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An Econometric Analysis Of The Influence Of Money Supply And And Money Demand Relations In The Determination Of National Income

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An Econometric Analysis Of The Influence Of Money Supply And And Money Demand Relations In The Determination Of National Income

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Content This d isssrtstf on h u boon m icrofilm ed ex actly «s rece iv ed 68-12,024 BOORMAN, John Thomas, 1941- AN ECONOMETRIC ANALYSIS OF THE INFLUENCE OF MONEY SUPPLY AND MONEY DEMAND RELATIONS IN THE DETERMINATION OF NATIONAL INCOME, University of Southern California, Ph«D., 1968 Economics, finance University Microfilms, Inc., Ann Arbor, Michigan AN ECONOMETRIC ANALYSIS OF THE INFLUENCE OF MONEY SUPPLY AND MONEY DEMAND RELATIONS IN THE DETERMINATION OF NATIONAL INCOME by John Thomas Boorman 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) January 1968 UNIVERSITY O F S O U T H E R N CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFO RNIA 0 0 0 0 7 This dissertation, written by ............JOHN. THOMAS.BOORMAN............ under the direction of h.%3....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 I L O S O P H Y ■ Z f t e t h c < ? ■ Dean Date J an u a ry . 1968 DISSERTATION COMMITTEE TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION .................................... 1 The Purpose of This S t u d y ............ 1 The Precedent in the Literature..... 1 The Wealth Constraint in Economic Theory . 8 The Structure of Our Model and the Mode of Our D a t a ......................... 10 An Overview of the Study.............. 13 II. REVIEW OF THE LITERATURE.................. 15 Simultaneous Equation Models ................ 15 The Klein-Goldberger Model of the United States................................ 16 Ronald Teigen's Structural Equation Model of Money Supply and Money Demand .... 20 The money supply equation ............. 21 The money demand equation ............. 23 The reduced form income equation .... 24 Critique.............................. 25 The Financial Sector Model of the Brookings Quarterly Econometric Model of the United States.......... 28 The financial submodel as a complete m o d e l .............................. 28 ii iii CHAPTER PAGE The financial submodel as integrated with the complete Brookings model . . 32 Summary.................................... 34 The Demand for Money.................. 35 A Review of Theory.................. 35 The Quantity Theory of Money..... 36 The Liquidity Preference Theory .... 39 The Inventory Theoretic Approach .... 43 The Portfolio Approach .................. 46 Empirical Investigations of Money Demand . 47 The definition of "money"....... 4 8 The determinants of the demand for money 4 9 The interest elasticity of the demand for m o n e y ..................... 49 Wealth as a constraint in money demand relations..................... 54 Conclusions and implications for our s t u d y ......................... 60 The Supply of M o n e y .......................... 61 A Review of the Theory of Money Supply Determination .................. 61 The deposit expansion mechanism .... 61 "Reserve Position" Theory ............. 64 iv CHAPTER PAGE Free reserves and the "Policy Target" debate.................................. 69 Specification of Empirical Money Supply Relationships ........................... 73 The study by Polak and White........... 74 Ronald Teigen's use of the "potential money stock" concept.................. 76 The money supply "Schema" of Karl B r u nner................................ 77 III. FORMULATION OF A MODEL OF THE MONETARY SECTOR 86 Money Supply.................................. 87 Development of the Accounting Framework . 87 The bank reserve equation............. 88 Intermediate influences between bank reserves and the money stock......... 93 Formalization of the assumed accounting structure............................. 94 Specification of a testable form for our m o d e l ............................. 100 Commercial Bank Holdings of Excess Reserves........................ 104 Excess reserves and vault cash......... 106 Constraints on commercial bank portfolio management............................. Ill V CHAPTER PAGE The determinants of desired excess reserve holdings ........................ 113 Member Bank Borrowing...................... 123 Commercial bank borrowing and free reserves............................... 12 3 A synthesis of theories of the deter mination of bank borrowing........... 12 5 Specification of the demand for borrowed reserves equation ........... 130 The Demand for Money......................... 134 The Demand for Demand Deposits .............. 135 Questions on the empirical measure of the interest r a t e .................... 136 Considerations on the empirical measure of the wealth constraint............. 140 The form of the functional relation . . 145 The influence of short run factors on our m o d e l ............................. 145 The Public's Demand for Currency ............ 147 The motives for holding currency .... 148 The determinants of the public's demand for currency........................... 151 The Demand for Time Deposits at Commercial B a n k s .................................... 155 vi CHAPTER PAGE Time deposits within our money supply framework......................... 156 The determinants of the public's demand for time deposits................ 161 IV. FORMULATION OF A MODEL OF THE REAL SPHERE . . 167 The Consumption Function .................. 167 The role of liquid assets in the consumption function .................. 169 Wealth and the "life cycle” hypothesis . 174 Professor Friedman's permanent income hypothesis......................... 179 The relation between Friedman's hypoth esis and our own study............ 182 The specification of the consumption function........... 184 The Determinants of Investment Expenditures ............................. 191 Gross non-agricultural business expen ditures on plant and equipment— a wealth model ........................... 195 Inventory investment expenditures . . . 203 The treatment of non-business construc tion expenditures .................... 210 The Term Structure of Interest Rates . . . 214 vii CHAPTER PAGE Traditional explanations of the term structure of interest rates ........... 215 The expectations hypothesis ........... 216 The liquidity preference theory . . . 219 The market segmentation hypothesis . . 222 The "Preferred Habitat" Theory ........... 225 The specification of the term structure equation................................. 227 Specification of the weight pattern and description of the "Almon" technique . 230 The Price Adjustment Equation ............. 233 The price level in classical analysis . 234 The price level in Keynesian analysis . 236 Specification of empirical tests on factors influencing the movement of prices................................... 239 Specification of the dependent variable 243 V. REVIEW OP THE MODEL AND METHODOLOGICAL PROBLEMS INCURRED IN ITS ESTIMATION .... 245 The Complete Model.......................... 245 Data employed in our estimates........... 246 Summary of the model ............... 249 Least Squares Estimates and the Specifica tion of the Error T e r m s ................. 254 viii CHAPTER PAGE Simultaneity and Least Squares Estimates . Estimation by Simultaneous Equation Techniques............................. 