31. Notice that the proof presented by Valavanis is similar to Hahn's ;proof. 71 Hahn, "The.Patinkin Controversy," 0£. cit., p. 39. 118 Let us try to put this in terms of a "conceptual experiment." Suppose that we ask each individual what his, demands and supplies, would be at each set of relative prices, supposing that his balances were in equilibrium. The answers give us our demand and supply equations. We also ask each individual what quantity of real balances he would demand at each level of transactions. This, assuming that the demand is linear, gives us the Cambridge equation. . , . Hence the absolute price level is a function of relative prices, but not vice-versa. We may ex press this as follows: the real part of the model tells us the volume of transactions for each set of relative prices if balances are in equilibrium; the money part of the model tells us what equilibrium balances are for each level of the transactions; we may solve the first part without the latter, of both simultaneously. We can see at once that the well- known argument which starts "if all money prices are doubled, there is disequilibrium in the money market but not in the goods market" does not prove incon sistency in this model: the goods market equations are only supposed to tell us what individuals do if their balances are in equilibrium; if we arbitrarily double money prices, their balances are not in equi librium, and the goods equations are not designed to tell us what happens.'2 iThe Outcome of the Controversy As with most debates, the outcome of the Patinkin controversy is not clear-cut. The controversy has been clouded because of what is essentially a semantic problem. iThe. earlier writings^ seemed to imply that a system ^Archibald and Lipsey, ". . . : Further Comment," op. cit., p. 53. ^Specifically, we have reference to Patinkin, "In validity . . . ,"o]3. cit.; Patinkin, "Indeterminancy . . . " op. cit.; Lange, "Say's Law . . . ," o£. cit.; Brunner, > "Inconsistency , . . ," o£. cit.; and Patinkin, "Relative Prices . . . ," o£. cit. _________ ! 119 i |exhibiting, the neoclassical dichotomy had no arithmetic i ! solution; a topic which has elicited several critical com- i ments. ^ Although it is not perfectly clear what each con- I tributor had in mind at the time of each contribution, it ;is clear that the existence of an arithmetical solution to the neoclassical system is no longer widely disputed. The !inconsistency referred to earlier is now given a different interpretation; in Patinkin's words: The first thing that should be noted is that the contradiction with which . . . [we are] concerned has nothing to do with the possible inconsistency of a system of static excess-demand equations in the sense that such a system may not have a formal mathematical solution; indeed . . . this type of question lies outside the interests of this book. Instead the notion of inconsistency with which the foregoing argument is concerned is the standard (and general) one of formal logic that a set of propositions is inconsistent if it simultaneously implies a proposition and its negative.75 Patinkin has reference here to the inconsistency between the implicit and explicit money demand functions; however, as Valavanis has pointed out, under certain inter pretations this need not be an inconsistency in a compara tive static sense. The. point, it appears, is this: It is ^^For example, see Valavanis, 0£. cit.; Archibald land Lipsey, ". . . : A Critique of Lange and Patinkin," op. cit.; and Hahn, "The Patinkin Controversy," o£. cit. ^Patinkin, Money, Interest, and Prices, op. cit., pp. 176-177. ! unfair to accuse the great majority of neoclassical writers ' of the Patinkin inconsistency; the questions asked by those who formulated the static general equilibrium system were different than those asked by Patinkin; when questions were asked similar to Patinkin's the rigid static framework was abandoned in favor of one that was capable of providing satisfactory answers. This is essentially the point raised by Archibald and Lipsey. Their critique of Patinkin, however, is un warranted in the sense that the Patinkin model is not capable of ever reaching a long run (full) equilibrium position; as Patinkin noted; It should, however, be clear that when in the course of time the individual comes to the marketing period in question, he will not generally act in accordance with the plans he now makes. For by that time new information will be available which will cause him to modify them. Thus, for example/ he will by. that time have information on a week— or on weeks— which is now beyond his economic horizon. In brief, we assume that every Monday each individual reconsiders the whole situation that will confront him during the ensuing month and formulates or revises his plan accordingly.7 6 But, even if the system were capable of reaching a |position of long run equilibrium, the disappearance of the ireal balance term from the demand functions is not valid; 7^Ibid.t pp. 60-61. 121 even after the individual reaches long-run equilib rium, he continues to determine his behavior in the light of his wealth restraint [including real bal ances] ; . . . accordingly his demand functions in the usual sense of the term continue to depend on wealth. . . . In other words, the individual de manding . . . [xin/P and x-^j (j=l, 2,..., m-1)] in long-run equilibrium does not conceive himself as acting in accordance with . . . [the demand func tions exclusive of real balances], but as buying the optimum amounts indicated by . . . [the demand functions including real balances] for . . . [his long-run equilibrium] level of wealth.77 In closing this section it will be worthwhile to summarize by means of a quote from H. G. Johnson which puts the whole controversy in its proper perspective: While a formally consistent theory can be constructed by interpreting velocity as an externally-imposed restraint on monetary behavior (an interpretation for which there is ample precedent in the literature) this treatment not only leaves velocity itself un- . explained on economic grounds, but precludes any analysis of monetary dynamics and the stability of monetary equilibrium by its inability to specify behavior in disequilibrium conditions. As the bet ter Classical monetary theorists saw, these problems are most easily handled by assuming that money bal ances yield services of utility to their holders; and Patinkin's major contribution has been to elab orate a rigorous formal theory of this approach.78 IV. STOCK VERSUS FLOW ANALYSIS In our attempt to introduce certain financial and non-financial variables into a general theory of economic 77ibid., pp. 435-436. 78Johnson, o£. cit., p. 340. 122 jbehavior we are faced with problems that, while not absent j from the traditional general equilibrium system, are not I explicitly treated in the literature that we have reviewed thus far. We. have reference here to the difficulties that arise when both stock and flow magnitudes appear explicitly in the same system. Consider, for example, the system of Section I of this chapter; ignoring the Cambridge'equation, that system purported to. explain the determination of price and quantity demanded and supplied per unit of time. These are pure flow magnitudes which should be carefully distin guished from pure stock magnitudes that are dated (dimen- sionless) variables rather than bearing the dimension per unit of time; i.e., flow variables have reference to a period of time (no matter how short the interval may be) |while stock variables have reference to a particular date. Suppose that we now introduce into the analysis an asset that is held as a stock but is not consumed. The :neoclassicals in fact did introduce such an asset; this ;asset was, of course, circulating money. The demand func- ;tion for money was normally stated in terms of a stock ;demand function (the Cambridge equation); no recognition of a flow demand for money was ever given.79 This treatment 79a flow demand for money function is not to be confused with Patinkin's "implicit money relation." The implicit money function is a reflection of the fact that ;individuals must adjust their demands and supplies of all 123 of a stock is completely satisfactory provided that the assumptions implicitly made by the neoclassicals are ful filled; specifically, their assumptions were that the flow supply of money is exogenous and, consequently, that the flow demand for money is equated to zero at all equilibrium positions by the price of money (i.e., the reciprocal of the general price level). In other words, in this type of system and with the given assumptions, flow excess demand and stock excess demand are equivalent; Let us now introduce another type of commodity into the analysis; a commodity that is both held as a stock and consumed— i.e., a stock-flow commodity. There are now two types of,demands and two types of supply to explain: a demsnd for the commodity as a flow (e.g., to be consumed) and a demand for the commodity to hold as a stock; and the same categories for supply. That the model of Section I is not capable of handling this situation is obvious. Thus, it appears that if we wish to analyze the workings of a system that contains stock-flow variables and/or wish to explain the disequilibrium behavior of a system containing only pure flow and pure stock variables, other goods and services in order to alter their stock of [ money. This is purely a definitional, as opposed to a behavioral relation. On Patinkin's demonstration of the equivalence of the 35^ and .functions, see his "Indeter minacy . . . ," oj>. cit., pp. 7-9. 124 we must modify the basic model- But, these are not the only cases in which an explicit recognition of the differ ences between stock and flow magnitudes is crucial. In the review of the Archibald-Lipsey critique of Patinkin in the preceding section, a distinction was made between short run (weekly) equilibrium and long run (full) equilibrium. These two. concepts of equilibrium are intimately related to the concept of stocks versus flows. Weekly equilibrium may be defined as a situation in which the algebraic sum of the stock and flow excess demands for each commodity is satisfied; whereas, in full equilibrium the additional con dition is specified that the stock excess demand must also be satisfied. This gives us another reason to differen tiate between stocks and flows. .The tendency in static analysis has been to disre- ;gard the factors mentioned above on the grounds that the period of analysis chosen is usually so short that stocks can be regarded as remaining constant. It is only when we move on to considerations of dynamic adjustments do we find stocks being mentioned explicitly. This is especially true !of modern monetary theorists who regard, following those :who have considered cyclical variations in investment, cer tain flows as adjustments of actual stocks to their desired level.. However, when the purpose of a model is to explain the holdings of stocks— or, for that matter, when the model 125 is designed for. comparative static analysis— the stock-flow |relationship cannot be ignored. The Relation of Stocks to Flows The stock of an asset at any point of time is the sum of all. the past positive flows not consumed. It fol lows directly that the only way in which a stock can be . changed is by means of a flow— it may be decreased by a negative flow (e.g., depreciation) and increased by a posi tive flow (e.g., production). An example of this is the relationship between a balance sheet and an income state ment. A balance sheet is a statement of the stocks held by i a particular enterprise as of a particular date, while.an income statement is a recapitulation of all the flows that took place during a given period of time. The balance : sheet is a result of all past flows and is, under certain 1 f t f t ;assumptions, the summation of all past income statements.00 We may also take an example from the physical world. Consider the act of filling a bathtub. At any igiven time the bathtub will contain a certain stock of ®®This is, of course, not strictly true. An income statement does not include transactions involving borrow ings or on capital account (including capital gains), but refers to flows of income and expense. We may, therefore, more accurately say that a balance sheet is the summation of all past income statements assuming that no borrowings, etc. have taken place. 126 water; the magnitude of this stock of water will depend on the rate of flow of water into the bathtub from the spigot and the amount of time that has elapsed from the time the spigot was first turned on and the particular time in ques tion. If the bather wishes more water for his bath he need only allow the flow of water to continue until the desired level of the stock of water has been achieved, or he may alter the rate of flow by adjusting the spigot. Suppose that we now find that the bathtub has a leak so that there is not only a flow of water into the tub via the spigot but also a flow of water out of the bathtub via a hole in the bottom. This more nearly approximates the situation when we turn from the physical to the eco nomic world. In other words, in economics we rarely find a pure flow are a pure stock variable; it is more common to find stock-flow variables. Additionally, in economics we must go one step further; we must investigate what influ ences the desired rate of flow and the desired level of the stock and, which is of more importance to us in this sec tion, what difference it makes to the desired rate of flow if there are stocks in existence, and vice versa. The Controversy over Stocks or Flows As with most other things in economics, there is considerable disagreement on the correct treatment of the 127 ! stock-flow problem; and, indeed, there is disagreement on : whether there is a problem at all. The more modern debate has taken place in the context of the controversy concern ing the equivalence of the loanable funds (LF) and liquid ity preference (LP) theories of interest rate determina tion, which can be traced back to J. R. Hicks' demonstra tion of their formal equivalence. Hicks, using Walras1 Law to eliminate one equation of the general equilibrium system, pointed out that if the excess demand function for money is eliminated we have a LF theory of interest, and if the : excess demand function for bonds (securities) is eliminated we are left with a LP theory of interest.81 it is not our f I intention here to review the LP versus LF debate; fortu nately both G. S. L. Shackle and Harry G. Johnson have pro vided us with excellent reviews.®2 ^he contributions to | this debate will be referred to only when they are capable of shedding some light on the role played by stocks and flows in economic analysis. The equations referred to by Hicks are both flow equations, while the LP theory is normally stated in stock terms. Willian Fellner and Harold M. Somers, however, have 81Hicks, ojd. cit., pp. 160-162. 82G. S. L. Shackle, "Recent Theories Concerning the Nature and Role of Interest," The Economic Journal, LXXI (June, 1961), 222-235; and Johnson, o£. cit., pp. 359-365. I 128 1 | argued that the excess demand equations can be identified I with the. desired change in the stock of money or securities, irespectively. If we assume that the system is in stock equilibrium at the beginning and end of the marketing period, it follows that stock analysis and flow analysis i are equivalent when considering monetary equilibrium.8- ^ The Fellner-Somers article touched off a debate with Lawrence Klein, Klein objected to the Fellner-Somers argument on two related grounds: (1) the Fellner-Somers :assumption that each market period starts with actual stocks equal to desired stocks, and (2) their disregard of dynamic adjustments which, according to Klein, is the real :difference between the LP and the LF theories. As Klein jsaid, it is one thing to hypothesize the dynamic relation (2.4.1) PjT ” PjT—1 = (^ji^ where the subscript T refers to the time period in ques tion, and quite another to hypothesize the relation84 T 1 (2.4.2) PjT PjT—1 = ■ ^ ^ ^ ^jT^ J t——m 88William Fellner and Harold M. Somers, "Note on 'Stocks' and 'Flows' in Monetary Interest Theory," The Re view of Economics and Statistics, XXXI (May, 1949), 145-146. 84Lawrence r. Klein, "Stock and Flow Analysis in Economics," Econometrica, XVIII (July, 1950), 247-248. 129 A subsequent article by Karl Brunner has served to clarify the Fellner-Somers-Klein controversy, and to lay the foundation for later work on the stock-flow question. Brunner considered a situation in which stocks are large relative to changes in flow demand and supply; therefore, Under these circumstances the momentary price will be determined by the stock relationship and not by any flow relationship. In general, a flow equilib rium price will still be accompanied by a stock disequilibrium, which will force a change in price till short-run stock equilibrium has been achieved. This situation will then be accompanied by a flow disequilibrium which will change the underlying stock relationship. So a new stock equilibrium will be formed, with a new price and a new flow disequilibrium and so on until the whole short-run system has eventually been adjusted.85 A model explaining such behavior can be stated as follows: (2.4.3) S(T) = (2.4.4) S ( T . ) = (2.4.5) S(T) = (2.4.6) s [p(T) ] where S(T) is the stock of the asset in question at time T; s(T) is the rate of change of S at time T (i.e., the flow supply); p(T) is the price of the asset at time T; S^Karl Brunner, "Stock and Flow Analysis: Discus sion," Econometrica, XVIII (July, 1950), 247-248. 130 j and D is the stock demand at time T. i . Equation (2.4.5) defines stock equilibrium and a ; "stock relation price"; equation (2.4.6) defines flow equi- ; librium and a "flow relation price." It is only in full or ^ stationary equilibrium (i.e., where both (2.4.5) and ' (2.4.6) are satisfied) that the stock relation price and the flow relation price are identical.^ Under Brunner's assumption that stocks are large relative to changes in flow demand and supply, short run' price determination is dominated by the stock equilibrium condition; long run price determination is dominated by neither, the stock nor the flow equilibrium conditions, but is dependent on both. In terms of Brunner's model, the Fellner-Somers argument is as follows: given that (2.4.5) is satisfied at ;the beginning of the period, price is uniquely determined i by (2.4. 6) in conjunction with the relations (2.4.3)- : (2.4.4) . Klein's critique consisted of questioning the validity of assuming that the stock relation (2.4.5) is satisfied at the beginning of the period, contending that the real difference between the LP and LF theories arose only when (2.4.5) is not initially satisfied. He then , 86It is interesting to note that Shackle uses a line of reasoning very similar to this to reach a different ;conclusion; Shackle concludes that it is possible that two i rates of interest (or prices) can prevail at the same point ;in time— one flow relation rate, and one stock relation rate. See Shackle, op. cit., especially pp. 227-228. _______ 131 asked Fellner and Somers which relation they referred to as determining the momentary price, (2.4.5) or (2.4.6). The Fellner-Somers reply was a restatement of their assumption previously criticized by Klein.^ Brunner got to the heart of the question when he wrote, If stock equilibrium in ([T] - 1) is a necessary condition for the proposition that flow equality implies and is implied by stock equality in . . . [T], then surely the stock relation has to form an integral part of the theory. The restriction imposed by Fellner and Somers obscures an impor tant question: what the general structure of economic processes is when demand and supply are not simultaneously equal for both stocks and flows.88 With regard to Klein's question, Brunner pointed out that the answer, according to Brunner's analysis, is dependent on the type of equilibrium considered; so that, in general, there is no equivalence between the LP and LF theories. The New Stock-Flow Analysis The new stock-flow analysis is due to the work of R. W. Clower and D. W. Bushaw, who have attempted to build 87william Fellner and Harold M. Somers, "Stock and Flow Analysis: Comment,” Econometrica, XVIII (July, 1950), 242-245. 88Brunner, "Stock and Flow,. . ." 0£. cit., p. 249. 1 132 j |a general theory of price determination in an economy con- jtaining pure flow, pure stock, and stock-flow commodities. The initial contribution was by Clower, who used an analy- ;sis very similar to Brunner1s to argue that productivity and thrift affect the price of bonds only in the long run. In Clower's model, the current price is determined, ceteris paribus, by the stock demand for bonds in relation to the existing stock supply of bonds. Since existing stocks are large relative to changes in flow demand and flow supply, :the current price will not be influenced by changes in productivity and thrift, except to the extent that changes in them affect expectations as to the course of future events. It is only over relatively long periods of time I that changes in productivity and thrift will materially affect the price of bonds. Consider changes in the atti tudes toward thrift that are cumulated over time? this I amounts to a shift if the stock demand curve which, ceteris paribus, will result in a different equilibrium price. ;Turning now to the productivity side, an increase in pro ductivity will normally make entrepreneurs more willing to incur debt (an increase in flow supply) and more willing to :carry larger stocks of debt (a decrease in flow demand— i.e., a decrease in the desired rate of retirement of ex isting bonds per unit of time). The net effect is a 133 rightward shift in. the stock supply curve over a relatively long period of. time.89 These results are completely con sistent with Brunner's model. Clower then teamed up with D. W. Bushaw to devise what they felt to be a general model of a stock-flow econ omy. The essentials of this model were first presented in an article in Econometrica, and later amplified in a book by the same two authors.90 From our point of view, the earlier, article contained two conclusions that are of im portance. In the first place, the system now contains two equations for each stock-flow commodity and two equilib rium conditions, which can be written (2.4.7) Xj + Xj = 0 (2.4.8) Xj = 0 where Xj is the flow excess demand for the j^ commodity and Xj is the stock excess demand for.the same commodity. This double equilibrium criterion has implications for both :the Patinkin controversy and the LP-LF debate; these will W.. Clower, "Productivity, Thrift and the Rate of Interest," The Economic Journal, LXIV (March, 1954), 107-115. " 9°R. W.. Clower and D. W.. Bushaw, "Price Determina tion in a Stock-Flow Economy," Econometrica, XXII (July, 1954), 328-343; and D. W. Bushaw and R. W. Clower, Intro duction to. Mathematical Economics (Homewood, Illinois: Richard D. Irwin, Inc., 1957). | 134 i 91 be discussed in more detail later in this section. The second conclusion that is of importance to us is that there is, in general, a fundamental difference be- ; tween models of a pure stock or pure flow economy and a model, of a stock-flow economy. Bushaw and Clower demon- | strated by an arithmetic example that there are situations in which a system is stable when considering stocks or flows, but unstable when considering stock-flow variables. This provides us with a concrete rationale for preferring | a stock-flow model over the. traditional pure flow model. The stock-flow model, as presented here, is devel oped along lines similar to the model in Section I of this chapter; it differs from the Bushaw-Clower presentation in that the consumption and production sectors are tied to gether, something that Bushaw and Clower do not do for their static stock-flow model. The major difference be tween this model and the model presented earlier is that ■ stocks of commodities are now considered as variables so that their level and rate of change are at the discretion 93-William j# Baumol later identified (2.4.7) as pertaining to weekly equilibrium, and (2.4.7) — (2.4.8) as pertaining to full equilibrium. See his "Stocks, Flows and Monetary Theory," The Quarterly Journal of Economics, LXXVI (February, 1962), 46-56. Bushaw and Clower refer to the situation where (2.4.7) is satisfied, but (2.4.8) is not, as an "apparent equilibrium" situation, and point out that ; no significance can be attached to it in a dynamic frame work. On this see Clower and Bushaw, "Price Determina- tion . . . o£. cit., p. 331. 135 of the individual economic units. The. interpretation of the "desired stock." Before proceeding with a consideration of the model, it is first necessary to discuss certain questions regarding the in terpretation of what we mean by the desired level of a stock— the D^j in our notation. The first question that comes to mind concerns the date that is affixed to the D - j _ j. Most writers in this field take the Fellner-Somers' view and interpret the D^j as pertaining to the end of the cur rent marketing period, so the stock excess demand— which is defined as D„- ^ minus the initial stock— is numerically • * " J equal to the stock adjustment component of the total flow demand for the commodity— the only required adjustment is the division by time to give it a flow dimension. Bushaw and Clower, however, disagree with this interpreta tion; in their system the D^j is to be interpreted as that stock that the individual (consumer or producer) wishes to hold at the. current prevailing market prices at the conclu sion of some period of time— the time period is presumably the individual's economic horizon. This interpretation in volves adding a new. variable to. the analysis; the time rate of change of existing stocks toward their desired levels, which is, of course, the relevant stock adjustment component of total flow demand in a static analysis. 136 A second question arises with regard to the type i of stocks that the Bushaw-Clower model in its present form | is capable of handling. Upon close examination of the ; model, it appears that the D^j are restricted to commodi- ?ties that are capable of being consumed; this leaves out j two general types of potential stocks: capital goods and financial goods. Consider the category of capital goods. The present model makes no allowance for calculations re- ; lating future periods of time— i.e., it consists of indi viduals with one period time horizons. As has been pointed out by F. H. Hahn, there is no place in a model of this type for interest rate determination in a one period analy- ; sis since it disregards one of the most important func- ; tions of the rate of interest— namely, it does not allow i for the equalization of discounted marginal utilities over time and makes the interest rate dependent only on individ uals 1 precautionary propensities; to provide a rationale for the interest rate, a period of time which encompasses the consumer's or producer's multi-period economic horizon imust be considered.But, it is well known that a ra- I tional entrepreneur will consider the future discounted ; value of capital goods as one of his criteria for invest- ; ment decisions. 92p. h . Hahn, "The General Equilibrium Theory of Money . . . ,” op. cit. 137 Now consider financial goods; the absence of a rate of interest in the model rules out the explanation of pricing of fixed income financial goods. However, this does not include those financial goods that do not bear a fixed rate of return, the most important of which is cir culating money. Patinkin and others, however, have pointed out that a rational individual does not derive utility from possessing nominal financial assets. Hence, to adequately handle financial goods, prices must be introduced into the utility functions of consumers and the decision functions of firms. Keeping this discussion in mind, we shall now con sider the basic Bushaw-Clower model. The basic model— the consumer. Consider a market in which there are n consumers (i=l, 2,..., n) and m goods (j=l, 2,..., m) , and where pure competition prevails in all markets. The i* - * 1 consumer enters the period with an ini tial stock of certain commodities T (2.4.9) S-Lj = Si j ( 0) + / x'^jtt) dt (j=l, 2,..., s) To where s £ m, and the is the time rate of change of the j* '* 1 stock. His operating income is derived from selling the services of his initial stock of commodities or the services of factors that cannot be held as a stock (pri marily labor services). Denote these initial flows of 138 > factor services by x*i2'***' x*iz^ ' where m t. z <. s* The consumer will allocate his operating income plus any proceeds from the sale of his initial stocks to purchase commodities (x^ z+i# xi z+2'***' xim^ r factor services (Xii, x^2,..., xiz) / stocks of commodities (Dj_i, Dis^ * As before, define the flow excess demand for the ith consumer as the quantity he consumes if it is a com modity (2.4.10) E * < = x. . (j=z+1, z+2,, • . •, m) XJ ij and the quantity he consumes less his initial endowment of services if it is a factor (2.4.11) Ef j = xi j — x*^j (j.=l, 2 z) Additionally, we have in this model various stocks of commodities over which the individual has a choice in determining their level. Define the excess demand for stocks as the desired level minus the initial endowment (2.4.12) Xij = Dij ~ s±j (j=l2,..., s) Bushaw and Clower claim that it would only be under unusual circumstances that the consumer would desire to accumulate the entire excess of D^j over the S^j in one period; it is more probable that the consumer's decision as 139 to the rate of accumulation is dependent on other economic variables. There are various hypotheses possible as to the factors that influence the consumer's decision; however, Bushaw and Clower choose (2.4.13) x 1 ±j = .x,ij{Xij) (j=l, 2,..., s) where dx'^j/dX.^ > 0, and x'-^j = 0 if and only if X^j = 0. The is termed "investment demand." For simplicity, Bushaw and Clower assume that investment demand is propor tional to the stock excess demand, so that (2.4.14) x'•• = b.-X.. (j=l, 2,..., s) J J J where 0 < _ b^j < 1, and constant. Following the convention developed in Section I of this chapter, we may write the budget constraint of the ith consumer as m (2.4.15) t Pj[Eij + bijxij3 E 0 The itb consumer's utility is a function of both stocks and flows, and the utility function can be written (2.4.16) u^ = u(xj_2_, x^2 r • • • i xim' ^ilr ^i2* * * *f ^is^ or alternatively as , 140 (2.4.17) u^ = u(E.q + x*j^f E^2 + x *±2'•••r Eiz + x*iz' E i.,z+l'***' Eim' xil + ®ilr xi2 ®i2'***/ xis + Eis^ The consumer wishes to maximize (2.4.17) subject to (2.4.15); form the new function m (2.4.18) Z± = u( ) X( pj [Eij + bijXij]). The results of the familiar maximization procedure yield 3Ui (2.4.19) — - - Ap. = 0 (j=l, 2,..., m) 8 E i j ' 3 3ui (2.4.20) gX- — AbijPj = 0 (j^l/ 2,.. . f s) m (2.4.21) -( . z p-[E, . + b- -X..]) = 0 Using one of the m+s+1 equations to eliminate the A, we may solve (2.4.19)-(2.4.21) for the independent vari ables E^ j and X^j in terms of the exogenous p j and j. (2.4.22) E- j _ j = E ij(Pi' P2'***/ Pm/ Silf S±2,..., Sis) (j=l . / 2 f... / m) (2.4.23) xi j xij(Pi' P2/*,*/ Pm 7 ®il' Ei2'***7 ®is^ ( j = l. / .2 y . . « f S) 141 | Making use of the s equations in (2.4.14) , we have m+2.s I equations in the m+2s unknowns Ej+ (j=l, 2,..., m) , X — j 1 J (j=l / 2r r s) ; and. x'-^j (j =1, 2, ... , s) » The homogeneity of the system.— The system (2.4.14) and (2.4.22)-(2.4.23) is homogeneous of degree zero in the : money prices. Since the proof is completely analogous to : that of equations (2.1.11)-(2.1.13), there is no need to ; repeat it here. The point is that the equimarginal cri terion used by the consumer is independent of the absolute prices, and dependent on the price ratios. The basic model— production. Once again, assume that within the same markets that consumers operate in, there are production units that combine factor services j (x-^, X2,..., xz) per unit of time— purchased from the n ! consumers— 'and primary and intermediate products (xz+i, xz+2,..•, xm) per unit of time— produced by the firm in : question or purchased from other firms— to produce quanti ties of products (xz+-^, xz+2,..., xm) per unit of time. The firm also wishes to hold stocks of certain commodities I (D^, D2,... Dg)— 'produced by the firm in question or pur- . j chased from other firms or from consumers— an example of ; which might be inventories of raw material, goods in pro- i j cess, and finished goods. As before, there are m-z indus tries (k = Z+l, z+2,..., m) , Nk firms within each industry I 142 I I I I (h=l, 2,..., and m-z goods (j=z+l, z+2,..., m) . The firm is assumed to have similar behavior pat- :terns towards the desired rate of change of the level of |stocks as does the consumer; that, is, the firm is assumed ,to desire to adjust to desired stock levels over several f - :periods of time so that equation (2.4.14)— with the appro priate change in subscript— pertains equally to consumer ; and producer behavior. The firm, therefore, wishes to make m (2.4.24) — 2^ pj (xhkj - khkjxhkj.) a maximum. The subscripts have the same meaning as in the first section of this chapter. The firm now. has the option of holding stocks of various commodities which is, in turn, significantly influ enced by the entrepreneur's subjective evaluation of risk, future sales volume, and other economic and non-economic phenomena. Hence, the entrepreneur now wishes to maximize ! (2.4.24), not subject to a transformation function— a tech nical relation between inputs and outputs— but subject to what might be called a decision function— a function which not only takes into consideration the technical coeffi cients of production, but also takes into consideration the subjective evaluations of the entrepreneur. Such a func tion may be written (2.4.25) g(xj_, X2,.. •, > ^1 r ^2r * * *f ^s^ ^ 143 To perform the indicated maximization, form the new function m (2.4.26 Vhk = ^ Pj(xhkj " bhkjXhkj) * The maximization procedure yields (2.4.27) Pi - — — = 0 <j=l, 2,..., m) 3 3 hkj (2.4.28) - P-i^hk- i " " y ■ --- = 0 (j= l.r 2, . . ., s) 3 3 9xhkj (2.4.29) g( ) = 0 Using one of the m+s+1 equations to eliminate y, we have m+s equations to solve for the m+s variables Ehkj - xhkj and the Xkkj as functions of the exogenous p^ and c 93 s i j - (2.4.30) Eh k j = p2,..., pm, Shkl, S., ) hks (g= 1, 2,..., m) ^Bushaw and Clower write their excess demand functions of the firm as functions of the p- alone as, "A direct consequence of the lack of 'income effect1 in the theory of business behavior." (Introduction to . . . , op. cit., p. 168.) This appears to be an invalid extension of pure flow theory to stock-flow theory? it does not seem plausible that an entrepreneur would not take his existing stocks (both levels and values) into consideration when formulating his plans. 144 (2.4.31) Xhkj =.Xhkj(p1, p2,.../ pm, Shki> s hk2 Shks) / .2 f ... . r S)' If there are Nk identical firms in the k^*1 industry, and taking into consideration the relation between the de sired level of stocks and their rate of change as expressed by (2.4.14), the excess demands of the k- * * * 1 industry for products, factors, and stocks are (2.4.32) Ekj = NkEhkj(P;L, P2r * * " ' Pm' Shkl' Shk2'***' ®hks^ = EkjtPi» P2'***' Pm' Skl' Sk2'***' Sks' { 3 = 1, 2,. .., m) ( 2 . 4 . 3 3 ) Xk j = N k Xh k j ( p a , P 2 , . . . , p ^ , S h k l , S h k 2 , . . . , Shks} = xkj(P]/ &2r' ''' pm' ®kl' ^k2'***' ^ks' Nk^ ( 3==' l -.r 2,..., s) (2.4.34) X'kj = NkbhkjXhkj (j=l, 2,..., s) The homogeneity of the system.— The system (2.4.32)- I 145 i I (2.4.34) is homogeneous of degree zero in the money prices. ;The proof of this statement with regard to the homogeneity of (2.4.32) - (2.4.33) is completely analogous to that of Section I of this chapter; with regard to (2.4.34), all quantities on the righthand side are independent of the prices except X^j which is itself homogeneous of degree zero in the prices. Hence, (2.4.34) exhibits the same homogeneity properties as does (2.4.32)-(2.4.33). The complete system. The market excess demands for products, factors, and stocks are the summation of the ex cess demands of the n consumers and the m-z industries, viz. (2.4.35) (2.4.36) (2.4.37) Ej - Eij (plf p2,. . . , pm , Si:L, Si8) m + k=z+l Ek3^P1, P2'***' Pm' Skl' Sk2 ®ksr Nk> (j=lr 2,..., m) n x- j “ -.2 xij(Pl' P2'***' Pm' sil' si2' * * • 'Sis) r=l m + 2 _ Xkj(Pi' ^2'*'*' pm' Sil/ Si2'* * *' k=z+l J Sks' Nk (j=l, 2,...., s) n m x1. = 2 x". . + 2 x'ki (j=l/ 2,..., s) J i=l 3 k=z+l J \ I 146 i ! The market functions (2.4.35) and (2.4.36) are, j i therefore, functions of the p^ (j=l.r 2,..., m) , S^j and Sj^j (3=1, 2, • •., s? i= 1, 2, • •., n; k—• z+1, z*l* 2,. • • , m) , and : the Nk (k=z+l, z+2,..., m) ; (2.4.37) is a function of these same variables— since it is a function of the Xj— and the j jparameters b^j and bj^j, which we assume, for the sake of simplicity, to be identical. Ignoring the effects of the initial distribution of stocks, these functions may be written (2.4.38) Ej = Ej(p^, P2,..., Pm* ®lr ^s* ^z+lf Ng^_2 / • • • 1 (j=l r 2,. .., m) (2.4.39) Xj = Xj (Pj_r P21 * * * • Pm' ®l' &2rm-mmr ®s' ^z+1' Ng+2 f • • • / ^ r 2 ,. . . , s) (2.4.40) ^' j = * j ^ 11 ^2 r • • • r P j j i ' ' ®21 * * * ' Ssf Nz+1 * Nz+2 r * • • r Njn, b^, i> 2 1 • • * t bs) (j=l, 2,..., s) Equilibrium requires that each market just clear; our equilibrium conditions are (2.4.41) Ej ( ) + x' j ( ) = 0 (j —• 1. , 2,. .. , m) 147 (2.4.42) X..( . ) = 0 (J=l, 2,... f s) The condition (2.4.42) implies and is implied by (2.4.43) x'.( ) = 0 (j=l, 2,..., s) D Equation (2.4.41) can be identified as the short run equilibrium condition; however, if (2.4.42) does not hold prices will not be stable over time which violates the concept of equilibrium. Consequently, for full (long run) equilibrium to prevail both (2.4.41) and (2.4.42) must hold. We shall also assume that there is free entry into and free exit from all industries; in the long run profits will be zero. We may then write the profit function (2.4.44) ( p . - j ^ , J? 2 1 * * • t = 0 (k=z+1, z+2,..., m) : as an additional long run equilibrium condition. i The system (2.4.41)- (2.4.43) and (2.4.44) contains 2m+s-z equations— whether they are equationally independent : or not is another question— and 2m-z unknowns, the pj (j=l, 2,..., m) and (k=z+l, z+2,..., m). The system seemingly overdetermined; however, as Samuelson has pointed out, it 'is sometimes necessary to investigate the dynamics of a ■ system in order to arrive at theorems in comparative sta- :tics.9^ Consider a situation in which (2.4.41) holds but 94This is Samuelson's "correspondence principle"; see Samuelson, 0£. cit., pp. 258 ff. 148 (2.4.42) does not; there is no reason to think that Ej = 0 and x1j = 0, it is more likely that Ej > 0 and x'^ < 0, or : Ej < 0 and x'j > 0. Suppose that one of these latter al- ; ternatives in fact prevails and that excess flow demand (i.e., the Ej) is satisfied ex post by unintended inventory accumulations or decumulations. Price as observed at an instant of time might be stable and the market as a whole might clear ex ante. However, the desired level and rate of change of the stocks would not be achieved; in the sub sequent period the economic units would find themselves with a level of stocks that they would not be willing to hold at the previous market prices; market prices would change which would in turn change the desired flow quanti ties and stock levels until a situation was reached where both (2.4.41) and (2.4.42) were satisfied. Hence, the ; seeming overdeterminacy disappears— both equilibrium condi tions are necessary for any type of stable (over time) equilibrium to be established. Walras 1 Law and stock-flow analysis.— Walras1 Law ! stems from the form of the budget restraints and the deci- : sion functions. Once a decision has been made as to the : quantities demanded or supplied of m-1 commodities, the quantity demanded or supplied of the m * " * 1 is automatically determined. Consequently, one equation of the system 149 (2.4.41) is not independent; once m-1 of the relations in (2.4.41) are satisfied, the m t * 1 must also be satisfied. It is interesting to note that the dependent equation cannot be one of the s equations in the. system (2.4.42) because of the absence of any stock variables in the budget restraints (2.4.15). The dependent equation is one that describes price determination in one market during the marketing period; without it the system is definitely underdetermined. Once again, we find that the model that we have been considering describes a barter economy; equations (2.4.41)-(2.4.42) and (2.4.44) are functions of relative prices, and there is no way that the absolute prices can be solved for in the present model. Later Developments in the Stock versus Flow Debate The content of the debate since the Bushaw-Clower contributions has not materially changed; there are still those who maintain the equivalence of the two approaches and those that maintain that there is a difference between stock and flow analysis. It must be remembered that this debate centers on stock analysis versus flow analysis, not stock-flow analysis versus some other type of analysis. Further, the debate was carried on in terms of stocks ver- ! 150 jsus flows of financial— not real— assets, primarily money and bonds. The former qualification makes little difference to our analysis; the latter, however, makes a great deal of difference. Taking the qualifications in reverse order, the first question to ask is what differences exist between financial and non-financial assets that might affect their treatment. One difference is that financial assets cannot be consumed (except if we take into consideration acciden tal destruction, which we ignore here) and can therefore be treated as pure stock items; on the other hand, non-finan- cial assets can in general be either consumed or held as a stock, or both. Clearly, from a purely mechanical point of view, when dealing with a pure stock variable, stock and ;flow analysis can be made equivalent if the correct assump tions are made; while, if we are dealing with a stock-flow variable, neither a stock analysis or a flow analysis is satisfactory— what is needed is a stock-flow analysis. However— and this refers to our first qualification— once a particular commodity is identified as a pure stock magni- I |tude, its correct treatment (from a purely mechanical point I of view) depends on the assumptions. If the Fellner-Somers i [view is taken, then stock analysis and flow analysis are lequivalent and it makes no difference which is used; if the |Fellner-Somers assumptions are rejected, a stock-flow 151 analysis is the only appropriate approach to take. We may conclude from these remarks that stock anal ysis and flow analysis are applicable only in special cases; it is, in general, more satisfactory to take the more gen eral stock-flow approach which is capable of handling all types of commodities under all combinations of assumptions. The preceding discussion has been carried on in terms of the pure mechanics (or mathematics) of the argu ment which completely disregards the economics involved. It is on the economic grounds that the participants to this debate have concentrated. Patinkin1s views on stock analysis versus flow analysis in monetary theory. Don Patinkin appears to be the foremost proponent of the equivalence of stock analysis and flow analysis in monetary theory. His views are most succinctly stated when he wrote: Stock analysis, as well as flow analysis, presupposes a period of time: namely the period between the mo ment .at which the individual is making his plans, and the moment for which he is making them. Hence . . . the periods presupposed by the analysis must be iden tical with that of flow analysis. This proposition holds also in the limiting case where the period is an instantaneous one. Conversely, if the periods presupposed by the two analyses are not the same, then the two excess-demand functions will also generally not be the same. . . . It should, however, be obvious that the different excess-demands in these cases are not the result of any alleged difference between stock and flow analysis 152 as such,, but rather the result of our using two different periods of time in our different analysis. Clearly, these same differences between excess- demands would remain even if we were to apply stock analysis— or flow analysis— to both cases. All this is the refection of the simple fact that the prices and interest rate which might equlibrate an economy over a period of a month need not do so over a period of a week— and conversely.95 ; Thus, Patinkin's analysis is a simple extension of the Fellner-Somers argument. Patinkin assumes, in essence, that desired stocks equal actual stocks at the beginning of the period and that the individual's economic horizon with regard to stocks extends only over the current period. W. J. Baumol has criticized Patinkin on this latter assump tion, claiming that the Patinkin analysis assumes that if the individual's excess of desired over actual stocks is X at the end of n periods, the adjustment will take place at the rate of X/n per period. ^6 This is seemingly a misrep resentation of the Patinkin model; if this were true the excess flow and excess stock demand functions of a pure ■ stock commodity would no longer be identical, they would be i related by the factor 1/n. 9^Don -patinkin, "Liquidity Preference and Loanable Funds: Stock and Flow Analysis," Economics, XXV, New j Series (November., 1958) , 306-307. Patinkin also gives a thorough,, tzhough purely dimensional, discussion of stocks and flows in his Money, Interest, and Prices, op. cit., pp. 515-523. ■ 96 Baumol, "Stocks, Flows and Monetary Theory," ■ 2E* Hit*» P- 55. i j | Patinkin's formulation has also been criticized by R. W. Clower on the grounds that Patinkin's statement of the problem ignores dimensions. According to Clower, the : Patinkin formulation may be stated T T-1 (2.4.45) / f(t) dt - / f(t) dt To To where f(t) is the flow of a certain commodity as a function of time. This quantity clearly has the dimension of a stock, and the number which measures the difference between the total stock of a given commodity at two given points of time also happens in this case to measure the flow of the commodity during the interval of time defined by the given points. Thus, a single (numer ical) symbol suffices to characterize a property of two distinct "things"— a "stock" in the first case, a "flow" in the second. But this does not mean that the two "things" referred to are identical; they are not.97 Patinkin replied that it was not my intention to argue that the difference between a stock at two different points of time has the dimensions of a flow, but rather that the change effected (or to be effected) in a stock over a given period of time has the dimensions of a flow.9^ Patinkin's formulation would then be ®^'R. W. Clower, "Stock and Flow Quantities: A Common Fallacy," Economica, XXVI, New Series (August, 1959), 25 i . ^Don Patinkin, "Reply to R. W. Clower and H. Rose," Economica, XXVI, New Series (August, 1959), 253. 