256 Other Methodological Problems ........... 259 Multicollinearity ...................... 259 Autocorrelation ........................ 2 60 Methodological problems introduced by the use of a "mixed m o d e " ......... 262 VI. A PRESENTATION OF OUR RESULTS............. 267 Estimates on the Final Form of Our Model . . 276 The Consumption Functions ................ 277 The Inventory Investment Equation .... 283 Residential Construction Expenditures . . 2 85 Business Investment in Plant and Equipment 286 The Term Structure Equation........... 290 The Price Adjustment Equation ........... 293 Money and Time Deposit Demand Equations . 297 The Bank Reserve Equations............. 304 Evidence on Some Disputed Points ........... 313 The money supply relation ............. 313 The interest elasticity of money demand 316 Simultaneous equation estimates vs. single equation results ............. 318 Estimates of Sectoral Submodels ........... 321 ix CHAPTER PAGE The real s e c t o r ..................... 322 The monetary s e c t o r ................. 323 A Comparison of Results ...................... 329 VII. SUMMARY AND CONCLUSIONS................... 337 The Bank Reserve Equations ............. 338 The Expenditure and Stock Demand Equations 340 Monetary Influences in the Determination of Real Sphere Expenditures........ 343 Suggested Directions for Future Research . 346 APPENDIX.................................................. 351 BIBLIOGRAPHY ............................................. 364 LIST OF TABLES TABLE PAGE I. Two Stage Least Square Estimates on Various Forms of the Interest Rate Constraints on Commercial Bank Holdings of Excess Reserves and Borrowings .................... 273 II. Short Run Elasticities of the Variables on the Left with Respect to (DD+CURR) and (Wealth) .................................... 282 III. Interest Elasticities of Business Expendi tures on Plant and Equipment........... . 2 89 IV. Bank Reserve Equations....................... 305 V. Short Run Elasticities of (DDa(jj) with Respect to (rB) and (rdisc) ................ 316 VI. The Per Cent Change in the Elasticities of the Endogenous Variables with Respect to Variables Listed from the Single Equation to the Simultaneous Equation Estimates . . 320 VII. Comparison of the Results of Submodel and Complete Model Estimates .................. 327 VIII. Elasticities.................................. 330 x CHAPTER I INTRODUCTION The Purpose of This Study Our primary purpose in this study shall be to de velop a theory of the determination of the money stock and to test that theory within the framework of a simultaneous equation model of income determination which postulates wealth as a significant constraint on individual economic behavior. The primary focus of the analysis shall be upon an explication of an accounting framework of the monetary system and a specification of the most important behavioral relations within that system which determine the use of the monetary base supplied by Federal Reserve policy. By inte grating the behavioral relations of the monetary sector of our model with "basic” behavioral relations explaining ex penditures in the "real sphere" of the economy and by test ing these relations within a simultaneous equation system, we hope to be able to derive relatively unbiased estimates of some of the more important structural parameters of the economy. The Precedent in the Literature Many of the relations which we wish to investigate 1 2 have already been subjected to a certain amount of empiri cal testing. Most of this work has been in the form of single equation least squares regressions on time series data. Studies employing these techniques have concen trated primarily on economic relations involving consump tion and investment expenditures and the demand for money. Much less work has been done in formulating even the most basic postulates of money supply theory in an operationally meaningful form and subjecting these formulations to empir ical analysis. However, the results of these investiga tions employing single equation techniques must be judged with care, for these techniques are subject to the criti cism that they may yield seriously biased or even meaning less results. The valid use of these techniques presup poses a one way interaction of the explanatory variables on the dependent variable if we are to be able to perform cer tain useful statistical tests on our estimates. However, in the usual situation, economic relations are not in real ity unidirectional. Rather, interdependence and mutual action and reaction (simultaneity) generally characterize the relations postulated by economic theory. The applica tion of single equation estimation techniques, therefore, introduces what has come to be called "simultaneous equa tions bias" into the estimates of the parameters involved.^ 1The source and nature of "simultaneous equations Hence, given the interdependent nature of all markets in the economy, it is highly unlikely that the estimates de rived from such tests will satisfactorily approach the true bias” may be illustrated as follows: Consider the usual supply-demand relationship as drawn below. time (t) time (t+1) time (t+2) supply S - demand D supply S' - demand D' supply S" - demand D” Observed price-quantity figures are A, B, C at times t, t+1, t+2, respectively. Q/r An attempt to fit a statistical demand or supply curve to actual real world observations will not, in fact, yield the desired relationships except in very special circumstances. The usual time series observations of prices and quantities do not correspond to either any one demand curve or any one supply curve, but rather, they are intersection points of various supply and demand curves which are almost continu ously shifting either randomly or systematically due to the influence of outside factors. Hence, attempts to derive single equation estimates of these curves on the basis of observed data will actually result in a statistical construct which is neither a supply curve nor a demand curve. For example: The least square regression line which could be fitted to the data above would be something like BB*. This line would have a nega tive slope in the situation drawn here only because of the tendency for the supply curve to shift relatively more than the demand curve. Yet a statistical study of the data in volved could easily be misunderstood by the unwary to rep resent the true demand relation. This would lead one to accept a biased estimate of the slope and, thus, of the elasticity of the demand curve. The only way in which such time series data could readily yield true structural estimates of either the sup ply curve or the demand curve would be in the very special circumstance where one of the curves is stable and the shifting of the other curve traces out points along the structural parameters which the investigator seeks to esti mate. Thus, we must view the recent results obtained by investigators using these techniques as preliminary and approximate at best, for it is impossible to know exactly how seriously these statistical inaccuracies bias the final estimates derived from the empirical observations. The fairly recent development of relatively inex pensive techniques for the estimation of relations postu lated within the framework of a complete simultaneous equa tion system, has afforded a variety of methods by which an investigator may take explicit account of those interdepen dencies of the economic system which seem most significant desired curve. P This is pictured below. P Q '/t To get around this problem, the true interaction of supply- demand relations in determining price-quantity figures must be considered. This can only be done by specifying a si multaneous equation model including both a supply equation and a demand equation, and taking care to observe the fa miliar rules for "identification." For a more complete discussion of this problem, see Jean Bronfenbrenner, "Sources and Size of Least Squares Bias in a Two-Equation Model," Studies in Econometric Meth od, editors, Wm. C. Hood and Tjailing C. Koopmans, Cowles Commission Monograph, No. 14 (New York: John Wiley & Sons, Inc., 1953), pp. 221-235. on a priori grounds. The availability of these techniques has led to the publication of a fairly large number of simultaneous equation models in the past few years. Each of these models has its own distinguishing characteristics, but the great majority of them have focused upon the basic consumption and investment expenditure relations of the real sphere. Only a very few of these studies have been carried out along the lines of our own inquiry, attempting to include some of the specific monetary relations of the economy within the structures postulated by their respec tive models. Three of the most important models which have made some progress along these lines are: (1) The Klein- Goldberger Model of the United States covering the period 1929-1952, (2) The Brookings Quarterly Econometric Model of the United States, and (3) Ronald Teigen's 1964 Model of the United States.^ Even these studies, however, are char- 2Lawrence R. Klein and Arthur S. Goldberger, An Econometric Model of the United States 1929-1952 (Amsterdam North Holland Publishing Company, I$S"5) ; J. S. Duesenberry et al. (editors), The Brookings Quarterly Econometric Model oT tKe United States (Amsterdam: North Holland Publishing Company7 1^65); and Ronald Teigen, "Demand and Supply Func tions for Money in the United States: Some Structural Estimates," Econometrica, XXXII, No. 4 (October, 1964), 476-509. Two additional recent works came to my attention near the completion of the present model. These are (1) Ronald Teigen's own expansion of his 1964 model to include an endogenous "real sphere": "An Aggregated Quarterly Model of the U.S. Monetary Sector: 1953-1964" (mimeo graphed), and (2) Stephen Goldfeld's Commercial Bank Behav ior and Economic Activity (Amsterdam: The North Holland 6 acterized by some seemingly very important omissions. In every case, they either fail to postulate explicit rela tions to explain the use of bank reserves in the determina tion of the money stock, or they fail to integrate the money supply relations which they do specify with the "real sphere" expenditure relations of the model. This is not to say that these models do not give some consideration to the financial sector of the economy; some even go so far as to include a specific money supply function within the struc ture of the model. This is the case in Ronald Teigen's work, for example. Yet, in each of these studies listed, the final structure specified in the model either elimi nates money supply as an endogenous factor or makes the real sphere independent of the relations which describe the determination of the money stock. In Chapter II, we shall review in detail the structures postulated in these three models. At that time, we shall see exactly how each of these models treats the monetary relations of the economy and just how completely these behavioral relations of the monetary sector are integrated with the expenditure rela tions of the real sphere in the final model. Publishing Co., 1966). These works contain many elements similar to those in our own model. Although no complete review and integration of these works was possible at this late date, some similarities between our own work and these models have been pointed out in Chapter VI. 7 Thus, we see that the two basic problems of money supply theory— the specification of the behavioral rela tions involved in the determination of the money stock and the explication of the transmission mechanism by which these monetary factors influence the variables of the real sphere— have not been successfully integrated within a single model in any of the empirical work done to date. Those works which have been noted above have, at best, covered only one of these problems; nonetheless, they pro vide a sufficient basis for us to attempt a combined anal ysis of these problems. For, under the impetus provided by these studies and by other works carried out by Brunner, Brunner and Meltzer, Polak and White, and Teigen,-* the tradition in macroeconomic models of assuming that the money stock is fixed unequivocally by the monetary author ities seems to be rapidly disappearing. In the combined product of these works, we find that the first steps have been taken towards achieving a more complete understanding ^Karl Brunner, "Schema for the Supply Theory of Money," International Economic Review, II, No. 1 (January, 1961); Karl Brunner and Allan H. Meltzer, "Some Further Investigations of Demand and Supply Functions for Money," Journal of Finance, XIX, No. 2 (May, 1964); Phillip Cagan, Determinants and Effects of Changes in the Stock of Money 1875-1960 (New York: nTb .E.R., distributed by Columbia University Press, 1965); J. J. Polak and W. H. White, "The Effects of Income Expansion on the Quantity of Money," I.M.F. Staff Papers, IV (August, 1955), 398 ff.; and Ronald Teigen, loc. cit. of the multitude of forces which bear an influence upon the determination of a given money stock and of the effect of changes in that stock upon the "real" variables of the economy. We propose to continue this trend by integrating an analysis of the behavioral relations describing those factors which either absorb or contribute to the supply of bank reserves within a complete "wealth constraint" model describing the determination of national income. The Wealth Constraint i n Economic Theory Our decision to focus upon wealth as the prime con straint on individual economic behavior grows out of the success which many theoretical and empirical studies have had in using this variable to explain activity in various sectors of the economy. In several recent studies, various behavioral relationships which postulate wealth or net worth (defined differently in these various studies) as one of the prime conscious restraints on the actions of diverse agents in different sectors of the economy have been tested successfully. Friedman's permanent income hypothesis,^ the work done by Modigliani, Ando and Brumberg on the life 4Milton Friedman, A Theory of the Consumption Func tion (Princeton, New Jersey: Princeton University Press, 1537). cycle of saving,-* Meltzer's time series study of money demand,® a recent dissertation written by Frederick Hammer^ which develops a wealth model of business investment, and some of the theoretical work done on portfolio analysis, all indicate a prominent role for some measure of wealth or net worth in the determination of individual economic be havior. The success of the theories presented in these works immediately suggests the interesting possibility of developing a model based on the results obtained by these individual investigators and structured around one unifying concept— the wealth constraint. So many investigators have constructed single equation models along these lines that it seems a sufficient basis has been established for inte grating some of their work and testing their ideas within a unified framework. Obviously, this does not mean that we must slavishly accept the specific structural forms origi nally presented in these works and try as best we can to 5Albert Ando and Franco Modigliani, "The Life Cycle Hypothesis of Saving: Aggregate Implications and Tests," American Economic Review, LIII (March, 1963). 