154 T T -1 T (2.4.46) ( / f(t) dt - / f(t) dt)// dt which has the dimensions of a flow. The argument against the equivalence of stock anal ysis and flow analysis. Most economists that have argued ;against the equivalence of the two approaches to monetary theory agree that from a purely mathematical point of view, under certain conditions and assumptions, stock analysis and flow analysis are equivalent. From the economic stand point, however, these contributors find a world of differ ence between the two approaches. The best statement of this position was made by Warren L. Smith. With respect to the question of stocks and flows in monetary interest theory, . . . two different facets of the problem should be distinguished. First, from a formal mathematical standpoint, it is often pos sible to present the same model either in terms of stocks or in terms of flows. If so, it is a matter of taste which formulation to use. Second, however, from the standpoint of economic behavior, a stock adjustment may be substantively different from a flow adjustment. To put the matter concisely, the statement that the value of one variable depends upon another variable is not the same thing as the^ statement that the rate of change of the first vari able depends upon the second variable.99 ;This is the same observation made by Lawrence Klein some ; eight years earlier. 9Warren L. Smith, "Monetary Theories of the Rate of Interest: A Dynamic Analysis," The Review of Economics and Statistics, XL (February, 1958), 21. 155 ! A Digression on the Implications of Stock-Flow Analysis Before concluding this section, it will be instruc- Itive to consider the implications of the stock-flow analy sis outlined by Bushaw and Clower to two controversies that :have raged among monetary theorists. Namely, we shall con sider the Patinkin controversy and the LP-LF debate. i The Patinkin controversy. The Bushaw-Clower model presented earlier in this section is essentially a neo classical model with stock-flow commodities explicitly in troduced. The question is whether or not the absolute price level is determinant in this model. This question has already been discussed under the heading of "Walras1 Law and Stock-Flow Analysis"; it was :concluded there that the double equilibria conditions ne cessitated by the presence of stock-flow commodities does not by itself make the absolute prices determinant in this :system. Hence, the Bushaw-Clower model does not rescue the neoclassical model from the Patinkin critique. The LP-LF debate. The Hicksian proof of the equi- ; valence of the LP and LF theories of interest rate deter mination comes into doubt in a stock-flow economy; since there are two equilibrium conditions for each stock-flow commodity, no matter which equation is eliminated by Walras1 156 Law the theory that remains is not a pure theory of either type. Cliff Lloyd used this conclusion to argue that the Hicksian proof holds only in situations where there is: (1) a pure flow economy, (2) a pure stock economy, (3) a stock-flow economy where money and bonds are either pure flow or pure stock variables— they do not have to be the same, or (4) a stock-flow economy where either the flow excess demands or stock excess demands for money and bonds are equivalent. Earlier, Patinkin made what appears to be the most sensible observation of this entire debate. He observed that in a general equilibrium system the same equilibrium rate of interest would prevail no matter what equation was eliminated; this is a reflection of the truly simultaneous nature of the system. He concluded, therefore, that the arbitrary classification of a theory as being either a LP theory or a LF theory on the basis of which equation is eliminated is meaningless. lOOciiff Lloyd, "The Equivalence of the Liquidity ; Preference and Loanable Funds Theories and the New Stock- iFlow Analysis," The Review of Economic Studies, XXVII (June, 1960) , 206-209. 1 ^Patinkin, "Liquidity Preference and'. . . op. ait., pp. 300-301. This interpretation fits in with an earlier objection to the Hicksian proof by Abba Lerner, who inquired what type of an interest theory would remain if the "peanuts" equation were eliminated. The source of Lerner's objection is seemingly untraceable; however, see Johnson, o£. cit., p. 361. ! 157 i i I Borrowing a page from Brunner's earlier analysis, I !W. J. Baumol has argued that under conditions of partial i disequilibrium a choice can be made as to the appropriate jtheory of interest rate determination; the choice, however, depends on empirical, rather than theoretical, considera tions . The relevant consideration is the relative rate of iadjustment of each market to an equilibrium position; if the bond market adjusts faster to changing market condi tions than does the money market, then the LF theory is the appropriate theory, and vice versa.I* - * 2 Conclusion The review in this section was not intended to be an exhaustive treatment of the relevant literature; rather it was intended to do two things; ( 1) to present a review of the differences between pure flow, pure stock, and stock- flow models of economic behavior, and ( 2) to present an 103 outline of the form that a stock-flow model would take. 1 0 2Baumol, "Stocks, Flows and Monetary Theory," jop. cit. - * • ^Particular attention should be paid to two arti- ;cles by Josef Hadar, who discusses the dynamics and compar ative statics, respectively, of a Bushaw-Clower t^pe stock- !flow model. The articles are: "A Note on Stock-Flow !Models of Consumer Behavior," The Quarterly Journal of Eco nomics, LXXIX (May, 1965), 304-309; and "Comparative Sta tics of Stock-Flow Equilibrium," The Journal of Political Economy, LXXIII (April, 1965), 159-164. 158 We have argued throughout this review that a stock-flow approach— as opposed to a pure flow or pure stock approach— is the more fruitful line for investigating economic phenomena. The reason given in the main argument of this section ran in terms of the generality of the stock-flow approach; however, there may be a more funda mental reason for preferring the stock-flow approach over alternative approaches. Consider, for example, a commodity that can be considered a pure stock quantity, namely bonds. If bond market behavior were studied by means of a pure stock model, this would imply that the demand for and sup ply of bonds are purely in response to discrepancies be tween desired and actual stocks of bonds and other pure stocks. But, consider for a moment the actions of a firm : that is in the process of deciding whether or not to issue ; new bonds to finance additional plant capacity; are the firm's present level of indebtedness, stock of capital goods, etc. the only things taken into consideration? The :answer is that they are probably not; anticipated flows of factor services, income, and other flow quantities undoubt- |edly play an important role. Thus, from a purely behav ioral point of view, it appears that a stock-flow approach is to be preferred in all but some exceptional cases. The stock-flow approach is of crucial importance to the present analysis in that it logically leads to the 159 I portfolio approach for the study of economic— and, in par ticular, financial— behavior, which is one of the corner stones upon which this work is based. A clue as to the workings of a stock-flow-portfolio model has been given by Karl Brunner from the standpoint of policy variable changes: Variations in policy variables induce a reallocation of assets (or liabilities) in the balance sheets of economic units which spills over to current output and thus affect the price level. Injections of base-money (or "high-powered" money) modify the composition of financial assets and total wealth ' available to banks and other economic units. Ab sorption of the new base money requires suitable alterations in asset yields or asset prices. The banks and the public are thus induced to reshuffle their balance sheets to adjust desired and actual balance-sheet positions. The interaction between banks and the public, which forms the essential core of money-supply theory, generates the peculiar leverage or multiplier effect of injections of base money on bank assets and de posits and, correspondingly, on specific asset and liability items of the public's balance sheet. The readjustment porcess induces a change in the relative yield (or price) structure of assets crucial for the transmission of monetary policy-action to the rate of economic activity. The relative price of base money and its close substitutes falls, and the rela tive price of other assets rises. The stock of real capital dominates these other assets. The increase in the price of capital rela tive to the price of financial assets simultaneously raises real capital's market value relative to the capital stock's replacement costs and increases the desired stock relative to the actual stock. The relative increase in the desired stock of capital induces an adjustment in the actual stock through new production. In this, manner current output and prices of durable goods are affected by the readjust ments in the balance sheets and the related price 160 movements set in motion by the injection of base money. The wealth, income, and relative price effects involved in the whole transmission process also tend to raise demand for non-durable goods.1 0^ V. THE STRUCTURE OF FINANCIAL MARKETS AND THE ECONOMICALLY RELEVANT COMPONENTS OF NET WEALTH In earlier sections of this work we have considered the role that real wealth— or, a particular type of real wealth, real balances— has played in economic analysis. No mention has been made, however, of what items should com prise "economically relevant wealth"— i.e., what items of wealth does a rational individual or group of individuals consider when formulating their economic decisions— and what relation, if any, do the components of net wealth have to the institutional set-up of an economy. It is the pur pose of this section to investigate these questions in more detail. 1 / , What is Economically Relevant Wealth? - - * - — In the final analysis, this is an empirical ques tion; however, as with most other concepts in an empirical science, it is instructive, and perhaps necessary, to first lO^Karl Brunner, "The Report of the CMC," The Jour nal of Political Economy, LXIX (December, 1961), 612.' 161 construct a theoretical (or abstract) system to analyze the I possible elements that make up an individual's, or group of individuals1, wealth to determine which elements should be included in the economically relevant category^ This is especially important in this case because of the lack of wealth data necessary to empirically test various hypothe ses concerning the definition of net wealth. , To begin the analysis, we shall make certain sim plifying assumptions: ( 1) the propensity to consume, save, etc. as a function of wealth is assumed not to differ from individual to individual; i.e., distribution effects are assumed away; ( 2) symmetry with respect to behavior of debtors and creditors is assumed; (3) the economy is as- : sumed to consist of two sectors: the private sector and the government sector; and (4) wealth in the form of human capital will be temporarily ignored. On the individual level, there is no question that items that appear on the asset side of the individual's (economic) balance sheet are net assets to the individual, and the items that appear in the liability section are net liabilities to the individual; there is a question, however, as to what items are true liabilities to an individual (see the discussion of the Pesek-Saving thesis later in this ;section). This implies that the net worth section of an individual's (economic) balance sheet is a valid measure of 162 the individual's net non-human wealth, and that this is the figure that should enter into his calculations that are influenced by his wealth position. When we sum over all individuals and consider aggregate behavior, the picture is not nearly so straight forward. It is clear that all tangible, physical assets owned by members of the economy should rightfully be con sidered as net wealth; the problem arises when financial instruments are introduced. One peculiarity of all finan cial instruments, or so it is claimed by some, is that they assume two roles: on the one hand, they are assets to the holders; on the other hand, they are liabilities to the issuer. Taking into consideration the four assumptions stated earlier, if this is true it directly follows that financial assets and liabilities exactly offset each other so. that the net wealth of the community as a whole is iden tically equal to their stock of tangible, physical as sets. ^-05 If the behavior of one sector in isolation is considered, this conclusion does not hold because the lia bilities of the other sector held by the sector in question are net assets of that sector. The fact remains, however, that when the fwo sectors are considered together, 105The process of arriving at this conclusion is what the accountant calls "consolidation." This procedure is discussed by Ralph Turvey, Interest Rates and Asset Prices (London: George Allen & Unwin, Ltd., 1960), chap. V. 163 the actions of creditors and debtors offset each other— if the assumptions stated earlier hold— and there is no net financial wealth in the. community. If this were the line taken by economists, there would be no place for monetary and financial theory except 1 in the study of the behavior of individual economic units. This has not been the case; the tendency has been to relax the assumption concerning distribution effects and to as sume that one sector does not consider its liability posi tion when making economic decisions. The sector usually chosen is, of course, the government sector. The Development of the Concept of Net Financial Wealth The early proponents of the wealth effect believed J that the balance sheets of the economic universe that they were concerned with must be consolidated rather than merely aggregated. In general, they were primarily concerned with ! the private {excluding banking) sector; they therefore ' treated the exogenous sectors as not being influenced by ! their own asset and liability positions. An example of their type of reasoning with respect to net financial wealth of the private sector is given by Pigou when he : wrote, It must be remembered, indeed, that not all the stock of money held by the public constitutes a net asset 164 to them. Part of it is offset by. debts: from them to. the banks in respect of advances and discounts.106 This was as far as the considerations of the com ponents of net financial wealth went until Lloyed A. Metz-, ler published his pathbreaking article in 1951. Metzler claimed that the method employed to alter the stock of money, in the context of a neoclassical system that in cludes a wealth effect, makes a great deal of difference: If the change is brought about by open market operations, interest theory is a monetary theory; if the change is brought about by printing money, interest theory is a real theory. The crucial point is whether or not the method of changing the stock of money alters the existing stock of other assets. For simplicity, Metzler assumed that government ob ligations are fixed in real terms and that interest pay ments on government holdings of its own debt are remitted to the private sector as income. Under these circumstances, if the money stock were (say) doubled via government pur chases (from the private sector) of its own obligations, the new equilibrium position would be characterized by 10€>-A. c . Pigou, "Economic Progress in a Stable En vironment," Economica, XIV (New Series (1947), reprinted in Friedrich A. Lutz and Lloyd W. Mints (eds.), Readings in Monetary Theory (Homewood, Illinois: Richard D. Irwin, Inc., 1951), p. 250. I 165 doubled prices, lower, real asset holdings,, the. same real ; quantity, of money, and a lower, rate of interest. The lower rate of interest implies a permanently lowered propensity to save and a higher propensity to. consume. Money, in this situation, is neither, neutral nor does the dichotomy hold. On the other hand, assume that the government (say) doubles the quantity of money by using the printing press, : and then uses the proceeds to purchase currently produced goods and services. In the new equilibrium position, : prices will be doubled, real asset holdings will be the same, real balances will be unchanged, and the rate of in terest will be the same. This is the neoclassical outcome; money is neutral, but the dichotomy does not necessarily hold.107 It was not long before Gottfried Haberler pointed out that Metzler's analysis implicitly assumed a distribu tion effect: specifically, the private sector is assumed ; to be influenced by its (and the government's) level of | debt, but the government is assumed to be unaffected by its debt. If the behavior with respect to debt was symmetrical between the private and the government sectors, a decrease 107Lloyd A. Metzler, "Wealth, Saving and the Rate of Interest," The Journal of Political Economy, LIX (April, 1951), 93-116. Notice that Metzler's results are com pletely consistent with the Patinkin model; for Patinkin's views, see his Money, Interest, and Prices., oj>. cit., pp. 288-294. I 166 I . i ; in assets, held by. the. private sector as a result of open 1 market operations would be offset by a decrease in liabili- | ties of the government— net assets and net behavior of the r community, as a whole would be the same.108 Subsequent writers have accepted Metzler's implicit assumption as valid, and a whole theory of financial behavior has been built upon this assumption. The Gurley-Shaw model. John Gurley and Edward Shaw continued the analysis from the point where Metzler left off. They argued that a model designed to explain monetary behavior cannot validly ignore the financial structure, and ; that there are important implications of the presence of a variety of financial assets to both monetary and growth I economics. The Gurley-Shaw model is an alternative to. the ; Patinkin model in that both purport to explain behavior in ; a monetary economy, but each place their emphasis on dif ferent aspects, of economic behavior: Patinkin1s emphasis , is on the. real balance effect, whereas Gurley and Shaw place their emphasis on the whole spectrum of financial I assets which are,, to an extent, differentiated by their lO&Gottfried Haberler, "The Pigou Effect Once Again," The Journal of Political Economy, LX (June, 1952), |240-246. ' 167 degree of liquidity.. Gurley and Shaw envisage an economy consisting of consumers, non-financial firms, non-monetary intermedi aries, and a monetary sector. These four sectors deal in five markets: A market for labor, current output, direct securities, indirect securities, and money. Each entity's demand for financial assets— with the exception of the monetary sector, which is assumed to be motivated by non maximizing considerations— is assumed to be governed by an attempt to balance their portfolio relative to their pref erences and market determined prices. There is nothing novel so far in this analysis, except there is one new actor on the stage— non-monetary intermediaries— and one new stage on which the actors may interact— the market for indirect securities. The process of intermediation. Crucial to the Gurley-Shaw analysis is an economic rationale for the pres ence and functioning of non-monetary financial intermedi 109 John G. Gurley and Edward S. Shaw, Money in a Theory of Finance (Washington, D.C.: The Brookings Insti tution, 1960). The same two authors previously published portions of their book in a series of articles; these in clude: "Financial Aspects of Economic Development," The American Economic Review, XLV (September, 1955), 515-538; "Financial Intermediaries and the Saving-Investment Pro cess," The Journal of Finance, XI (March, 1956), 257-276; and "The Growth of Debt and Money in the United States, 1800-1950;. A Suggested Interpretation," The Review of Eco nomics and Statistics, XXXIX (August, 1957), 250-262. ____ 168 aries; they accomplish this task by appeal to the nature of the saving-investment process. Consider a pure barter economy; any saving out of current output that an individ ual does in this situation must take the immediate form of some tangible asset. If an individual wishes to dissave without depleting his current stocks, there is no way in which the savings of a surplus individual can be trans ferred to the dissaver short of an outright gift. Or, to put the matter a little differently, no member of the economy can be either a surplus of deficit unit in the sense that, for each individual, beginning stocks plus in come is identically equal to consumption during that time period plus ending stocks, ex ante and ex post— and this must hold for each and every period. From an economic standpoint, such a system is obviously suboptimal; an effi cient allocation of resources dictates that resources should flow to those who can earn the highest returns from those who have less attractive alternative uses for their savings. When circulating money is introduced into the econ- omy, the situation is somewhat improved with regard to the saving-investment process. The transfer of savings from |surplus to deficit units, however, can only take place i |through an indirect mechanism; this indirect mechanism would work through the medium of price changes. For 169 example, the process of saving from current income means that excess supplies will appear and prices will fall; as suming that supply is relatively inelastic in the short run, real resources will be transferred from savers to the rest of the economy via the decreased price level. This is rather an inefficient means of mobilizing savings; what is needed is some lending instrument so that the transfer can be made directly— for example, a bond. The type of bond that we have reference to here is what Gurley and Shaw call a "primary security," which include[s] all liabilities and outstanding equities of nonfinancial spending units, that is of spending units whose principal function is to produce and purchase current output, and not to buy one type of security by issuing another.HO Bonds and equities, then, give an opportunity to those who wish to incur a deficit on current account to borrow from those who wish to run a surplus. But, in a complex society it is not always possible or convenient for borrowers to tailor their security issues to meet the needs and preferences of lenders. Consider, for a moment, the problems that would be faced by a firm that wished to float a $100 million bond issue if they had to issue literally thousands of different securities to meet the needs of the thousands of ultimate lenders. nOQUr].ey an^ shaw, Money in a Theory of Finance, op. cit., p. 59. 170 Economic efficiency alone,, along with other, considerations, would suggest that institutions specializing in these types of transactions should emerge on the economic scene. Thus, financial intermediaries enter the picture. According to Gurley and Shaw, The principal function of financial intermediaries is to purchase primary securities from ultimate borrowers and to issue indirect debt for the port folios of ultimate lenders. and Financial intermediaries may be divided into two main groups: the monetary system and the nonmone tary intermediaries. The monetary system . . . purchases primary securities and creates money . . . nonmonetary intermediaries, in contrast, perform only the intermediary role of purchasing primary securities and creating nonmonetary claims on themselves, which take the form of savings deposits, shares, equities, and other obligations.. These claims are nonmonetary indirect debt or financial assets, depending on whether, they are looked at from the standpoint of the issuer or the holder. The function of financial intermediaries— whether they are monetary or non-monetary— is, then, to channel savings from surplus units to deficit units by selling in direct debt and purchasing direct securities. The transfer process is different depending upon whether, the function is performed by a monetary or non-monetary intermediary. If it is performed by a non-monetary intermediary, the trans fer is direct; i.e., the same dollars that are given up by 111Ibid., pp. 192-193. the lenders are received by. the ultimate, borrower. On the other hand, if. the transfer, is performed by a monetary in termediary— ignoring reserves— no act of saving (either past or present) need have occurred; the transfer is accom plished by price changes. This result is a direct conse quence of the acceptability of the indirect debt of mone tary intermediaries as a medium of exchange. A view that appears, at first glance, to be contra dictory to the foregoing has been expounded by Karl Brunner and Allan Meltzer. In qualitatively investigating the financial adjustment mechanism in the context of a wealth (portfolio) adjustment scheme, they conclude that their model "refutes . . . the widespread interpretation of 'net inflows' to time and savings accounts as a savings flow. Such flows are shown as a by-product of an asset allocation process only tenuously related to saving (i.e., growth in [net] w e a l t h ) . 0n closer examination, however, it is clear that these two positions are not contradictory; Brunner and Meltzer are merely making a distinction between I past saving that flows to non-monetary intermediaries as a result of a portfolio adjustment (i.e., a disinvestment in other assets), and saving that flows to non-monetary ^■■^Karl Brunner and Allan H. Meltzer, "The Place of Financial Intermediaries in the Transmission of Monetary Policy," The American Economic Review,: LIII (May, 1963), . 38!. 172 ;intermediaries that is currently produced (i.e., saving :from current income)— a distinction that is perfectly com- patible with the statement in the previous paragraph. j The process of deposit creation. As noted previ ously, the Gurley-Shaw definition of financial intermedi- i Iaries does not distinguish between the monetary and non monetary institutions. This flies in the face of tradi tional banking and financial theory which has given a unique role to the monetary sector— that of the ability to create deposits. According to Gurley and Shaw, however, it is more correct to say that all financial intermediaries create deposits; the only difference being that monetary financial intermediaries create money, while non-monetary intermediaries create non-monetary indirect "assets." For illustrative purposes^ consider the balance sheets of a ! commercial bank (CB) and a non-monetary financial interme diary (NMI) in the process of acquiring primary deposits and making investments. For simplicity, assume that the CB ; is subject to a 20 per cent currency reserve requirement |and that the NMI has no reserve restriction. Now assume that a depositor comes to the CB and to the NMI with $100 in currency that he wishes to deposit. This transaction is illustrated in Figure 2. 173 CB NMI Currency $100 Deposits $100 Currency $100 Deposits $100 FIGURE 2 DEPOSIT CREATION PROCESS— INITIAL DEPOSIT The institutions will attempt to invest their ex cess funds, and assuming that the desired level of excess reserves is zero, their respective balance sheets will be CB NMI Currency $100 Deposits $180 Earning $100 Deposits $100 Assets Earning Assets 80 FIGURE 3 DEPOSIT CREATION PROCESS— LENDING There is no doubt that "deposit creation" has taken place in both instances: in the case of the CB, the public now i |has eighty dollars more than in its initial position; while in the case of the NMI, the public has the same amount of ;nominal money balances, but $100 more in non-monetary fi nancial assets. This mechanical illustration of deposit creation is well known and not disputed; the substantive question from the standpoint of monetary theory is whether or not the 174 I liabilities of NMI are substantially different from those ! of a CB. Gurley and Shaw would say that the liabilities of i , the two types of institutions are very similar in certain ; respects; however, their view has been attacked on basically ;two points. One school of thought maintains that NMI are purely passive agents that maintain a standing offer to the public to provide certain services, as does a broker or a merchant . . . the rate of growth of outstanding obligations of intermediaries arise mainly out of changes in economic and financial conditions that affect the extent to which customers desire to take advantage of the standing offer of the intermediaries, rather than out of any particular decisions or actions on the part of the intermediaries themselves. . . . Discipline over financial intermediaries is exercised in an immediate and direct manner by their creditors. Until someone brings money into a savings and loan association to exchange for its obligations, the association cannot lend money. When the creditor comes back to the association and requests the re turn of his money, the association must similarly | contract its loans. A change in the volume of demand deposits, in contrast, is initiated by banks when they change the volume of their debt holdings; the banks' creditors, as such, play no active role in the process. . . . The commercial banks do not need to "borrow loanable funds from spending units with surpluses" in order to extend credit.113 No more need be said about this view except that, if it were valid, it would imply that the supply schedule ■ for non-monetary indirect debt and the demand schedule for m . Culbertson, "Intermediaries and Monetary ■Theory: A Criticism of the Gurley-Shaw Theory," The Ameri can Economic Review, XLVIII (March, 1958), 136-137. 175 |demand deposits are infinitely elastic, a view that would | find very few supporters among economists. The second, and related). criticism of the Gurley- ;Shaw theory is concerned with their assertion that NMI create loanable funds; a criticism that is based on the * 1 1 E I idea that NMI perform only a brokerage function. The . 'Gurley-Shaw position o this point is worth reviewing be cause of its crucial importance to their theory. The ac cepted definition of the supply of loanable funds is: (2.5.1) Supply of loanable funds = Planned saving of spending units + Increase in the stock of money - Increase in economy1s demand for money (hoarding). By an appropriate rearrangement and substitution, (2.5.1) becomes (2.5.2) Supply of loanable funds = Spending units' in- j crease in demand for primary securities + Non-monetary intermediaries' increase in | demand for primary securities + Monetary ! I 1140n this point, see John G. Gurley and Edward S. jshaw, "Reply [to J. M. Culbertson]," The American Economic jReview, XLVIII (March, 1958), 136-137. I i I ! llSculbertson, op. cit., p. 122; and Joseph Aschheirrv ! "Commercial Banks and Financial Intermediaries: Fallacies jand Policy Implications," The Journal of Political Economy, jLXVII (February, .1959), ,64-67. 176 system's increase in demand for primary i securities.. Thus, NMI do create loanable funds as long as their i increase in demand for primary securities is not offset by ;a corresponding decrease in demand by spending units and :the monetary system. There is no reason to think that the monetary system would decrease their demand as a result of an increase in demand by NMI; however, there are reasons to believe that the spending units would decrease their de mand, perhaps by the exact amount of the increase in demand of the NMI, as a result of the increase in demand of the NMI. Gurley and Shaw get around this by assuming that money and non-monetary indirect debt are close substitutes so that an increase in demand on the part of spending units :for non-monetary indirect debt is accompanied by a decrease in demand for real balances that spills over into the pri mary security market. This is an empirical question, and one that we shall have more to say about in the latter chapters of this work. It is interesting to note that the idea that the presence of NMI reduces the demand for money is not new. For example, twenty-five years before the publication of the Gurley-Shaw work, J. R. Hicks wrote: Those persons who have command of large quantities of capital, and are able *to spread their risks, are not only able to reduce the risk on their own capi tal fairly low— they are also able to offer very 177 good security for the investment of an extra unit along with the rest. . . . They can, therefore, provide the safe investments which their fellow- citizens need. . . . The appearance of such safe investments will act as a substitute for money in one of its uses, and therefore diminish the demand for money.US Inside versus outside money. One contribution made by Gurley and Shaw that has enjoyed a great deal of popu larity is their distinction between "inside money" and "outside money." Inside money is money that is based upon internal debt, while outside money is money based on the debt of some exogenous sector (e.g., the government or foreign units). This distinction is important for our dis cussion because inside money does not represent net finan cial wealth to the community (at least in the Gurley-Shaw view), but outside money does. Perhaps an example will make the distinction clear; assume a three sector economy where the business sector is the only.issuer of bonds (standardized perpetuities paying $1 per period) which are purchased by the consumer and government (monetary) sectors. The balance sheets of the 11®J. R. Hicks, "A Suggestion for Simplifying the Theory of Money," Economica, II, New Series (1935), re printed in Friedrich A. Lutz and Lloyd W. Mints (eds.), Readings in Monetary Theory (Homewood, Illinois: Richard D. Irwin, Inc., 1951), p. 23. For the derivation of (2.5.2) from (2.5.1), see Gurley and Shaw, Money in a The ory of Finance, op. cit., pp. 218-220. 178 various sectors might appear as follows Business Sector Consumer Sector Money (Mb) $. 50 .Bonds (B/i) $500 . Money $125 (Mh) Tangible 900 Net Worth 450 Bonds 400 (Bh/i) Net Worth $525 $950 $950 $525 $525 Government (Monetary) Sector Bonds (B^/i) $100 Money (M) $175 Net Worth -75 $100 $100 FIGURE 4 INSIDE VERSUS OUTSIDE MONEY iwhere B = B^ + Bg and M = Mb + Mh. In this example, there i is $75 of outside money— the monetary sector's monetary : liabilities less their holdings of domestic debt— and $100 of inside money— the monetary sector's holdings of domestic | debt— to make a total of $175 in nominal balances held by the non-monetary sectors. It should be noted, however, 117These balance sheets are reproduced, with cer- : tain corrections, from Don Patinkin, "Financial Intermedi- j ; aries and the Logical Structure of Monetary Theory,” The American Economic Review, LI (March, 1961), 102. that the presence of outside money in this system is pred icated on the assumption that the monetary sector1s be havior is not influenced by changes in their liability i I position; i.e., a distribution effect is assumed in this model. The foregoing discussion implies that the relevant , monetary wealth constraint should be written (2.5.3) [Mq - (l/i)Bg]/P | where the "o" subscript indicates intitial quantities, P is I i the price level, and the other notation has the same mean- j ing as in Figure 4. It is obvious that in a pure inside ; i • I money economy, net financial wealth is zero; while in a j | pure outside money economy, net financial wealth is Mq . In the intermediate case, net financial wealth is less than ! Mq , but greater than zero. The implications of inside-outside money to the j wealth effect, the dichotomy, and neutrality. The price ! induced wealth effect, or what we have called the Pigou effect, is the effect on consumption, investment,, etc. of a j i change in net wealth due to the effect on nominally fixed J priced assets of a change in the price level. The nomi nally fixed priced assets that comprise net wealth, accord-! ing to the currently popular view, are primarily outside money and outstanding government debt. As long as the 180 government engages in monetary operations based on their own debt and/or has outstanding obligations, there is a financial wealth effect. However,, consider for a moment a | situation in which there is only inside money and no inter est paying government debt? a change in the price level will only redistribute financial wealth among the various sec tors of the economy (i.e., the expression (2.5.3) vanishes), there is no operative financial wealth effect. Thus mone tary theory, if it is to be concerned with anything at all, rests on the existence of government obligations. Further, the inside-outside money distinction has important implications to our view of how a monetary econ omy functions; specifically, the distinction bears directly on the validity of the classical and neoclassical dichotomy and the conditions under which money will be neutral. With! regard to the types of money that can exist within an econ- omy in the present context, there are three possibilities: 1. If the money supply consists entirely of inside! money and there are no other outstanding government obli gations, the dichotomy is valid and, therefore, money is neutral. The reason for this result is that the real bal ance term, equation (2.5.3), is identically equal to zero at all possible price levels, and consequently disappears from the real sphere equations. The dichotomy is valid since, although the price level does not appear in the 181 commodity. equations, it does appear in all monetary equa tions, including the bond equation.118 2. If the money supply consists entirely of out side money, but no other government obligations are out standing, the dichotomy is not valid but money is neutral. The dichotomy breaks down because (2.5.3) no longer van ishes; money is neutral because a (say) doubling of the money supply doubles all prices leaving the real value of net financial wealth— which is, by assumption, identical with the stock of outside money— unchanged. This is essen tially the Patinkin system analyzed in Section III of this chapter. 3. If the money supply consists of both inside and outside money, and/or if there is government non-monetary debt outstanding, neither the dichotomy nor neutrality holds. As Modigliani said, Just how a change in the money supply or in the de mand for money will affect the real variables of the system depends on which component of supply is changed and on the relative size of the components and of the national debt.119 1180n this point, see Ibid., p. 107.; and Franco Modigliani, "Liquidity Preference and the Theory of Inter est and Money," The Critics of Keynesian Economics, ed. Henry Hazlitt (Princeton: Princeton University Press, 1960), pp. 183-184. 11®Modigliani, "The Monetary Mechanism . . . ," op. cit., p. 87. This section is essentially based on this work, and especially pp. 84-88. 182 Following Modigliani's example, assume that the money sup ply is entirely of the inside variety and that the govern ment does have a positive debt position. A (say) doubling of the money supply would tend to double the price level, thus lowering the real value of net financial wealth; i.e., the doubled price level would reduce the real value of outstanding government obligations by one-half. The new equilibrium position would tend to have a higher level of saving and investment, and a lower rate of interest and consumption. The conclusion that money is not neutral in an economy which contains a mixed money supply and/or govern ment obligations rests entirely on the test for neutrality that one accepts. As Harry Johnson observed, The neutrality debate can be reduced to any arbi trarily low level by arguing that they depend on distribution effects, and that the appropriate test of neutrality is an equiproportional change in inside money, the assets backing it, and outside assets.120 The latter portion of Johnson's observation is the view taken by Patinkin, who argues that it is probably more re alistic to assume proportional changes in inside and out- 120h . q. Johnson, "Monetary Theory and Policy," The American Economic Review, LII (June, 1962), 342. side money, than to assume non-proportional, changes.1^1 Net money versus gross money doctrine. Gurley and Shaw make another distinction that is of interest to us: this is the distinction between "net money doctrine" and "gross money doctrine." Net money doctrine "nets out all private domestic claims and counterclaims before it comes to grips with supply and demand on the money market."; while gross money doctrine "avoids such consolidation of financial accounts."122 terms of Figure 4, net money doctrine would measure the money supply as $75; gross money doctrine would measure it at $175. Gurley and Shaw favor a gross money approach on the grounds that net money doctrine would deny that aggregative real demand for money depends on accumulation of private domestic securi ties . Growth in the stock of such securities would be considered irrelevant, except in short periods, to aggregate demand for money, just as growth in the monetary system's holdings of such securities would be considered irrrelevant to the stock of (outside) money. and that, in the absence of outside debt, an economy becomes money-less and bond-less. It is in effect a 121gee Patinkin, Money, Interest, and Prices, op. cit., pp. 298-301? and, by the same author, "Financial In termediaries . . . ," op. cit., p. 108. 122Gurley and Shaw, Money in a Theory of Finance, op. cit., p. 134. 184 barter society., without a determinate price l e v e l . 3 Don Patinkin has taken exception to the Gurley-Shaw preference for the gross money doctrine, accusing Gurley and Shaw of confusing financial variables as dependent variables (M^, M*1, B*1, and B) and as independent variables (M*5, m*1, B^1, and B ) , and that "the absence of distribution o o o o effects implies that at the level of aggregate behavior it is only the sum total of financial assets in the economy that matters."124 To more specific, Gurley and Shaw might state their aggregate demand functions for commodi ties, bonds, and money, respectively, as (2.5.4) C = C(yQ, i, Mq/P, Bq/P) (2.5.5) B/iP = B(y0, i, Mq / P , B q / P ) + B<3/iP (2.5.6) M/P = M(y0, i, MQ/P, BQ/P) where yQ is real national income (assumed to be fixed ex ogenously) , i is the rate of interest, and the other nota tion has the same meaning as in Figure 4. Patinkin, on the other hand, states his correspond ing functions in the form 123Ibid., pp. 137, 142. 124patinkin, "Financial Intermediaries . . . ," op. cit., p. 104. 185 (2 . 