6Allan Meltzer, "The Demand for Money: The Evi dence from the Time Series," Journal of Political Economy, LXXI, No. 3 (June, 1963). ^Frederick Hammer, "The Demand for Physical Capital Application of a Wealth Model" (unpublished Doctoral dis sertation, Carnegie Institute of Technology, Pittsburgh, 1963) . 10 integrate them with one another. Rather, general consider ations of wealth as a constraint on individual economic benavior will be applied in each of the various sectors of the economy which we consider. On the basis of these broad considerations, specific structural forms will be derived and tested: first by single equation techniques, and then, after likely modifications suggested by these initial results, with simultaneous equation methods. The Structure of Our Model and the Mode of Our Data The formulation of a simultaneous equation model which includes explicit relations to explain the determina tion of the money stock and which is constructed around some measure of wealth as the basic behavioral constraint in the various sectors included within that model, will permit a variety of tests on several of the more important questions currently in the fore of the discussions of mone tary theorists. For example, with real, non-monetary wealth, monetary wealth, and the rates of return on various fixed value assets appearing as arguments in several equa tions, specific measures of the interest elasticity of the supply and demand for money and of the endogenous expendi ture variables can easily be calculated. Likewise, the disaggregation of total non-human wealth into its exogenous non-monetary component and its endogenous monetary compo 11 nent will allow a test of the sensitivity of consumer ex penditures to real balance and real wealth effects. The significance of these tests is indicated by the fact that although most Keynesian economists have generally been willing to accept the theoretical possibility of these wealth and interest rate effects, they have most often de nied the empirical relevance of such effects. As Lawrence Klein writes: My theoretical predilections are very much in favor of a theory of the real economy. The monetary economy, if in good housekeeping order, will not have a dominant influence on real affairs. Never theless, I have tried hard over the years, in sev eral models, to give the benefit of every doubt to money and interest rates when making statistical estimates. My empirical verdict, thus far, is that little evidence can be found for the actual influence of money or interest on real activity.® Hence, inclusion of these separate measures of monetary and non-monetary wealth within our consumption expenditure equations should permit a more precise estimate of the strength of these wealth and real balance effects. We shall further attempt to more effectively rep resent the specific behavioral responses postulated by eco nomic theory by estimating our relations in a form which takes explicit account of differing sectoral responses to ®Lawrence R. Klein, "A Postwar Quarterly Model: Description and Application," Studies iri Income and Wealth, XXVIII (Princeton, New Jersey: Princeton University Press, 1964), p. 56. real and monetary changes. We shall postulate that there exists no "money illusion" in the decisions made by con sumers and investors in determining their real expenditures or in the decisions made by the non-bank public to hold various components of the money stock. On the other hand, we shall assume that Federal Reserve policy determines only the nominal stock of unborrowed bank reserves and that com mercial bank behavior is directly responsive only to the monetary value of the arguments which enter into the deci sion function. Consequently, rather than restricting our data to either nominal or real values exclusively, as was done by the authors of the models referred to above, we shall employ a mixed mode in our estimates. That is, all variables entering both the expenditure relations of the real sphere and the stock demand functions of the non-bank public in the monetary sector shall be measured in real (deflated) terms. All variables entering the commercial bank behavioral relations such as deposit liabilities and reserve measures shall be specified in nominal terms. The price level connecting these real and nominal values shall be included as an endogenous factor within this system.® ^The specification and testing of the system in this form was encouraged in a conversation with Professor Milton Friedman. 1 am most grateful to him for pointing out some of the various ways in which this "mixed mode" could be employed. 13 In this way, we hope to be able to separate the real and the monetary factors affecting price changes and to effec tively isolate both the price induced movements in real balances and the final effects brought about by these move ments. An Overview of the Study In the following chapters, we develop a macroeco nomic model of the United States economy which integrates the real and the monetary spheres of that economy and which focuses upon a wealth variable as a prime constraint in the aggregate expenditure and stock demand relations. Using quarterly data for the postwar period, we derive estimates of the parameters of our model from two stage least squares regressions on the simultaneous relations postulated within the model. In Chapter II, we present a detailed review of the simultaneous equation models introduced above. In addition, we review and summarize those theoretical and empirical studies on "money demand" and "money supply" theory which relate specifically to our own work. In Chapter III, we first develop an accounting framework of the commercial banking system of the United States. Within this framework, we then derive structural equations for the behavioral re lations which explain the sources and uses of commercial 14 bank reserves and the determination of the money stock. After considering some of the theoretical and empirical work done by other authors on "wealth” theories of consump tion and investment expenditures in Chapter IV, we derive our own structural relations to explain these real sphere flow variables. In Chapter V, we present the complete model as specified in the previous two chapters and we dis cuss some of the specific statistical problems incurred in estimating this model. In Chapter VI, we present our re sults. Here we discuss the implications of these results for the theoretical issues noted above, and we compare our estimates with the estimates derived by the authors of the works reviewed in Chapter II. Finally, in Chapter VII, we sum up our results and suggest directions for further re search. CHAPTER II REVIEW OF THE LITERATURE I. REVIEW OF SIMULTANEOUS EQUATION MODELS Since a rather limited amount of empirical and the oretical work on money supply has appeared in the litera ture, it is possible to review in some detail the more im portant contributions in this field. The references to the works by Brunner, Polak and White, Cagan, and others cited in the first chapter will be considered in more detail in Part III below when we present a complete review of the more important econometric models presented in recent years which take specific consideration of the financial or mone tary sector of the economy as an endogenous element. These will include the Klein-Goldberger model, the Brookings quarterly model, and Ronald Teigen's 1964 model. In con sidering the first two models, we will restrict our atten tion to those parts of the models immediately relevant to the monetary factors which we shall study. In the case of Teigen's model, its small size and simple structure will allow us to review the entire work. We consider first the oldest and still most famous of these works, the Klein-Goldberger model. 