5.7) C = ;F(y.o, i, . [Mq - (l/i)B^]/P) i 1 (2.5.8) B/iP = G(y0/ i, [M0 - (l/i)Bgj/P) + B^/iP | ! (2.5.9) M/P = L(y0, i, [MQ - (l/i)Bg]/P) We will have to agree with Patinkin that "the net money doctrine does not imply that an economy with only in side money is 'money-less and bond-less,' so that its price i level is indeterminate''; ^ 5 indeed this is precisely the valid dichotomy that we considered earlier. We cannot agree, however, wtih Patinkin when he claims that Mq and B0 should be netted out before they appear as arguments in the demand functions. What Patinkin appears to be doing is confusing a "wealth approach" with a "portfolio approach"; granted that these two approaches are not mutually exclu sive, but neither is an assertion that one is superior to i the other on strictly a priori grounds a valid conclusion. : That "net-money doctrine overlooks the bearing of portfolio balance on real behavior"126 cannot be denied; and, in view of Gurley and Shaw's continual emphasis on the portfolio balance approach, it seems as if Patinkin's criticism is : completely unwarranted. 25Ibid.,, p. 106 . 126Qurley and Shaw, Money in a Theory of Finance, op. cit., p. 144. ■ 186 ] | A Different Conception of | Net Financial Wealth After reviewing the contributions to modern mone tary theory and its dependence, via the real balance effect^ on the presence of government debt, Harry Johnson very ! perceptively observed that This tradition leaves modern formal monetary theory rather awkwardly dependent on adventitious institu- ! tional or historical details; and the question naturally arises whether this is the best that can be done . . . [and that] the more elegant approach to monetary theory lies along inside-money rather than outside-money lines. . . . : Johnson goes on to observe that the assumed distribution effect with regard to government debt is predicated on the idea that the government can always (1) pay its debts by issuing new debts— i.e., it can always issue new money since it controls the money supply— and (2) meet its inter- i Iest payments since it has the taxing power. With regard to the latter. It provides grounds for denying that interest-bearing government debt should be treated as net assets of the public. The existence of government debt implies the levying of taxes to pay the interest on it, and in a world of reasonable certainty these taxes would be capitalized into liabilities equal in magnitude to the government debt; hence, if distribution effects between individuals are ignored, a change in the real amount of government debt will not have a wealth- effect. |and, with regard to the former, If this logic applies to interest-bearing government debt, why should it not apply to the limiting case of noninterest-bearing government debt, which is equally a debt of the public to itself, and to the commodity moneys, which are the same thing though based on custom rather than law? 127 Thus, net financial wealth appears to be nonexistent, and monetary theory vanishes. The Pesek-Saving thesis. Boris P. Pesek and Thomas R. Saving have taken exception to the foregoing analysis as it pertains to net financial wealth; they maintain that, under certain conditions, a debt producer— whether the pro ducer is the government or some private concern— can create net financial wealth. Commodity and fiat money. Consider a pure barter economy? now assume that one capital good is specified as (commodity) money. The commodity in question still retains its value as a commodity, but it now takes on a new addi tional value by reason of its performing the functions of money. Specifically, money allows the holder to engage in exchange without the time and bother involved in barter transactions; the individual can now consumer more leisure or use his added free time to earn more income. Thus, com modity money represents net wealth to the community since its holders are made better off by reason of its possession, 127Johnson, 0£. cit., pp. 342-343. 188 | I while its non-holders are no worse off. The only way there f I could be an offsetting liability is if the producer of the commodity money incurred a liability of equal magnitude to the proceeds from its sale. This cannot be the case since the sale of money in this case is analogous to the sale of any other capital good; if the sale of commodity money is offset by a liability of equal magnitude, so is the sale ; of all non-monetary goods, and the net wealth .{both mone- ; tary and non-monetary) of the community is reduced to zero; "Such a definition of debt,” according to Pesek and Saving, "is clearly not a useful one."^-2* * Fiat money is also a part of net wealth. To see this, assume that commodity money is replaced by fiat money; those that held commodity money, being recompensed with ; fiat money for their losses, are no worse off than before, ■ and those that held no commodity money in the first place i are no worse off. Hence, fiat money takes on the monetary : function of the commodity money and is, therefore, a part ; of net wealth of the community. It might be objected that this analysis does not hold in the case of a price change. For example, assume that the price of money doubles, i.e., the price level 128Boris P. Pesek and Thomas R. Saving, Money, Wealth, and Economic Theory (New York: The Macmillan Company, 1967) , p. 51. 189 decreases by one-half. Those that do not hold any money are no worse or better off than before; however, those that do hold money balances are now better off than they were before. This conclusion is due to the peculiar technical property of money that "a physical unit of . . . [money] yield[s] physical income, the size of which . . . [is] per fectly proportional to the price of , . . [money] in terms of other commodities."129 Thus, a change in the price of money is indistinguishable from a change in the quantity of money; if the latter is a change in wealth, so must the former be. Private money production. Suppose that we now in troduce private money producers, who produce private money (M) and sell it for income earning assets (y/r), into the r economy. Assume that the marginal cost of producing (either pieces of paper or bookkeeping entries) is zero, and that interest payments on it are prohibited (if inter est payments were permitted, the "borrowing rate" and the "lending rate" would be driven into equality, and money would deteriorate into a pure debt). Pure competition.— It is a familiar proposition of value theory that a purely competitive firm will produce 129Ibid., pp. 60-61. where price equals marginal cost; if marginal cost is zero, the firm (and the industry) will, in general, produce a finite output and sell it at a zero price. If the commod ity in question happens to be money, the price of money will drop to zero, and its reciprocal, the price level, is infinite. In other words, a purely competitive banking industry will destroy itself; monopolistic influences are a necessary condition for the existence of money. Monopolistic competition.— Assume now that there are restrictions placed on the private money producers so that there is no longer unrestricted money production. Pesek and Saving assume that this restriction takes the form, in addition to the prohibition of interest payments, of an "instant repurchase clause"— i.e., the private money producer must stand ready, willing, and able to repurchase ;their output with "dominant money" upon request. Dominant money (M^) is fiat money produced by the government. Even in the absence of a required reserve, the money producers :will still wish to hold a reserve of so that they can 'make good on their instant repurchase clause. An individual will purchase M^ from a money pro- iducer with and y/r; at the margin, the individual will I ' !be indifferent as between the private money that he gains j |and the dominant money and other assets that he gives up. I The change in real wealth of the i^*1 individual after such 191 | !a transaction is j (2.5.10). Aw^ = Mp/P - AM^/P - Ay/r which is equal to zero. On the other hand, the change in real wealth of the k1 - * 1 money producer is (2.5.11) A w j ^ . = Ay/r + (AM^/P - Yf/Pr) where the Y^ is the nominal income that is foregone by the money producer by reason of his holding reserves in the ;form of dominant money. The last two terms of (2.5.11) :exactly offset each other since the capitalized value of :income foregone on the reserves is equal to the amount of the reserves themselves. To arrive at the change in net real wealth to the community as a whole, we add (2.5.10) to (2.5.11), yielding (2.5.12). Aw = (Mp/P - AMd/P - Ay/r) + (Ay/r + AJ^/P - Yf/Pr) = Mp/P - AMd/P i.e., the change in the community’s net real wealth posi tion as a result of a sale of private money is "precisely equal to the total sales of private money minus the de- 130 crease in the stock of the dominant money outstanding." 192 |This applies, of course, only to the extent that prices do i i not change because of the monetary expansion; price move ments consequent on monetary expansion, however, is a dif- i ferent question than we are addressing here, and it affects |all fixed valued claims in the same way. In terms of sectoral balance sheets, the above transactions would appear as Private Non-Monetary Sector Private Money Producer - AMd/P + Ay/r + AMd/P + Yf/rP + M /P Net Worth + Ay/r Net Worth P — — + AW FIGURE 5 MONEY AND NET WEALTH where the Aw in the net worth section of the private money I producer's balance sheet represents his "monopoly profit" and is an addition to the net real wealth of the community. Do non-monetary financial intermediaries create net j wealth? The process of deposit creation and lending of a i ! i non-monetary financial intermediary (NMI) can be broken up into two separate transactions; in the first place, an in- :dividual comes to the NMI and exchanges money (either Md or jMp) for an earning asset— a liability of the NMI. 193 (2.5.13) Aw = yj/r - Am^/p - y^/r + AMp/P where r is to be interpreted as the "market" rate of inter est; the change in net real wealth due to this first trans- i action is zero. When the NMI lends the money that they : received from the first transaction— assuming that they I I maintain no money reserves— the intermediary receives an I income earning asset (the liability of the borrower) and j gives up money balances ! (2.5.14) Aw = y2/r - AM /P - y2/r + AM /P - s ’ • ^ ** ! which is also equal to zero. The net change in real wealth to the community is the sum of (2.5.13) and (2.5.14); the ; amount of the change in real wealth depends on the relation | of y-^ to y2* Empirically, one would expect to find that y2 > y-^f so that, as a first approximation, the change in net real wealth is * (2.5.15) Aw = y2/r - y^/r > 0 If equation (2.5.15) were in fact the true relation, ;the instruments issued by an NMI would be "money-debt”; the ;amount of the money-ness that they would possess depends on |the amount of the divergence of the interest that they pay on their deposits and the market rate of interest (r). The fact that the observed rates do diverge, however, does not mean that the deposits of NMI possess some attributes of 194 i ■ i i money; the fact that the deposits issued by NMI cannot be iused as a medium of exchange means that a rational individ- | ual would not pay a premium for (say) a savings and loan I share relative to the price of similar assets. The dilemma is solved by noting that NMI typically offer deposits plus services for sale; the services consist, among others, of insurance against price fluctuations, investigation of the credit worthiness of the ultimate borrowers, and the re moval of indivisibilities of financial assets. Hence, the correct formulation of the change in community net real wealth is (2.5.16) AW = Y2/r Yj/r “ c/r = .0 where c is the real cost of the services provided by an NMI. We may conclude, then, that in a purely competitive ' economy non-banking financial intermediaries do not create net wealth. That a different result was obtained when con- ; sidering private money producers (i.e., commercial banks) ; is due to the idea that for money to exist there must be monopolistic influences present in the market. No such condition is necessary for the existence of non-monetary debt. : Conclusion i . This section has been devoted to the consideration i ! of the components of net financial wealth: on the individ 195 ual level there is no problem; on the aggregate level, how ever, there has been a good deal of disagreement as to what constitutes net financial wealth, and, at one extreme, as to whether there is any net financial wealth at all. In tuitively, this latter assertion appears to be nonsense; however, it has only been recently that a theoretical ra tionale has been.given for considering certain parts of gross financial wealth as a portion of net community real wealth. This conclusion is of considerable importance to the state of monetary theory; if net financial wealth were non-existent, an important link between the real and mone tary spheres would disappear and monetary theory could be reduced to the study of individual economic units. The only way that monetary theory could be saved in this situa tion is to introduce the real value of financial instru ments into the aggregate demand and supply functions by hypothesizing a portfolio balancing scheme (which is, of course, Gurley and Shaw's "gross money" doctrine); the portfolio approach— both on the theoretical and empirical levels— however, is still in its infancy; a great deal of work still remains to be done in this area before the port folio approach can take its rightful place among its col leagues . The relevance of this section to the major theme of 196 j | this dissertation lies in the implications that it has for I I the steps taken between the individual excess demand func tions and the market excess demand functions. Specifically, this section was designed to help answer the questions con cerning the correct arguments and wealth constraint for the | market functions. VI. THE APPROACH As has been emphasized elsewhere in this work, the basic hypothesis that we are working under is that the "portfolio approach" is a relevant method to use when studying financial phenomena. This hypothesis is not orig inal; it has been gaining momentum since Keynes' emphasis on treating money as an asset [and] has been followed by subsequent theorists as a means of bringing money within the general framework of the theory of choice.131 However, neither was Keynes original in his treat ment of money as one asset out of several to choose from; to reach the beginning of the portfolio approach in economic l^ljohnson, op. cit., pp. 335-336. It is well known that the Keynesian monetary theory takes a portfolio ap proach in the sense that individuals are assumed to have only two alternative means of holding their savings— money or "bonds." James TObin has pointed out that the Cambridge approach can be given a similar interpretation; the choice is now between- money and capital goods. See James Tobin, i"Money, Capital, and Other Stores of Value," The American Economic Review, Li:(May, 1961), 27. 197 analysis we must go back to a classic article by J. R. Hicks. Hicks observed— as did Keynes later— that economic theory was traditionally dichotomized into two separate and seemingly unrelated branches: value theory and monetary theory. He then asked the very pointed question: Why not apply the simpler and generally better developed tools of value theory to the problems encountered in monetary the ory? Hicks could see no reason why it should not be, after all, Money is obviously capable of quantitative expression and therefore the objection that money has no mar ginal utility must be wrong. People do choose to have money rather than other things, and therefore, in the relevant sense, money must have a marginal utility.132 Hicks found the solution to his problem in a combination of value theory and banking theory. As he said, In value theory, we take a private individual's in come and expenditure account? we ask which of the items in that account are under the individual's own control, and then how he will adjust these items in order to reach a most preferred position. On the production side, we make a similar analysis of the profit and loss account of the firm. My suggestion is that monetary theory needs to be based again upon a similar analysis, but this time, not of an income account, but of a capital account, a balance sheet. We have to concentrate on the forces which make assets and liabilities what they are.133 The more recent contributions to the portfolio 132Hicks, "A Suggestion for . . . ," o j d . cit., p. 15. ^-^Ibid. f pt 25. ! 198 approach have followed the exposition of the original i I Hicksian approach as presented by Jacob Marschak and Helen j Makower, who set forth the adjustment processes and equi librium conditions for portfolio balance of the individual and the market under varying conditions.'*'^ That this ap- ; proach is gaining stature within the profession is attested to by the numerous journal articles and books that have come out on the subject,135 an<^ j - , y ^he fact that it has found (implicit) official recognition in at least two semi- Jacob Marschak, "Money and the Theory of Assets," Econometrica, VI (October, 1938); and Jacob Marschak and Helen Makower, "Assets, Prices and Monetary Theory," Eco nomica, V. New Series (August, 1938), reprinted in George J. Stigler and Kenneth E. Boulding (eds.), Readings in Price Theory (Homewood, Illinois: Richard Irwin, Inc., ;1952), pp. 283-310. 135a listing of the relevant articles and books is ,much too long to undertake here; a partial listing can be found in Johnson, 030. cit., pp. 361-362 and p. 364. In ;addition to those listed by Johnson, several other sources : deserve mention here: Karl Brunner, "Some Major Problems :in Monetary Theory," The American Economic Review, LI (May, ; 1961), 47-56; Karl Brunner and Allan H. Meltzer, "The Place of Financial Intermediaries in the Transmission of Monetary iPolicy," The American Economic Review, LIII (May, 1963), ‘372-382; James S. Duesenberry, "The Portfolio Approach to the Demand for Money and Other Assets," The Review of Eco- Inomics and Statistics, XLV, Supplement (February, 11T63), 9-31; and Ralph Turvey, Interest Rates and Asset Prices (London: George Allen & Unwin, Ltd., I960)~ TKis list is ;not meant to be exhaustive, but to merely indicate some of the better known sources in this area. official reports.136 Considerations of Portfolio Balance The literature to date has gone in two directions: on the one hand, the criteria for. choosing an optimum port folio, assuming wealth constant, have been considered; on the other hand, the reactions of individuals, assuming risks and preferences constant, to changing yields and quantities of assets— and their implications for market. outcomes— have been considered. The two approaches are not mutually exclusive, the former rightfully precedes the lat ter; nevertheless, the investigations of each have gone on more or less independently. , The optimum portfolio. Considerations of the cri teria used by a rational individual in choosing an optimum ^Committee on the Working of the Monetary System Report [The Radcliffe Report], Presented to Parliament by the Chancellor of the Exchequer by Command of Her Majesty August, 1959 (London: Her Majesty's Stationary Office, 1959); and Money and Credit: Their Influence on Jobs, Prices, and Growth (A Report of the Commission on Money and Crediti Englewood Cliffs, N.J.: Prentj-ce-Hall, Inc., 1961). The word "implicit" appears in the text because of the emphasis on "liquidity" in.the above references, rather than the outright advocation of the portfolio approach. For a discussion of the idea that the former implies the latter, see Abba P. Lerner, "Discussion [of Brunner, Meltzer, et al.], "The American Economic Review, LIII (May, 1963) , .401-403. 200 ] 37 I portfolio is primarily due to Harry M. Markowitz; the I Markowitz model, in essence, is applicable to a situation j in which an individual has a given amount of resources to I invest and wishes to diversify his portfolio such that i risk (measured by the standard deviation of past yields or ; some other appropriate magnitude) is minimized and expected yield maximized— i.e., each individual is seeking a saddle point with respect to his portfolio composition. A port folio that exhibits the before mentioned properties is called an "efficient portfolio," which will represent an optimum allocation of the individual's wealth. The Markowitz model, however, does not readily answer the types of questions that we are addressing in the imodel developed in this study; granted, it does indicate ; that if the price of a security increases relative to the prices of other assets, we would expect it to. become less attractive, ceteris paribus, to the individual consumer or producer. However, the model does not tell us how market price changes might come about and how an individual— or : group of individuals— allocate increments in their real | wealth-due to price changes, etc.— between consumption and ^"^Harry M. Markowitz, "Portfolio Selection," Jour nal of Finance, VII (March, 1952), 77-91; and, by the same author, Portfolio Selection: Efficient Diversification of Investment (New York: John Wiley & Sons, 1959); also see W. F. Sharpe, "A Simplified Model for Portfolio Analysis," Management Science, IX (January, 1963), 277-293. 201 asset acquisition expenditures. Additonally, there is no mechanism for the determination of the allocation of income between consumption and saving in this model. These are the types of questions that we are interested in investi gating. The portfolio approach. We have reserved the term "portfolio approach" for the approach that is capable of answering the types of questions alluded to in the last section. In other words, we are interested in the affects on market outcomes of the rearrangement of individual port folios in an attempt to reach an efficient position, and in the effects of market outcomes on individual behavior to wards consumption, physical investment, financial assets, and existing tangible assets. To this end, preferences and ! evaluations of risk for each individual are taken as data. It is to be emphasized that the Markowitz analysis under- !lies this type of model— we are taking some of his vari- |ables as data (e.g., risk) in the same way that he took some of our variables as data (e.g., wealth); an analogous relationship is the connection between microeconomic analy sis and macroeconomic analysis. From an Operationally Meaningful to an Operationally Feasible Hypothesis 3 i The model presented in Chapter III of this work is I 202 I ! a very general construct of one hypothesis of the correct i representation of how an economy operates; it is an opera- ; tionally meaningful model in the sense that it could, in principle, be tested; but it is not an operationally fea sible model in the sense that it cannot, under present con ditions, be actually tested. But, this is of no great im- ; \ portance to us since our purpose is to devise an approach to the study of financial phenomena that is consistent and capable of investigating a large number of different ques tions . Obviously, the basic model must be simplified in :order that our objective be realized. The method of sim plification proposed in this study is not dissimilar to :that used by Ralph Turvey and others who have followed the suggestions of Hicks, Marschak, and Makower in their inte gration of money and value theory. Turvey, for example, begins his analysis in a general equilibrium framework but I at a highly aggregative level; he then expands his model to include those variables that he wishes to explain (endoge nous variables) and those that he feels significantly in fluence his model but are not significantly influenced by it (exogenous variables). The present model, on the other hand, begins at the individual level, builds up to a gen eral equilibrium market model, and, finally, contracts to focus on the problem at hand. 203 The. exact form that the simplification will take is ! dependent upon the question being addressed. Turvey points this out when he said: j The point is that the theory as stated above cannot be directly applied to particular circumstances, without modification and that the. nature of the modification required will vary from case to c a s e . 8 ' Although there are an infinite number of potential simpli- :fications possible for any one study, they can be catego rized into two broad types: aggregative models that divide the economy into various sectors, and disaggregative models that only consider a subset of equations but are aggregated and/or consolidated over some of the variables. The method chosen, of course, is dependent on the hypothesis that is being tested. The problem. It will be recalled that when review ing the Gurley-Shaw work it was pointed out that their con- i tention that non-monetary intermediaries create loanable funds is dependent upon two empirical hypotheses: (1) An |excess supply of money appears when the demand for the lia bilities of non-monetary intermediaries increases; and ( 2) i |an excess supply of money is partially cured by increased ;spending on consumption and investment goods. It is with ithe former of these hypotheses that we are concerned with 138Turvey, 0£. cit., p. 60. j 204 in this work; specifically, we shall ask the question: Are j i money (narrowly defined— i.e., currency outside of commer- I cial banks plus demand deposits adjusted) and the liabili- : ties of non-monetary financial intermediaries (the so- :called "near-moneis") substitutes, and, if so, are they ;close or weak substitutes? If two goods are substitutes in demand, we would expect a rise in the price of one to be accompanied by an increase in the demand for the other, ceteris paribus. Traditional economic theory tells us that one way of in- vestigating this is to consider the cross elasticities of demand for the various goods under consideration. This suggests that the appropriate method of simplification in ithis case is to select the relevant demand functions from I the set of general equilibrium equations and to simplify them by consolidation and aggregation to the point where !they can be estimated and tested. We are not without help in this direction; Edgar L. ;Feige has empirically investigated the relationship between ithe demands for liquid assets. Feige computed single equa- ;tion least square estimates of the per capita demand for demand deposits, time deposits at commercial banks, and savings and loan association shares as functions of per capita "permanent income," the rates of return on demand deposits (a negative term measured by the service charges levied relative .to average total demand deposits), time deposits, deposits, savings and loan shares., and mutual savings bank deposits, and a series of dummy variables rep resenting geographical regions in the United States (cross sectional data were used in the study). The savings and loan share demand function also had per capita advertising expenditures by savings and loan associations as one of its arguments. He then investigated the substitutability be tween the various assets as measured by cross elasticities of demand and found that, although certain assets are weak :substitutes, there is no reason to accept the hypothesis that, in general, non-monetary liabilities are substitutes for money narrowly defined. Feige also undertook the task of investigating the stability of the various demand func- ;tions over time; his conclusion was that there is no reason to believe that the demand functions for demand deposits, savings deposits at commercial banks, and savings and loan association shares are unstable over t i m e . 1^9 No one would deny that Feige has made a significant contribution to. our knowledge of financial phenomena; how- 13 9gdgar L. Feige, The Demand for Liquid Assets: A j Temporal Cross-Section Analysis (Englewood Clxffs, N.J.: IPrentice-Hall, Inc., 1964). Feige also computed "efficient iestimates."— the so-called Aitken estimates— and "restricted jestimates"— estimates that are constrained so that the icross price coefficients in a linear estimation are equal, ii.e., so that (9xi/3pj) is equal to (SXj/8pi). 206 ever, we do disagree with his reasoning concerning the cor rect arguments in his demand functions. In particular, we ; favor a portfolio approach to this problem; Feige does in fact acknowledge the theoretical importance of a portfolio balance, but he does not introduce this concept explicitly ; into his functions. In other words, Feige writes his de mand functions ( 2.6.1) Aj — Aj t f 2 ' • • • * (j=1 1 .2 , . . . . , s) ! where Aj is the (stock or flow) demand for the j1 -*1 asset, ■ rj is the rate of return of the jth instrument, and w is nominal wealth. A portfolio approach, on the other hand, implies that the demand functions should be written ; (2.6.2) A j — Aj (r^, r ^, • »•, ^g / ® ^ 2 r' ' ’r i (j= l. r 2, . . . , S') where the Sj are the real values of the initial stock of the jth instrument. This not only has implications for ispecification and estimation, but it also has implications for the measure of substitutability or complementarity used. One indicator of whether two goods are substitutes ' t or complements, and the one used by Feige, is the concept of cross elasticity of demand (2.6.3) e^ = (3A^/9r j) (rj/A^) (i^j) ! which is the responsiveness of the quantity demanded of the : ith instrument for a (small) change in the yield of the j*1 * 1 ; instrument. The cross elasticity, under certain circum- ; stances, is an unambiguous indicator of any substitutability i or complementarity between two goods, but it is not an un ambiguous measure of the degree of substituability or com- ; piementarity between two goods. Hence, what is needed is ;some measure of these characteristics. The portfolio approach gives us such a measure. Consider an individual who possesses a certain portfolio of financial instruments at the beginning of the period in question, and assume that we wish to investigate the degree of substitutability or complementarity between demand de- ;posits and savings and loan association shares in his port folio. We have in mind the following conceptual experiment:: ;keeping prices constant, vary his initial stock of savings and loan association shares in such a way that his total real wealth is held constant— by varying his initial stock of other, non-related stocks— and then observing how his desired stock of demand deposits behave. If movements in ihis desired stock of demand deposits parallel the movements sin his initial stock of savings and loan association shares, i Ithe two goods are complements in portfolio balance; if the jmovements in the two goods are in opposite directions, they |are substitutes in portfolio balance. I 208 | | The cross portfolio balance term coefficients in \ ( 2.6.2)— i.e., the coefficient corresponding to S^, i^j— I are an aggregate measure of a series of experiments of this ! ! type and, as we shall discuss at some length in Chapter IV of this study, are also a measure of the degree of inter dependence in demand between two. goods for portfolio pur poses. This measure is one of the bases of the criteria that we shall use in testing the Gurley-Shaw hypothesis. CHAPTER III THE THEORY Using the material reviewed in Chapter II as a basis, we are now ready to embark on one of the major tasks of this work; this is the construction of a general equi librium market model that is well suited to the investiga tion and explanation of financial phenomena. The model is built up from a few simple behavior assumptions, and, con sequently, bears a vague relationship to the realities of day to day life. This is the price, however, that any the orist must pay; a model, after all, is only a representa tion of the real thing, and is constructed to facilitate understanding of the phenomenon in question— the more com plex the phenomenon, the less the model resembles it. One criterion for judging the worth of a theory or model is its degree of simplicity; if the model were as complex as real ity itself, it would be more convenient to study reality directly than go to the additional bother and expense of building a model. This model is constructed in the neoclassical tra dition in the sense that we assume a world of pure competi tion, perfectly flexible wages and prices, and unitary elasticity of expectations. These assumptions are certainly 209 ! 210 i ' not fulfilled in any existing economy today, nor is it | likely that they prevailed in any economy that existed when the classical and neoclassical economists wrote. This, however, is really beside the point; if we in fact repre sented this model as a perfect replica of any existing economy we would be intellectually dishonest both to our selves and to the reader. But, no economist has ever ■ claimed that these assumptions are or ever have been ful filled in their discussions of "pure economics," although, in a normative sense, many do feel that such a world would be the best of all possible worlds. The point, however, is this: The economic world is much too complex for the human mind— even with the aid of electronic devices— to compre- ; hend; as an expedient to understanding, economists con struct models that purportedly focus on the relevant fac- : tors, but that are simplified enough so that the appro priate questions can be readily addressed. It is not al ways easy to identify the factors that are important and : those that can be disregarded— to a great extent, this is where "economics as an art" comes in. We need not be con tent, however, with other peoples' conjectures of how things "really" work. Empirical evidence can and should be brought to bear on alternative hypotheses in an attempt to distinguish between "good" theories and "bad" theories. In relation to the emphasis of the present study— i.e., on financial assets and liabilities— the neoclassical assumptions bear little more relation to reality than they do in the study (e.g.) of supply and demand conditions in the steel industry. The money and capital markets are cer tainly not perfect markets; although the prices of finan cial instruments are more flexible than steel prices, they are, in general, sticky to a greater or lesser extend; and, perhaps most important of all, anticipations of future price and yield changes probably materially influence present interest rates. If the neoclassical assumptions are not fulfilled, why bother going to the trouble of building a theory around them? The answer is quite simple: Simplicity. In other words, .we feel that the factors left out of the model are of a lower order of importance in the explanation of the phenomena that are being considered than are the factors that are included. Our anticipations may be proved incor rect; if they are, it is then that the assumptions should be questioned and revised. That economics is an art is not in question, but all art must stand the test of acceptance — acceptance in this case requires that our "art" be ca pable of explaining the things that it is supposed to. Because this model's focus is on the financial sphere, we shall concentrate our discussion on those topics most relevant to financial variables. This does involve a 212 cost;, namely, the de-emphasis of the. real sphere relations. This is not to be taken as. evidence, that we feel that one sector is more important than the other, or that one sector can be validly, considered in partial or complete isolation; the spirit of this work is truly in the tradition of gen eral equilibrium. The only justification for this emphasis is that the real sphere relations have, by themselves, re ceived the lion’s share of the analysis in the past, and, therefore, are better understood than their financial cousins. I. THE MATHEMATICAL METHOD USED J. R. Hicks defined a "method" as a family of models. A model may be defined as a construction, in which certain elements of the state (or process) that we desire to examine (or to con template) are selected, such that the interrelations and interactions of those elements may be deduced by reasoning (especially, but not necessarily, math ematical reasoning) . . . in the hope that our gen eral understanding of the state (or process) may be enhanced by an understanding of that aspect of it which is presented by these particular elements. 1 Hicks noted— as other, economists had done earlier^— that there are several methods that could possibly be applied to -*-John. Hicks, Capital and Growth (New York: Oxford University Press, 1965), p. 28. 2See especially Gerhard Tintner, "Maximization of Utility Over Time," Econometrica, VI (April, 1938), 154- 158. 213 any given problem. In the. oontext of dynamic economic analysis,: he distinguishes between four different methods: 1. The .static (or classical) method. The static method is composed of studying a series of single periods, each of which, is. assumed to be in static equilibrium. The. crucial assumption of this method is . that the equilibrium of. time t could be taken to be determined by current param eters only; or, as we may put it now that we are using a sequential framework, that the equilibrium of a single period may be treated as self-contained.3 2. The temporary equilibrium method. This method is essentially that used in Value and Capital, and is characterized by the fact that "the mar ket is in equilibrium . . . even in the very short period, which is what its single period must be."^ This characteristic is this meth od's major weakness. 3. The fixed price method. This is most easily identifiable with Keynesian type models, where the traditional demand and supply equations are: abandoned and prices are assumed to be exoge- 3Hicks, 0£. cit.., p. 32. ^Tbid., p. 76. 214 nously. determined. Fixed price systems have a tendency to. go "macro," and their major advan- . tage is the. ease with which they are capable of handling stock adjustment relations— i.e. , they are best suited to balance sheet disequilibrium situations as illustrated by the portfolio bias of the liquidity preference theory of the in- . terest rate. Flexible prices (flex-price sys tems) can also be handled in this framework, but usually at the expense of assuming away all stocks. 4. The growth equilibrium method. This method abandons the assumption of fixed prices, and investigates equilibrium over time— i.e., it is concerned with moving equilibria. Whereas in the static and temporary equilibrium methods time is usually assumed to be discrete, the growth equilibrium method considers time to be a continuous variable in the restrictive sense that "the fundamental data (tastes and technol ogy) are to be taken as unchanging; the only change that is admitted is a uniform expan sion."^ As examples of the application of this 5Ibid., p. 132. 215 . type of method, .we may cite those .invest iga- . tions that have used the. calculus of. variation and the. turnpike theorems. Although Hicks was writing about growth economics, his fourfold classification has a great deal of relevance to the methods available for the study of financial theory. With regard to this work, the alternative methods available are reduced to two: the. static method can be discarded be cause of its inability, to. handle the function of financial instruments as a vehicle for redistributing consumption and investment over time, and the fixed price method is not ap plicable because of its inability to handle flexible prices and stocks simultaneously. Of the remaining two alterna tives, only the temporary equilibrium method— actually a modified version of this method— has the properties, that are most desirable for the purposes that we have in mind. Specifically, the ultimate aim of this study, as we have said before, is to develop a model that is adaptable enough so that empirical evidence may be easily brought to. bear on 6Since Ramsey's early application of the calculus of variation to. economic theory (F. P. Ramsey, ."A Mathemat ical Theory of Saving,” The Economic Journal {1928)), it has found many diverse economic applications. For an applica tion to monetary theory, see Boris P. Pesek and Thomas R. Saving, Money., Wealth, and Economic Theory (New York:. The Macmillan Company, 1967), chaps. 13-16. The standard work on the turnpike theorem is Michio Morishima, Equilibrium, . Stability, 1 and Growth (Oxford: The Clarendon Press, 1964). 216 any particular hypothesis relating to financial phenomena. To this end, the model considered in this chapter envisages an economy that is assumed to possess a series of discrete equilibria? that is, in the absence of changing data, the economy is assumed to move through a series of short term equilibrium positions, eventually reaching a long term equilibrium position characterized by. zero net investment— this is the classical stationary state. For obvious rea sons, the growth equilibrium method is not the ideal method to apply to this type of situation. With this discussion as a background, we are now ready to consider the basic model.. II. THE MODEL We shall be concerned here with an economy that consists of three sectors— the consumer sector, the produc tion sector, and the financial sector— which is a closed i economy in the sense that all production is for use by en- \ dogenous units and all consumption, investment, and finan- : cial transactions are satisfied out of domestic production ! or changes in domestic stocks (except for the demands for "dominant money"). As before,, we must make certain insti tutional and behavior assumptions and possess certain data before the system can be solved for the. equilibrium values of the. variables. Our institutional assumptions are that 217 pure competition prevails in all markets— with the excep tion of the supply side of the market for the medium of exchange— in the sense that no single buyer' or seller can influence market prices through his own actions and that there are no barriers to entry to, or exit from, any indus try, and that wages and prices adjust freely and instanta neously to. changing supply and demand conditions. The behavior assumptions are that each individual wishes to maximize his utility— if he is a consumer— or his profits— if he is a (financial or non-financial) producer— and that everyone expects the current prices to prevail in all fu ture periods with probability 1.0 0, i.e., we assume unitary elasticity of expectations on the part of each economic unit. Another behavior assumption that is made here, and one that is almost always made implicitly in economic mod- ■ els, is that everyone expects that their current desired behavior will in fact be realized. When it comes to. the consideration of what are data and what are variables, the distinction is not so clear-cut; the. classification that any one item falls into depends, in some cases, upon what period of time is under consideration. Basically, this model allows for the consideration of two different periods of. time: the short run which, in equi librium, is characterized by the condition that total flow demand equals total flow supply, and the. long run which, in 218 equilibrium, satisfies the additional condition that actual stocks equal desired stocks. Now, consider the short run; for the consumer the data are his (cardinal) utility func tion, his (positive) time preference rate, his initial portfolio, his initial endowment of factor services, and the market prices of all goods and services; the variables are the amounts consumed, the desired levels of stocks., and the amount of factor services sold. For the individual producer, the data are his decision function, his initial portfolio, his initial endowment of factor services, and the market prices Of all goods and services; the variables are the quantity of inputs purchased, the desired level of stocks, and the quantity of output produced and the quan tity sold. In adjustments to long run equilibrium, the de sired portfolio, consumption, etc. must be considered over a number of periods ancr therefore, the initial portfolio and the initial endowment of factor services that are di rectly attributable to the elements of it are no longer data, but become variables of the analysis. Although market prices appear as parameters to the individual economic units, when the actions of all units taken together are considered market prices become vari ables of the analysis. The above statement of the model might, at first glance, appear to indicate that the individual economic unit. 219 achieves his desired portfolio in each and every period. : In one sense this interpretation is correct, in another sense it is completely incorrect. The individual is con ceived of as being confronted with a spectrum of prices and interest rates? he will choose a portfolio composition and level such that, with the given prices and interest rates, his satisfaction will be maximum. If the costs of port folio adjustments were negligible he would probably adjust immediately? however, costs for at least some items can be iquite substantial for very rapid adjustments. In an at tempt to maximize his satisfaction over time, the individ ual will then choose some rate of adjustment of his actual portfolio to its desired level and composition, and, in so doing, he will simultaneously select the appropriate port folio for each and every period until long run equilibrium is established. It is in this sense that the individual is content with his portfolio in each period, even though it is not the desired portfolio that he ultimately wishes to ;reach. T^e Adjustment Process In order to rationalize price behavior as it has been postulated above, we shall borrow the Hicksian device iof'the "week" and the "month." A week is defined "as that !period of time during which variations in prices can be 7 neglected." The week, then is a period of time in which short run equilibrium is attained; i.e., where an equality of flow demand (consumption plus investment demand) and flow supply (production plus changes in inventories) is attained. To insure price stability over, the week, we as sume, following Hicks, that the markets are only open on "Monday" so that all contracts must be entered into on this one day; production and deliveries take place throughout the week, but no new contracts, can be signed until Monday of the following week. By a process of tatonnement it is possible to visualize the attainment of a short run equi- 1 v librium even though such a situation could never be actu ally observed. For our purposes, a month is defined as a series of weeks long enough so that a long run equilibrium position can be attained; i.e.', long enough so that, in addition to the equality of flow demand and flow supply, actual stock's reach their desired level at the prevailing market prices. As we shall see later, the analysis must extend over a period of time longer than a month because the number of weeks in a month itself is a variable of the. analysis which, in turn, is dependent upon costs and utility. A typical adjustment process might proceed as ^J. R. Hicks, Value and Capital (2d ed.; Oxford; The Clarendon Press, 1946), p. 122. follows: assume an autonomous shift in some parameter so that on Monday of the first week under consideration excess demands appear in some markets at the prices that prevailed in the immediately preceding week. Individuals that come to market on this first Monday find that the market no longer clears at the old prices, and by a process of trial and error new contracts are signed at new prices that sat isfy the flow equations. At the new prices individuals find that their existing portfolios are no longer at their preferred level and composition; they therefore make plans to adjust their existing portfolios to the new desired position that is consistent with the now prevailing prices. In general, this adjustment of portfolios will proceed over several weeks due to the cost and inconvenience involved in; immediate portfolio adjustment. On Monday of the second week, individuals again find that excess demands appear in certain markets at the prices that prevailed in the immediately preceding week— due, of course, to the changed level and composition of their initial portfolio. This appears as somewhat of a shock to them since, by assumption, they expected last week's prices to be maintained in all succeeding weeks. This is one of the major weaknesses of this analysis in that it is assumed that people do not learn from experience; however, for simplicity we do assume that they do not. In 222 any event, new prices and quantities exchanged are deter mined, once again, by a process of trial and error and new contracts are signed. The new prices will involve a re assessment of desired portfolio level and composition, and, in general, a different rate of change of existing port folios toward their preferred level. As the weeks pass, and in the absence of any addi tional autonomous shifts, there is a convergence of actual to desired portfolios until long run equilibrium is re established; this is the classical stationary state. Whether or not there is a convergence to long run equilib rium, is primarily a question of stability, a question that will not be considered in this study.