15 16 The Klein-Goldberger Model of the United States The financial sector of the Klein-Goldberger model consists of four equations: (1) the household liquidity preference equation, (2) the business liquidity preference equation, (3) a "term structure of interest rates” equation in which the long term rate is determined by several lagged values of the short term rate, used as proxies for expected short term rates on the assumption that expectations are primarily determined by recent experience, and (4) a money market adjustment equation. In examining household liquidity preference, Klein and Goldberger follow the empirical practice established by James Tobin of separating total money balances into two component parts: transactions balances and idle balances.^* They first calculate the ratio between cash balances and income in 1929. Then, under the assumption that "no bal ances are idle during this period of brisk turnover and brisk trade,this ratio is taken to be an estimate of the classical parameter expressing total cash balances as a 1James Tobin, "Liquidity Preference and Monetary Policy," Review of Economics and Statistics, XXIX (February, 1947), 124-1517 ^Lawrence R. Klein and Arthur S. Goldberger, An Econometric Model of the United States, 1929-1952 (Amster dam! North Holland-PubTisHing Company, 1955), p. 25. 17 proportion of income. Consequently, transactions balances may be defined as the product of this estimated parameter and real disposable income. "Idle balances," then, are defined as the difference between total liquid asset hold ings of households^ and this measure of transactions bal ances. Hence, as derived by Klein and Goldberger, this is the equivalent of the monetary concept of "idle balances" defined by Tobin, plus other items more usually classified as liquid assets or money substitutes (a concept, therefore, which is even broader than Friedman's concept of "temporary abodes" of purchasing power). The business liquidity preference equation is de veloped on the premise that "the major business choice be tween securities and goods is a short run decision, whether to hold inventories for a short period or to hold short term securities (commercial paper); whether to borrow for a short period or to forego the possibility of inventory 4 gains." The cost of borrowing or the return on securities is measured by the short term rate of interest; the gain or loss on inventories is measured by the price changes occur ring during the period in which the inventories are held. ^Total liquid assets are here defined as savings deposits + United States Government Bonds + savings and loan shares + demand deposits + currency. ^Klein-Goldberger, 0£. cit., p. 27. 18 Furthermore, by viewing the business transactions motive as substantially similar to the motive of households in hold ing cash, and by calculating the minimal ratio of currency and demand deposits to the wage bill (a proxy for total business transactions) as an estimate of the classical pa rameter, a measure of idle liquid balances held by business enterprises can be derived. In this way, a very broad concept of idle liquid balances (again, not the more familiar concept of idle money balances) is related in a multivariate linear equa tion to the rate of change of prices, the short term inter est rate, and a lagged measure of end-of-year total liquid assets held by enterprises. Thus, on the demand side of the money market, Klein-Goldberger focus on liquid assets, both money and money substitutes, as the measure to be explained. They are concerned with "money" in the more popularly defined sense of demand deposits plus currency only insofar as they wish to separate out that part of this money stock used for transaction purposes by businesses and households from the total stock of liquid assets. These derived liquidity measures appear in only two other equations of the model: "total liquid assets" held by households appears in the con sumer expenditures equation as a proxy for wealth, and "total liquid assets" held by enterprises enters the 19 investment demand equation as a measure of the funds other than recent profit receipts available for internal financ ing of investment projects. Bank behavior is brought into the Klein-Goldberger model only in the last equation mentioned above— the money market adjustment equation. Again, however, Klein- Goldberger are not concerned with specific money supply relations. Rather, they concentrate on the rate of change of interest rates as a function of the per cent of reserves held in excess of requirements by the banks of the Federal Reserve System. This money market equation is developed as analogous to the adjustment equation in the labor market where the rate of change of money wage rates is made a function of unemployment— a measure of excess labor supply — and other variables. Thus, the purpose of the equation is to express price changes as a result of "the fundamental law of supply and d e m a n d"5 rather than to express the "stock" relations evident in the market. As Klein- Goldberger note, "the relation . . . is relatively weak and possibly calls for more intensive research."** Thus, we see that Klein-Goldberger focus not on the supply and demand for money balances defined as demand de posits plus currency, but rather, upon the demand for a ^ I b i d . , p. 29 ®Ibid., p. 30. 20 much broader class of assets— total liquid assets held by households and businesses— and the price of these assets in the market. As will be seen below, our study will focus on the more restricted concept of money balances which has become widely accepted as "money" in the literature— demand deposits adjusted plus currency outside banks. Furthermore, the arguments of our consumer expenditures, investment de mand and other equations will include more complete meas ures of wealth than the proxy measure, "liquid assets." Ronald Teigen1s Structural Equation Modelof Money Supply~and Money Demand A much quoted work which develops a structural model of the monetary sector of the economy is the recent presentation in Econometrica by Ronald Teigen. In this work, an attempt is made to get around the problems of si multaneous equations bias by estimating a simple supply- demand model of the monetary sector by means of the Theil- Basmann method of two stage least squares. In this model, an aggregate money supply relation, an "interest-responsive?1 transactions demand function, and a reduced form income equation are estimated jointly for the postwar and inter war periods. Of the three models under review here, this paper is the closest in spirit to the research proposed for this work. It deals specifically with supply-demand rela- 21 tions influencing the money stock; it attempts an inte gration (not completely successful) of these monetary rela tions into a simultaneous equation model which includes a "real sphere" equation; and it has as one of its main pur poses the desire to estimate the structural relations of the monetary sector free of the simultaneous equations bias inherent in the research results of the single equation estimates found in the literature. The money supply equation. In this work, Teigen tries to reduce the analysis of the factors affecting money supply down to the truly exogenous factors over which the Federal Reserve actually has some direct control, rather than assuming (as is usually done in econometric studies) that the Federal Reserve has direct control over the size of the money stock itself. Accepting the insti tutional arrangements (such as reserve requirements) and certain behavioral relations (such as the desired ratio of currency held by the public to the total money supply) as given at any particular time, the author conceives of total reserves in the system as determining a maximum attainable money stock. This, however, can be broken into two parts: (1) an exogenous element based on reserves supplied by the Federal Reserve authorities (unborrowed reserves), and (2) an endogenous element based on reserves created by member bank borrowing. His purpose, then, is to focus on the 22 relations determining bank borrowing so as to explain the ratio of the observed money stock, M, to the exogenously determined component of the total potential money stock, M*. To accomplish this, Teigen views the commercial bank as motivated primarily by profit and risk considera tions. Hence, the major determinant of the degree to which banks will expand the money supply by borrowing from the Federal Reserve and creating "endogenous" reserves is the differential between the cost of borrowing (or holding se curities instead of loans in their portfolio) and the re turn from making loans. As he states: The expected relationship between the ratio M/M* and its proposed functional arguments is straight forward. When the return on loans rises, ceteris paribus, banks presumably will shift the composi tion of their portfolios in such a way that rela tively fewer securities will be held, the margin of excess reserves kept as a buffer against un foreseen contingencies will be cut down in size, and, in general, an effort will be made to expand loans and deposits, causing a rise in the money stock relative to M*. T he opposite effect will result from an increase in the cost of making loans.7 His final money supply function, which is used in the em pirical tests, is a linear relation between the above men tioned ratio and the differential between the cost of borrowing (represented by the discount rate, r) and the 7Ronald Teigen, "Demand and Supply Functions for Money in the United States: Some Structural Estimates," Econometrica, XXXII, No. 4 (October, 1964), 481. 23 return from making loans (represented by the four to six month rate on prime commercial paper, r_) plus two dummy variables included to account for changes which are felt to have occurred in the basic structure of the money supply mechanism over time. The money demand equation. In investigating the determinants of the demand for money, Teigen bases his analysis on the studies done on money demand theory by Tobin and Baumol.® Specifically, he postulates that "under present institutional arrangements, there should exist only a transactions demand for money."® However, the interest foregone by holding money instead of interest bearing assets is a real cost and should be considered in deciding the size of transactions balances. Hence, transactions balances (total money demand) are viewed as interest elas tic and the postulated behavior "leads to the well known square root inventory formula for transactions demand which Baumol and Tobin have derived."10 8william J. Baumol, "The Transactions Demand for Cash: An Inventory Theoretic Approach," Quarterly Journal of Economics, LXVI (November, 1952), 545-556; and James Tobin, "TheInterest Elasticity of the Transactions Demand for Cash," Review of Economics and Statistics, XXXVIII (August, 1956), ?4T^247. ^Teigen, o£. cit., p. 483. lOlbid. 24 Teigen's final structural demand for money equation is a generalization on Tobin's formula. An aggregate de mand for money function is approximated to his derived theoretical relation by considering the demand for money to be determined by the product of the interest rate and a function of income. In treating total money balances as the variable to be explained, Teigen is following the cur rent practice of not trying to separate out idle and active balances. Following the inventory approach, he in fact denies the existence of such idle money balances. In his empirical tests, Teigen estimates two basic models: one in which the demand relation is nonlinear, containing as arguments the term (r_.Y)— the product of the O rate of interest and the level of income, the level of in come itself, and the lagged money stock; and one which is linear in the natural logarithms of these variables. The equations also include seasonal dummy variables which nor malize the model seasonally bn the fourth quarter. (The data employed were series of quarterly estimates not ad justed for seasonal variation.) All of Teigen's estimates are derived from regressions employing levels of all vari ables measured in nominal terms. This contrasts with our proposed use of a "mixed mode.” The reduced form income equation. The structural income relation which appears in the model is a linear 25 function of current exogenous expenditure, net worth, and lagged income. This is a reduced form equation derived from a very simple aggregate expenditures model. The con sumption function is based on formulations derived by Modigliani, Brumberg, and Ando and specifies disposable income and net worth as independent variables. Imports, all taxes, transfers, undistributed corporate profits, and social insurance contributions are viewed as fixed propor tions of Gross National Product, depreciation as a fixed proportion of net worth, and inventory valuation adjustment as a fixed proportion of the change in G.N.P. Investment expenditures, government expenditures and exports are as sumed exogenously determined. The complete model, then, appears as follows: (1) - - f <r - r ) M* C D (2) MD = M <rY, Y, Mt_1) (3) Y - Y (E, NW, Yt-1) where rc, rD, Y, and M are defined above; E is total exoge nous expenditures; and NW is net worth. The net worth measure employed is that derived by Albert Ando for his study of consumer expenditures. Critique. As one of the first attempts in the 26 literature to face the problem of simultaneity in the money supply— money demand relations in the economy, Teigen1s work contains much that is of interest to us. As one of the first attempts along these lines, however, it quite naturally leaves much undone. One of its most seri ous shortcomings, but one that was fully recognized by the author, is the lack of complete simultaneity between the "monetary" and the "real" sectors of the economy. The in come variable appears as an argument in the money demand equation making the monetary sector responsive to changes in the real sphere. The income equation, however, is de void of any monetary influences. Hence, there is no mecha nism in the "real" sector to show the influence of monetary factors. This is a great oversimplification, particularly as regards investment expenditures. As the author himself notes: Ideally, the interaction of the money stock and interest rate with income should also be taken into account. In making income an endogenous variable, the model recognizes this interrelationship; how ever, the treatment of investment as an exogenous variable results in one way causality from the in come equation to the rest of the model, with no true interaction. To the extent that two way causal relationships between money, the rate of in terest, and income exist, failure to recognize this introduces bias into the estimates.11 Teigen feels that the lags involved in the effects running 11Ibid., p. 487. 