® The Consumer Sector We shall consider a market in which there are n consumers (1=1, 2,..., n) and m goods and services (j=l/ 2 m) . The i’ * '* 1 consumer enters the first week of the period under consideration with an initial stock of tan gible goods "I (3.2.1) Sij = / x'i;j(t) dt (j=v+l, v+2,.. ., s) ®However, see Josef Hadar, "A Note on Stock-Flow Models of Consumer Behavior," The Quarterly Journal of Eco nomics, LXXIX (May, 1965), 304-309. 223 and an initial stock of financial assets (if Sij>0). and liabilities (if S^j<0) -I (3.2.2) Si;j = / x'ij(t) dt (j=l, 2,..., v) where v<s<m. The convention is adopted here that "T" re fers to a particular date, while "t" refers to a period of time. For example, the stock at the beginning of the first week under consideration— week zero— will bear the super script "-1," the ending stock will bear the superscript "0," and the flow quantities during the week will bear the superscript "0." In general, the initial stock of the tt ^ 1 week bears the superscript "T-l,” the ending stock bears the superscript "T," and the flow variables over that week bear the superscript "t." The consumer derives his operating income in any one week from the sale of the services of his initial stock of goods or the services of factors that cannot be held as a stock-— primarily labor services. Denote these initial flows of factor services in the tth week by (x*ifV+lf x*f c , x*^_), where m>z|s. The consumer's total in- l,V+£ X jS • — come in any one week consists of his operating income plus any proceeds (either positive or negative) from the sale (purchase) of his initial stocks plus any income received (paid) from his holdings of financial assets (liabilities) of the previous week; he will allocate his total income +*h t for the t week to purchases of commodities (x. ., 1 / ZtJ . x? • • • r r factor services (x^ ,, , xt1 ,..., x^ ), i,z+2' im' 1 ,v+1 ifv+2 iz m and stocks of financial and non-financial goods (D7 , D? ,. . ., D? ). i2 is' Define the excess flow demand of the i ^ consumer in the t*-* 1 week as the quantity he consumes if it is a com modity (3.2.3) E- ! " . = (j.=z+l, z+2,..., m) and the quantity he consumes less his initial endowment of services if it is a factor (3.2.4) E^- = x^. - x*!". (j=v+l, v+2,..., z) 3 1-3 i3 In the cases where the Ef c refer to the factor ser- vices that flow from a stock (i.e., where z<s), the formu- ilation of (3.2.4) implies that the x " ! : . must be interpreted ;as the quantity that a consumer wishes to consume plus the services that are neither consumed nor sold. Correspond ingly, the E^j is the quantity of the factor service that actually reaches the market during a given period of time, land can be measured without reference to the x*^j* Thus, this conception of the demands for and supplies of factor I services that flow from a stock has the advantages of ex plicitly recognizing the opportunity cost of not using or selling available factor services (due to the interpreta tion of the x-Jj mentioned above) and, since our attention is focused on the excess demands, of not having to come to grips with the slippery concept of the amount of factor services that can potentially flow from a given stock during a particular period of time. It should also be pointed out that the initial flow of factor services that eminate from a stock becomes a variable in a multiweek analysis; however, once the level of the stock itself has been determined the initial flow is also determined. This model is developed in terms of the demands for. capital goods as a stock, rather than in terms of the demands for the initial flows of the services of these capital goods. Finally, notice that the x£j (or x*^.) is not the same thing as depreciation due to use. We *3 reserve consideration of depreciation for the discussion of the production sector. The stock excess demand is defined as the desired level at the end of the week minus the initial stock T T T-l (3.2.5) XIj = Df. - ST. (j=l, 2,..., s) 3 1 3 Investment demand— the flow counterpart of stock excess de mand— is defined as (3.2.6) x'Jj = x* /I <j=l, 2,..., s) where the one in the denominator has the dimension "time." To repeat what was said previously, relation (3.2.6) does not imply that full stock equilibrium is achieved at ! the end of each week; it only implies that the individual ; plans to add increments to his stocks each period until s ' full stock equilibrium has been reached. The necessary T t icondition for full stock equilibrium is that X^j and x'^j be zero, and this will only happen when the desired and ;actual stocks are the same at the prevailing prices in each and every week. The utility function. The utility function is a relation expressing the amount of satisfaction (utility) I that is derived by an individual consumer from the consump tion and possession (either present or future) of goods and services. In traditional economic analysis the utility function was expressed as depending on current, or in the case of an intertemporal approach, future, levels of goods 'and services consumed. Various contributors have added to the list of candidates for inclusion in the utility func tion, and before proceeding on to our version of the util ity function it might be wise to comment briefly on each of I these candidates. Samuelson and Patinkin have suggested that the real lvalue of financial assets should rightfully appear in the individual's utility function. First of all, consider non monetary financial instruments; traditional theory has treated them as if their only function is a vehicle to re distribute consumption over time and to. earn an income so that more could be consumed at a later date. As such, the instruments themselves would possess no direct utility. However, as Patinkin has so aptly pointed out, non-monetary instruments do perform another function in a non-specula tive, relatively certain world; they, help satisfy the pre cautionary motive, and, in this respect,, they are a pur veyor of utility. With regard to money, the rationale for including real balances in the utility function has been given in terms of the precautionary motive and the avoidance of trouble and embarrassment of default in the event the indi vidual finds himself unable to meet an obligation when due because of a lack of money on hand (the so-called "trans actions motive"). These two motives are probably very real, but they do disregard a potentially very important source of utility; Pesek and Saving have pointed out that the major reason that real balances appear, in any portfolios is that money allows the individual to avoid the inconvenience 9 ■ of barter. The question naturally arises as to why people :hold a stock of money when they could hold interest earning !assets until the moment before the money was needed to com ^Pesek and Saving,. cit., p. 48. 228 plete a transaction. The answer, of course, runs in terms of the costs and inconvenience involved of switching back and forth befween money and other financial or real as sets. 10 Bushaw and Clower went one step further when they suggested that the real value of all stocks should appear in the individual's utility function. The Bushaw-Clower model is strictly intratemporal, and their stocks are pre sumably to be interpreted as the full equilibrium stocks; on this basis, however, it would seem more proper to in clude only the beginning level of the stocks plus the in crement added to actual stocks this period in this period's utility function. On the other hand, the model that is presented here takes an intertemporal approach, and, for this reason, it appears more proper to include the levels of stocks that the individual anticipates that he will en joy in each week over the period under consideration in his utility function. 11 In other words, we are suggesting that 10For a demonstration of this using the concepts of inventory theory, see William J. Baumol, "The Transactions Demand for Cash: An Inventory Theoretic Approach," The Quarterly Journal of Economics, LXVI (November, 1952), 545-556. “ 11This is essentially the approach taken by Josef Hadar in his articles, "Comparative Statics of Stock-Flow Equilibrium," The Journal of Political Economy, LXIII (April, 1965), 159-164;. and "A Note on Stock-Flow , . . . loc. cit. There is, however, a fundamental difference 229 the initial stocks and the time rate of change of actual stocks to. their desired level are the appropriate arguments in the individual's utility function. But,, beyond this, we are suggesting that it is the. discounted real value of fu ture stocks that should appear in the utility function, and not their undiscounted, values. That is, .we are suggesting that the individual consumer is concerned with maximizing the present value of his satisfactions over his time hori zon rather than maximizing the total utility derived over the same period of time. On Monday of week zero the individual will form his plans as to the level of stocks that he desires to hold at the existing prices and interest rates and the rate at which he wishes to achieve the desired level. Alterna tively, it could be said that on Monday of week zero the individual formulates plans as to the values he wishes to assign the following variables (3.2.7) = (Sjj + x*<?j)/(l+r* ) 0 (j=l, 2,..., s) d} . = (ST3: + x'°. + x' ) / (1+r. ) 1 13 ID ID 13 i between Hadar's conception of what the consumer wishes to ; maximize and the conception presented here. Hadar assumes ! that the consumer wishes to maximize total utility during ; the time under, consideration, we assume that the. consumer ■ wishes to maximize the present value of total utility over the entire period under consideration. 230 D?. = .(STJ + x1?. + x^. + x'?.)/l+r.) >2. ID ID ID ID ID -1 0 1 M M (sij + x'±j + x'i;j +...+ x'ijj/d+ri) where r^ is the time preference rate of the i^*1 consumer and is, by assumption, greater than zero. The number of weeks that are chosen for the analy sis— M+l weeks in this case— is of considerable importance. Consider, for example, a case where, with a particular set of prices, it takes ten weeks after the initial disturbance for a given good to return to a position of full stock equilibrium. Now assume that relative prices change so that the equilibrium adjustment period becomes fifteeen weeks; the "month" for this good has increased by 50 per cent. It appears as if it is necessary to make q— the num ber of weeks in a month— a variable in this analysis, for if it were not, it would be necessary to have outside in formation on the equilibrium adjustment periods for every possible combination of prices. The period of analysis M, therefore, is defined as a number of weeks that is long enough so that all stock adjustments under all conceivable price combinations will have taken place. Treating the problem in this fashion allows the q for each stock to 231 become a variable in the sense that q can be determined by observing the week in which x'^j becomes zero and remains zero thereafter from equation (3.2.7). It should also be noted that M must be identical for all individuals in the economy; if this were not the case it would be possible to arrive at the strange conclusion that if two individuals had identical utility functions, the one with the lower initial stock could end up with the highest total utility, which is, of course, nonsense. There is good reason to believe that the number of weeks required to achieve full stock equilibrium— the q— will be the same for most, if not all, stocks. This con clusion stems directly from the portfolio approach that is being taken here.. To illustrate this point, assume that at the end of some week all stocks are in full equilibrium except two; on the Monday of the following week all markets will not clear at the prices that existed in the previous ; week— there is an excess demand in the markets that had not : achieved full equilibrium at the end of the immediately preceding week. Prices will then change and, along with them, so will the desired portfolios so that, in general, stock disequilibrium prevails in all markets. It is pos sible that there are some goods that are independent of the ; level and composition of the portfolio exclusive of the good in question; however,.this appears a priori to be the 232 exception rather than the rule, so that, in general, q may be considered to be the same for each stock. In the event that empirical evidence refutes this hypothesis, no damage is done to the model under consideration sicne one model could contain any number of different q's, so long as M is the same for all individuals. Letting (3.2.8) ait = l/(l+r1)t and K0 - (1 + a±- L + ai2 + ai3 +...+ aiM) K1 ” fail + ai2 + ai3 +***+ aiM* KM — ^aiM^ the discounted present value of the amount of the j* " * 1 stock that the i ^ consumer will receive satisfactions from over the M weeks can be written — 1 0 1 2 M (3.2.10) KoSi+ + + K2x'ij+...+ K ^ . (j=if 2,..., s) Th utility of the i* -* 1 consumer is a function of his real consumption flows over the period in question and the 233 real values of the stocks, that he. enjoys over the same period. Although one would expect that intertemporal sub stitution in consumption goods is much more limited than intertemporal substitution in stocks, the individual con sumer derives utility from his discounted consumption flows. Taking into consideration the relations (3.2.7)-(3.2.10), the utility function may then be written (3.2.11) u± = Ui[a.tK|., + V ' i c + V 1 +--- + Kmx’^ )/P, (K.S71 + K.x1? + K.X'-J- M ic 0 iv 0 iv 1 iv + ...+ KMx'iv)/P, KQSid + K0x'id+ K _x'l_+. . .+ K 1 id M id (j=v+l, v+2,..., m; c=l, 2,..., v-1; d=v+l, v+2,..., s; t=0, 1,..., M) Assuming that each non-monetary financial instru ment is issued in a single denomination of 0- , . and that each instrument yields $1 per week, the prices of financial assets and liabilities— the Pj (j=l, 2,..., v)— is given by .{3.2.12V p. = ■ S l/(l+r.)t + 0/(l+r.)tj 3 t=l 3 , 3 (j=l , 2,. .., v-1) where tj is the number of weeks to maturity, and the rj is the market rate of interest on the j* '* 1 instrument. The money price of the vth financial instrument, which we shall assume is the medium of exchange, is identically equal to unity. Notice that in using (3.2.12) as the definition of the prices of financial instruments, S7^ and x'^j (j=l, 2,..., v) are to be interpreted as the number of financial instruments, not their money, value. The price level of tangible goods and services P is defined by the relation m (3.2.13) P = I w.p. j=v+l J where the Wj (j-y+1, v+2,..., m) are given weights. Substituting from (3.2.3)-(3.2.4), the utility function may be stated as (3.2.14) u± = u.ta.^Ef. + x+.), p.(K0sTj + K0x'°o + Klx,io+- " + V i o > / p' (K0SIv + KOx’iv + K1x + v+...+ KMx'fv)/P, K0s ^ + Kox'id+ Kix'id +---+ V i a 1. ■ (j=v+l, v+2,..., m; c=l, 2,..., v-b d=v+l, v+2,..., s; t=0, 1, ..., M) The budget - donstraint. A consumer must live with in his budget constraint each and every peiod; i.e., his 235 total money income (operating income plus proceeds from i sales, interest and divident receipts, and borrowings) must ;be exhausted on the purchase of goods and services for con sumption and asset acquisitions. To formulate a specific budget constraint, we must make some assumptions about the :details of interest and divident payments; the assumption made here is that payments are made each Monday on the in struments owned the previous Monday. For the Monday of the t^k week, this would mean that interest and dividends would be received (or paid) on the initial stock of financial assets and liabilities of the Monday of week t-1 (i.e., sTt2) plus the acquisitions of that day (i.e., x't'T^)— in lj 13 other words, interest and dividends will be received (or T—1 paid) on S (j=lf 2,..., v-1) . ij Mathematically, the budget constraint for the t" 1 -*1 week is ■maximize his utility as expressed by (3.2.14), but he must (3.2.15)— one for each week of the period. Form the new function (3.2.15) m z j=v+l t-1 Z x'^.) = 0 t=0 ^ Consumer equilibrium. The i^*1 consumer wishes to do so subject to a series of budget constraints of the form 236 m (3.2.16) Zi = u, ( ) ~ 1 (3.2.15) t=0 t The results of the familiar maximization procedure are (3.2.17) (ait) 9ui/3E^ xtPj = 0 (j.=v+l, v+2,..., m; t=D, 1,. .., M) (3.2.18) Kt(Pj/P) au-j/ax1^ “ XtPj = 0 (3=11 .2 / • . •. / v-i / t=0, 1, . . . , M) (3.2.19) Kt(l/P) aUi/ax’^ - xt = o (t= 0, 1,..., M) (3.2.20) (K.) au /gx'^. - = 0 l ij t j (j=v+l, v+2,...., s? t=0, 1,..., M) m . s v-1 1 (3.2.21) E P^y. + i P-^'J. - 2 (S?r + j=v+l 3 j=l J J j=l 13 t-1 s x'f.) = 0 (t=0, 1,..., M) t=0 13 The system (3.2.17)-(3.2.21) consists of a system of (M+l) (m+s-v+1) equations in the same number of vari ables. Using M+l equations to eliminate the (M+l) A's, the remaining equations may be solved for the (M+l)(m+s-v) un- j Iknowns— which are the E. . (j=v+l, v+2, ...f m; t=0, 1,..., M), 13 237 and the (j=X, 2,..., s; t=0, 1,..., M)— in terms of the exogenous variables— the p. (j=l, 2,..., m) , P, p.S.^/P 3 3 *^3 (j=l, 2,.,., v-1) , siy/p^ Sij (j-=y+l» v+2,..., s) , and the Kt (t=0, 1, . . . , M). The way in which the variables enter the demand functions depends on the way that they appear in the system (3.2.17)-(3.2.21) after the a 'x have been eliminated. Di viding (M+l)(m+s-v) of the equations by the remaining (M+l), and dividing (3.2.21) through by P, leaves the pj (j=v+l, v+2,..., m) , P, and the s”^ (j.-l, 2,..., v) remaining only ID in the form of ratios. Taking eI t^ (j=v+l, v+2,..., m; t=0, 1...., M) , pjXr|j/P (j=l, 2,..., v-l; t=0, 1,..., M) , x'^/P (t=0, 1,..., M), and x'j[j (j=y+ir v+2,..., s; t=0, 1...., M) as the dependent variables, the excess demand functions appear as (3.2.22) E^_. = (pir p2,..., Pv_x/ pv+1/P,..., pm/P, PlSil1/P- ‘- Pv-lSi”v-l/P' siv1/p' S?"1 , S?- 1 , K., a. ) i,v+l' is t it (j=y+l, v+2,..., m? t=0, 1,..., M) (3.2.23) x'ij = j^ x' j ' &2 ' * ’ *1 ^v-lf ^> v+l^P, 238 f T-1 , T-1 t-1 siv /P' Si,v+ 1 Sis ' Kt' ait> (j=l, 2,..., v-1; t=0, lf..., M) (3.2 • 24 ) X — (P.) X 1 (P-^ r P2 r • ' • r Pv— 1 ' Pv+l^P r ' * * ' Pxti/Pf Pisn /?.'•••' Pv-l^i,v-l/P/ gT—1/p gT—1 gT—1 - w - a 1 iv ' ' i,v+lf * *'' is ' *t' it' (t=0 , 1, . .. , M) (3.2.25) x*ij = x'ij(Pi' P2'’*"' ^V-l' Pv+l/P/* * *' Pm^P' ^l^il1^' • • • r Pv-lsi,v-l/P/ SL 1/P' Si”v+1' * * *' Sis' Kt' ait) (j=v+l, v+2.,... f s; t=0, 1,..., M) In this system, M+l of the equatipns are not inde pendent. To see this, consider a single period budget constraint of the form (3.2.15); it can be readily seen that once a decision as to the amount purchased (or sold) of any (m+s-v-1) goods and services, the amount purchased (or sold) of the remaining good or service is automatically determined. This holds for every week of the period under consideration. Thus (M+l) (m+s-v-1) of the above equations can, given the values of the parameters, be solved for (M+l)(m+s-v-1) of the excess demands; the remaining (M+l) excess demands directly follow from the equations solved. Remembering that the pj (j=l, 2,..., v-1) are really interest rates, by inspection it is obvious that the systems (3.2.22) and (3.2.25) are homogeneous of degree zero in the p. (j=v+l, v+2,..., m), P, and the (j=l, J lj 2,..., v), but not homogeneous of any degree in the Pj (j=v+l, v+2,..., m) alone. The systems (3.2.23)-(3.2.24) are homogeneous of degree one in the same variables. The Non-Financial Production Sector Within the economy under consideration, there are ;non-financial production units that combine factor services (xv+l' xv+2f’**' xz) per time— purchased from other firms, the n consumers, and from the firm in question— and primary and intermediate products (xz+^, x^,. xm) per I unit of time— purchased from the firm in question or from other firms— to produce quantities of goods and services (xv+i/ xv+2,..., xm) per unit of time. Assuming that cer tain factors can also be final goods and services, this model contains m-v non-f inancial industries (k=v+l, v+2. , ..., m), firms within each industry (h=l, 2,..., N^) and 240 where (k=v+l, v+2,..., m), and m-v non-financial goods and services (j=v+l, v+2,..., m). Each firm within each industry enters the first period under consideration with an initial portfolio? the level of the j^h stock at the beginning of the first week (I.e., T=-l), if it is a tangible good, is given by T "I (3.2.26) Sh£j - f x'hkj(t) dt (j=v+l, v+2,..., s) and, if it is a financial stock, by 1 "I (3.2.27) S~£ =./ x'hkj (t) dt (j=l, 2,..., v) ^ — 00 In a similar fashion as in the case of the con sumer, define the excess flow demand (i.e., the excess de mand for factor inputs or commodity and service outputs) of the hth firm of the kth industry in the tth week as Ehkj 5 xhkj - x*hkj (j=v+1- v+2'--' 21 (3.2.28) t=0, 1, ... ., M) e£_ „ = (j=z+l, z+2,..., m; hk3 hkj t=0, 1,..., M) jNotice, once again, that for all z less than or equal to s ;the must be interpreted as the quantities the firm ■wishes to use plus the quantities neither used nor sold. If in one week the firm produces below capacity, the entre preneur must make the decision whether to rent out the excess capacity or allow certain machines to remain idle; typically, a firm that e.g., makes steel will not be in terested in going into the business of renting out the ser vices of open hearth furnaces. Nevertheless, idle machines do represent a cost in the form of foregone revenues which the entrepreneur must take account of, and this method of handling excess capacity reflects this in the sense that the firm is assumed to consider the costs of idle capacity in the same way that it considers the cost of its normal inputs. What this definition of the excess demands implies is this: the firm really makes two decisions with respect to its factor service inputs. In the first place, it must decide upon the desired level of service inputs in each week; in the second place, it must decide upon what propor tion of the service inputs will be purchased in the market :place and what proportion will flow from plant and equip ment owned by the firm in question. No matter what the source of the service input, the price to an individual firm is the same— in the case of hired inputs, the price represents a cost in the accountant's sense of the word; in :the case of service inputs that flow from plant and equip ment owned by an individual firm, the price represents a cost in the form of an opportunity cost. It will be no ticed that this treatment of stocks and the services that flow from them is analogous to the treatment of tangible inputs— or, in the case of the consumer, tangible goods consumed— in that there is no differentiation between tan gible inputs that are currently purchased and those that are taken from existing stocks. Net stock excess demand is defined as the desired level at the end of the week minus the initial stock (3.2.29) x£kj = D^kj - (j=l, 2,..., s; T=0, 1, . . . , M) Gross investment demand, on the other hand, is defined as the desired change in the level of the stock (either posi tive or negative) plus the decrease in capital stock due to the use of plant and equipment in the productive process, i.e., (3.2.30) x'J . = X?k -/1 + D? h,(xj ) hk] “Xu hk] 3 hkj (j=l, 2,•.. , Sf T,t=0, 1,..., M) where the one in the denominator of the -first term on the right has the dimension "time," and h^( ) is a deprecia tion function that will be explained in more detail later in this section. Of course, certain stocks are non-depre- ciable— for example, financial stocks— so that, in these cases, the hj( ) are identically equal to zero. The decision function. A typical firm may be viewed as endeavoring to make a maximum profit with a given 243 I I | level of net worth; or, what is saying the same thing, it I iwill endeavor to minimize net worth for a given rate of profit. When a businessman says that he desires to "maxi mize the return on invested capital," he has this in mind. A more technical way of stating this concept is to say that :the firm seeks a saddle point with respect to the relation :of profits to the level of net worth. This being the case, an entrepreneur is willing to add equal increments to his stocks of assets and liabili ties as long as the additions contribute a positive incre ment to his profit flows. Thus, an entrepreneur will in vest if the capitalized value of the new asset is greater than the capitalized value of the liability that he assumes. If the decision is whether to reinvest profits in the en terprise or to distribute the earnings to the owners, the reinvestment decision will be made only if the rate of re turn available on internal (to the firm) investment is igreater than the rate of return available on the best al ternative investment. If the relevant rates of return are equal— as they would be at the margin— the entrepreneur is iindifferent as to his course of action. In order to reach its goals, each firm will possess a positive stock of various goods at any point in time. The level and composition of the portfolio, however, will depend, in addition to any outside constraints, upon the 244 subjective preferences, anticipations, and evaluations of the individual entrepreneur, and upon various purely eco nomic factors. It is a basic human trait that no two per sons will react to a given stimulus in ,the same way; for example, entrepreneurs' evaluations as to the risks in volved in a particular undertaking will differ, as will their anticipations with regard to changes in market condi tions. Some entrepreneurs may have a high preference for risk aversion, others a low preference; some entrepreneurs may value liquidity highly, others may place a low value on it, and so on. The decision function, then, reflects each entre preneur's preferences and evaluation, but this is not all. Each firm is further constrained in its actions by techni cal relationships between inputs and outputs which are gov erned by the current "state of the arts"? the. decision function also reflects these technical relations. Thus, the decision function is a combination of a "preference" function and a production function. The individual in his role as an entrepreneur does not gain any satisfaction from producing output or possess ing stocks of various goods, his sole concern with these acts is to the extent that they add to the profitability of the firm. The entrepreneur will plan his inputs, outputs, and stocks for each week in the period in such a way that the present value of profits over the period will be a maximum. On Monday of week zero he will plan the stocks that he wishes to hold in each week; i.e., he will plan the following quantities: Dhkj = Shkj + [x'hkj " Dhkjhj *xSk'jJ 1 Dhkj shkj + ^x'hkj " " Dhkjhj^xhkj^ + ^x'hkj " " ^hkjkj (xhkj^ (3.2.31) ! (j=l, 2,..., s) M -1 0 0 0 Dhkj = Shkj + ^'hkj “ Dhkj^j ^xhjk^ + [x'hkj " Dhkjhj(xhkj* 1 +••*+ M M M [xVj - Dhkjhj<xhkj>i t T i “ « where the - D^kj^j ^xhkj^ ; * ’ s tiie net investment m the jth stock during the t^h week. Since the entrepreneur gains no satisfaction from possessing these stocks, the above quantities are not dis counted; or, to put the matter a little differently, it makes no difference to the entrepreneur when investment takes place except to the extent that the time stream of I 246 i investment influences profits. Thus, the decision function is dependent upon the real value of the flows of inputs and outputs, the real value of the initial stock in week zero, : and the flow of net investments. Taking into consideration , the relations (3.2.28)-(3.2.31), it may be written (3.2.32) . g h k ^ j , PcD^c/P- I>hkv/p' Dhkd> = 0 (j=v+l, v+2,..., m; c=l, 2,..., v-1; d=v+l, v+2,..., s; t,T=0, 1,..., M) It should be pointed out that, in the case of the first v stocks (i.e., the financial stocks), the depreciation term drops out so that the desired level at the end of any par ticular week is the sum of the initial stock plus all gross (which, in this case, is identical to net) investment in that good up to and including the week in question. The quasi-profit function. We use the term "quasi profit function" in this study to indicate that these func- :tions not only express the difference between sales and costs, but also express certain other behavior patterns that are related to the operations of a business enterprise. For example, asset acquisitions do not normally appear in a profit and loss statement, but they do appear in our quasi profit functions. These functions are probably closer to a cash flow concept than they are to a profit concept. 247 As has been said before, the individual firm wishes to maximize its return on invested capital. To this end he| will purchase inputs, produce outputs, and hold stocks of various assets and liabilities with the view to maximizing the excess of the market value of outputs over inputs while minimizing his net worth. The firm, however, does have a time preference with respect to its income and expenditure flows; a dollar paid or received today is worth more than a dollar paid or received tomorrow. Define the operating income of the ht * 1 firm in the k1 " * 1 industry over the time period under consideration as the discounted market value of the excess of outputs over inputs, i.e., m (3.2.33) Z Pj(E2kj[l/(l+rhk)°] + Ehk. (l/d+r^)1] j=v+l + •••+ ^4jtV(l+rhl.)Ml) where the r^k is a market determined rate of interest that reflects the firm's foregone income by reason of receiving a dollar tomorrow rather than today; or, in the case of payments by the firm, it represents the income that could be earned on a dollar that is paid tomorrow rather than today. Using the alternative cost doctrine, the rkk is the rate of return on the firm's next best alternative invest ment which, at the margin, is driven into equality with the firm's cost of capital. Hence, the rkk maY be defined as a weighted sum of the return paid on the firm's liabilities v- 1 (3.2.34) = I whkjr. m for all D^kj less tIlan zero. The whkj are assumed, for simplicity, to be given weights. Letting (3.2.35) a£k = l/(l+rhk)t (3.2.33) may be restated as m M • (3.2.36) Z p Z ahk Ehkj 3=v+l J t=0 J The typical firm also owns financial assets and has outstanding liabilities upon which interest and dividends must be paid and received. " Assuming, as we did in the case of the consumer, that interest and dividends are paid in week t on the initial stock of that week (i.e., T=t-1), the present value of net receipts and payments of interest and dividends over, the period is given by V-1 o -1 1-1 0 M (3.2.37) j— 1 tahk Shkj + &hk (Shk^ + X'hk3 +***+ ahk (Shkj + x'hkj + x'hkj +*'*+ x'hk3)] Letting - 0 . • .1 ^ . 2 • ^ ^ .* (3.2.37) may be stated as v-.l ? Q^hkj - r ^ hkj - ». 2- hkj (3.2.39) 2 (K' S”i- + K'.X'O + K' x’J, K ' x ' 51’ 1 ) M hkj' The firm is not only concerned with its operating income, but it is also concerned with the level and compo sition of its portfolio and the rate at which it adjusts the existing portfolio to its desired position. In an at tempt to maximize the return on invested capital, the firm will attempt to minimize increments added to its net worth and maximize increments added to its profit flows; i.e., the firm wishes to maximize the. difference between its operating income as defined by (3.2.33) and its net worth in each and every period, subject, of course, to the insti tutional, preference, and perhaps technological factors which are reflected in its decision function. In the non-financial production sector, the desired level of certain stocks is no longer the simple sum of the beginning stock in week zero plus all desired increments of 250 investment up to the time in question; certain stocks-— ; namely plant and equipment— depreciate with use, and this i represents a net deduction from the firm's stock of capital. | It is now necessary to make some assumption as to the be havior of depreciation? one of the simplest assumptions is I to assume that the rate of depreciation is dependent upon the rate of utilization of the services that flow from the I particular type of equipment. Thus, denote the rate of depreciation of one unit of the j* * * 1 stock in week t by (3.2.40) hj (x^j) a hj(Ehkj* (j=Y+l/ v+2,..., s; t=0, 1,..., M) Even though the firm may hire the services of a particular ; stock from outside sources, it still seems plausible to assume that the firm's existing stock of that equipment will 'be more intensively utilized the higher the level of the service input. To further simplify matters, we shall as sume that the rate of depreciation is a constant proportion of the rate of input, i.e., (3.2.41) h-|(Ehkj) = HjEhkj <j=v+l, v+2,..., s; t=0, 1,..., M) ' ! It should be pointed out that, in the notation used here, xhkj ^enotes "the services that flow from the stock (i.e., the services that flow from D^kj). We can get by wi,th this simplification in notation by assuming that those stocks from which salable services flow are not directly an assumption that is probably close to reality. Relations (3.2.40)-(3.2.41) are not to be confused I taken out of inventory for production purposes--which, in • this analysis, is a problem of portfolio composition— but represent the physical depreciation due to use of the equipment— or, more accurately, the services that flow from the equipment— in the production process. Further, notice that this does not pertain to depreciation due to obsoles cence, which is ruled out of this analysis by the assump tion of constant technology. net worth; the incremental net worth function may be writ- Expanding the above expression, substituting from (3.2.30) | consumed nor enter into the production process directly; with the actual quantities of e.g., raw material that are The entrepreneur, then, is concerned with the mini- ; mization, subject to the profitability considerations dis cussed earlier, of the present value of his additions to ten (3.2.42) M i = I T,t=0 and (3.2.35), and collecting terms, (3.3.42) may be ex pressed as 252 S M t t j=i pj A ahk*'hk3 which, because it is a minimization problem, appears in the quasi-profit function as a negative quantity. The quasi-profit function is the sum of (3.2.36), (3.2.39), and (3.2.43), i.e., m M V"1 ^ (3.2.44) *hk = S Pj J ajk E ^ + 2i (K'0Shkj + 3=v+l t=0 3=1 J ■ +• * -+ “ 1 hkj M hkj s M t t Z p . Z a, , x' , . j- 1 3 t =0 hk Non-financial producer equilibrium. In its endeavor to maximize the return on investment, the individual firm will wish to maximize (3.2.44) subject to (3.2.32). Form the new function (3.2.45) Vhk = irhk - yghk The first order conditions for a maximum are (3.2.46) a^Pjd-Hj) - p3ghk/3Et]cj = 0 (j=v+l, v+2,..., s; t=0,1,..., M) (3.2.47) ahkPj “ u95hk/yEhkj = 0 (j = s+l, s+2, . . ., m; t=0, 1, • • •, M) 253 (3.2.48) K -.t+ 1 - a^kPj - M(p ,/P) sg^/ax'^. = 0 (j=l, 2,..., v-1; t=0, 1,..., M) (3.2.49) - - tid/PJsgnfc/sx'^ = .0 (t=q, 1,..., M) (3.2.50) - aJj-Pj - = .0 (j=y+l, v+2:,..., s; t=0, 1,,.., M) (3.2.51) ghk( ) = 0 The system (3.2.46)-(3.2.51) consists, of (M+l) (m+s-v)+l equations in the same number of unknowns. Using one of the equations to eliminate the u, the Pj (j=y+l, v+2,..., m), P, and Skkj (j=l, 2,..., v) appear only as ratios. Choosing the E^j (j.=v+l, v+2,..., m; t=0, 1, • • ., M) , pjX*kk j /P (j . =l, .2,. .. , v-1; t=0 , 1, • • ., M) , x'kkv/P (t=0, 1,..., M) , and (j=v+l, V+2,..., s; t=0, 1,..., M) as the dependent varibles, the above system can be solved for the unknowns in terms of the exogenous vari ables. (3.2.52) Pv_jl# Pm/P' Plshkl/p' • • •' ^v-^h^v-l^' shkv/p' Shk,v+1'***' Hj, K't+l' ahk^ (j.=tff+l, v+2 ,. • • , my t=0, 1, •»• , M) 254 (3.2.53) x'hkj = ^/P'j)x,ij'(P-1r. P 2 " - m ' r pv-l' pv+l/P' T-l • * * r Pm/p' Plshkl/p' * * * > .T-l _T-1T-l Pv-lshk,v-l' p ' Shkv/Pf shk,y+l' *•' sSks- Hj- • K't+v ahk) (j=l, 2,..., v-1; t=0, 1,..., M) (3.2.54) x'hkv = ■^p^x'hkv^pl f p2'*-**f pv-l' Pv+l/^' • • • f Pm/p« ' PlShkl/P' * * * f Pv-l^hkry-l/pf shkv/p' Shk^y+l'***' shKs' Hj' KW ahk> (t=0.f. I,...., M) (3.2.55) x'hkj ~ ^'hkj^'l' $ 2 ' ' pv-lf pv+l^p' *** pir/p' T—1 T-l T—1 Plshkl/p' • * *' Pv-lshk,v-l/p' shkv/p' shkyv+l'*•* *' Shks' Hj' K,t+1' ahk^ (j=v+l, v+2,..., s; t=0, 1,..., M) As before, M+l of the above equations are not inde pendent. Consider the decision function (3.2.32); in any ione week, once a decision has been reached with respect to j the values assigned to any (m+s-v-1) variables, the. value iof the remaining variable is automatically determined. 255 | Consequently, given the values of the parameters, (M+l) i | (m+s-v-1) of the above equations can be solved for the ; excess demands; the values of the remaining (M+l) excess I ■ i j demands will directly follow. The above system of equations exhibits the same i homogeneity properties as do the excess demand functions of the consumer sector; (3.2.52) and (3.2.55) are homogeneous T—1 : of degree zero, the Pj (j.