27 from interest rate changes to investment changes to effects on income make such bias relatively small in a quarterly model such as this. This, of course, is an open question until further research is undertaken. Teigen's model is also open to criticism for the way in which the structural relation describing money sup ply is formulated. First of all, the assumption that cur rency holdings and deposits in non-member banks can be represented as constant proportions of the total observed money supply seems like an overly rough approximation to the true behavioral relations involved over the period covered by the model. Secondly, the model throws little light on the seeming contradiction between the assumption that banks are profit maximizers (given their relative aversion to risk) and the observed behavior of bank borrow ing at times when the discount rate is below the rate of return from making loans (and sometimes even below the rate of return on securities held by banks). We will return to this point below. Lastly, the inclusion of dummy variables, other than seasonal adjusters, in the money supply relation indicates the need for further work to more explicitly explain the nature of the structural changes involved. None of this is meant to detract from the basic accomplish ment of Teigen's research. It is meant, however, to point up the great need for further research along the lines 28 suggested above. The Financial Sector Model of the Brookings Quarterly Econometric Model of the United States The particular focus of attention on total liquid assets which we noted as characteristic of the Klein- Goldberger model is maintained in the financial sector sub model of the complete Brookings model. Here, however, the basic stock of liquid assets is disaggregated into its major components and supply-deraand relations for most of these components are investigated. The financial sector of this model, both in its original form and as finally con densed and modified for inclusion into the complete model, was constructed by Frank de Leeuw of the Federal Reserve in Washington. The financial submodel as a complete model. This financial submodel deals with demand and supply relations in seven United States' financial markets and with five broad groups of transactors in the seven markets. "The typical behavioral equation of the model deals with quar terly changes in one sector's holdings of some asset or liability, expressed as a per cent of a measure of the 29 sector's wealth.For example, the change in total time deposit holdings as a per cent of wealth is expressed as a linear function of the stock of time deposits in the pre vious quarter, last period's disposable income, and non farm residential construction plus expenditures on consumer durables, all deflated by lagged wealth, and the rates of return on time deposits and three month treasury bills. The nineteen equations contained in the submodel may be summarized as follows: 1. Seven portfolio equations like the one above for the nonfinancial sectors: currency, demand deposits, time deposits, saving and insurance claims, household holdings of U.S. securities, household borrowing from financial institutions, and business holdings of U.S. securities. 2. Five portfolio equations for the financial sec tors: holdings of U.S. securities by banks and non-bank finance, bank holdings of excess re serves, bank borrowing from the Federal Reserve, non-bank finance holdings of private securities, non-bank finance holdings of U.S. securities. 3. A term structure equation for U.S. security rates. 4. An equation for the interest rate on private securities and one for the rate on time de posits . 5. Four identities. The basic structuring of these financial equations is based on the assumption that "banks do attempt to con trol the volume of deposits and loans, but they do so. 12Frank de Leeuw, "A Model of the Financial Sector," The Brookings Quarterly Econometric Model of the United States, editors, J. S. Duesenberry et al. TAmsterdam: North Holland Publishing Company, lSTsTT p. 466. 30 according to the present model, mainly by altering the yields they pay on time deposits and the terms on which they expand loans, rather than by direct decision to buy or sell deposits and loans." Hence, "... for four items in the balance sheet— demand deposits, time deposits, the required reserves derived from these deposits, and loans and investments— banks are assumed to accommodate any quar terly changes which the public wishes to make."^-3 This leads to the following structure within the model for the elements most closely related to the supply and demand for money (as we have defined it): 1. On the demand side a. A demand deposit demand equation b. A currency demand equation c. A time deposit demand equation 2. On the supply side a. An equation for bank borrowing from the Federal Reserve b. A bank excess reserve equation c. An equation to determine the yield on time deposits. The supply of "high powered" money (unborrowed re serves plus currency) is assumed to be exogenously deter- 13Ibid., p. 507. 31 mined by the Federal Reserve. It should be noted that there is no explicit supply of money equation within this framework since the Federal Reserve determines the "reserves plus currency" stock and the public can divide that total however it wishes. Like wise, there is no supply of demand deposits relation. Thus, the money stock is determined only in the broadest sense by the establishment by the Federal Reserve authorities of a certain size stock of high powered money. The ability of people to change their currency holdings and, thereby, bank reserves, and the ability of banks to borrow weaken the relation between Federal Reserve action and the actual money supply. As de Leeuw notes: The Federal Reserve open market identity, of course, set limits to a weighted combination of currency, time deposits, excess reserves and demand deposits, but there is no additional control (within the model) over the supply of demand deposits alone. 4 It is interesting to note that the separation of reserves into two components— exogenously determined unbor rowed reserves plus currency and endogenously determined bank borrowing— is similar in spirit to Teigen's formula tion. In fact, de Leeuw shows that a reduced form equation for the supply of money, similar to that of Teigen and closely related to that derived by Karl Brunner in his 14Ibid., p. 484. 