=V+l, v+2,..., m) , P, and S^kj ; (j=l, 2,..., v), while (3.2.53)-(3.2.54) are homogeneous of : degree one in the same variables. The Financial Production Sector The economy in question also contains financial production units that combine factor services (^v+1, Xv+2, ; ..., xz) per unit of time— purchased from other firms, the n conumers, and from the firm in question— and primary and |intermediate products (xz+1, xz+2,..., x^) per unit of time ; — purchased from the firm in question or from other firms— I to produce quantities of financial instruments and related I " : !services per unit of time. Financial producers do not have a monopoly in the ;production of financial instruments; both consumers and inon-financial producers are capable of, and in fact do, •produce a variety of financial assets and liabilities. For example, a consumer creates a financial instrument when he 256 borrows from a commercial bank to purchase an automobile, I i | as does a non-financial producer when he extends open book j credit or sells bonds to finance capital expansion. To [ | differentiate between the financial and non-financial sec- j tors, we shall adopt the. distinction used by Gurley and I Shaw: The non-financial sectors are defined as consisting of units whose principal function is to produce and pur- : chase current output;, the financial sector is defined as I comprising those units whose principal function is purchas ing one type of security by producing another. Hence, the asset side of the balance sheet of a non-financial unit would be expected to. consist primarily of non-financial assets, whereas the asset side of a financial unit's bal- ; ance sheet would be expected to be composed of mostly fi nancial assets. These are not the only differences between the ifinancial and non-financial sectors. Consider a non-finan- ! cial unit;, the act of production or consumption does not necessarily mean that a portfolio readjustment is required in the sense that production or consumption can be financed out of current income. On the other hand, every time that a financial producer engages in the act of (flow) produc- jtion it directly follows that his portfolio level and/or composition is. altered. Consequently, the level of output of a financial producer, or of the financial sector, is i intimately related to the level and composition of the ex- ! ! isting portfolio relative to the desired level, a fact that | makes financial producers unique among economic units. I Further, this unique characteristic of financial production units means that their output of financial instruments is denoted by (x^, x'2(v ( x'v^ ratlier bY (x2/ * 2 '" • ' t ! xv ) . Within the financial sector itself it is necessary to distinguish between monetary financial intermediaries (MI) and non-monetary financial intermediaries (NMI). The basis of the distinction is the character of the intermedi ary's liabilities; the liabilities of the former serve as a ; medium of exchange, while the liabilities of the latter do not. The non-monetary intermediary sub-sector. Non- imonetary intermediaries produce non-monetary financial in- ; struments that they exchange for financial instruments pro- : duced by other economic units and, to a minor extent, for | factor services, raw material, etc. from which they produce their financial instruments and attendant services. In general, the marginal cost of producing financial instru ments is close to zero in terms of physical inputs; the I major proportion of cost arises from the promises that ac company the instrument— namely,, the promise to pay a fixed return per unit of time to the holder. The decision function— The decision function of a NMI expresses the preferences and technological factors faced by the individual entrepreneur with regard to port folio balance, the rate of change of existing stocks to their desired level, and the quantity of flows used or pro duced per unit of time in the same manner as relation (3.2.32) expressed these same factors as faced by the indi vidual non-financial producer. The decision function of the h^*1 firm in the non-monetary financial industry contains identical arguments as does (3.2.32), and may be stated (3.2.56) ghfc( ) = 0 The quasi-profit function— An NMI can be looked upcn as dealing in income streams; it will exchange its promise to pay a fixed income each week for a given number of weeks for the promise of some other economic unit to pay the NMI a fixed income per week for some other given number of weeks. The NMI's profit on the transaction is the difference in the capitalized values of the promise that it receives and the promise that it makes, the capitalization rates are the market rates of interest applicable to the particular fi nancial instrument in question. If we assume that all fi nancial instruments yield $1 per week, and that the face amount of the instrument is paid in the week, the. pres ent value of an instrument that is due to mature in n weeks is defined by (3.2.12), which is nothing more than the 259 Pj (j=l, w,.. ., v-1) . Consequently, a valid measure of the NMI's profit on any given transaction is the price of the asset received times the quantity received minus the price of the asset given up times the quantity given up. Notice that no inference concerning profits made can be drawn from the relative face amounts of the instruments traded, the relative market rates of interest must be known before any conclusion can be reached. Extending the above discussion over all financial instruments and the M weeks of the analysis, it can be said that the individual NMI will attempt to maximize the pres ent value of the stream of profits over the period in ques tion which is, in this case, equivalent to the attempt to maximize the present value of net worth over the same period. Another way of saying the same thing, however, is that the individual NMI wishes to maximize the present value of the excess of the market value of its non-monetary financial assets over the market value of its liabilities over the period, or (3.2.57) V [p.tsSjj + ) l/(l+rhk)° + j = l pj ( x ' h k j ) 1/ ( I + r h k ):L + - - + Vd+rwc)*1] Substituting from (3.2.35), the above expression may be rewritten as i v-1 • , M t t j (3.2.58, I I A typical NMI will also use certain inputs and sell j !certain services in the same manner as any other producer :would; the NMI's actions with respect to these quantities !are described by equation (3.2.36), which is reproduced here as m M :(3.2.59) ,4« l Pj t=, a>* In addition to the above mentioned types of activ ities, an individual NMI is also responsible for paying in- j terest and dividends on its outstanding liabilities and will receive interest and dividend payments on the finan cial assets that it holds. At first glance it might appear that maximizing the net present value of the portfolio is ;equivalent to maximizing the net present value of dividend and interest receipts; however, this is not so. The former is a profit concept, the latter is a cash flow concept; the difference between these two concepts, in this case, is the 'result of the disparity between the market rate of interest and the stated rate of interest on outstanding financial instruments. If the stated rate of interest on all out- ;standing financial instruments was a variable so that it always equaled the market rate of interest, the maximiza tion of the net present value of the NMI's portfolio would 261 be equivalent to maximizing the net present value of its interest and dividend receipts; obviously, this condition is not fulfilled in the case of most outstanding financial instruments. If an individual NMI wishes, to maximize the present value of its dividend and interest receipts, it will wish to maximize ( 3 .2 .6 0 ) ^ + R' l x ' hk j + K’2X'hkj + - ” + M-l which is to be interpreted in the same manner as (3.2.39) was. Assuming that an NMI finances its stocks of non- financial assets and the medium of exchange out of retained earnings (i.e., it is assumed that an NMI issues no capital stock or other "conventional" financing instruments), a typical NMI's incremental net worth that is attributable to non-financial assets and the medium of exchange function is s M £ (3.2.61) £ pj z 3=v J t=0 J which is the same as (3.2.43) except that the sum now goes from v to s instead of from one to. s. The above mentioned assumption is made on the basis of the normal relative un importance of capital stock, open book credit, etc. in the balance sheets of most NMI's and, for that matter, in the 262 i j balance sheets of most private Mi's. However, there are ; exceptions to this— e.g.,, closed end investment companies and capital stock insurance companies— that at least de serve mention here. To adjust the model to take care of these situations, it would be necessary to identify these non-intermediary liabilities and capital items— this term is used here for the lack of a better one— and include them : in (3.2.61) instead of in (3.2.58). It might appear that a rational MNI, under the as- sumptions of this model, would only purchase the highest yielding financial instruments, which would presumably be long term securities. However, this is probably not the case. As was pointed out earlier, each entrepreneur has preferences regarding .his willingness to assume risks, and these preferences are reflected in his decision function. If each financial instrument had the same degree of risk and there were no legal or other restrictions on the in vestment policies of any financial intermediary, undoubtedly1 ;long term instruments would be the only financial purchases made by any financial producer; but, the financial instru ments considered in this analysis are assumed to differ in the risks inherent in each instrument. Thus, each entre preneur must evaluate the risks involved in each instrument in relation to his preferences before deciding upon his optimum portfolio. Another consideration that is relevant 263 — and one that is not considered in this analysis— is the "cash drain" that all financial intermediaries are subject to. The quasi-profit function of the ht * 1 firm in the NMI industry is the sum of (3.2.58)-(3.2.60) and the negative of (3.2.61), V ~1 -1 M t t (3.2.62) „hk = Pj(Sh^ + ^ a£kX'tk .) m M t t + S Pj S ajj^ j=v+l J t=0 J V”1 _i o M-l + ^ ^'o^hkj + ^ lx hkj K Mx j^j) 3 M t t " j!v pj ti0 ahkx hkj NMI producer equilibrium.— In an attempt to real ize its goal of maximizing its return on invested capital, an NMI will wish to maximize (3.2.62) subject to (3.2.56); form the new function (3.2.63) Vhfc = T r hk - pghk The first order, conditions for a maximum are (3 .2 .6 4 ) - wSghk/3E^k . = 0 (j.=v+l, v+2,.. ., s; t=0, M) 264 (3 .2 .6 3 ) a£kPj - V^hk/*E^. = 0 (j=s+l, s+2,..., m; t=0, 1,..., M) (3 .2 .6 6 ) + K 't+1 - M(P j/ P ) Sghk/ Sx ' t k .. = 0 {j=1. r v-1; t=0, 1,.. . , M) (3.2.67) - - y(l/P)3g /ax*t =0 hk • hk hkv (t=0, 1 , , M) (3.2.68) - aJkPj - y.8ghk/9x'£kj = 0 (j=v+l, v+2,..., s; t=0, 1,..., M) (3.2.69) ghk( ) = 0 It is interesting to note that the only difference between the equations that describe non-financial producer and NMI producer equilibria is one term in one equation; namely, a£kPj is negative in (3.2.48) and positive in (3.2.66). This is a reflection of the idea that non-finan cial producers' output behavior directly influences their portfolio composition, whereas non-financial producers' ioutput behavior does not necessarily result in portfolio i changes. The system (3.2.64).-(3.2.69) consists of (M+l) (m+s-v)+l equations in the same number of unknowns. Using one equation to eliminate the y., and choosing the Ehkj 265 t (j.=y+I, v+2,...., m; t=0, 1,..., M) , PjX'hkj/P 2 v-1? t=Of 1,... ., M) , X'^kv/P (t=0, 1,..., M) , and (j=v+l, v+2',... ., s; t=0, 1,..., M) as the dependent vari ables, the above system can be solved for the unknowns as functions of the exogenous variables. (3.2.'70). Ehkj = Ehkj^pl' p2,*’’, pv-l' Pv+l/p'***' Pn/P' plshkl/p-• • •' Pv-lshk^y-l/p' shkv/p' nT“ 1 cT“l TT TT I at \ bhk,v+l* • • • * bhks' t+1' hk; (j.=v+l, v+2,..., m; t=0, 1,..., M) (3.2.71) x'hkj ~ . (P/Pj)x'hkj ^P1' p2' * ‘ *' ^v-1' pv+l//fp' ' T-l t-1 • • • / Pm/p' Pl^hkl/p' * ’ *' Pv-l^hk,v-l/p' qT-l T-l T-l bhkv' ' hk,y+l' * • *' - bhks' ■ j' * t+1' ahkJ (j=l, 2,..., v-1; t=0, 1,..., M) (3.2.72) X 1 — (P.) X 1 ( p - ] _ , P2 r • • • / Py—^/ Pv+l/p' flKV • * *' Pn/P' plEhkl/Pf * *•' Pv-lEhklv-l^P ' CT—1 gT-1 qT— 1 TJ X f 1 shkv/p' hk,v+l/* * *' hks' j' * t+1' a^k) (t=0, 1,..., M) • * • r V P' PlSWcl/p •• • / (j.=v+l, v+2 s; t=0, 1 M) As in the case of the non-financial production sec tor , the form of the decision function (3.2.56) causes (M+l) or the above equations to be not independent. Given the values of the exogenous variables, (M+l) (iri+s-v-1) of the equations can be solved for the values of the excess demands; the reamining (M+l) excess demands will directly follow. equations is reflected in the homogeneity of the system. Systems (3.2.70) and (3.2.73) are homogeneous of degree v), and (3.2.71)-(3.2.72) are homogeneous of degree one in the same variables. the mechanics of operations, there is not much difference between an NMI and an MI; both purchase the liabilities of other economic units by issuing their own instruments, and As before, the non-independence of certain of the zero in the pj (j=y+l, v+2 m) , P, and <j=l, 2,. The monetary intermediary sub-sector. In terms of 267 | both wish to maximize the present real value of their net j non-monetary financial portfolio. However, the simple ex tension of the analysis that was applied to an NMI to an i ; MI leads to some very strange results. To illustrate this, assume, for the sake of argu- :ment, that the output of an MI are liabilities so that (3.2.63)— with the modification that the sum in the first term of (3.2.62) is taken from one to v to reflect the. nature of the Mi's output, and, correspondingly, the sum in the last term of the same .expression is now taken from v+1 : to s— is the function that the entrepreneur wishes to maxi mize. One of the first order conditions for a maximum is (3.2.74) atkpv - li.9ghk/3x’Jkv = 0 (t=0, 1,..., M) where pv has been previously defined as being identically equal to unity. It is now necessary to take a closer look i at the interpretation that is to be placed on pv as it ap- ■ pears in the modified version of (3.2.62). In general, the cost that attaches to. the output of : any financial intermediary is the capitalized value of the : income stream that accompanies the financial instrument in ! question; if there is nO accompanying income stream, the cost to the producer is zero. Since the money that has been discussed so far in this analysis has been assumed to bear no dollar return per period, this is the interpreta- 268 tion that is to be placed on the pv in (3.2.74).; i.e., pv equals zero when looked upon from the cost side. Thus, (3.2.74) reduces to (3.2.75) -^ghk/ *'£kv = 0 (t=0, 1,..., M) There are three possibilities; (a) y equals zero, 9ghk/3x'hkv eguals zero' or v equals 9ghk/3x'£kv equals zero. If y equals zero, this implies, by (3.2.65) and (3.2.68), that the firm has an infinite cost of capital and/or the prices of non-financial stocks and the prices of goods and services that are not capable of being held as a stock are zero; clearly, neither of these are acceptable conclusions. Hence, 9^hk/9x'hkv must ec2ual zero; i.e.., an individual MI is willing and able to substitute other goods and services for the medium of exchange without limit. In other words, unless somehow constrained, money producers will supply an infinite amount of their output each period as long as the price of money in terms of other goods and services is above zero; or, which is saying the same thing, unrestricted money production will drive the price of money in terms of other goods and services to zero and the price level will become infinite. This type of reasoning lead Pesek and Saving to conclude that private money producers must be constrained 269 1 2 in their pricing policies if private money is to. exist. The methods used to control private money production on the contemporary American scene/ and the ones discussed by Pesek and Saving, are the prohibition of interest payments on privately issued money and the requirement that all pri vately issued money must be instantly exchanged by the pro ducer for other assets upon the demand of the holder. In order, to constrain the private money producers in the present model, it is necessary to make certain as sumptions regarding the degree of freedom allowed an indi vidual MI in its actions. In line with the above discus sion, we shall assume that interest payments on private money issues are prohibited— an assumption that has been implicitly made throughout this analysis— and that an MI is required to keep a reserve of "dominant money" equal to some percentage— call it "b"— of their outstanding issue of private money. This latter assumption is equivalent to the "instant exchange clause" alluded to earlier. For simplicity, we shall assume that dominant money (L) does not circulate outside of the monetary production system; its only function is to serve as a pure reserve base. Dominant money is issued by some exogenous agency who fixes the total stock in existence at any one point in 12peSek and Saving, op. cit., especially p. 250. V 270 time, but does not control, or attempt to control, the dis- I | tribution of it among the individual monetary producers. i I Denote the total stock supply of dominant money, during the period in question by j (3.2.76) L = constant and the initial stock held by an individual MI at the be- . T-l ! ginning of the t1 -1 1 week by . The desired stock at the T 1 end of the week is then denoted by Lj^, and the desired : rate of change of the actual to the desired level over the week is (3.2.77) L'£k = (L^ - L*^)/l where the one in the denominator has the dimension "time." ;The money price of dominant money— pL— is set identically !equal to unity, so that private and dominant money exchange on a one to one basis within the MI sector. The decision function.— As in the case of other economic units, the decision function of an MI expresses | |the preferences and technological factors faced by the in dividual entrepreneur with regard to portfolio balance, the jrate of change or existing stocks to their desired level, j and the quantity of flows used or produced per unit of time, jIn addition to the variables that are the subject of deci sions on the part of non-monetary units, an MI must make a 271 decision with regard to the actual level of dominant money held relative to the required level in each and every week. In the case of dominant money, the entrepreneur is not only concerned with the net affect upon the stock of his output of additions or subtractions that occur each week, but he must also be concerned with being sure that actual reserves are at least as large as required reserves each week; it is then up to the discretion of an individual entrepreneur whether or not he desires to hold any excess reserves. Defining (3.2.78) Jgk = (L*^ + ^ l & ) / b « £ v + j 0 X'hkv> where b is the proportion of the outstanding private money issue of an individual MI that must be held as a reserve in the form of dominant money, the decision function of the hth f^rin the v* " * 1 industry may be written (3.2.79) Ghv(E^kj , PcDkkc/pr Dhkv//P' Dhkd' Jhk^ H 0 (j-y+1, V+2:,.... . , m; c=l, 2,.... , v-1; d=y+l, v+2,..., s; t,T=0, 1,..., M) Notice that the expression (3.2.78) must be greater than or equal to unity; the reason for this is that this model does not take into consideration any penalty rate or other means of controlling the actions of monetary producers with re spect to the: relation of actual to required reserves other 272 than by outright decree. Further, notice that although the ! price level does not explicitly appear in (3.2.78), the j i entrepreneur is concerned with the real values of his out- ; | put and of his holdings of dominant money; this is because | it is with the real income that flows from these stocks | that he bases his decisions upon. | The quasi-profit function.— As in the case of the NMI sector, an MI deals in income streams; it will receive a promise to pay a fixed income per week for a given number : of weeks.from some other economic unit in exchange for a piece of paper that, in essence, promises nothing other | than that the MI will hold as a reserve against their money1 issue an amount of dominant money equal to some proportion of the nominal value of the pieces of paper issued. Of i j course, the other party to this transaction receives a | stream of income from the pieces of paper— i.e., from the |private money— in the form of a non-pecuniary return; if :the capitalized value of the stream of non-pecuniary income • from the private money were hot greater than or equal to j the capitalized value of the income stream given up, no ra tional individual would purchase the output of an MI. The I |crucial point is, however, that the amount and value of the iservices that flow from the Mi's output are independent of !the cost of production in terms of physical inputs incurred :by an MI. 273 The actions of an individual MI are similar to the actions of any other financial producer in that an MI will also attempt to maximize the present value of its financial portfolio of earning assets. To this end, it will issue private money— which is assumed to have a zero marginal cost of production— and purchase income earning finnacial assets from other economic units. This does not mean that the cost of issuing an additional unit of private money is zero; on the contrary, for every unit of private money issued an MI must hold a fractional reserve of non-interest bearing dominant money which represents a cost to the firm in the form of income foregone. It is the capitalized value of this foregone income stream that is the cost of producing a unit of the medium of exchange. An MI, then, wishes to maximize the present value of its financial asset holdings while, at the same time, minimizing the present value of its holdings of dominant money. Consider, first of all, a function that describes the behavior of the value of an Mi's non-monetary financial portfolio over the period in question; this may be termed :a financial net worth function v-1 , M v-1 . (3.2.80) NWf = NWf (p. E S~T. ., p. E E x hki) 3 j= 1 hk: 3 t= 0 j= 1 *1*3 Taking into consideration present values, this expression has the same form as (3.2.58), i.e., Next, consider a function that describes the behav ior of the desired holdings of dominant money by an indi vidual MI over the period in question; this may be termed a desired reserve function - 1 ^ t 0 1 M „ (3.2.82) DR = DR(S.. , 2 x' ^ , J.., jr,,..., J. . , b) hkv t_Q hkv hk' hk' hk It is obvious from (3.2.78) that the level of desired re serves at any one point in time is dependent not only on the increment of private money issued that week, but also on the initial stock of outstanding private money at the beginning of that week; hence, (3.2.82) takes the form M t (3.2.83) E J?k [b(Sr£w + E x't )] T=0 t=0 hkv It might appear at first glance that (3.2.81) and i ■ |(3.2.83) refer to two different mathematical concepts that I i imply different behavior assumptions; to be more specific, it might appear that (3.2.81) refers to a function appli cable to any one week in the period under consideration, while (3.2.83) might appear to refer to the integral of a function that describes the behavior towards desiered re serves in one week. This is, however, a misinterpretation both (3.2.81) and (3.2.83) refer to a period of time that 275 consists of M weeks; the difference in form arises from the T dependence of the variable Jkk (T=0, 1/..., M) in (3.2.83) upon all past values of x'^kv/ an^ not on just the value of x,b in the present week. On the other hand, no such re- hkv lationship links the independent variables in (3.2.81); the value of NWf can be found with no additional information other than prices, initial stocks at T=-l, and the time stream of additions to the stocks. Taking into consideration that it is present values that the entrepreneur is concerned with, expanding (3.2.83), substituting from (3.2.35), and letting ,,0 . _ 0 T0 , 1 ,1 , . M Bhk ahk^hk + ahk^hk + ••• + ahkJhk 1 i _i M M Bhk “ ahk hk * *,+ ahkJhk (3.2.84) rM _ M M hk " hk hk (3.2.83) may be written (3.2.85) b<Bhkshkv + Bhkx'hk + Bhkx'hkv + Bhkx'hkv + , .M v ...+ Bhkx'hkv) ' An individual MI, then, will wish to make v-1 _ M (3.2.86) s pj(Shkj + 1 ahkx'hkj) " b(BhkShkv j=l J t=0 a maximum. Although "cash drains" out of the MI sector are assumed, in this analysis, not to exist,, there are still the "clearing drains" between the individual Mi's to ac count for. Most probably, reserve changes experienced by commercial banks are best explained by some type of sto chastic process; however, for the sake of simplicity, we shall assume that each private monetary producer, based upon past experience, believes with certainty that his re serve changes are explained by the following function (3.2.87) L'£k= nix't-l) - t(x'£kv) where x'^”^ is the aggregate expansion in the stock of the medium of exchange in the period t-l, and is viewed as a parameter by an individual MI. In words, (3.2.87) says that an individual MI believes with certainty that his holdings of dominant money this week will be increased by a constant proportion of the expansion of the medium of ex change brought about by all other Mi's last week (the ex pansion by the MI in question may be ignored from this term on the grounds that it is very small relative to the total expansion), and diminished by a constant proportion of the medium of exchange production engaged in by the MI in ques- 277 tion this week. Alternatively, these quantities may be viewed as the mean value of some probability distribution 13 that purportedly describes their behavior. In view of the above discussion, (3.2.78) must now be rewritten as <3.2.8 8) j£k = ;<L*-£ + ^ tnfx't'1) . ♦<i'^kv)- 1)./b ( S ^ + tl0 X'WCV> In addition to purchasing income earning financial assets and producing and selling the medium of exchange, a typical MI will also use certain inputs and perhaps sell certain services that are associated with the major func tion of their operations, receive and pay interest and div idends, and hold certain non-financial stocks. An Mi's behavior toward these activities is analogous to the behav ior of any other profit maximizing producer, and may be expressed, respectively, as m M - t - H - (3.2.89) e p s a£k j=Y+l J t=0 J v-1 - 1 0 m-1 (3,2.90) s (K'nSbk. + K' x' . . +...+ K' x.', .) j_l u nx] i hk] M hk] ^For a suggestion as to another possible approach to a behavioral theory of the money supply, see Karl Brunner, "A Schema for the Supply Theory of Money," Inter national Economic Review, II (January, 1961), 79-109. 278 s M t j . (3 .2 .9 1 ) - p. ^ 4 _ l _ The quasi-profit function of the h monetary pro ducer is the sum of (3.2.86) and (3.2. 89) - (3.2.91) , V_1 -1 M t t n -1 (3.2.92) ' " ' h k “ pj*Shkj + ahkxhkj^ “ b^ahkshkv M m M t t + • \ Bhkx 'hkv> + . * Pj * ahkEhkj t=0 3=v+l t=0 J v-1 _i n m—l + I +...H- K^x'^.) s M t t E Pj 2 ahkx'hkj j=v+l J. t=0 J Notice that the form of (3.2.92) implies that an individual ■ MI issues no capital stock, etc.? this formulation suffers from the same weakness that was discussed in the presenta tion of the NMI sector. MI producer equilibrium.— An individual MI will ;wish to maximize (3.2.92) subject to (3.2.79); form the new function ( 3 .2 .9 3 ) Vhv = x hv - »Ghv The first order conditions for a maximum are (3 .2 .9 4 ) 4 kP-jU - Hj) - 3 Egkj = .0 (j.=V+l, v+2.,..., s; t=0, 1,.. ., M) 279 (3.2.95) (3.2.96) (3.2.97) (3.2.98) (3.2.99) (3.2.100) where B'j^ respect to : (3.2.101) a£ p. - U3Gu, /3eJ\. = 0 hk*3 H hk' hkj (j=s+l, s+2, . . . ., m; t=0, 1 , , M) ahkpj + K't+i - 1 1 <P/P) 3W 8x'hkj = 0 (j=l, 2,..., v-1; t=0, 1,..., M) M — h fB1 ^ — + 7 R 1 ^ f ^ -jr i ^ i [ hk,v’ hkv + hk + B hk,x’ hkv] - i a (1/P) 3Ghk/8x'^kv = 0 (t=0, 1,. .., M) ahkPj " "9Ghk/3x,hkj = ° (j=v+l, v+2,..., s; t=0, 1,..., M) M - b TB1 °'^ S_1 + E R 1 ^f ^ x 1 ^ 1 hk,L' hkv T=t hk,L' hkvJ - y(l/P) 9Ghk/3L'^k = .0 (t= 0, 1. , . . . , M) Ghk( ) = 0 x i is the first partial derivative of B^k with B'hk!x- = aL (3JWc/3x'hkv> T t T and B1^ L, is the first partial derivative of B^k with re spect to L'^, i.e., M (3.2.102) B ' ^ l, = £ a^OJ^/SL'^) T=t = J t aWc [1 /b (S hkv + Jo X'hkv>] The superscript "T" affixed to flow variables in (3.2.97), (3.2.99), and (3.2.101)-(3.2.102) is meant only to clearly indicate which variables are to be summed. The relative complexity of the expressions (3.2.97) and (3.2.99) is due to the explicit recognition given to the t t j fact that a change in or L'hk not only affects the relation of the present stocks of private money issued and holdings of dominant money, but it also affects all future values of these stocks. In other words, an increase in e.g., x'jjkv for t=7 means that this new value influences the relationship between the private money issue and the holdings of dominant money in weeks 8, 9,..., M, and, for 281 a given J^k (T=8, 9,..., M), L'^k must vary accordingly; +■ T or, for a given I*'kk (t=8, 9,..., M) , must vary accord ingly. Of course, in any actual circumstance, given the values of any one of these variables over time, the other two will adjust in such a way as to insure that the indi vidual MI reaches its most preferred position. The functions (3.2.94)-(3.2.100) do not place any restriction upon the values that Jkk may assume; therefore, to fulfill the institutional assumption that actual re serves must be at least as large as required reserves, it is necessary to assume that the form of the decision func- m tion is such that Jj^ is not defined for values less than unity. Under the "certainty" assumptions of this model, it might appear at first glance that no profit maximizing MI would hold any excess reserves; as long as reserve changes are explained by (3.2.87), an entrepreneur knows exactly what his stock of reserves will be during the ensuing week on Monday for each one of his alternative courses of .ac tion, and he feels that he can predict any changes with perfect certainty. However, there are costs and inconve niences involved in switching in and out of assets from week to week. Thus, for the same reasons that consumers do not hold interest earning assets instead of the medium of exchange up to the moment before a transaction is to take 282 place, an MI is likely during certain periods of time to hold a stock of excess reserves. The system (3.2.94}-(3.2.100) contains (M+l)Cm+s- v+D+l equations and the same number of unknowns. Using one equation to eliminate the y, and choosing the E^j (j=v+l, v+2,...,' m; t=0, 1,..., M) , p^x'^/P (j=l, 2,..., -1; t=0, 1,..., M), x'£kv/P (t=0, 1,..., M) , L'^/p (t=0, v 1,..., M) , and (j=v+l, v+2,..., s; t=0, 1,..., M) as the dependent variables, the above system may be solved for the dependent variables in terms of the exogenous variables.; (3.2.103) Ehkj = E hkj^plf P2J***' pv-l' pv+l^P,!**# Pn/Pf PlEhkl/pr•••' Pv-l^hk,v-l/ ^ f ®hkv/p' t*T-1/i5 qT- 1 c,T-l t t at L hk /p' hk,v+l' ' * ’ ' hks' Hj ' ahk' b, < j > , n, K't, KJt+1) (j=V+l, V+2,..., m; t=0, 1,..., M) V (3.2.104) x't^ = (p/Pj)x,kkj{Pa^ P2r*.., Pv-i/ Pv+l/P^ T-l T-l * ‘ '' plShkl/pf * * *' pv-lshk,v-l/p T-l rn_ 1 T-l T-l Shkv^p’ L*hk /p' ®hk,v+1• " •• Shks' Hjr aL ' b> x v-1' +' K’t' K,t+i> (j=l, 2,..., v-1; t=0, 1,..., M) 283 11 (3,2.105) x't = (P)x'gkv(Pl/ p2,..»., P ^ , Pv+i/Pi- hkv plShkl/p' * • •' Pv-lShkJv-:i/P' s££/P, L ^ / P , Sj^v+1,.,., s££, Hj, A ahk' b' x'v 4>* • nr . K't, K't+i) (t=0, 1,. . . , M) (3.2.106) L1^ = (p) ' hk ^ 1 f p2r ’ * *' pv-lf Pv+l/Pr T-l T—1 •••/ Pm/p' plshkl/p' *r *' Pv-lshk,v-l/p' CT-1 /n T *T“ 1 /tj qT-1 cT" 1 T T hkv' ' L hk 'p' shk,v+l'* • • ' &hks' j' ahkf x’v f ^ ^f ^'tf ^'t+l^ (t=0, 1,..., M) (3.2.107) x'hkj = X'hkj^Pl/ P2f***' Pv-1' Pv+l/P/ T-l T-l • Pm/Pf PlShkl/P#•••/ Pv-lshk,v-l/p' qT“ 1 /T) T *^_ ^'/'D cjT—1 _ _ hkv' ' hk /p' shkfv+l,,*,/ Shks' Hj•, ahk' b/ x'v 11' K't' K't+1^ (j=v+l, v+2,..., s; t=0f 1,..., M) t In the above system, 2(M+l) of the equations are not independent; to see this consider the decision function 284 (3.2.79). Once a decision is made as to the. values as signed to (m+s-v-1) of the variables that appear in this function in any one week, the value of the (m+s.-v)^ is automatically determined;, and, remembering the relation (3.2.87) , once the value of x'^v is determined,- the value of L'^k follows directly from (3.2.101). Hence, given the values of the parameters, (M+l)(m+s-v-1) of the excess de mands can be found, the remaining 2(M+l) excess demands are linear combinations of the other solutions. Again, the non-independence of certain of the equa tions has implications for the homogeneity of the system. Systems (3.2.103) and (3.2.107) are homogeneous of degree T—1 zero in the p. (j=v+l, v+2,..., m), P, S,. . (j=l, 2,..., J HK} v) , and but not homogeneous of any degree in the Pj (j=y+l, v+2,..., m) alone. The system (3.2.104)- (3.2.106) is homogeneous of degree one in the same, vari ables. The Complete System The market excess demand functions for goods and services are a "combination" of the corresponding excess demand functions of the n consumers and the m industries. The word "combination" is used here to indicate that the traditional method of algebraically summing over all eco nomic entities within the model— or, what is equivalent 285 from the standpoint of this work, consolidating the balance sheets of all economic units— is not necessarily the rele vant method of aggregation for market considerations. To investigate the implications of the application of this traditional means of aggregation in the context of the present model, consider the market excess demand for a financial instrument— say the 7t * 1 instrument. Assuming that there are no distribution effects and that there are Nj, identical firms within each industry, the excess demand function in the tt ^ 1 week would appear as + . n + m (3.2.108) x'S = 2 x 1 ; (3. 2. 23) + I N. x ' hV7 (3. 2. 53) 7 1=1 17 k=v+l k h k 7 V_1 t + 2 Nkx hk7(3*2-71) + Nvx'hv7(3*2*53) k=l which becomes (3.2.109) x1 7 = = (P/P j) x1 ^ ' ^2 7 * * * 7 ^v—1f ^v+17 ^ 7" * * 7 Pm/P/ ST 1/p Sq Kt' K,t'’ K't+1' ahk' Hj' b' V ♦' "> where the variables with a single subscript denote market quantities, and the K., K1. , K 1 , a^, , and N. are to be t t t+1 hk k interpreted as vectors taken over all consumers and firms, and the H_. as a vector taken over all depreciable stocks. The first thing that strikes one upon examination 286 of (3.2.109) is the absence, with the exception of the m _ I terra S /P of any financial stocks as arguments— i.e., v (3.2.109) implies that the demand to add to or subtract from a particular financial stock in the aggregate is inde pendent of the existing level of that stock and of the portfolio composition that exists at that time. The ra tionale used for this type of aggregation is based upon the assumption of a lack of distribution effects; if the ac tions of debtors and creditors exactly offset each other, then the level of internally produced and held debt washes out when all internal economic units are considered simul taneously. Thus, the stock quantities that appear as argu ments in (3.2.109) represent the net real wealth of the community as a whole. This line of reasoning is fine when it is applied to considerations of the wealth effect taken in isolation; however, it would be extremely hard to rationalize on a priori grounds that the demand for changes in the level of a stock is independent of the existing level of that stock and the relation of the level to the levels of all other stocks. It would be only under rather peculiar circum stances that the actions of creditors and debtors with re gard to portfolio behavior would exactly offset each other. In general, one would expect to find that the higher the level of any existing financial stock, the lower 287 would be. the desired flow quantity demanded and the lower would be the desired flow quantity supplied, ceteris paribus. To simplify matters, consider a closed economy in which there are only two endogenous economic units; in such a two person world it is easy to see that the only way in which the actions of the issuer and the holder of a partic ular debt instrument with regard to the desired rate of change versus the level of a stock can exactly offset each other is if the flow supply curve and the flow demand curve are identical in the ST~^-xl1: plane. If this were not the case, the supply and demand curves would intersect at one point in the plane— assuming of course, that we stick to the uniqueness of solution assumption— which would; be dependent upon the existing level of the stock in ques tion. Extending this to an n+N^m person world, the absence of initial ’ financial stocks in the market excess demand functions for financial instruments implies that the aggre- gate flow demand and flow supply curves in the S -x1 plane are identical— an assumption that appears dubious on theoretical grounds. When it comes to the question as to whether or not initial financial stocks should appear as arguments in the market non-financial excess demand functions, the applica tion of a similar analysis leads to the conclusion that their absence implies that the aggregate excess demands for ! changes in non-financial stocks, consumption goods and ser- ! vices, and inputs are independent of the level of initial financial stocks— i.e., the flow supply and flow demand ' curves for each of the aforementioned goods and services are identical in the S^“^-x,-t (or xt) plane, where j=l, | 2,..., v. This, once again, appears to be a rather dubious ; assumption. The explicit recognition of financial and non- financial stocks in the analysis, then, leads to the con clusion that all initial stocks should appear in each mar ket excess demand function. Consequently, the market functions cannot be arrived at by the simple algebraic summation of the individual excess demand functions; they must be derived by a process that does not wash out inter- ■ nally generated debt outstanding against the amount of it ; held internally. On the other hand, the aggregation pro cedure should not count a financial instrument once as a liability and once as an asset, each instrument should only be counted once. In terms of absolute magnitudes, it makes : no difference whether a particular instrument is looked upon as an asset or as a liability since the magnitude of ; any pure debt instrument held as an asset is identical to the magnitude of the liability attributable to this instru ment of its issuers. If internally held liabilities of exogenous units (or exogenously held liabilities of endoge 289 | nous units) are added to the analysis, the size and perhaps! sign of certain of the coefficients would change, but the arguments in the functions would be unaltered. The market functions. What the previous discussion! has been leading up to is what Gurley and Shaw refer to as I "gross money doctrine," which is a natural outgrowth of the! portfolio approach to the explanation of economic phenom- i ena.l^ to derive market excess demand functions that ex hibit the properties of gross money doctrine, the method | of aggregation chosen in this case is, first of all, to setj T—1 T-l ! each initial stock of a liability— i.e., each or S^j,| less than zero— that appears as an argument in the indi vidual excess demand functions identically equal to zero, ! and then algebraically sum over all economic entities. It ; should be noted that this method of aggregation is not a ' ' l I general method; it works in the case under consideration j because there is no internally generated debt instruments that are held by exogenous units. ! Assuming that there are no distribution effects with regard to the holding of stocks and performing the | j indicated operations, the market flow excess demand func tions appear as John g. Gurley and Edward S. Shaw, Money in a Theory of Finance (Washington, D.C.: The Brookings Insti tution, 1960), pp. 137-149. (3.2.110) E (3.2.111) x (3.2.112) x (3.2.113) L 290 j = Ej(pl' p2'"*' Pv-1' Pv+1/P'’*‘' Pm/P PlsT-i/p,...f s^-Vp, L/P, CT_1 qT—1 x ' t“l , \ V+l'* S r Vr n> (j=v+l, v+2,..., m; t,T=0, 1,..., M) = (P/Pj)x't(pif p2,..., Pv_lf P^/P, ***' pm^P# P1E1 /Pr* * *' pv - l W P' S^-Vp, L/Pf S^,...., sf"1, A, b, x'^”1, q) (j= 1, 2,..., V-l, t, T=0, 1,..., M) 'J = (p)x'^(pi, £> 2,..., pv_1/ Pv+1/Pf..., Pm/*V plSl"1/P'**-' pv-lS?-l/p^ Sv’Vp, L/P, / . . • , ^ X'v , ' f * , ^ (t,T=0, 1,..., M) = (P)L'^(p^f P2 / • • • , P^_ p / P^.j.p/P , • • • , Pm/^ PlSl"1/P>" ' Pv-lSV-l/P' Sv'V p - L/P, T-l m_ " I t—l * • •, Sg , A, b/ x y f < [ > / t i ) (t,T=o, 1,..., m) 291 j (3.2.114) 35' j = x,j^l/ ^2' * " * f Pv-1' ^v+l^*' * * *' pjS^'Vp,..., pv-is^:i/pf s^_1/P/ l/p, T-l T-l fc -1 ^y+1/ • * * , ^ X'v r ^^ {j=y+l, v+2.,. . ., s; t,T=0, 1,..., M) where A is a "matrix of vectors"; i.e., (3.2.115) A = ,[[Kt] [K't] [K\t+1] [ajkl [H ] [N^] 3 The elements of this matrix are to be interpreted as vec- . . . tors taken over all economic entities, and, in the case of the Hj, over all depreciable goods. It is also possible to derive market stock demand functions from individual behavioral assumptions and data in the same way that market flow excess demand function 1 R were derived. These are;iJ (3.2.116) Dj1 = (P/pj) D __(p-^, ^2', m ’ * Pv~l/ Pv+1/Pf ■ * * ' ^ic/^ ' P l ^ l ’ * * * 7 ^ v - l ^ v — 1 ^ P ’ S^/P, L/P, S^i,...,_ Sg"1, A, b„ x'^"1, < i > , n) (j=*l, 2,..., v-l? t,T=0, 1,..., M) ■^Whether or not the initial stock appears in the j^h stock demand function depends upon the form of the utility and decision functions. We assume here that the initial stock is included in the corresponding stock demand function. 292 (3.2.117) Dv — (P . ) D , ^ . ( p .^ , P2 f. . . • f P-y—lf Pv+l^P* * * r r qT— 1 /.p qT~1 /p qT~ 1 /p qT— 1 PlSl /P/*.-r PV_1SV_1/P' Sv /?' v+1r . .., S^”1, A) (t,T=0, 1,. .. , M) (3.2.118) L = (P.) L (P-t P 2 r * * * r Py—j _ ’ Pv+l^P 1 • • • t Pjfl/P / eT-1. e*"1/® eT-l/p qT-l 11 Pv-1 V“P ' V /P' v+lf .../ Sg , A, b , x'-y , ( J ) , n) (t,T=0, 1,..., M) (3.2.119) D_. = p^tp.^jr. P2r • • • r Py-l' Pv+l/P' * * * ' Pm^pf PlSrVP-.., Pv-lSv-l/p- S^-Vp , L/Pr Sy+1,..., S^"1, A, b, X'£-1, n) (j=v+l, v+2,..., s; t,T=0, 1,...,M) By inspection it is obvious that the above system exhibits the same homogeneity properties as does the indi vidual stock demand and flow excess demand functions; namely, (3.2.110), (3.2.114), (3.2.116), and (3.2.119) are homogeneous of degree zero in the p. (j=v+l, v+2,..., m), P, and Sj” 1 (j.=l, 2,..., v) , and (3.2. Ill) - (3. 2 .113) and (3.2.117)-(3.2.118) are homogeneous of degree one in the same variables. Also, notice that the system (3,2.110)- 293 (3.2.119) includes, besides the portfolio balance terms, an implicit measure of the community's real wealth; ex plicitly written, it becomes Market equilibrium. When moving from the analysis of an individual economic entity to the analysis of the economy as a whole, prices and interest rates can no longer ; be considered as parameters; they now become variables of the analysis. ior in the sense that, with given market prices, each con sumer consumes and accumulates exactly what he had planned to, and each firm produces, sells, and accumulates exactly ;case of each and every economic unit. This, in turn, im- ;plies that each market just clears. As we have discussed earlier in this chapter, this model involves two concepts of equilibrium: short run (flow) equilibrium and long run (full stock) equilibrium. We now turn our attention to the consideration of these two (3.2.120) I sT"1 j=V+l 3 + (ST_1 - L)/P + L/P = v Market equilibrium is characterized by the condi tion that actual behavior will correspond to desired behav- what it had planned to; in other words, market equilibrium implies that both utility and profits are maximized in the 294 different equilibria. Short run (weekly) equilibrium.— Short run equilib rium is characterized by the. condition that all flow mar kets clear; i.e., (3.2.121) E^(3.2.110) : + X,1T(3,.2.114) =0. 3 3 (j=v+l, v+2,..., s; t=0, 1,..., M) (3 .2.122) Ej (3. 2.110). = 0 (j=s+l, s+2,..., m; t=0, 1,..., M) (3.2.123) (P/pj)x'^(3.2.Ill) = 0 (j=l, 2,..., v-l; t=0, 1,..., M) (3.2.124) (P)x'^(3.2.112) = 0 . (t=.0,. 1,..., M) (3.2.125) (P)L,t(3.2.113) =0 (t=0, 1,..., M) Equations (3.2.123)-(3.2.125) might, at first glance, appear contradictory in the sense that they seem to imply that financial stock equilibrium is achieved in each and every week. This is the same conceptual problem that was encountered in the initial specification of this model;i it eminates from the interpretation given the x'j (j=l, 2,... s). The short run equilibrium conditions indicate that prices will adjust so that the total flow demand will just match the total flow supply for each good and service; in the case of financial goods, they indicate that desired additions to financial stocks during any given week will be just offset by desired deductions from existing stocks and newly produced financial goods. These conditions, however, say nothing about the relation of actual stocks to their desired levels at the existing prices, and prices will con tinue to change from week to week until actual and desired stocks are brought into equality; for stable prices, this condition must be fulfilled both for individual and aggre gate stocks. The system (3.2.121)-(3.2.125) forms a block re cursive system consisting of (M+l) simultaneous blocks, each block being related to all previous blocks by reason of the relationship between initial stocks and past behav ior; i.e., (3.2.126) S?- 1 = ST1 + 2 [ x ' t - D ?H j(x5l 3 3 T,fc=0 j 3 3 2 (j . =l./ 2,..., s) Each simultaneous block consists of m+l equations in m unknowns: the p^ (j=l, 2,..., v-l, v+1,..., m) and P. However, because of their relationship to the individual excess demand functions, two of the market equations are linear combinations of the other m - 1 functions; hence, an individual block contains only m- 1 independent equations. This seeming underdeterminacy is removed when it is remem bered that the price level is a function of the pj (j=v+l, 296 v+2,..-r m) as defined by (3.2.13); therefore, by the counting rules adoped in this work, each simultaneous block in (3.2.121)-(3.2.125) and (3.2.13) forms a consistent and determinant system. Given the initial quantities of stocks at time T = -1 and the values of the other paramters, the system may be solved recursively for the equilibrium spectrum of prices and the price level for each week in the period under con- sideration. Given this information, the appropriate inter est rates may be solved for by relation (3.2.12), and the cost of capital for each firm may be obtained with the aid of (3.2.34). Long run (full) equilibrium.— Full equilibrium is characterized by stable prices from week to week, which, in turn, implies that actual stocks have reached their desired; levels in addition to all flow markets just clearing. The only production that takes place under these circumstances is for consumption and to replace any assets that have de preciated in the current week. On the financial markets, the only activity is associated with the replacement of financial instruments that have matured with identical in struments; the money supply is constant since each money producer and each money holder have reached their optimum portfolio at the currently prevailing (stable) market 297 prices. This is the classical stationary state which, in the absence of any autonomous disturbances, will continue on indefinitely with constant stocks, income, prices, etc., and zero net investment. In the context of the present model, the long run equilibrium conditions are (3.2.127) E^T (3.2.110) = 0 3 (j=v+l, v+2,..., m; t=0, 1,..., M) (3.2.128) x't(3.2.114) = 0 j (j=V+l, V+2,..., z; t=0, 1,..., M) (3.2.129) (P/p.)dT(3.2.116) - (P/p.)S^"1 = 0 J 3 ^ 3 (3.2.130) (P)D^(3.2.117) - (P)S^"1 = 0 (T.=0 , 1, . . . , M) (3.2.131) (P)LT(3.2.118) - (P)L = 0 (3.2.132) Dj(3..2.119) - ST 1 = 0 3 3 (T=0, 1,..., M) (j=V+l, V+2,..., s; T=0, 1,..., M) 298 ; and the zero profit condition‘ d (3.2.133) ^k^l* ^2 ' * ’ * ' ^v—lr ^v+1^^1 r * * * / ^m/^*' Pl®l /P r , PV_^SV_^/P, Sv /P, L/P , } I Sv+1' * * *' Ss_1' A, b, x'^"1, < f > , n) = o I (k=l, 2,..., m; t=0, 1,..., M) The v+1 to z index in (3.2.128) indicates that this condi- ! I tion applies to stocks of depreciable goods. ; With the exception of (3.2.127)-(3.2.128), it is j not necessary to explicitly state the flow equilibrium con-j ditions in long run equilibrium because (3.2.129) - (3.2.132) imply the flow conditions (3.2.123)-(3.2.125) and (3.2.134) x1^(3.2.114) = 0 j (j~z+l, z+2,..., s; t=0, 1,..., M) Hence, a restatement of these conditions in this section would be redundant. Since in long run equilibrium everything remains constant, it is not necessary to consider the entire system! for M+l weeks; the solutions of the equations for any one dpor the rationale of including this in the long run equilibrium conditions, see Chapter II, Section I. 299 week will satisfy the equations describing the behavior in any other week. Considering one week in isolation, the aforementioned system contains 2m+s-2v+z+l equations in 2m unknowns: the p^ (j=l, 2,..., v-l, v + 1 , m ), P, and the N^. (k=l, 2,..., m) . However, due to their relation to the individual excess demand functions, two of the above equa tions are linear combinations of the remaining 2m+s-2v+z-rl market functions. Keeping in mind the price level equation (3.2.13) , the system then contains 2m+s-2v+z independent equations to determine the 2m unknowns; there appears to be an excess of s-2v+z equations. Is the system overdeter mined? The answer is, of course, no. The s-2v+z seemingly excess equations are a result of the double equilibrium conditions necessary to obtain dynamic price stability for those goods that can both be held as a stock and consumed and for those stocks that are subject to depreciation. As Bushaw and Clower have pointed out, if a particular stock market happened to be in equilibrium at a particular set of relative prices but the corresponding flow market was not, ex post stocks must be changing, and prices cannot be 17 stable from week to week under these circumstances. % W. Clower and D. W. Bushaw, "Price Determina tion in a Stock-Flow Economy," Econometrica, XXII (July, 1954), 330-331. 300 . Thus, these "extra" equilibrium conditions are necessary to| i insure that the conditions of long run equilibrium are ful-j filled. i I Given the values of the paramters, then, the system; (3.2.127)-(3.2.133) for any t and (3.2.13) may be solved | for the long run equilibrium values of the set of relative ; prices, the price level, the prices of financial instru ments, and the number of forms in each industry. Once this: has been accomplished, the long run equilibrium stock j levels may be solved for by substitution in (3.2.116)- (3.2.119). As before, the long run equilibrium values of j 1 the interest rates and the costs of capital may be found by substitution in (3.2.12) and (3.2.34). Before closing this section, there is a possible ambiguity that should be cleared up. The zero long run I profit condition for the money production industry does notj imply that the price of money in terms of other goods and services is zero; or, what is saying the same thing, it does, not imply that the price level is infinite. It does mean, however, that the price of money in terms of other j goods and services is competed down to the marginal (which i equals average), costs of production, which, in this case, is equal to b (the required reserve ratio) dollars per one dollar produced; in other words, the price level becomes a direct function of the required reserve ratio. Alterna- 301 tively, the zero profit condition for the money production industry could have been omitted— implying that there are some restrictions to entry into this market and, therefore, a possibility of making pure economic profits in the long run— which would mean that the firm numbers (the N^, k=l, 2,..., v-l, v+1,..., m) would appear as relatives in the system (3.2.110)-(3.2.114) and (3 .2.116) - (3.2.119) ; i.e., they, would appear as Nj/Nv, N2/Nv,. . . ., Nm/Nv. III. CONCLUSION The model that has been developed in the preceding sections of this chapter has been couched primarily in mathematical terns, which might tend to obscure the eco nomics involved. It is the purpose,. then, of this final section to relate this model to the mainstream of monetary and financial theory as reviewed in Chapter II of this work. The basic hypothesis of this work is that to "ade quately characterize the relevant social space" of an econ omy which uses financial instruments, the presence and levels of all stocks must, at least in principle, be ex plained. This is because, to carry the analysis one step backwards, financial instruments possess two characteris tics (among others) that differentiate them from, and are shared with, other economic goods: ( 1) the existing stock of any financial instrument at any given point in time is | normally large relative to the flows of newly created in- j struments during some (short) interval of time; and ( 2) economic units usually view their desired level of a given j i stock as being related to the levels of all their other stocks— individuals and institutions do explicitly consider; i and discuss their "portfolio" and its actual versus its optimum "composition." Admittedly, both of these observa- i tions are based on "casual empiricism"; one would suspect, | I however, that they would be substantiated by the available j evidence. I E i This model, then, is a theoretical attempt to por- i tray a monetary economy in which each unit has the alterna tive of saving or dissaving and investing or disinvesting, ; i \ and in which each unit has the choice of a variety of fi nancial instruments and non-financial assets by which he j may accomplish the aforementioned acts. A verbal outline of the path taken by such an economy after an initial dis turbance has already been sketched in Section IV of Chapter; II of this study, and other verbal treatments have been presented by other contributors. Por example, the conclu- j sions reached by Milton Friedman regarding the potential efficacy of monetary policy appears to be based on a theo retical construct resembling the present model. In dis cussing the cyclical behavior due to a rise in the rate of : 303 change in the money stock brought about by open market operations (i.e., an increase in flow supply), Friedman describes the adjustment processes as follows: It seems plausible that both nonbank and bank holders of redundant balances will turn first to securities comparable to those they have sold, say, fixed- interest coupon, low-risk obligations. But as they seek to purchase these they will tend to bid up the prices of those issues. Hence they . . . will look farther afield: the banks, to their loans; the non- bank holders, to other categories of securities— higher-risk fixed-coupon obligations, equities, real property, and so forth. As the process continues, the initial impacts are diffused in several respects: first, the range of assets affected widens; second, potential creators of assets now more in demand are induced to react to the better terms on which they can be sold, including business enterprises wishing to engage in capital expansion# house builders or prospective homeowners, consumers who are potential purchasers of durable consumer goods— and so on and on; third, the initially redundant money balances concentrated in the hands of those first affected by the open-market purchases become spread throughout the economy. As the prices of financial assets are bid up, they become expensive relative to nonfinancial assets, so there is an incentive for individuals and enter prises to seek to bring their actual portfolios into accord with desired portfolios by acquiring non financial assets. This, in turn, tends to make ex isting nonfinancial assets expensive relative to newly constructed nonfinancial assets. At the same time, the general rise in the price level of non financial assets tends to raise wealth relative to income, and to make the direct acquisition of cur rent services cheaper relative to the purchase of sources of services. These effects raise demand curves for current productive services, both for producing new capital goods and for purchasing cur rent services. The monetary stimulus is, in this way, spread from the financial markets to the markets 304 for goods and services. Turning our attention now to the more technical aspects of the model, Harry Johnson has observed that, Neither the Brunner-Clower nor the Clower-Bushaw [i.e., the existing stock-flow theories] theory really solves the stock-flow problem: the former subordinates the flow analysis entirely to the stock, the latter simply adds stock and flow anal yses together. The defect common to both is the absence of a connection between the price at which a stock will be held and the current rate of change of the stock held, and correspondingly between the price at which a stock will be supplied and the current rate of change of the stock supplied; such connections would yield a simultaneous equilibrium of stock and flow evolving towards full stock equi librium {zero net flow).^9 At first glance the model presented here might appear to suffer from the same weaknesses; however, upon closer examination it is evident that it does not. It is true that the short run equilibrium conditions— equations (3.2.121)-(3.2.125)— are flow equations; but, in the case of goods that are capable of being held as a stock, these l^Milton Friedman and Anna J. Schwartz, "Money and Business Cycles," The Review of Economics and Statistics, XLV, Supplement (February, 1963) , 60-61. Also see Milton Friedman, "The Lag in the Effect of Monetary Policy," The Journal of Political Economy, LXIX (October, 1961), 447- 466. For further references to works that take this same approach, see H. G. Johnson, "Monetary Theory and Policy," The American Economic Review, LII (June, 1962), 364. Also see the quotation from the work of Karl Brunner in Chapter II, Section IV. l ^ J o h n s o n , q cit., pp. 363-364. For a review of the relevant references concerning the Brunner-Clower and Clower-Bushaw theories, see Chapter II, Section IV. 305 flow equations are derived directly from the stock excess demand functions in such a way that the economy as a whole is willing to hold the existing stocks while experiencing a certain rate of change in the levels of their stocks at the existing prices. That the prices are not stable over a period of several weeks is an indication that peoples' expectations are not being fulfilled; hence, a new desired level and a new rate of change emerges in each of the suc ceeding weeks until a position of zero net rate of change for all stocks is achieved at the full equilibrium posi tion. The long run equilibrium conditions are equations (3.2.127)-(3.2.133) , which are seemingly dominated by the stock relations. However, the structure of the micro sys tem once again insures that the equilibrium values of the long run equilibrium system also satisfy the short run system; disregarding the zero profit condition, the system (3.2.127)-{3.2.132) will yield the same long run equilib rium values as will the solution of the recursive system (3.2.121)- (3.2.125) in conjunction with the stock demand functions (3.2.116)-(3.2.119). It should also be noted that the model presented in this chapter is free of both Patinkin's Invalidity I and 306 20 Invalidity II. The system isf therefore, logically con sistent and, by the counting rules, mathematically consis tent and determinant. Although the comparative static properties of this model will not be worked out in this study, it is possible to briefly consider the effects in a shift in some exoge nous variable on the market outcomes. Assume, for example, that the "monetary authorities" wish to increase the supply of the medium of exchange, and that they effect this de sired change by lowering the required reserve ratio (b). In the first instance, each MI will find that their stock of dominant money at the new b is larger relative to the outstanding stock of the medium of exchange than they would like it to be, and they will attempt to diminish their holdings of "excess reserves" by purchasing income earning assets and, perhaps, non-financial goods and factor ser vices— see relations (3.2.103)-(3.2.107). As the MI sector expands, interest rates' on financial instruments that are demanded by Mi's will be bid down and the prices of non financial goods and services will be bid up. At the new, lower interest rates on certain finan cial instruments, the non-MI sectors will find that their desired portfolio and the rate of change of actual to 20Invalidity I and Invalidity II are reviewed in Chapter II, Section III. 307 | desired levels are now different than they were before the j I expansion in the MI sector. The non-financial sectors willj i probably wish to hold a relatively smaller portfolio of i financial assets, and increase their borrowings to finance j the holdings of non-financial stocks (i.e., an increase in ; physical investment) and their consumption levels— see | (3.2.22)-(3.2.25) and (3.2.52)-(3.2.55). This will have j the effect of attenuating the increase in prices of non- j monetary financial instruments brought about by the MI sec-j tor's expansion, and of bidding up the price level of non- | i financial goods and services. | ! Assuming that the portfolios of Mi's are concen trated in relatively short maturity instruments, the af fects on the NMI sector will be a switching from short term; securities, whose prices have risen, to the long end of the: i ! spectrum of financial instruments— see (3.2.70)-(3.2.73). The NMI sector will also desire to increase its (stock and flow) supply of its liabilities due to the change in rela- : tive rates of return of financial instruments of varying j maturities. ; | The increase in the supply of the output of the NMIj j sector will tend to force the price of these short term instruments down; however, in the final long run equilib rium position, the prices of financial instruments and/or the price level of physical goods and services must have 308 j i risen to the extent necessary for the non-MI sectors to be j j willing to hold the increased stock of the medium of ex- ; change. Thus, the increase in demand for financial instru-j ments, and especially those instruments that are close i substitutes' for the medium of exchange, must outweigh or at! least offset the increase in supply of these instruments by! all sectors. In the final long run equilibrium position one would expect to find that production and prices of non- j | financial goods and services have increased, stocks of non-| financial goods and consumption have increased, and stocks j ! of financial goods have also increased. The adjustment process as it has been outlined above leads to the conclusion that money is not "neutral" in this system in the sense that a change in the supply j I conditions of money affects both financial and non-finan- i cial variables. This conclusion is based- on the idea that a change in b that results in a larger stock of outstanding: \ ‘ ; private money results in an increase in net real wealth; i * ~ ! this result, in turn, rests on the assumption that there are monopolistic influences present in the money production! sector. Hence, if pure competition prevails in the money production sector (i.e., if there is free entry and exit), money is "neutral" and the argument b vanishes from the real sphere long run equilibrium conditions (3.2.127)- 309 j (3.2.128) and (3.2.132); if, on the other hand, there are j barriers to entry, money is not "neutral" and b appears as j j an argument in the above long run equilibrium conditions. However, the question naturally arises as to j whether this conclusion holds for other types of changes in! the supply of the medium of exchange. Assume, for example,! that the stock of dominant money is (say) doubled auto- j nomously. Now, consider the long run equilibrium condi- ! tions (3. 2.12-7) - (3. 2.132) ; assuming that the system was j initially at a position of long run equilibrium, these j i functions would also be satisfied with a doubled stock of l | at the initial rates of interest and relative prices if all| prices and stocks of financial instruments exactly doubled and if the stocks of non-financial goods remained unchanged.; This latter requirement implies that the stock demands and j stock supplies of non-financial goods are completely un- | responsive to changes in relative prices, the spectrum of interest rates, and the level and composition of financial | portfolios even in the short run, for if non-financial stocks deviated from their initial long run equilibrium j values during the adjustment period there is no mechanism j to insure that they return to this level in the new long run equilibrium position. Therefore, it seems that it is very doubtful that money is "neutral" for a change in L even if the money production sector operates under condi tions of pure competition. Any other changes in the supply conditions of the medium of exchange that are capable of analysis within the | j framework of this model are equivalent to the two cases j | considered in this section. Thus, it appears that even I i though it is possible that the real variables in this modelj could be invariant to changes in money supply variables in the long run, it would be only under rather unusual circum- | stances, that this result could be achieved. For all prac- j tical purposes, therefore, money is not "neutral" in this model. The emphasis in the model presented here has been ! on portfolio adjustments which, it has been argued through out this work, appears to be a much more "realistic" expla-j nation of observed changes in economic (and particularly , monetary and financial) variables than the alternative approaches to monetary and financial theory. However, de spite the advantages of the approach used here there are i certain weaknesses. We shall reserve comment on these j i I points until the final chapter of this study— Chapter VI. j 311 APPENDIX I GLOSSARY OF SYMBOLS Superscripts T refers to a specific date; in particular, T refers to the end of the t * - " * 1 week, T-l refers to the beginning of the t week, t refers to a period of time— a week. Subscripts i an index that refers to a particular consumer, ( — i# ^ • f h) • j an index that refers to a particular good or service, (j.=l, 2,. .., m) . h an index that refers to a particular firm. (h=l, 2,..., Nk). k an index that refers to a particular industry, (k=l, 2,..., m). v the total number of financial goods, (j=l, 2, . . ., v) ; the. v" * " * 1 good is the medium of exchange, z refers to the last factor service, (j=v+l, v+ 2,, z; 2—s). s the total number of goods that may be held as a stock, (j=l, 2,..., s). m the total number of goods and services, n the total number of consumers in the economy. 312 Variables D?j (hkj) t^ie desired quantity of the j* - * 1 good to be held as a stock by the i- * - * 1 (hk^) unit at time T. Si j (likj) t* ie actua^ quantity of the good held by the ith (hk^) unit at time T-l, which is equal to the initial stock at the beginning of the first week under consideration (a paramter) plus all past increments of net investment. T T T—1 Xij(hkj) Dij(hkj) “ Sij(hkj) m the desired quantity of dominant money to be held as a stock by the h ^ monetary inter mediary at time T. L*kk'L the actual stock of dominant money held by the h* " * 1 monetary intermediary at time T-l, which is equal to the initial stock at the beginning of the first week under consideration (a parameter) plus all past increments of net additions of dominant money. t* ie desired gross additions to the stock ij(hkj) by the i^h (hk^*1) unit during the t* - * 1 week; i.e., gross investment demand. L'J\ the desired additions to the stock of dominant hk money of the h’ * - * 1 monetary intermediary during the t1 " * 1 week. 313 xij(hkj) desired rate (flow) of consumption of the jth good or service by the ith unit during the tUii week, or the desired rate of input or out- * f * h 4 * T - i put of the jgood or service by the i (hkth) unit during the tth week. Eij(hkj) tlie excess flow demand for the jth good or service by the ith (hkth) unit during the tth week. Note: The market variables, corresponding to the above m T-l T t T-l - f - + • are denoted by , S. , K., L , L* , x'L' , 3 ' 3 r . 3 f . j' t t xj , and E_^, respectively. Pj the market price of the j^*1 good or service. P the price level of non-financial goods and services. J . " j — r^ the market rate of interest of the j finan cial instrument. the number of firms in the k^h industry, q the number of "weeks” in a "month." X a Lagrangian multiplier, u a Lagrangian multiplier. r ^ the "cost of capital" to the h^* 1 firm in the kth industry. hk the present value of the profit made by the hth firm in tjjg ^th inaustry over, the period in question; industry profits are denoted by 314 T J,. the desired ratio of actual reserves of domi- hk th nant money to required reserves of the h monetary intermediary in the tt ^ 1 week. x*ij(hkj) unit's initial endowment of *th_ factor services during the t week that ema- T—1 nate from (j-v+1' v+2,..., s) . Parameters STl^kj) the initial quantity of the j’ * ' * 1 good held by the i* - * 1 (hkth) unit at the beginning of the first week under consideration; the corre sponding market quantity is denoted by ST^ L*“^ the initial quantity of dominant money held by the h* 1 * 1 monetary intermediary at the beginning of the first week under consideration. L the aggregate amount of dominant money held by the monetary production sector. x*ij (hkj) t*le {hk’ * - * 1) unit's initial endowment of the jth factor service flowing from j (irkj) tiiat could be marketed or used during the O^h week, the ith unit's initial endowment of the jth factor service that does not emanate from a stock and that could be marketed or used dur ing the t* ' * 1 week; this refers primarily to labor services. i - i - j r^ the time preference rate of the i consumer. 315 + • V i the number of weeks to the maturity of the j financial instrument; tj automatically de creases by one with the passage of each week, weights that reflect the relative importance of each non-financial good or service in con sumption, production, and stocks, a weight that reflects the relative importance of the j* * * 1 financial instrument in the lia- bility and equity section of the hk unit's balance sheet. the relation between the intensity of the use of the j* * * 1 physical asset and its rate of depreciation. the required minimum ratio of dominant money holdings to outstanding private money, a number of weeks chosen so that all stocks will reach an equilibrium position within this time period. the fraction of an MI's money production that will result in losses of dominant money; the loss being equal to i j > times the amount of this week's money production. the proportion of the aggregate money produc tion last week that will be gained in the form of dominant money by an individual Mi this week. 316 0 the face amount of all non-monetary financial instruments. Definitions ait hk K. 1'/ < 1+ rhk> M E a. . t=t K1 M E a. t=t hk B hk M y at TT T,t=t hk,x 1 hk' hkv ,T,t ' hk, L' 3 BL/8L,hk [[Kt] [KVt] [K't+1] [:ajk] [Hj ] [N^] ] I CHAPTER IV AN APPLICATION OF THE THEORY As we have repeatedly stressed throughout this study, a construct of the degree of generality of the model presented in Chapter III is of importance only as a frame- ; work from which qualitative conclusions can be drawn, and as a guide for empirical research. For this type of model ! to be "operationally feasible," it must be modified in such a way that the variables are directly measureable and/or suitable proxies that are themselves directly measureable are available. However, measureability is not the only criterion; all of the variables in system (3.2.109)— (3.2.117) are directly measureable, but no one would sug gest that these functions are appropriate for empirical in-j vestigations. Hence, the term "operationally feasible" also implies that the model that is to be subjected to em pirical investigation be simple in the sense that only the most important explanatory variables are considered. Of course, a model of this type also implies that the form of the equations has been adequately specified and that any significant restrictions on the coefficients are enumerated.! Of the criteria that an empirical model could be judged by, the following would undoubtedly appear toward 317 the head of the list: (1) the model should be adequately specified— i.e., each variable should be unambiguously de fined and measureable, and the form of the equations indi cated clearly; (2) only those explanatory variables that are "important" to the explanation of the phenomena under study should be included; and (3) adequate data— either already existing data or data that can be gathered— should be. available. Basically, any modifications to the model developed in the preceding chapter that are designed to adapt it for empirical purposes can proceed in two directions: it may be aggregated over sectors and variables (macro models), or specific equations may be chosen and then aggregated over certain of the independent variables (micro models). It is the purpose of this chapter to present an example of each of these two alternatives. I. A MACRO MODEL In this section we shall develop a Keynesian type short run income determination model that will be built up from the market relations (3.2.110)-(3.2.114), (3.2.116)- (3.2.119) and the equilibrium conditions (3.2.121)- (3.2.125). As is customary, we shall consider a closed, purely competitive economy that may be considered as con sisting of three aggregate markets: the goods and services 319 market, the labor market, and the money market. The model ; presented here is similar to that presented by Don Patin- kin;"*" however, there are certain differences, especially in; i the money market equations, that stem from our emphasis on i the portfolio approach. In addition, the discussion of | this section pays particular attention to the "operational i feasibility" of the theoretical construction. Define rg a weighted average of "short term" i interest rates. ; r^ : a weighted average of "long term" I interest rates. ! r a weighted average of market interest G rates on government obligations. P the implicit GNP deflator. C real consumption. Ipatinkin develops his aggregate model in his Money,; Interest, and Prices (2d ed.; New York: Harper & Row, Pub-; lishers, 1965), chap. 9. The workings of the model are discussed in chaps. 10-13 of the same work. Also, cf. Franco Modigliani, "The Monetary Mechanism and Its Inter action with Real Phenomena," The Review of Economics and Statistics, XLV, Supplement (February, 196377 80. 1 2 An interesting approach to the simplification of a model is given by Walter D. Fisher, "Simplification of Economic Models," Econometrica, XXXIV (July, 1966), 563- 584. Fisher's approach is probablistic in nature and re quires that the model to be simplified is capable of esti- | mation; hence, his approach is of no use in the case under consideration. real saving. real government expenditures. real physical investment. real gross national income or product. the nominal wage rate (a weighted average). a measure of industrial plant capacity utilization. the ratio of actual reserves held by com mercial banks to their required level, an index of the tax rate on individual and corporate total taxable income, the demand for labor, the supply of labor. nominal tax receipts of the government, the nominal stock demand for the medium of exchange. the nominal stock supply of the medium of exchange. the nominal stock demand of government interest bearing obligations. the nominal stock supply of government interest bearing obligations. the initial stock of nominal government obligations. the nominal stock demand for long term credit instruments . 321 the nominal stock supply of long term credit instruments. the nominal stock demand for short term credit instruments. the nominal stock supply of short term credit instruments. the initial stock of nominal medium of exchange.■ the initial stock of nominal short term credit instruments. the initial stock of nominal long term credit instruments.. the initial stock of capital equipment, the initial stock of nominal dominant money (i.e., reserves at commercial barks). In order to construct an empirical model of this type, it is convenient to consider demand and supply func- | tions rather than the excess demand functions that were ! used in the analysis of Chapter III. In general, the argu ments that would appear in a particular demand or supply function in a model of that type would be identical to the arguments that would appear in the corresponding excess demand function. In the remaining analysis of this section, i j the excess demand functions of Chapter III will be treated ! as if they were demand or supply functions; any differences B SL B DS B SS B* M B*BS B* K* L* BL 322 in the arguments will be noted in the discussion. The Goods and Services Market The aggregate demand for final newly created, non- financial goods and services in this model is the total desired rate of consumption and gross investment in the economy over the period in question. The period that will be discussed here is the "week," although the model may be extended to cover a period of more than one "week." As is customary in this type of model, we shall break aggregate demand up into two components: consumption (which is asso ciated with .the consumption function), and investment (which is associated with the marginal efficiency of capi tal schedule). The consumption function appropriate to a week may be identified, with a few modifications, with the summation of the system (3.2.110) over all commodities and services for any t. However, the system (3.2.110) includes demand functions for raw material and intermediate products, cate gories that do not belong in a consumption function. To get around this problem, we shall follow Patinkin in as suming that all firms'are vertically integrated to the ex tent that each is completely self-sufficient in all inputs 3 except labor and capital goods. Disregarding the parameters A, $, and n because they are not likely to significantly change during the period under consideration, and b and x'^"1 because they are unlikely to significantly influence the demands under consideration, and summing (3.2.110) for any t over all final, newly created goods and services, the consumption function may be written (4.1.1) C = C(rs, rL, B*M/P, y) It is, however, more convenient to work with the converse of this function; the saving function may be stated (4.1.2) S = .S(rs, r , B*M/P, y) The micro counterpart of the investment function is the system of equations (3.2.114). Once again, however, a strict translation of the micro functions into a macro function is not permissible; (3.2.114) reflects demands for and supplies of existing physical assets as well as for newly created physical assets. Summing (3.2.114) over the demand for newly created physical stocks and disregarding the parameters of that function, the investment function is 3Patinkin, o£. cit., p. 205. 324 (4.1.3) I = I(r , r , B*M/P, y, K*, H) S 3 li I It may seem strange that (4.. 1.1) - (4.1.3) do not explicitly contain a wealth constraint, especially since this form is implied by systems (3.2.110) and (3.2.114). j The real value of total wealth, however, is defined as the i capitalized value of the real income stream that emanates from it, or, in this case (4.1.4) w = yn/rn + yh/rh + B*^/P + B*G/P where w is total real wealth, Yn/rn anc^ Yft/3 ^ are the com- | i ponents of total real wealth due to non-human and human j physical real wealth, respectively, and the last two terms on the right represent net real financial wealth. The measure of income and interest rates used in (4.1.1)- i (4.1.3) includes the first two terms on the right in ; (4.1.4); hence, to include income, interest rates, and wealth as arguments in the consumption and investment func tions is to be guilty of double counting— or, to use the statistical terminology, multicollinearity would be intro duced. The decision to use income as an. argument in these | functions rather than wealth is based upon the scarcity of reliable statistics on wealth and upon the a priori judg ment that portfolio balance is relatively unimportant in these relationships. Turning now to the supply side of the market, the j 325 aggregate supply function is the summation for a given t ofj the supply counterparts of (3.2.110) and (3.2.114) over all! newly created commodities and services. Assuming that all : firms are vertically integrated to the extent indicated ; earlier, the output of any firm— and, therefore, all firms j taken together— is dependent upon the technical relation ships of production. Thus, we may write the aggregate sup ply function as ! (4.1.5) y = y(N, K*) Equilibrium in the goods and services market is achieved when aggregate demand is equal to aggregate supply,: or (4.1.6) y = C + I Alternatively, the equilibrium conditions in this case may be stated (4.1.7) S = I Notice, however, that equilibrium in this market implies nothing with regard to the level of employment; for this information, we must investigate the labor market. The Labor Market Because of the simplifying assumptions spelled out in the discussion of the goods and services market, labor 326 1 and capital goods are assumed to be the only factor inputs I that are subject to market pricing in this model. However,:: changes in the stock of capital are assumed to be small relative to the existing stock of capital in the short run | | so that, given the initial stock of capital, real gross i i national product is uniquely determined once the level of j employment is determined. Each firm within the economy will hire the services| of labor in such a way that their profits will be a maxi mum, and this will be where the marginal product of labor is equal to the prevailing real wage rate. Aggregating over all firms, this relation may be stated ! (4.1.8) D/P = Sy/SN i The demand for labor function is the inverse of | i this function, or i j (4.1.9) Nd = Nd(D/P, K*) On the other hand, the supply of labor function is the summation for a given t of (3.2.110) over all suppliers I of labor, who are, by assumption, confined to the consumer sector. As before, disregarding the parameters of (3.2.110) and performing the indicated operations, the sup- ply of labor function is (4.1.10) Ns = NS(D/P, r.g, rL, B*M/P) j 327 j The first thing that will be noticed about the sup-j ply of labor function as it is presented here is that it is! markedly different from the traditional presentation in that there are additional arguments other than the real wage rate. However, the arguments that appear in (4.1.10) j i are directly implied by the supply counterparts of the sys-j tern (3.2.110); it is true that the level of employment and : the real wage rate will be uniquely determined by the in tersection of the and Ng curves in the employment-real j i wage rate plane, but it appears plausible that the position! of the supply curve in that plane is significantly influ- | enced by the level of real wealth and the opportunity-cost i of not working. This is all that (4.1.10) tries to reflect. For equilibrium to prevail in the labor market, the usual condition that demand equals supply must be fulfilled,! j i.e., | (4.1.11) % = Ng The Money Market The money market, as the term is used here, refers : to the markets for all financial goods. For purposes of | analysis, this market has been subdivided into three sub- markets: the market for the medium of exchange, the market for "short term" obligations, and the market for "long tern" obligations. In any empirical estimation of this 328 system, some scheme for determining what is "long term" and what is "short term" must be devised. One possibility that suggests itself is to define those financial instruments that are usually regarded as near monies, (e.g., time de posits at commercial banks, savings and loan association shares, and deposits at mutual savings banks) as short term obligations, and all other instruments considered in the analysis as long term. However, there are an infinite num ber of other possibilities; the actual classification cho sen would depend upon the purposes of the estimation and the individual investigator's predilections. The short run micro flow excess demand functions for financial instruments are given by systems (3.2.111)- (3.2.112), and the short run stock demand functions for the same goods are given by systems (3.2.116)-(3.2.118). On the theoretical level, we may use either stock or flow ag gregate demand and supply functions without encountering any conceptual difficulties. The problems concerning the equivalence of stock analysis and flow analysis, which were discussed in Chapter II, Section IV of this study, are not present in this model because of the concept of a "short run desired stock level" introduced in Chapter III. How ever, on the empirical level the observed changes in the stock of a particular financial instrument measures changes in the quantity of flow demand that are satisfied out of 329 newly created financial instruments and changes in the quantity of flow supply of newly created financial instru ments. However, the flow systems (3.2.Ill)-(3.2.112) also include demands that are satisfied out of existing stocks and supplies of existing stocks. Any estimation of these functions from existing statistics would, therefore, tend to bias the estimates of the coefficients in a downward direction.^ For this reason it was decided to cast the macro financial relations in stock terms. The aggregate demand function for real balances (medium of exchange) is a simplified version of (3.2.117) for a given T, (4.1.12) Md/P = MD(rs, rL, y, B*M/P, B*BS/P, B*BL/P) On the basis of the analysis of Chapter III, it is possible to derive a short run stock supply function of real balances that would contain similar arguments as does (3.2.117), except that there would also be terms to account for the influence of institutional and legal constraints on private money production. In this case we have ^Similar problems arise in the specification and estimation of the supply and demand functions of other stock-flow goods. In the case of investment, however, it is probable that trading in existing goods is so small relative to investment transactions involving newly created goods that the estimation of the flow functions from exist ing statistics introduces no significant bias. 330 <4.1.13) Ms/P = Ms(r ; rL, Y, B*M/P, B*Bg/P, B*bl/P, L*/P, b) The aggregate demand function for short term and long term obligations are derived by summing (3.2.116), for a given T, over the appropriate instruments, or (4.1.14) Bds/P = BDS(rs,-rL, y, B*m/P, B*b£ ,/P, B*BL/P) and (4.1.15) Bdl/P = BDL(rs, rL, y, B*K/I?r B*Bg/P, B*BL/P) By a similar derivation as was used in arriving at (4.1.13), we may state the stock supply functions of short term and long term obligations, respectively, as (4.1.16) Bss/P = Bss(rs, rL, y, B*M/P, B*Bg/P, B*BL/P) and (4.1.17) Bsl/P = BSL(rs, rL, y, B*M/P- B*bl/P) As before, equilibrium requires that all markets clear; hence, the equilibrium conditions are (4.1.18) Md = Mg (4.1.19) Bds - Bgg (4.1.20) BDL = Bsl 331 ! Solutions and Conclusion i One of the fundamental assumptions of short run models of the type presented in this section is that in vestment flows are so small relative to existing stocks that stock quantities can be regarded as constant. Remem- j J bering that reliable aggregate statistics are available at best on a quarterly basis, a good case can be made for this; assumption as it pertains to physical investment, but not, it will be argued here, in the instance of financial stocks.! i The length of the production period of physical 1 capital and its average life expectancy would tend to indi-j cate that the amount of physical investment that is likely to take place in some relatively short period of time (e.g., one year) would be small relative to the existing stock. However, there is no technological reason why the | i quantity of any financial instrument— or all financial in- j I struments— could not (say) double in a relatively short period of time. Then, it might be asked, why do initial real balances appear in the "real sphere" equations rather 5 ! than the current values? j It is true that the level of real balances is ^The portfolio balance terms in the money market equations should be considered as constants in a short run analysis, although they do become variable over the long run. For a discussion of this point, see supra, Chapter III. 332 j j likely to remain relatively constant in the short run due to the probable behavior of the price level consequent to a monetary expansion? this is especially true in an economy! that is initially operating near the full employment level.: i But the point is that for a short run monetary adjustment mechanism to be operational in this model, the current values of nominal balances (a variable) should appear in the indicated equations instead of their initial values (a parameter). j As an example of how this short run monetary ad justment mechanism might operate, assume that L* is auto- j 1 nomously increased to the extent necessary to cause a doubling of the desired stock supply of the medium of ex change at the prevailing prices and interest rates. If we assume the normal signs to the respective partial deriva tives, the initial response will be a lowering of the shortj i term interest rates— which will eventually spill over into the long markets— and an increase in real balances. This will cause individuals and firms to increase their desired levels of consumption and physical investment; however, j short run aggregate supply is likely to be relatively in- j elastic so that this increase in real demands will be atten uated by an increase in the price level, as well as by a leakage of money expenditures into the securities markets. The values assumed by the variables in the new short run 333 j j equilibrium position will depend upon the exact system con-I i sidered. First of all, consider the system that has been discussed so far in this section— i.e., equations (4.1.2)- (4.1.3), (4.1.5), (4.1.7), and (4.1.9) - (4.1.20) . An exami-| nation of the real sphere relations— equations (4.1.2)- (4.1.3), (4.1.5), (4.1.7), and (4.1.9)-(4.1.11)— indicates | that the real magnitudes are invariant to changes in the I supply of money as long as the price level moves propor- j tionately with changes in the money stock. An examination j of the money market equations indicates that the price ! level will increase in proportion to the change in the j quantity of money. Thus, money is "neutral" in this system, and the final equilibrium position will be characterized by unchanged real variables, lower real stocks of non monetary financial instruments, and the same real quantity i of money. ! Now, consider the system that is developed later in; this section— equations (4.1.26)-(4.1.46)— which differs from the initial system in that a government sector has been added. It is obvious that money is not "neutral" in t j this system since B*G/P appears in some of the real sphere j equations. In this system, the adjustment process might proceed as follows: as the price level increases, due to the increase in the stock supply of money, the real value j 334 of outstanding government bonds decreases which, in turn, decreases the desired level of I and increases the desired level of S. However, the decrease in real wealth shifts the N_ function to the right, lowering the equilibrium real s wage rate; thus, we are faced with a situation of falling aggregate demand and a rising aggregate supply. In the financial markets, a decreasing level of real wealth is tending to decrease both the supply and de mand functions; however, this tendency is somewhat counter acted by the decrease in the real value of outstanding instruments and the increase in real income. In the final equilibrium position, demand in the financial markets will have decreased relative to supply sufficiently to be com patible with lower interest rates.® The effect of lower interest rates on the goods and services markets is to increase I and decrease S. There fore, the new equilibrium position would probably be char acterized by higher prices (but not twice as high as the initial values), lower interest rates, perhaps greater real balances, a lower real wage rate, and a larger level of ^It should be pointed out that the monetary equa tions in this system— as well as those in Chapter III— would not be acceptable to a Quantity Theorist in that the Md function depends on the (lagged) money supply. For a Quantity Theorists's views on this, see Milton Friedman, "The Quantity Theory of Money— A Restatement," Studies in the Quantity Theory of Money, ed. Milton Friedman (Chicago: The University of Chicago Press, 1956), pp. 3-21. 335 real income. The model as it has been presented has disregarded j a sector which is empirically quite important, the govern ment sector. In recognizing the presence of the government,: many degrees of sophistication and complexity are possible; j . i the government sector presented here, however, is minimal j in the sense that real expenditures, tax revenues, and government financial transactions are considered in rather j a rigid and unrealistic fashion. That being the case, the i expenditure and tax receipts equations are (4.1.21) G a G0 (4.1.22) T/P = T(y, d) i where GQ is automonous government real expenditures on newly created goods and services, T is the nominal tax re- j i ceipts, and d is an index of the tax rate on individual j and corporate taxable income. So that the. government may run a deficit or surplus of expenditures over receipts, we shall assume that the j government finances all deficits by issuing interest bear ing obligations and disposes of all surpluses by retiring a portion of their outstanding instruments. The real stock supply of government bonds would then be (4.1.23) BSG/p = b*g//P + G ~ T//P 336 The real stock demand function for government obligations j can be stated as (4.1.24) Bdg/P -= BDG(rs, rL, rG, y, B*M/P, B*Bg/P, BW P> | and the equilibrium condition is (4.1.25) bdG= BSG | i Taking into consideration the addition of the government j sector, the model may now be restated as (4.1.26) S = S(rs, . rL, rG, Ms/P, B*g/P, y) (4.1.27) I = I(rs, rL, rG, Ms/P, B*G/P, y r H, K*) (4.1.28) G = G0 (4.1.29) T/P = T(y,d) (4.1.30) y = y(N, K*) (4.1.31) S-I = G - t/P (4.1.32) Nd = Nd(D/P, K*) (4.1.33) Ns = Ns (D/P, rs, rL, rG, ,MS/P, b*g/p) (4.1.34) % = Ns 337 (4.1.35) Bdg/P =.BDG(rs, rL, rQf. y, B*M/P, B*G/P, b*bs/p , b*bl/p) (4.1.36) Bsg/P =.B*g/P + G - T/P (4.1.3 7) Bdg = Bsg (4.1.38) Md/P = MD(rs, rL, rQ, y, B*m/P, B*g/P, B*bs/P' B*bl/P) (4.1.39) Ms/P = Ms(rs, rL, rG, B*M/P, B*BS/P, B*BL/P, L*/P/ b) (4.1.40) Md = Mg (4.1.41) BDS/P = BDS(rs, rL, rG, y, B*M/P, B^P, b*Bs/P' b*bl/p) (4.1.42) Bgg/P = Bgg (rg/ rL, rG, y, B*M/P/ B*q/P, b*bs/p' bW p) (4.1.43) BDS = Bgg (4.1.44) Bdl/P = BDL(rs, rL, rQ, .y, B*M/P, B*G/P, b*bs/p, b*bl/p) 338 (4.1.45) BgL/P = BSL(r.s, rL, rG, y, B*m/P, B*G/P, B*BS/P' BW P> (4.1.46) Bdl = .BgL This system of twenty-one equations contains twenty endogenous variables— rs, rG, P, y, S, I, G, T, D, N^, V b d g ' b s g ' V V b d s ' b s s ' b d l ' 30 ,1 Bsi--and ten exog- enous variables~B*M, B*Qf B*BS' b*BL' k*' l*' K, d, and G0; it is, by the counting rules, seemingly an overdeter mined system. However, by Walras1 Law, one of the above equilibrium conditions is not independent; therefore, there are only twenty independent equations. Hence, under cer tain conditions the above twenty independent equations can be solved for the twenty unknowns. With regard to the specification of this system, it should be pointed out that all of the equations, with the exception of (4.1.33), satisfy the order condition for "over" identified relations; equation (4.1.33) satisfies the order condition for a "just" identified relation. This is only true, of course, if all of the specified coeffi- 7 cients are significant. Having considered one of the many possible deriva tor the order conditions for identification, see Gerhard Tintner, Econometrics (New York: John Wiley & Sons Inc., 1952), p. 157. 339 tions of a "macro" system from the analysis of Chapter III, it is now time to move on to a consideration of a "micro" system. We shall have more to say about the model of the next section because the analysis will be carried one step further; i.e., we shall attempt to bring empirical evidence to bear on the hypotheses presented there. II. A MICRO MODEL In the review of the Gurley-Shaw work presented earlier in this study, it was pointed out that one of their most important, and certainly most controversial, hypothe ses was that money (narrowly defined) and the liabilities of non-monetary intermediaries are close substitutes in demand.® This section will be devoted to the construction of a model that is capable of empirically testing this hypothesis. The context in which the "Gurley-Shaw hypothesis" becomes most important is that of monetary policy. Assume, for example,_that the monetary authorities wish to pursue a "tight" monetary policy in order to drive the spectrum of interest rates up, and that they do this by selling private domestic instruments. 8John G. Gurley and Edward Shaw, Money in a Theory of Finance (Washington, D.C.: The Brookings Institution, 196"0]r 340 At the higher interest rate, spending units have lower real demands for money [narrowly defined] and nonmonetary indirect assets; the aggregate real size of intermediaries is reduced. At the same time, how ever, the uncontrolled intermediaries are now willing to supply more claims on themselves at their prevail ing deposit rate. Given this deposit rate and the deposit rates of the monetary system, a higher inter est rate and a lower price level can be reached at which spending, units are temporarily satisfied with their real holdings of financial assets. This higher interest rate would "stick" if nonmonetary interme diaries were prevented from taking further action. But at their present deposit rate there is now an excess supply of nonmonetary indirect assets. This leads to a rise in their deposit rate, which in creases spending units1 real demand for nonmonetary indirect assets and reduces their real demand for money [narrowly defined] and primary securities. The short run effect is to lower the interest rate below what it otherwise would be and to raise the price level. In this way the effectiveness of mone tary policy is watered down by the activities of uncontrolled intermediaries.9 The effectiveness of monetary policy is, therefore, reduced for two reasons: the increased elasticity of the demand function for narrow money due to the presence of close substitutes, and the shifts in the demand function for narrow money due to changes in the prices of closely related goods. Thus, for a given change in the quantity of money, the relevant interest rates will change less if there are close substitutes for money than they would in the absence of any close substitutes. It should be empha sized that financial intermediaries do not render monetary 9Ibid., p. 240. 341 policy useless, it just diminishes its effectiveness. If, on the other hand, the presence of non-monetary financial intermediaries decreased the stability of the demand for money function, monetary policy would be severely hampered. The Equations that our concern should be with the demand functions of the financial instruments whose substitutability is to be in vestigated. For the same reasons given in the first sec tion of this chapter, we shall work once again with stock demand functions; these are reproduced below— from (3.2.116)-(3.2.1 1 7)— for non-monetary financial instruments and the medium of exchange: The nature of the problem outlined above indicates (4.2.1) (P/Pj) Dj (p^, P2 ,..., Pv_^ / ' * * * ' P]j/P Pi3?"1/?..... Pv-lSv-l/P' sv"1/p' L/P' v+l' ' s?"1, A, b,: x**"1, < j > , n) (j=l, 2 v-1, T=0, 1 / * • • r M) (4.2.2) T (P)Dv (p^, p^, • • • , Pv_]y Pv+l//fp,***f Pm^p' PxS^-Vp ; • * * (T=0, 1 M) f • • • f 342 | I The first question that arises concerns what finan-| cial instruments, in addition to the medium of exchange, ! should be considered. Undoubtedly, most financial and non-; financial goods are substitutes to some extent; however, from the point of view of the Gurley-Shaw hypothesis, it is j only short term, highly liquid financial instruments that are of interest. This still leaves a rather wide range of choice; on the basis of the interest shown in the litera ture, however, the most likely candidates are time deposits| at commercial banks, savings and loan association shares, | in and deposits at mutual savings banks. For reasons that j will be discussed in the next chapter, only time deposits at commercial banks and savings and loan association shares will be considered in this study. Now consider the system (4.2.1)-(4.2.2) for any T; j in the consideration of substitutability or complementarity j between various goods, the prices and interest rates of goods and services that are not being explicitly considered may be placed in the ceteris paribus conditions, and the “ i stocks of these same goods may be aggregated into a net wealth figure without introducing a significant bias into the estimates. We may also ignore the matrix A and the lOsee Edgar L. Feige, The Demand for Liquid Assets:, A Temporal Cross-Section Analysis (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1964). 343 parameters b, $, and r j because they are unlikely to signif icantly change over relatively short periods of time; and, finally, the parameter x'^-^ may be ignored on the grounds that it is unlikely to significantly influence the subject demand functions. Using interest rates instead of prices, and letting T m rP rp D'j equal PjDj and S'^ equal P j S j , the simplified stock demand functions may be stated as (4.2.3) D*d = (P)D'd(rd, rt, rg, S'd/P, S't/P, S'g/P, y/p ) (4.2.4) D't = (P)D't(rd, rt, rg, S'd/P, S't/P, S'g/P, Y/P) (4.2.5) D’s = (P)D's(rd, rt, rg, S*d/P, Sft/P, S's/P, y/p) where D'd, D't, and D's are the nominal demands for demand deposits, time deposits at commercial banks, and savings and loan association shares, respectively; rd (a negative quantity), rt, and rg are the rates of return on demand deposits, time deposits at commercial banks, and savings and loan association shares, respectively; S'd* an<^ S't/ and S's are the initial nominal stocks of demand deposits. 344 time deposits at commercial banks, and savings and loan association shares, respectively; and y is nominal net wealth— in this case we use nominal "permanent", income as a proxy for nominal net wealth. The nature of the data used in the estimations per formed in Chapter. V is such that reliable estimates of price deflators are not available (cross sectional data on a statewide basis are used). We would, therefore, like to state the arguments in (4.2.3)-{4.2.5) in nominal terms; explictly multiplying through by P (the price level), a typical demand function would appear as (4.2.6) D'j = Prt, Prs, S'd, S't, S's, y) But, as was pointed out before, price level statistics are not available on the data used in this study; hence, the unadjusted interest rates are used in the estimation. One would suspect, therefore, that the estimated interest rate coefficients are larger than they would have been if the correctly specified stock demand functions were in fact estimated. Thus, the demand functions that will be used in this study are: ■^Tf a price index were used, the. estimated coeffi cients would be larger, smaller, or unaffected, depending upon how the price level behaved relative to the base period. 345 (4.2.7) D 1 d = D'd(rdf rt, rs, S'd, S't, S*s, y) I (4.2.8) D 1 = D'.j_(rd, rs# ^'d* ^'t* ^'s* ^ (4.2.9) D's = P's(rd, rt, rg, S'd, S't, S's, y) A linear form of these relations will be estimated and tested in the next chapter. However, one important ques tion still remains unanswered: What is an appropriate measure of the degree of substitutability?— a question thati we shall now turn our attention to. i Alternative Measures of j Substitutability ; The traditional definition of substitute or com plementary goods is in terms of the shapes of their indif ference curves: goods that are perfect substitutes are characterized by linear indifference curves, while goods that are perfect complements are characterized by indiffer ence curves that are pairs of straight lines that meet at right angles.12 The shapes, of the indifference curves for pairs of goods that do not conform to these two extremes will lie somewhere between a straight line and a pair of I 1^This definition of perfect substitutes and per fect complements is due to Irving Fisher. See his "Mathe matical Investigations in the Theory of Value and Prices," Transactions of the Connecticut Academy of Arts, and Sci ences, IX (July, 1892), pp. 76-85. 346 right-angled straight lines: the "flatter" the curve, the closer substitutes are the two goods; the "less flat", the curve is, the closer, complements are the two goods. This definition of substitutes, and complements has led to the development of various indicators that are capa ble of showing whether two goods are complementary, substi tutes, or independent in demand. One is the sign of the jth price coefficient in the i* ” * 1 demand function, and an other is the cross elasticity of demand. If consumers act rationally— i.e., if A is a substitute to B, then B is a substitute to A— these two indicators are equivalent in the sense that they will both give the same answer; this is be cause, assuming that all prices and quantities consumed are positive, the sign of the cross elasticity will be deter mined by. the sign of the cross price coefficient. To illustrate the criteria for judging the type of interdependence in demand involved, if any, and the poten tial pitfalls in their interpretation, consider the follow ing two demand functions. X1 = cllpl + c12p2 (4.2.10) x2 = c21pl + c22p2 where x^, X2 and p-^, P2 are the quantity demanded and prices, respectively, of goods 1 and 2, and the c's are the 347 respective coefficients. Considering only the first rela- i tion in (4.2.10), the rules are as follows: If (9x1/3p2)(p2/xi) > Of or if c12 > 0, the goods are substitutes in demand. If (3x1/3p2) (P2/Xl) < °f or c 12 < the. goods are complements in demand. If (9x^/3p2)(p^/xj) = 0, or if c^2 = the. goods are independent in demand. Except in the case of perfect substitutes— where j i the cross elasticities are infinite— neither the coeffi- i cients nor the cross elasticities are capable of giving anyj indication of the degree of substitutability or complemen tarity between the goods in question. In the case of the K cross price coefficients, this is obvious from the' non comparability of the units in which quantity and prices are measured; in the case of cross elasticities, this is easily demonstrated ,by a simple example. Assume that two goods are in fact close substitutes, and that the respective prices and quantities in the neighborhood under considera tion are as follows: p^ = 10, p2 = 5, x^^ = 1,0 0 0, and x2 = 100,000. If it is assumed that the quantities are measured in the same units and,that the demand functions are linear, one would expect that the cross price coeffi- 348 cients would be identical; assume that c^2 = ci2 ~ ' 0 0 0 * 13 The cross elasticities are then e-^ = t5 ®21 = i Are we to assume from this that good 1 and good 2 are relatively close substitutes, but that good 2 and good 1 are not? This is, of course, a misinterpretation of what information a cross elasticity is designed to convey. The point is that cross elasticities or the magnitude of the cross price coefficients are incapable of being used | as a measure of the degree of substitutability or comple- j mentarity. When turning our attention from goods in general to financial goods, however, certain modifications in the in terpretation given to an indifference map are necessary. One of the basic points made in Chapter III of this study 1 was that individuals are concerned with the real value of financial instruments— i.e., price times quantity deflated by the price level— rather than with the quantity of finan cial instruments. This means that indifference curves for , financial goods lie in the real price times quantity planes,; 13This refers to the so-called "integrability con ditions" of rational consumer behavior which, under, certain conditions, may be extended to the market function. On this, see Henry Schultz, The. Theory and Measurement of De mand (Chicago: The University of Chicago Press, 1938T, pp. 575-582, 630. 349 j and not in the quantity planes as is the case of physical goods and services. Thus, a point on an indifference curve can no longer be used to compute the amount of one good that an individual is willing to give up in order, to gain another amount of a different good. In the case of stocks ; of financial goods, an indifference curve represents levels; of indifference in the relative stocks that an individual holds in his portfolio— any trading that takes place will be done on a one dollar to one dollar basis. No rational j individual would e.g., trade $3 worth of General Motors j bonds for $1 worth of demand deposits. It is also possible to consider indifference maps between a financial stock and a non-financial stock, and indifference maps between financial flows and consumption flows. In both of these cases the slope of an indifference: curve does, as in the case of non-financial flows, repre- j sent ratios at which the individual is willing to trade. The. case that is being considered here, however, is the case of two financial stocks, and in investigating their substitutability or complementarity. For price changes, the reinterpretation of an indifference map does not change the definition of substitutes or complements in terms of the shapes of the indiffernce curves; however, the portfolio approach does suggest another concept that is potentially quite important in the study of the interdepen-j 350 dence in demand of two stock goods. To illustrate the implications of the portfolio approach to considerations involving financial instruments, consider the following indifference map of an individual economic entity. FIGURE 6 THE "PORTFOLIO EFFECT" Assume that goods 1 and 2 are only two of several elements in an individual's portfolio, and that neither of these goods -are inferior with respect to wealth. Each in dividual is constrained in his portfolio holdings by his level of real wealth, and the wealth constraint for any two goods is determined by the proportion of total wealth that 351 I is allocated to these two goods in the individual's port- i folio during the present week; hence, the intercept on both; axes is given by + an<3, the constra^nt lines aa and bb form a forty-five degree angle with both axes. I With a given initial stock, income, prices of other stocks,^ etc., the individual is initially in equilibrium at A. Nowi assume that p2 falls— thus the wealth constraint shifts parallel to itself because the goods still trade on a $1 to: $1 basis— so that, given the initial conditions and assum ing no constraints on the actions of the individual, the individual is now in equilibrium at B. It should be j pointed out that it is not necessary for P2Q2/P at B to be 1 larger than P2Q2/P at A for a fall in P2; economic theory dictates that the quantity demanded should increase as price decreases for non-inferior goods, but there is no ; requirement that price times quantity also increase— this is a function of the price elasticity of quantity demanded. Hence, a point such as Z is a possible equilibrium position at the new level of Pj. Assuming that the individual adjusts to his new preferred position during the current week, at the begin- ; ning of the next week the individual will find that he now has a different initial stock of these two goods; he now has Oe of good 1 and Of of good 2. One of the initial con ditions has been altered, and the entire indifference map 352 will shift at the beginning of this new week, and the indi vidual will reappraise his entire portfolio level and com position. If the indifference system shifts so that the new equilibrium position is C— i.e., for a larger initial stock of good 2 the individual desires a larger stock of good 1— we shall say that the two goods are complements for portfolio purposes; if, on the other hand, the indifference system shifts1 so that the new equilibrium position is D— i.e., for a larger initial stock of good 2 the individual desires a smaller stock of good 1— we shall say that the two goods are substitutes for portfolio purposes. Or, to turn the argument around, for a smaller initial stock of good 1 the individual wishes to hold a smaller stock of good 2 if they are complements (point C), and for a smaller initial stock of good 1 the individual wishes to hold a larger stock of good 2 if they are substitutes (point D). The points C and D may lie above, below, or on the wealth line bb; their exact position relative to bb is determined by the equilibrium distribution of net real wealth between the rest of the individual's portfolio and goods 1 and 2 in the new week. However, it seems more probable that they would lie on or above bb in that a movement to below bb would imply that the real wealth elasticities of p-^Q^/P and P2Q2/P are greater than one (i.e., both goods would have to be "luxury" goods for C and D to lie to the left of bb). 353 It should be pointed out that indifference curves such as those drawn in Figure 6 are not capable of being used to separate out the income, substitution, and wealth effects. To accomplish this, it is necessary to work with indifference curves drawn to quantity axes— an attempt was made to do this in Figure 1. Further, it should also be pointed out that, assuming that the same two goods are con sidered in both cases, the indifference curves in Figure 1 are entirely different than those in Figure 6 because of the difference in the independent variables of the analysis real values of the stocks are used in the latter, whereas quantities are used in the former. To keep the argument straight, the movement from A to B in Figure 6 will be referred to as the "price effect," and the movement from B to C (or D) will be referred to as the "portfolio effect"; the price effect can, of course, be separated into the income, substitution, and wealth effects With regard to the price effect, the traditional indicators of interdependence in demand discussed earlier will not give an.unambiguous indication as to whether two goods are substitutes or complements on the. individual level when the two goods in question are financial stocks. For non-inferior financial stocks, one would expect the wealth effect to work in the opposite direction than the income and substitution effects; thus it is possible that 354 the cross elasticities or cross price coefficients could give an erroneous indication if the wealth effect out weighed the income and substitution effects. For example, ! assume that goods 1 and 2 are in fact close complements, | and that p£ falls relative to p^? if the wealth effect out-! weighed the income and substitution effects, it is possible; that the desired dollar value of the stock of good 1 would also fall, which would yield a positive cross elasticity ; implying that the two goods are substitutes. An indication; of the presence of a situation in which the wealth effect ] outweighs the income and substitution effects is available j in the sign of the own price coefficients; if the own price! coefficient has the "wrong" sign (i.e., if it is positive),! and price times quantity variables are being used, there is; •good reason to suspect that the wealth effect outweighs the other two effects. Where price times quantity is the unit j of measure, we would expect to observe this phenomenon in situations where the price elasticity of quantity demanded is less than unity. If it is assumed that debtors and creditors react symmetrically for changes in their real wealth positions, ' the non-monetary financial wealth effect disappears from the aggregate demand and supply functions, and the cross elasticities and cross price coefficients will, give an un ambiguous indication of the type of interdependence in 355 ! I demand involved. To relate the above discussion to the empirical demand functions that will be estimated in the next chap ter, we shall write the relations to be estimated in linear; form, viz. (4.2.11) D'd = c10 + ci;Lrd + c12rt + c13rs + c14S'd + c15s't+ c16s's + C17Y (4.2.12) D't = c20 + c21rd + c22rt + c23rs + c24S'd j + c25S't + c26S's + C27Y (4.2.13) D's = c30 + c31rd + c32rt + c33rg + c34S'd + c35S't + C36S's + C37y The interpretation of the cross portfolio balance ; term coefficients in these functions— e.g., c3^ and c33 in (4.2.13)--is not comparable with the type of adjustment just outlined in that the arguments in (4.2.11)-(4.2.13) imply that total real wealth and interest rates (prices) are held constant. However, suppose that the individual is initially in equilibrium at point A in Figure 6 and.that, after the markets have all closed in some "week," his stock of good 2 is increased by df, and that his total real wealth is held constant by taking an offsetting amount of 356 good 3 away from him. He is now at point E in Figure 6 which, by the appropriate choice of df, we shall assume is an equilibrium point with the given indifference map. Before the markets open on "Monday" of the next "week" (i.e., before prices have an opportunity to change.), the individual is asked what stock of good 1 he now desires to hold with the changed initial stock of good 2. If the new equilibrium position lies above line cAE, the goods are said to be the complements for portfolio purposes; if the new equilibrium position lies below line cAE, the goods are said to be substitutes for portfolio purposes. If a number of conceptual experiments of this type are performed on an individual, a series of points in the S'j-D1^ (i^j) plane will be generated. The portfolio bal ance term coefficients in (4.2.11) - (4 .2.13) are a measure of the slopes of the lines generated by a series of such experiments aggregated over all individuals. The signs and magnitudes of the cross portfolio balance term coefficients are therefore a measure of the portfolio effect. Now, consider (4.2.11); provided that the portfolio balance (independent) variables and the dependent variable are measured in the same units and the functions are linear, the interpretation is as follows: for every, one unit of time deposits added to the aggregate portfolio, economic units wish to add (subtract) c^ units of demand deposits, 357 ceteris paribus; and, for every one unit of savings and loan association shares added to the aggregate portfolio, economic units wish to add (subtract) c^g units of demand deposits, ceteris paribus. The interpretation of the port folio balance coefficients in the other equations is com pletely analogous. Using the standard definitions of perfect comple ments and perfect substitutes,14 perfect substitution or complementation for portfolio purposes may be defined by the form and slope of the function describing changes in D’ j for changes in S1^ — what we call the "portfolio * balance relation." If the goods are perfect substitutes for portfolio purposes, the portfolio balance relation will be linear and negatively sloped; if the goods are perfect complements for portfolio purposes, the portfolio balance relation will be linear and positively sloped. For purposes of investigating the Gurley-Shaw hy pothesis, however, it is desireable to distinguish between varying degrees of substitutability or complementarity. The division used here is completely arbitrary and perhaps has use only in the investigation of the questions ad dressed in this study; alternative dividing lines may be more useful in the study of other questions. Perfect sub stitutes and perfect complements of the first degree are 14Ibid., pp. 570-571. 358 I defined by the condition that the slope of their portfolio j balance relation is plus or minus unity, respectively. A distinction of this type is important in considering the following type of situation: Suppose that the monetary I authorities wished to decrease the supply of money relative j to the demand for money to drive "the" interest rate up. Assume, however, that the value of cjg in (4.2.11) was minus unity, so that one unit of demand deposits is "equiv-i alent" to one unit of savings and loan association shares I : • ' | for portfolio purposes. Depending on the supply conditions j in the savings and loan association share market, it is ; conceivable that the non-monetary sector could decrease their demand for demand deposits (with a one week lag) by adding to their holdings of savings and loan association shares to the extent necessary— which, in this case, is adding one dollar of savings and loan association shares | j for every dollar of the medium of exchange given up— to | keep the rate of interest fixed at its original position. Obviously, the larger (in a negative direction) the cross r portfolio balance term coefficients in the demand function for the medium of exchange, the greater, the possibility of completely frustrating monetary policy without driving the ! interest rates on alternative instruments down; the smaller these coefficients, the less likely it becomes because of the probable adverse interest movements as the demand for alternative instruments increases. 359 However, care should be taken in the interpretation of any given coefficient. Assume, for example, that the coefficient 0^5 has the value - 5 ; logic would dictate that the corresponding cross portfolio balance coefficient in the time deposit demand equation, i.e., C2 4, would have the value of - 1 / 5 . In other words, a large coefficient for any one portfolio balance term implies a small coefficient for the corresponding cross portfolio balance term. Hence, any measure of the degree of perfection of the interdependence in demand must take due account of the potential absolute deviations from (plus or minus) unity, which, of course, depends upon whether the deviations are toward or away from zero— i.e., whether, for example, c^g or C24 is considered. This discussion also implies that there are certain a priori restrictions that should be placed on the cross portfolio balance coefficients. If the interpretation pre sented above is correct, one would suspect that the coeffi cients bear the following relationships to each other: ( 4 . 2 . 1 4 ) c15 = 1 / c 2 4 c 16 = I / C 34 c26 = I / C 35 1 Conclusion It has been argued above that the traditional indi cators of substitutability and complementarity are inca pable of measuring the degree of interrelationship in de mand between two goods. In the case of stock-flow goods, 360 however, there is another concept that is useful in the study of interdependence in demand; this is what we have i called the portfolio effect. It was found that the cross portfolio balance term coefficients are a measure of the substitution or complementation trade-off ratios between two goods in the sense that they represent an "equivalency" factor in portfolio composition. This measure has certain desirable properties for an investigation of the Gurley-Shaw hypothesis. As was pointed out earlier, monetary policy could be drastically I impaired if the "equivalency" factor between demand depos- | its and some near money— e.g., c-^g— were 250 to one. The stock demand functions derived from a portfolio approach give a measure of these "equivalency" factors. In the second place, it is not altogether certain whether the price effect is the most important influence effecting changes in quantity demanded and quantity sup plied of financial instruments? it is possible that the longer run portfolio adjustments are the determining factor j in price-quantity determination. Once again, the portfolio approach as reflected in (4.2.11)-(4.2.13) takes into con sideration portfolio adjustments. The form of the equations specified in this section, however, does suffer from the weakness that it assumes that all adjustments take place in one "week." It is possible, for example, that some distributed lag arrangement might explain the adjustment path better than the scheme pre sented here. In the final analysis this is an empirical question, and a good deal of empirical experimentation with different functions will be needed before any answer can be given. No attempt will be made in this study to address this question. In the next chapter, we shall attempt to empiri cally test the Gurley-Shaw hypothesis using the functions and criteria developed in this section. Additionally, the testing procedure will bring evidence to bear on the "va lidity" of the portfolio approach as an explanatory frame work in economics. CHAPTER V ESTIMATION AND RESULTS In the empirical investigation being conducted in this chapter, there are basically two hypotheses; the first hypothesis is that demand deposits and certain other highly "liquid" financial instruments are close substitutes in demand, and the second hypothesis is that the portfolio * approach is a superior vehicle for studying and explaining financial behavior than are the alternative approaches one finds discussed in the literature. Although these are two separate and distinct hypotheses, the structure of the model developed earlier indicates that they cannot be considered as being independent in the sense that the test used to determine the degree of substitutability or complementarity for portfolio holdings depends on the usefulness of the portfolio approach. In other words, if the restrictions implied by the portfolio approach on the coefficients of the cross portfolio balance terms— which were developed in Chapter IV, Section II— do not hold, the empirical conclu sions derived from the estimates concerning the degree of substitutability or complementarity for portfolio purposes of the various instruments cannot be taken as valid evi dence . 362 363 As was pointed out in the introductory chapter of this work, economists are at a great disadvantage when it comes to the testing of their theories for the reason that,I in general, laboratory experiments are not feasible. The tests that economists do perform, therefore, are likely to ; be biased due to the inaccuracy or unavailability of data and the relatively crude statistical techniques that are available for handling their particular problems. For ex- : ample, regression analysis has been the standard tool for the testing of economic theories even though it is well known that the assumptions of regression analysis are sel- ; i dom if ever fulfilled by economic data. In spite of these difficulties, we shall attempt to estimate linear stock demand functions as expressed by (4.2.11)-(4.2.13) by a least squares technique, and to test the two hypotheses. If the efficacy of the portfolio ap proach as an explanatory device is substantiated, we would expect the respective cross portfolio balance term coeffi cients to be reciprocals; and, if demand deposits and the other financial instruments considered are "close" substi tutes in portfolio holdings, we would expect the absolute value of the coefficients of the cross portfolio balance terms in the demand deposit equation to be greater than or equal to (minus) unity. These are the criteria we shall employ in judging the results. 364 I. DATA USED AND DEFINITION OF VARIABLES The data used in this study is a ten year time series of cross sectional observations obtained from the Feige study cited earlier, and was gathered for the years 1950-1959 for the then thirty-one states of the United States that did not have mutual savings banks operating within them and the District of Columbia.^ Although obser vations are also available on mutual savings bank interest ; rate and quantity variables, their inclusion in this analy-j sis was rejected because it was felt their presence would introduce multicollinearity into the estimations. The potential multicollinearity arises from the necessity of introducing a dummy variable into each estimated equation i to account for the absence of observations on mutual sav ings bank variables in thirty-two cells in each cross sec- , tion; thus, a high degree of (non-linear)' correlation is achieved between the dummy variable and both the interest rate and quantity variables. For example, assume that the dummy variable (V) is assigned the value of one for mutual savings bank states, and zero for non-mutual savings bank states; a scatter diagram between V and the yield on mutual' savings bank deposits (rm) would have the following shape: ^dgar L. Feige, The Demand for Liquid Assets: A Temporal Cross-Section Analysis (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1964), pp. 66-87. 365 3 2 O FIGURE 7 THE IMPLICATIONS OF DUMMY VARIABLES The fact that the size of the standard errors relative to the coefficients in almost all cases is lower in the esti mations that were made exclusive of mutual savings bank variables than in comparable functions that included mutual savings bank variables tends to confirm this hypothesis. The variables are defined as follows: D1^ The dollar value of per capita commercial bank deposits outstanding in the current period. D't The dollar value of per capita commercial bank time deposits outstanding in the current period. 366 D's The dollar value of per capita savings and loan association shares outstanding in the current period. r^ The "actual" interest rate on commercial bank demand deposits in the current period— a negative quantity. The "actual" interest rate on commercial bank time deposits in the current period. rt rs The "actual" interest rate on savings and loan association shares in the current period. S 1 a The dollar value of per capita commercial bank demand deposits outstanding in the immediately preceding period. S't The dollar value of per capita commercial bank time deposits outstanding in the immediately preceding period. S's The dollar value of per capita savings and loan shares outstanding in the immediately preceding period. y "Permanent" per capita personal income. The "actual" interest rates on time deposits at commercial banks and savings and loan association shares were computed as the ratio of total interest payments j |during a particular period to the average balance outstand- I i ing of the instrument during the period. In the case of demand deposits, the numerator is the total service charges |levied on this type of instrument; hence, the interest rate on demand deposits is a negative quantity. "Permanent" personal income is a weighted average of present and past levels of personal income. The weights used in the calcu- i llation are those computed by Milton Friedman in his work 367 on the consumption function.^ Our data are essentially of two different types: cross sectional observations and time series observations. Unfortunately, neither type consists of enough data points to allow much confidence to be placed in any estimates de rived from them; thus, to obtain a sufficient number of degrees of freedom— something that the econometrician is always short of— from which fairly reliable inferences may j be drawn, certain of the estimates that follow will be de rived from a direct pooling of the cross-sectional and time series data. We now turn our attention to certain problems that arise when this type of data are used. i II. METHOD OF ESTIMATION The technique employed in testing the hypotheses discussed earlier is to compute single equation estimates of the demand functions for demand deposits, time deposits i | at commercial banks, and savings and loan association j | shares, specifying that they have the arguments and form j indicated in (4.2.11)-(4.2.13). The sample used in the estimation procedure is a ten year time series of cross j sectional data; each cross section consists of thirty-two | ] observations. I ^jytiiton Friedman, A Theory of the Consumption Func- \ tion (Princeton: Princeton University Press, 1957). 368 3 Following the work of Nerlove and Balestra, we may assume that we have observations on N individuals (n=l, 2, . . ., N) all taken over T periods of time (t=l, 2, , T). The variable that is to be explained will be denoted by ynt/ which is assumed to be explained.by K truly exogenous ,1 Jnt' . rr variables z ^,..., an<^ lagged values of the dependent variable. To express the relationship in matrix form, let y = an NT x 1 vector; z = *11 yiT- Nl ■NT I K Z • • • Z i i II 11 z1 iK NT NT an NT x K matrix of truly exogenous variables; ■^See Pietro Balestra and Marc Nerlove, "Pooling Cross Section and Time Series Data in the Estimation of a Dynamic Model; The Demand for Natural Gas," Econometrica, XXXIV (July, 1966), 585-612; and Marc Nerlove, Estimation and Identification of Cobb-Douglas Production Functions (Chicago: Rand McNally & Company, 1965), ppT 157-190. an NT x c matrix of lagged values of the dependent variable; and UNT an NT x 1 vector of residuals. Also, let a be a K x 1 vec tor of constant coefficients of the exogenous variables, and 3 a c x 1 vector of constant coefficients of the lagged endogenous variable. Throughout this discussion we shall ignore the constant term. The relation to be estimated may now be written (5.2.1) y = otZ = 3YC + u For purposes of arriving at the characteristics of the estimates of a and 3, it is necessary to make certain as sumptions regarding the residual vector u. We shall assume that each individual unt may be separated into two statis tically independent parts: an individual effect, and a remainder, viz., 370 (5.2.2) un£ - i i n + v ^ and that each part has a zero mean, and is independent (5.2.3) for all n, t It is further assumed that there is no serial correlation among the v and that each part is independent from one individual to another, If no lagged values of the dependent variable ap pear as independent variables in (5.2.1)— i.e., if £ is identically equal to zero— ordinary least square, estimates of the coefficients are, under the above assumptions, un biased and consistent; but they would not be minimum vari- 4 ance or, xn general, asymptotically effxcxent. If, on the other hand, lagged values of the depen dent variable do appear as arguments in (5.2.1)— i.e., if ^For an estimation procedure that is designed to increase the efficiency of the estimates, see Arnold Zell- ner, "An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias," journal of the American Statistical Association, LVII (June, 1952), T4T9- n=n1 and t=t' 0, otherwise EUnVn' 0, . otherwise n=n 371 p does not identically equal zero— the ordinary least square estimates of the coefficients are no longer consistent. This is because the lagged values of the dependent variable "are correlated with the current values of the residuals unt since they are determined to the same degree as the 5 current value of the dependent variables by un." As Nerlove goes on to point out, this is the same problem that arises in the estimation of one of a system of simultaneous equations that involves more than one endogenous variable of the system. In Nerlove's own words, In this case, if one of the endogenous variables is chosen as dependent, and the rest are treated ae if independent in a least-squares regression, the re sults are inconsistent because of the correlation between the endogenous variables treated as indepen dent and the residual of the equation. One solution to this difficulty is to use as instrumental variables a sufficient number of other exogenous . . . variables appearing elsewhere in the system in the formation of the "normal" equations so that the current endogenous variables in the equation need not be used for this purpose. The difficulty, of course, is that there are usually more than enough predetermined variables for this purpose, and a choice must be made among them. One of Theil's contributions in the development of two-stage least-squares was to show how such a choice could be avoided by selecting as instrumental variables those linear combinations of all predeter mined variables most highly correlated with the cur rent endogenous 'variables whose values they replaced in forming normal equations.6 ^Nerlove, 0£. cit., p. 177. Ibid., pp. 177-178. For a discussion of the iden tification problem couched in these terms, see E. Malinvaud, Statistical Methods of Econometrics (Chicago: Rand McNally i & Company, 1966), pp~534-540. 372 i i Nerlove’s answer to the problem that arises when lagged values of the dependent variable are introduced also; runs in terms of a two-stage least square estimation pro cedure. The t * '* 1 equation for the n ^ individual may be j written K k c (5.2.5) ynt = ^ „k Z„t + ^ 6C ynt_c + unt which, under certain conditions, has the solution K C O (5.2.6) ynt = ^ c^ ^ t-C + Wnt Relation (5.2.6) for n=l, 2,..., N, and t=l, 2,..., T, may be looked upon as the reduced form of (5.2.5); or, to put the relation in more conventional notation, the first stage is given by K - k (5.2.7) y*_j_ = 2 z„+. + . . . nt " A0 nt The lagged values of (5.2.7) may then be used as instru mental variables in the estimation of K c (5.2.8) y t - z ak znt + 2 3 Y*nt-C + unt k=l C=1 u It can be shown that the ordinary least square estimates of 7 the coefficients a and 3 in (5.2.8) are consistent. 7 See Nerlove, ojd. cit. , pp. 180-182, 373 This method of estimation is not to be confused' with the so-called "extraneous estimates" often found in demand studies., where e.g., time series data is used to ad just coefficient estimates obtained from cross sectional g data. This is a method to eliminate multicollinearity; the method proposed here, on the other hand, is merely to insure consistent estimates when lagged values of the en dogenous variable appear as arguments in a single equation estimation using a pooled sample of cross section and time series data, and nothing more. III. RESULTS MID INTERPRETATIONS The pooled estimates of the demand functions for demand deposits, time deposits at commercial banks, and 1 savings and loan association shares are based on the fol- I lowing assumptions: j \ I 1. The form of the demand functions is linear, and : the slope and intercept coefficients are the ^For an example of a type of extraneous estimation procedure often used in demand analysis, see Richard Stone, | Measurement of Consumers1 Expenditure and Behavior in the United Kingdom, 1920-1938 (Cambridge: Cambridge University Press, 1954), pp. 272-278. For an analysis of the validity of this procedure, and an indication of the relationship of cross section and time series estimates, see Edwin Kuh, "The Validity of Cross-Sectionally Estimated Equations in Time Series Applications," Econometrica, XXVII (April, 1959), 197-214; and Edwin Kuh and John R. Meyer, "How Extraneous Are Extraneous Estimates?" The Review of Economics and Statistics, XXXIX (November, 1957), 380-393. 374 i same for each state and time period for the variables included in a particular function. 2. The level of the supply curve differs between states and time periods, and is independent of the variables that shift the demand curve. This, in essence, assumes away the identifica tion problem, and assumes that we are observing I the market outcomes of the interactions of a stable demand curve and an unstable supply j curve. 3. The variance of each variable is constant and j i equal between states and time periods; i.e., we [ assume homoscedasticity. 4. The economic behavior of any economic entity in a given state is only influenced by economic conditions in that state. 5. To conduct significance tests, we assume that the residuals un^ are normally and randomly distributed. Although only pooled estimates of the deamand func- ; tions are given in the text of this section, estimates of 5 the same functions derived from cross sectional data for the years 1950-1959 are presented in Appendix I of this chapter. Also, pooled estimates of these same demand func tions exclusive of the portfolio balance terms are presented 375 for comparative purposes in Appendix II. Following the distinction usually found in studies ; of demand relations, the estimates derived from cross sec- | tional data may be identified with relations that describe I the shape of the demand function at a particular point in time— i.e., these are short run demand functions. On the other hand, estimates, that are derived from time series data may be identified with relations that describe the shape of the. demand function over several periods ot time— j i Q i.e., these are long run functions. The pooled estxmates ; presented here, however, constrain the short run estimated j j coefficients to be constant over time which, in general, will lead to lower empirical multiple correlation coeffi cients. The. estimates derived in this study are truly "single equation estimates" in the sense that all of the independent variables in each demand relation are assumed to be exogenously determined; this, of course, contradicts the spirit of simultaneity stressed throughout this study. The implications of this assumption to the empirical re- I j suits is that, unless each demand function is completely ! specified, there is a strong possibility that the estimated ^For example, see Henry Schultz, The Theory and Measurement of Demand (Chicago: The University of Chxcago Press, 1938), pp. 61-63; and Kuh, 0£. cit., pp. 207-208. 376 coefficients are subject to single equation bias. The available evidence, which will be discussed later in the chapter, tends to indicate that this is the case. Single Equation, Pooled Estimate— Demand Deposits The pooled estimate of the demand deposit stock demand function is: (5.3.1) D'f l = 280.35 - .11 S 1 a - .52 S'. + .46 S' a (.03) 3 (.08) 4 (.05) S + .58 y + 274.42 r^ - 31.38 r. (.03) (60.3) (15.7) - 89.56 r (19.4) where the numbers in parentheses under the. coefficients are; standard errors. The coefficient of multiple determination adjusted for degrees of freedom is .796, and is significant at the .05 level.The Durbin-Watson statistic was computed, and. it was found that the null hypothesis of non-autocorrelated residuals cannot be rejected. 1 All of the coefficients in (5.3.1) are signifi cantly different from zero, and the own price and income •^The .05 level will be used in all significance tests. 377 coefficients have the expected sign. The first thing that j i strikes one upon examination of this empirical function is j the high degree of significance (judged by the size of the standard error relative to the size of the coefficient) of the cross portfolio balance term and income coefficients relative to the significance of the interest rate coeffi cients. This tends to give support to the hypothesis that portfolio composition is a significant determinant of stock demand. Judging by the sign of the cross interest rate co- I efficients, both time deposits at commercial banks and i j savings and loan association shares appear to be substi tutes for demand deposits. This agrees with the results obtained by T. H. Lee, who, in a recent article, computed alternative stock demand functions for the medium of ex change (currency plus adjusted demand deposits at commer- j cial banks) in log-linear form; the arguments that appeared! in his functions were "permanent" income and various inter est rate differentials. Using the coefficient of multiple determination as his measure, Lee concluded that "savings and loan shares are the closest substitutes for money, whereas time deposits at commercial banks are modest sub stitutes for money. " ■ * ■ ■ * • Savings and loan association shares H t . H. Lee, "Alternative Interest Rates and the Demand for Money: The Empirical Evidence," The American Economic Review, LVII (December, 1967), 1172. 378 are still the closest substitute for "money," according to i Lee, when money is defined broadly— i.e. , when money is defined as the medium of exchange plus time deposits at commercial banks. For portfolio purposes, time deposits at commercial: banks and demand deposits appear to be "weak" substitutes in the sense that one unit of time deposits is "equivalent" to .52 units of demand deposits in portfolio holdings. On ; i i the other hand, savings and loan association shares appear j to be "weak" complements for demand deposits (the coeffi cient is + .46). However, as Feige has pointed out, a com-j plementary relationship in the demand deposit demand func- i tion is consistent with a hypothesis suggested by Tobin and Brainard.They point out that an increase in the return on the liabilities of a financial intermediary may have the; direct effect of inducing individuals to reduce their de- ; mand for demand deposits, but it may also have the indirect; effect of increasing the demand for demand deposits as re- > serves for the intermediary. Thus, if the indirect effect i outweighs the direct effect, a complementary relationship will be observed on the market even though the subject ■^Feige, ojd. cit. , pp. 25-26. The hypothesis was originally put forth in James Tobin and W. C. Brainard, "Financial Intermediaries and the Effectiveness of Monetary Controls," The American Economic Review, LIII (May, 1963), 383-400. 379 instruments are substitutes in portfolio choices of the non-financial sector and of the intermediaries taken sepa rately. It appears, therefore, that the portfolio comple mentary conclusion drawn from the estimate of the stock demand function for demand deposits may be subject to in fluences that would tend to bias the results. Since, how ever, the estimated stock demand function for savings and loan association shares is not subject to this same bias, ; | the results obtained from it would seem to be better evi- ! dence on the type of interdependence in demand between j demand deposits and savings and loan association shares. Turning our attention now to the cross sectionally derived estimates of the demand deposit demand relations presented in Appendix I, the most striking features are the: high degree of significance of the coefficients of S'3 , theJ low degree of significance (and insignificance) of the other explanatory variables, and the high (relative to the pooled estimate) coefficients of multiple determination. Although the results are somewhat ambiguous, if one were to ; take these estimates at face value he would be forced to conclude that the short run stock demand for demand depos its is, in general, independent of portfolio composition and the spectrum of interest rates (including the service charges levied against demand deposits), but is signifi- 380 cantly influenced by. the initial stock of demand deposits. However/ there is good reason to believe that these estimates may be seriously biased, and that the direction of the bias is indeterminant a priori. This is due to the simultaneous presence of a lagged value of the dependent variable as an argument in the function and autocorrelated residuals. ^ There is in fact evidence of autocorrelated residuals in most of these estimates; the Durbin-Watson statistics that were computed lie either below the lower limit or in the indeterminant range of the distribution in all cases. In those cases where the statistic lies below the lower limit, the null hypothesis of non-autocorrelated residuals must be rejected; in the indeterminant cases, no positive assertion can be made in either direction. In any event, these estimates cannot be viewed with too much caution. It should also be pointed out that the higher ad justed coefficients, of multiple determination for these cross sectional estimates, and for the other cross sec tional estimates considered in this study, cannot be used as a basis for claiming that these estimates are superior to the pooled estimates; this is because the use of per capita data would naturally introduce more artificial cor- l-^See J. Johnston, Econometric Methods (New York: McGraw-Hill Book Company, Inc., 1963), pp. 215-216. relation into the cross sectional estimates than it would into the pooled estimates. Single Equation, . Pooled Estimate-Time Deposits The pooled estimate of the stock demand function for time deposits at commercial banks is: (5.3.2) D', = - 37.18 - .22 S', - .20 S' + .02 S'd r (.03) a (.03) ^ (.04) + .40 y - 35.98 rd + 41.91 rt - 63.91 rJ (.0 2) (40.7) (10.4) (12.9) ; i , where, once again, the numbers in parentheses under the coefficients are standard errors. The coefficient of multiple determination adjusted for degrees of freedom is .778, and is significantly dif ferent from zero. The Durbin-Watson statistic indicates that the null hypothesis of non-autocorrelated residuals cannot be rejected. All of the coefficients are significant with the exception of the coefficients for S's and r^. That the coefficient for rd is not significantly different from zero j in this relation seemingly contradicts the implications of a significant rf c in (5.3.1); however, this may not be the case. The variable rd represents the service charges levied against demand deposits, and a change in rd may 382 cause individuals to shift into and out of the closest sub stitute for demand deposits--which is, of course, currency — rather than into or out of alternative interest earning assets. In other words, a change in the rate of service charges may cause individuals to rearrange their portfolios with regard to how the medium of exchange is held rather than causing them to shift out of (or into), the medium of exchange to (or from) some other type of instrument or physical asset. Thus, defining D'^j, S'^, and r^ as quanti ties pertaining to demand deposits, rather than the medium of exchange, may cause certain difficulties in interpreta tion and may have a distorting influence on the estimates. On the other hand, the insignificance of the co efficient of S's implies that time deposits at commercial banks and savings and loan association shares are indepen dent for portfolio purposes, a conclusion that is substan tiated by the insignificance of the coefficient for S ' - j . in the estimated stock demand relation for savings and loan association shares. This conclusion is rather hard to be lieve on the basis of prevailing dogma; however, noticing that the coefficient of rs in (5.3.2) is significant and negative, this phenomenon might be explained in terms of shifts in tastes and preferences. Very few people would disagree with the statement that the acceptability of sav ings and loan association shares has undergone a drastic 383 change in the last two decades, and especially in the de cade of the "fifties" (the period covered by the data used in this study). This being the case, one would expect to observe large fluctuations in the holdings of savings and loan association shares relative to holdings of time de posits at commercial banks (hence, the insignificant coef ficients) , even though more recent data might indicate a stable relationship. The coefficients of the own price and income vari ables have the expected sign, and are both significant. One is struck, once again, by the degree of significance of the cross portfolio demand deposit term coefficient (S's is not significant) relative to the significance of the co efficients of the cross interest rate terms. This tends to further substantiate the importance of portfolio composi tion as an explanation of financial behavior. The interest rate coefficients indicate that time deposits at commercial banks and savings and loan associa tion shares are substitutes, but that time deposits at com mercial banks and demand deposits are independent in demand (which, as was pointed out earlier, contradicts the conclu sions drawn from the estimated stock demand function for demand deposits). On the other hand, the cross portfolio balance term coefficients indicate that time deposits at commercial banks and demand deposits are "weak" substitutes 384 for portfolio purposes (which agrees with the findings from the demand deposit equation), but that time deposits at commercial banks and savings and loan associaiton shares are independent for portfolio purposes. This latter rela tionship was discussed at some length earlier. With regard to the cross section estimates pre sented in Appendix i, it appears that the short run stock demand for time deposits at commercial banks may be best explained by the initial stock of time deposits, the rates of return on time deposits at commercial banks and savings and loan association shares, and, perhaps, permanent in come. Once again, however, not much reliance may be placed in these estimates; although a majority of the Durbin- Watson statistics lie in the indeterminant range, there is a strong presumption that the residuals are autocorrelated which, coupled with the inclusion of S'^. as an argument, would lead to seriously biased estimates. For what it is worth, these estimates do in general indicate that time deposits at commercial banks and savings and loan associa tion shares are substitutes for price changes. Single Equation, Pooled Estimate — Savings and Loan Association Shares The pooled estimate of the stock demand function for savings and loan association shares is: 385 (5.3.3) D'g = - 415.43 + .45 S'd + .11 S',. + .40 S' (.05) {.08) ^ (.06) - .05 y - 86.62 r- - 7.91 r.. + 100.50 r (.05) (64.1) (16.3) (20.0) s where the numbers in parentheses under the coefficients are, as before, standard errors. The coefficient of multiple determination adjusted for degrees of freedom is .606, and is significantly dif ferent from zero. The Durbin-Watson statistic was computed,; and it was found that the null hypothesis of non-autocorre- ; lated residuals must be rejected. i The coefficients of S't, y, r^, and rf c are not sig nificantly different from zero, but the own price term co efficient has the expected sign and is significant. The. coefficient of S'd is, once again, highly significant, and i indicates a "weak" complementary relationship between de- j mand deposits and savings and loan association shares. This conclusion corresponds with the results obtained from (5.3.1). | The presence of evidence indicating autocorrelated j residuals in this relation, however, is strong evidence that the form of (5.3.3) has been misspecified; i.e., it is probable that the true stock demand for savings and loan association shares is non-linear. Although the estimates under these circumstances will, in general, be unbiased, 386 they will have a low degree of precision. The reason that I the presence of S's as an argument in this relation, in conjunction with the autocorrelated residuals, does not lead to biased estimates is that the estimation procedure outlined in Section II is designed to eliminate the corre- ! lation between S1s and the residuals. Further, if tastes with respect to savings and loani j association shares have in fact changed substantially over j the period covered by this study as was claimed in an ear lier portion of this section, it is probable that the ob- servations correspond to intersections between a shifting i demand and a (perhaps) shifting supply schedule. If this is the case, what has been estimated here is a relation de scribing the locus of points of intersections, and not a demand or supply relation; hence, the presumption is that the coefficient estimates are subject to single equation bias. j The evidence presented in the Feige study tends to substantiate this hypothesis; although Feige does not take j a portfolio approach, he does include among his arguments \ in the savings and loan share demand equation (in addition ! to dummy variables that indicate various geographical re gions within the United States) a measure of per capita advertising expenditures by savings and loan associations, which is probably a rough proxy for tastes. Feige then 387 j tested the stability of these functions over time and found; that there is no reason to reject the stability hypothe- ' 1 A ! sis. This, however, is not conclusive evidence in that Feige's tests may have indicated a stable relationship be- ; tween demand and supply, and not a stable demand function. ! When we turn to the cross sectional estimates of D's in Appendix I, things get worse. All of the Durbin- Watson statistics, except that for 1953, lie in the inde terminant range; however, if a larger cross sectional i sample were used it is probable that, they would indicate j autocorrelated residuals. This and the presence of S's as ; an argument in the functions leads us to conclude, once again, that not much confidence may be placed in these cross sectional estimates. Keeping this in mind, the esti mates indicate that, in general, S1s and perhaps rs are the; I only variables considered in this study that significantly j i influence the stock demand for savings and loan associatxon; shares. IV. CONCLUSIONS Before considering the conclusions of this study relative to the two hypotheses enumerated at the beginning of this chapter, it is desirable to consider in more detail 1 l^Feige, 0£. cit., chap. 3. 388 the possible inaccuracies that have crept into this analy- | sis. These possible inaccuracies may be considered under five categories: 1. Multicollinearity— The possibility of multi- i collinearity existing among the independent variables in- I eluded in (5.3,1) — (5.3.3) is strongest in the case of r^ versus r . This conclusion is based upon the observation s that savings and loan associations at least believe that j i time deposits at commercial banks is their closest competi-! i tor for the saving ( s . ) of the non-monetary sectors, so that j one would expect that the differential between rt and rs is i relatively constant. This hypothesis was tested, and it was found that rt and rs are in fact "fairly" highly cor- 15 related; hence, the standard errors (relative to the size of the coefficients) of these two variables are likely to ; be overstated in the estimated demand functions. A certain amount of.multicollinearity is also j likely to be introduced by reason of the correlation be tween the wealth constraint and the initial portfolio terms, and-the correlation between the interest rates and the : i initial portfolio. However, these effects are likely to be; minimal because both the wealth term and the interest rate terms are quantities ovserved this period, whereas the l^The coefficient of correlation adjusted for de grees of freedom is .619 in a regression of rs on r^ j 389 portfolio terms are quantities observed last period. 2. Single equation bias— This topic was discussed in the section on the stock demand for savings and loan association shares, and it was concluded there that this estimate may be severely biased because of an inadequate treatment of the identification problem. Moreover, there is reason to suspect that we have the same problem in the other estimates presented in this chapter. As has been pointed out earlier, there is reason to believe that, with a larger sample, the cross sectional estimates presented in Appendix I would exhibit autocorre lated residuals. An alternative interpretation of the cause of this phenomenon— alternative to the interpretation that it arises from the incorrect specification of the form of the function estimated— is that variables that influence the relation but that are excluded from it are correlated with the residuals. This hypothesis tends to be confirmed by the relatively low adjusted coefficients of multiple determination for the pooled estimates, which also suggests that there are other variables that were not included in these estimates but that significantly influence the stock demand for the fiancial assets considered here. It is possible that the estimation procedure used in deriving the pooled estimates which is designed to do away with the correlation between the lagged value of the 390 dependent variable and the residual term, aided in the "identification" of each of the pooled estimates in the sense that it made the lagged value of the dependent vari able a true exogenous variable. However, this still does not solve the identification problem as it pertains to the pooled estimates because of the treatment of the indepen dent variables in the estimation procedure— they were all treated as if they were truly exogenous. The evidence, then, points to the presence of a single equation bias in all of our estimates; however, more work needs to be done in this area before any positive . assertion can be made. 3. Errors in measurement— We have reference here to the correct specification of the dependent variable in (5.3.1). The question naturally arises as to what we are really interested in: the relation in demand between de mand deposits and other financial assets, or the relation in demand between the medium of exchange (defined as demand deposits adjusted plus curency outside of commercial banks) and other financial assets? According to theory the cor rect variable to consider would depend on the degree of substitutability between demand deposits and currency; however, even though they are not perfect substitutes, the weight of current opinion favors the use of the medium of exchange. 391 The use of demand deposits as the dependent vari able in (5.3,1), then, leads to a persistent understatement of the magnitude and an understatement or overstatement (depending on the variability of currency holdings relative to holdings of the medium of exchange) of the variability of the dependent variable. Hence, the coefficient esti mates in (5.3.1) and the coefficient estimates of S1^ in (5. 3.2) - (5.3.3) are likely to be distorted. 4. The linearity of the portfolio balance relation — The linear form used in the estimation of (5.3.1)-(5.3.3) has the effect of forcing the slopes of the portfolio bal ance relation (for a definition of this term, see Chapter IV, Section II): to be constant; this, in turn, implies that the financial goods subjected to this analysis are perfect substitutes or perfect complements for portfolio purposes if the respective cross portfolio balance term coefficients are significant. Obviously, there is no a priori reason to think that any of the goods considered here are perfect substitutes or perfect complements in this sense, and any estimates that assume this are going to produce distorted estimated coefficients. Ideally, one should have some knowledge of the shape of the portfolio balance relations prior to the esti mation of the demand relations. To this end, it would be instructive to experiment with various forms in the 392 planes; however, this exercise will be left for some other time. 5. The use of nominal values— As was discussed in Chapter IV at some length, the use of nominal, instead of real, values in the estimated functions is likely to dis tort the interest rate coefficients. Since, in general, price indices are used in empirical work, one would expect the estimated interest rate coefficients to be larger, smaller, or unchanged relative to the value of the esti mated coefficients if real magnitudes had been used depend ing on the behavior of the price index relative to the base period. With these possible errors in mind, we shall now turn to a consideration of the. evidence as it pertains to the portfolio approach and the Gurley-Shaw hypothesis. The Portfolio Approach— The Evidence On the basis of the evidence presented in this study, we must tentatively "accept" the hypothesis that the portfolio approach is a valid framework from which to study financial phenomena; we use the word "tentatively" to indi cate that there are certain inconsistencies that must be resolved before this approach may gain the status of a "theory." Our "acceptance" is based upon the high degree of 393 j significance of each cross portfolio balance term coeffi cient in the pooled estimates (with the exception of S's in i (5.3.2) and S' in (5.3.3), which are both not signifi- x. ' cantly different from zero), and upon the consistency of j the signs of the estimated coefficients of the cross port- ! folio balance terms. On the other hand, the a priori cri teria suggested for judging the coefficients of these terms — which we rewrite here as ! i (5.4.1) °t,a = ■ • L/°a,t °s,a = 1/ca.s cs,t = 1/0t.s| i where the first subscript indicates the particular port- | folio balance term in question, and the second subscript indicates the equation in which it appears— were not ful filled; however, due to the possible distortions of the estimated coefficients outlined above, this cannot'be taken! as evidence that would refute the hypothesis that the port- ] i folio approach is a valid vehicle for studying financial phenomena. The Gurley-Shaw Hypothesis— ' The Evidence | Disregarding the estimated stock demand function for savings and loan association shares on the grounds that it is likely to be the least reliable of the pooled esti mates, the evidence indicates both time deposits at commer-. cial banks and savings and loan association shares are sub-; 394 stitutes for demand deposits for price changes. With regard to changes in initial stocks, the evi dence suggests that demand deposits and time deposits at commercial banks are "weak" substitutes, whereas demand deposits and savings and loan association shares are "weak" complements. Further, it appears that time deposits at commercial banks and savings and loan association shares are independent for portfolio purposes, but that they are substitutes for price changes. Contrary to the findings of the Feige study (which used the same data), we must conclude that the evidence presented here cannot be used to refute the Gurley-Shaw Hypothesis. APPENDIX I SINGLE EQUATION ORDINARY LEAST SQUARES ESTIMATES "PORTFOLIO APPROACH" STOCK DEMAND FUNCTIONS CROSS-SECTIONAL SAMPLE* 1950 D'd = - 139.28 + .79 S'd - .16 S' + .18 S's + .23 y (.06) (.09) r (.19) (.05) + 42.35 rd + 9.40 rt + 15.40 rs (83.6) (34.0) (19.9) R2 = .98032 DW = 1.725 D' = - 102.34 - .07 S'd + .91 S't - .04 S' + .09 y ^ (.02) (.03) (.04) (.02) + 8.45 rd + 24.18 r.u + 12.90 rg (29.8) (12.1) (7.1) R2 = .99218 DW = 1.417 D's = - 19.60 - .009 S'd + .002 S't + 1.12 S's + .007 y (.005) (.008) (.01) (.004) - 6.84 rd + 3.53 rt + 4.05 rs (7.74) (3 .14) (1.84) R2 = .99853 DW = 1.687 *The coefficient of multiple determination adjusted for degrees of freedom is denoted by R2; the Durbin-Watson statistic is denoted by DW. ~ 395 1951 396 D' = - 151.95 + .89 S'd - .12 S't + .25 S' + 14 y a (.04) (.07) (.08) (.04) + 34.88 rd - 1.85 r^. + 33.93 rs (62.4) (19.3) (14.4) R2 = .99141 DW = 2.079 D 1 j _ = - 78.13 - .02 S'd + .99 S't - .04 S's + .05 y (.01) (.02) (.02) (.01) + 1.19 rd + 12.50 rt + 13.64 r_ (17.2) (5.3) (4.0) R2 = .99779 DW = 2.162 D' = - 12.74 - .01 S'd - .007 S',. + .1.22' S' + .006 y (.005) (.01) (.01) (.005) - 12.47 rd - 5.36 rt + 3.92 rs (8.9) (2.8) (2.1) R2 = .99875 DW = 1.507 1952 D'd = 87.02 + 1.02 S'd - .08 S1^ - .31 S' + .008 y (.06) (.08) (.09) S (.05) - 35.05 rd + 3.11 r^_ - 25.21 r (81.5) Q (17.9) ^ (17.7) R2 = .98415 DW = 2.077 397 D' = 53.10 + .004 S', + .94 S't - .03 S' + ^ (.03) a (.04) (.04) S ( + 13.74 r. + 31.07 rt - 27.36 (40.7) a (S'. 9) (8.8) R2 = .98783 DW = 2.145 D* = 10.11 + .02 S'd + .006 S't + 1.06 S' - (.015) (.02) (.02) - 18.35 + .27 r*. ~ *24 r (21.1) (4.6) (4.6) R2 = .99411 DW = 2.168 1953 D' = 107.27 + .98 S'd + .06 - .05 S' - d (.05) Q (.07) ^ (.07) ( + 151.95 rd - 12.77 - 3.36 (65.5) (16.9) (17.1) R2 = .98534 DW = 2.287 D't = 47.41 - .007 S'd + .96 S'^ + .01 S’s + (.01) (.02) (.02) ( + 48.73 rd + 19.66 rt + 20.17 (19.4) (5.0) (5.1) 01 y 03) rS . 01 y (.01) 04 y 05) .01 y .01) R2 = .99636 DW = 2.034 398 D' = 5.17 + .016 S'd + .02 S't + 1.08 S's - H (.014) (.02) u (.02) ( +3.67 rd + .75 r. + 2.88 rs (19.8) (5.1) ^ (5.2) r2 = .99442 ' DW = 2.812 1954 D'd = - 160.87 + .94 S'd - .10 S \ + .02 S' H (.04) (.05) (.06) + 30.40 r. + 25.52 r + 19.88 (42.8) (14.2) (13.1) R2 = 99239 DW = 1.993 D' = - 44.08 - .008 S'd + .98 S'j. + .05 S' H (.01) (.02) (.02) + 17.56 + 16.11 rt + 3.15 re (17.0) (5.7) (5.2) R2 = .99652 DW = 1.816 D1 = - 26.53 - .002 S'. - .01 S't + 1.15 S's (.01) (.02) (.02) - 6.66 rd - 2.60 + 7.26 r (16.8) (5.6) (5.2) 013 y 01) .10 y (.03) .02 y (.01) + . 01 y (.01) R2 - .99605 DW = 2.316 1955 399 D'd = 70.12 + .87 S' - .03. S' + .14 S' + .04 y (.06) a (.09) r (.06) s (.05) + 22.30 rd - 23.07 rt - 2.50 rs (69.0) (26.0) (21.4) R2 = .97838 DW = 1.653 D't = 4.66 - .026 S'd + .95 S'. + .029 S's + .027 y (.01) (.02) (.015) (.012) - 5.73 rd + 10.10 rt - 9.86 rs (16.5) (6.2) (5.1) R2 = .99663 DW = 1.868 D' = - 3.39 - .01. S'd - .01 S't + .1.17 S's + .004 y (.02) (.03) (.02) (.02) - 27.27 rd - 1.23 rt + 1.16 rs (24.5) (9.2) (7.6) R2 = .99374 DW = .2.492 1956 D'd = 42.33 + .96 S'd + .03 S’^ + .05 S'H ■- .01 y {.04) (.06) (.03) (.03) ~ 6.75 rd - 3.05 rt - 4.60 rs (38.5) (16-2) (16.2) R2 = .99173 DW = .2.292 400 D't = - 16.72 - .01 S'd + .95 S'. - .015 S' + .029 y (.01) (.02) (.014) (.012) + 28.50 rd + 14.02 x. q 74 rs (15.3) (6.5) r ”(615) R2 = .99654 DW = 2.657 D'g = - 2.10 + .015 S'd + .06 S't + 1.08 S' - .019 y (.012) (.02) (.01) (.011) - 7.84 rd - 17.32 r. + 13.30 r_ (13.3)) (5.6) r (5.6) R2 = .99819 DW = 2.062 1957 D'd = 54.59 + .94 S'd - .12 S't + -085 S's + .0,48 y (.05) (.07) (.042) (.040) + .47.37 rd + 29.30 rt - 41.82 rs (42.9) (18.6) (19.6) R2 = .98640 DW = 2.324 D'. = - 10.29 + .05 S’. + 1.00 S V + .002 S's - .0006 y (.03) a (.04) (.027) (.025) + 8.69 rd + 37.87 rt - 20.40 rs (27.2) (11.8) (12.4) R2 = .98668 DW = 2.320 401 D' = - 23.98 - .006 S'- + .0002 S'. + 1.12 S' s (.015) (.022) (.01) 1958 + .012 y + 26.31 rd + 2.26 r. + 4.60 r (.012) (13.1) (5.7) r (6.0) R2 = .99817 DW = 2.459 D'd = - 26.03 + 1.13 S'd - .096 S' - .055 S' (.05) (.072) r (.040) .001 y - 47.27 rd - 5.23 ry + 6.47 rs (.039) (43.7) (20.2) (15.9) R2 = .98766 DW =2.032 D't = - 56.41 + .01 S'd + 1.01 S't - .024 S' + .031 y (.02) (.03) (.015) b (.015) +10.77 rd + 32.80 rt - 9.46 rs (16.8) (7.8) (6.1) R2 = .99573 DW = 1.756 D' = - 45.29 + .013 S'd + .022 S't + 1.09 S's + .002 y (.014) (.020) (.01) (.01) I + 1.04 - 3.28 r^. + 13.92 rs (12.0) (5.6) (4. 4 ) R2 = .99879 DW = 2.183 402 1959 D' = - 196.37 + .86 S'd + .02 S' + .016 S' a (.03) (.05) ^ (.023) + 51.11 rd + 38.86 + 32.32 (29.6) (19.6) (16.2) R2 = .99441 DW = 1.584 D't = 23.61 + .03. S'd + 1.01 S't - .08 S' + (.01) (.02) (.01) ( - 5.54 + 8.63 r. - 11.30 r (12.8) a (8.5) ^ (7.0) R2 = .99780 DW = 1.911 D* = - 47.57 + .02 S1d + .022 S't + 1.10 S's S (.014) (.020) (.01) - 16.11 rd + 1.33 r* + 11.81 (13.2) (8.8) ^ (7.2) + .049 y (.027) 003 y 01) - .008 y (.01) R2 = .99896 DW = 1.973 APPENDIX II SINGLE EQUATION ORDINARY LEAST SQUARES ESTIMATES "NORMAL" STOCK DEMAND FUNCTIONS POOLED SAMPLE* D*d — 93.96 + .54 y + 377.62 rd - 39.48 r-^ ~ 27.89 r~ (.02) (69.0) (18.5) (21.9) R2 = .71055 DW - 1.863 D' = - 56.52 + .30 y - 107.90 rd + 44.25 rt - 71.18 r ^ (.01) (43.3) (U. 6) (13.8) R2 = .71940 DW = 2.053 D' = — 436.88 + .24 y + .1.43 rd - 6.61 rt + 95.8 rs (.02) (69.8) (18.7) (22.2) R2 = .44654 DW = 1.298 The coefficient of multiple determination adjusted for degrees of freedom is denoted by R2; the Durbin-Watson statistic is denoted by DW. 403 CHAPTER VI CONCLUSION In the preceding pages of this work, an attempt was! i made to fill what we felt was a void in the area of mone tary economics and finance. As is testified to by the length of the review of the literature section in this work, i a great deal of study has gone into the investigations of I monetary and financial relationships in a general economic framework; but each one of these investigations has failed i to incorporate stocks, as well as the traditional flows, ini a consistent and meaningful manner. It was felt that the ■ best approach to filling this void was to follow J. R. Hicks' early suggestion that, in the study of financial phenomena, a study of the balance sheet was more appropri- I i ate than the more common income statement approach— i.e., ! he suggested that a portfolio approach is the appropriate method of studying those itmes that comprise a portfolio.^ The model that is presented here has taken Hicks' sugges- i tion, and has, in addition, considered the income statement ; j •*-J. R. Hicks, "A Suggestion for Simplifying the Theory of Money," Economica, II, New Series (1935), re printed in Friedrich A. Lutz and Lloyd W. Mints (eds.), Readings in Monetary Theory (Homewood, Illinois: Richard D. Irwin, Inc., 1951), especially p. 25. 404 405 and its relation to portfolio size and composition. j The market functions that are derived from the "micro" model are not surprising in the sense that they contain precisely the same arguments that one would intui- j tively suspect should appear in market excess demand func- j i tions that emphasize the portfolio approach. In essence, both stock and flow market excess demands are found to be ! ! functions of relative prices, interest rates, and the real j i value of each asset in existence. Thus, these theoretical j functions follow what Gurley and Shaw have termed "gross j 2 money doctrine." To be of any use in an empirical science such as economics, a theoretical construct must be capable of em pirical refutation. Obviously, the model referred to in the previous paragraph is much too general to meet this j criterion; however, this very generality has the advantage that the model may be simplified in a variety of ways so that it is capable.of focusing on a variety of economic problems. Two approaches were suggested and illustrated, and empirical evidence was brought to bear on one of these illustrations. The results of the empirical investigation | indicated that: (1) the portfolio approach is an effica- ^See John G. Gurley and Edward S. Shaw, Money in a Theory of Finance (Washington, D.C.: The Brookings Insti- : tution, 1960), especially pp. 140-149. 406 cious framework for the study of financial phenomena; and (2) the Gurley-Shaw hypothesis cannot be rejected. The former conclusion is based upon the high degree of signifi cance of the cross portfolio balance term coefficients in the estimations, and the latter conclusion is based upon the signs of the estimated cross interest rate term coeffi cients . For changes in initial stocks, the results indi cate that demand deposits and time deposits at commercial banks are "weak" substitutes, whereas demand deposits and savings and loan association shares are "weak” complements. This complementary relationship might be explained by the hypothesis that savings and loan associations increase their stock demand for demand deposits in response to an increase in the initial stock of their liabilities by more than the other sectors decrease their stock demand for de mand deposits for an increase in the initial stock of savings and loan association shares. However, there is evidence that these estimates are distorted by the data and the methods of estimation used. These distortions are most noticeable in the savings and loan association share stock demand function, and in the inconsistency of the magnitudes of the estimated coeffi cients of the cross portfolio balance terms. All this points to the need for further empirical research in this area. 407 The theoretical model and empirical work presented j in this study is only a very small step in the direction i that we feel future investigations into monetary and finan-j cial phenomena should take. We shall now turn our atten tion to a few suggestions along these lines. I. SUGGESTIONS FOR FUTURE RESEARCH Inasmuch as this study has been divided roughly into1 a theoretical and an empirical portion, the discussion re garding the lines which future research might take will be | j similarily dichotomized. j I In a critique of any theoretical system (provided, of course, that there are no logical errors committed), any observations must be directed at the assumptions themselves j or the interpretations put on the conclusions. With regard i to the present study, of the three basic assumptions that ; form the basis of the theoretical model developed in Chap ter III— i.e., pure competition, perfectly flexible wages and prices, and unitary, elasticity, of expectations--the one; that appears to do the most damage to financial theory is the assumption regarding anticipated price changes. It is ‘ true that none of these assumptions correspond to the real world; however, it can be effectively argued that the mar ket for certain financial instruments (e.g., the market for securities listed on the New York Stock Exchange) approach 408 the position that their behavior can best be explained by assuming perfectly, competitive markets and perfectly flex ible prices. On the other hand, it is generally agreed that expectations do play an important, and perhaps the dominant, role in price and quantity determination, at least during some periods of time, in financial markets. The first suggestion therefore, is that alternative assump tions should be made concerning the anticipated behavior of future prices and interest rates, perhaps along the lines 3 developed by Hicks. Another weakness of this model is its handling of the supply of money function. In this model, commercial banks are conceived of as facing one reserve drain--the clearing drain— which they can predict in any one period with certainty. A more fruitfull approach to commercial bank portfolio behavior would seem to lie in the direction of stochastic processes.^ In this case, a commercial bank, instead of being certain of the amount of its reserve losses in any one period, would be faced with a probability distribution describing their potential losses in each ^J. R. Hicks, Value and Capital (2d ed.; Oxford: The Clarendon Press, 1946), especially chaps. XV-XXIII. 4 See, for example, Daniel Orr and W. G. Mellon, "Stochastic Reserve Losses and Expansion of Bank Credit," The American Economic Review, LI (September, 1961), 614- 623. 409 period. The process could be a true stochastic process in ; the sense that the distribution is e.g., time dependent, orj it could be a situation where there is one probability dis tribution for all periods. In certain circumstances, and in particular when studying regional financial markets or individual units, ’ the assumption of perfect competition would probably have to be relaxed. It is true that when dealing with broad ! aggregates certain markets do behave as if they are per- ; fectly competitive; but, as the aggregation is performed j over fewer and fewer units this becomes, in general, less j and less true. Take, for example, the commercial banking industry in a small town; by the nature of the industry's customers and the nature of the banks themselves, it is probable' that this situation could be best examined and ex plained by monopoly theory.^ In certain cases, this is also true in the study of "national" markets. This study has also neglected any precise treatment of the qualitative aspects of the theoretical model. A j rigorous comparative static analysis of this model would be helpful in fully understanding the implications of this approach to individual behavior and market outcomes. In ^For an interesting analysis of the commercial banking industry, see David A. Alhadeff, "The Market Struc ture of Commercial Banking in the United States," The Quar terly Journal of Economics, LXV (February, 1951), 62-86. 410 ; this connection, it may be more convenient to abandon the "temporary equilibrium" method used here in favor of a "growth equilibrium" method. Turning now to the empirical portion of this study, it was pointed out that there is reason to believe the | estimated coefficients presented here are subject to vari- j ous distortions due to the method of estimation used and the time period covered by the data; hence, our suggestions; for future empirical research are designed to remedy these.| I shortcomings. ' In the first place, it is suggested that a simul- i taneous estimation procedure should be used in this type of’ study. In the case under consideration, this would call for a specification of the corresponding supply functions. Secondly, it would be desirable to use more recent j data. This is especially important in the estimation of ; the stock demand for savings and loan association shares because of the possible structural shifts that occurred in this market during the forties and fifties. Thirdly, the medium of exchange is the relevant variable to be explained, not demand deposits. The use of ’ the latter as the dependent variable in one of the esti mated functions can, as was pointed out earlier, lead to some rather strange conclusions. Finally, it would be informative to extend the 411 analysis beyond the three financial instruments included in this study to other financial, or perhaps real, assets. B I B L I O G R A P H Y 412 BIBLIOGRAPHY A. BOOKS Ackley, Gardner. 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"Financial Intermediaries and the Saving-Invest- ment Process," The Journal of Finance, XI (March, 1956), 257-276. ________. "The Growth of Debt and Money in the United States, 1800-1950: A Suggested Interpretation," The Review of Economics and Statistics, XXXIX (August, 1957), 250-262. . "Reply," The American Economic Review, XLVIII (March, 1958) , llF^lIT: Haberler, Gottfried. "The Pigou Effect Once Again," The Journal of Political Economy, LX (June, 1952), 240-246. Hadar, Josef. "A Note on Stock-Flow Models of Consumer Behavior," The Quarterly Journal of Economics, LXXIX (May, 1965)^ 504-309. ________. "Comparative Statics of Stock-Flow Equilibrium," The Journal of Political Economy, LXXIII (April, 1965), T5¥-TM; Hahn, F. H. "The General Equilibrium Theory of Money— A Comment," The Review of Economic Studies, XIX, No. 50, 179-185. — ________. "The Patinkin Controversy," The Review of Eco nomic Studies, XXVIII (October, 1960), 37-43. Hickman, W. Braddock. 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"Financial Intermediaries and the Logical Struc-j ture of Monetary Theory," The American Economic Review,i LI (March, 1961), 95-116. ________. "Further Considerations of the General Equilib rium Theory of Money," The Review of Economic Studies, XIX, No. 50, 186-195. ________. "The Indeterminacy of Absolute Prices in Classi-; cal Economic Theory," Econometrica, XVII (January, J 1949), 1-27. ' j ________. "The Invalidity of Classical Monetary Theory," Econometrica, XIX (April, 1951), 134-151. _______. "Liquidity Preference and Loanable Funds: Stock and Flow Analysis," Economica, XXV, New Series (Novem ber, 1958), 300-318. "A Reconsideration of the. General Equilibrium 421 | Theory of Money," The Review of Economic Studies, XVIII, No. 45, 42-61. j Patinkin, Don. "Relative Prices, Say's Law, and the Demand; for Money," Econometrica, XVI (April, 1948), 135-154. | "Reply to R. W. Clower and H. Rose," Economica, j XXVI, New Series (August, 1959), 253-255. j Phipps, Cecil G. 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Chicago: The University of Chicago Press, 1956. Pp. 3-21. Jaffd, William. "Leon Walras* Theory of Capital Accumula tion ," Studies in Mathematical Economics and Econo metrics , Oscar Lange, el; al., editors. Chicago: The University of Chicago Press, 1942. Pi. 37-48. Lange, Oscar. "Say's Law: A Restatement and Criticism," Studies in Mathematical Economics and Econometrics. Oscar Lange, et al., editors. Chicago: The University of Chicago Press, 1942. Pp. 49-68. Modigliani, Franco. "Liquidity Preference and the Theory of Interest and Money," The Critics of Keynesian Eco nomics , Henry Hazlitt, editor. Princeton: Princeton University Press, 1960. Pp. 183-184. D. FOREIGN DOCUMENTS Committee on the Working of the Monetary System Report [The Radcliffe Report]. Presented to Parliament by the Chancellor of the Exchequer by Command of Her Majesty, August, 1959. London: Her Majesty's Stationary Office 1959. E. UNPUBLISHED WORKS Friedman, Milton, and Anna J. Schwartz. "Trends in Money, Income, and Prices." Preliminary draft of a work to be published by the National Bureau of Economic Research, Inc., New York, 1966.

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Creator Watson, William Roger (author)

Core Title The Interaction Among Financial Intermediaries In The Money And Capital Markets: A Theoretical And Empirical Study

Degree Doctor of Philosophy

Degree Program Economics

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Economics, theory,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor DePrano, Michael E. (committee chair), Tintner, Gerhard (committee member), Trefftz, Kenneth L. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-641183

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