32 "Schema" (to be reviewed below) can be derived from the portfolio equation for bank borrowing from the Federal Reserve, the bank excess reserve holding equation, the re quired reserve identity, and the Federal Reserve open mar ket identity. Furthermore, the lack of true simultaneity or complete interaction between the money market and the real sphere of the economy which characterized Teigen's model is also true of de Leeuw1s financial submodel. For, ". . . the equations do not deal with the effects of credit market developments on other markets and thus they do not by themselves have anything to say about the effects of monetary or debt management policies on aggregate income, employment, prices, or foreign transactions.1,15 The financial submodel as integrated with the com plete Brookings model. But what restrictions are placed upon this financial submodel when it is integrated into the complete Brookings model? The relationships which will result obviously depend on the modifications which are made in the submodel to fit it into the larger model. It is at this point that the hopes inspired in us by the fine struc turing of the financial model are depressed. The submodel as finally modified for integration within the rest of the ISibid., p. 527. 33 model contains only the following five relations: 1. The demand for demand deposits in slightly modified form 2. The original time deposits relation 3. The required reserve identity 4. An equation to determine the rate paid on time deposits 5. A slightly modified term structure of U.S. security rates equation In the final condensed form, de Leeuw's model exhibits the following relations with the rest of the model: The short term interest rate appears in equations for housing construction demand and government in terest income; the long rate is in the investment functions and business interest income equation; and cash balances affect consumer demand. These variables and others that are necessary are in de Leeuw's condensed model. His equations show the influence of monetary policy on the money mar ket variables through reserve requirement coeffi cients, time deposit maximum rates and maturity structure of the public debt.16 From these considerations we can see that if we analyze the financial submodel apart from the rest of the Brookings Model, it is possible in the way described above to derive a reduced form equation for money supply. l®Gary Fromm and Lawrence R. Klein, "The Complete Model: A First Approximation," The Brookings Quarterly Econometric Model of the United States, editors, J. S. Duesenberry et al . ~~TAmsterdam; North Holland Publishing Company, 196TT, p. 726. 34 However, there is no possibility of studying the inter action between monetary and credit variables which appear as dependent variables with the real sphere variables such as income, employment, etc., which appear only as exoge nously determined factors. When we turn to the complete Brookings model, there is true interaction and simultaneity between the monetary and credit variables and at least some of the other endoge nous variables of the model such as housing starts, invest ment in inventories, etc. However, in the reduction of the financial sphere from the nineteen equations of the com plete submodel to five equations which emphasize primarily the demand side of the market, the relation between money supply and the other factors has been lost. The focus of the complete model eliminates the interaction between money supply factors and the real sphere variables. This is the interaction which we hope to analyze in our own study. Summary Each of the above models, then, suggests a defi nite framework within which the financial sector and, more specifically, the money supply relations in the econ omy may be structured within an econometric model. With Klein-Goldberger, the focus is on the demand for "idle" liquid assets; with de Leeuw, in the complete submodel at 35 least, disaggregation emphasizes demand and supply rela tions for most of the components of the liquid asset stock; for Teigen, analysis is restricted to supply-demand rela tions for money as we have defined it. But in each case, something of the total money supply— money demand— income determination relation is lost. This is what we will at tempt to provide in our own analysis and testing. As a beginning, we turn to explicit consideration of the theo retical work which has been done in money supply and money demand determination and to a review of the single equation estimates which have been presented as evidence of the validity of some of these theories. II. THE DEMAND FOR MONEY A Review of Theory Empirical investigations of money demand functions have attempted to test the relationships postulated by many diverse theories developed to explain the behavior of in dividuals in holding monetary balances. Despite differ ences in the derivation or statement of each of these many theories, they may be conveniently grouped under four broad headings: the Quantity Theory of Money; the Liquidity Preference (asset demand) Theory; the inventory theoretic approach to the demand for transactions balances; and the Portfolio approach to the demand for money. 36 The Quantity Theory of Money. The Quantity Theory starts with the postulate that since money yields no util ity to the holder, under perfectly static market equilib rium conditions when receipts and expenditures would be synchronized, there would be no need to hold money balances. Only the introduction of time and the disparity between receipts and expenditures in the actual dynamic economy can explain the existence of such balances. More com pletely, it is both the randomness of the timing of re ceipts and expenditures and the possibility of unforeseen contingencies.which causes people to hold money, rather than to convert all cash balances into income earning as sets immediately upon receipt of those balances. We may cite Patinkin for a concise statement of the Classical theory. In its cash balance version . . . neoclassical theory assumed that, for their convenience, indi viduals wish to hold a certain proportion, K, of the real volume of their planned transactions, T, in the form of real money balances. The demand for these balances thus equals KT. Correspondingly, the demand for nominal money balances is KPT, where P is the price level of the commodities transacted. The equating of this demand to the supply of money, M, then produced the famous Cambridge equation, M = KPT. In the transactions version— associated primarily with the names of Newcomb and Fisher— the velocity of circulation, V, replaced its re ciprocal, K, to produce the equally famous equation of exchange, MV = PT.l? i^Don Patinkin, Money, Interest, and Prices (Evan ston, 111.: Row, Peterson and Company, 1956), p. 57. 37 In this view, then, the demand for monay was seen to vary directly with the level of transactions or income: M = KY. M = nominal money stock Y = current dollar value of national income The relationship which was assumed to exist between mone tary balances and income, as summarized by the parameter, K, was thought to be the result of historical, institu tional, and behavioral factors. These included the length of the period between wage and salary payments, the degree of sophistication of the population in the use of credit, the extent to which the working class accepted the use of banking facilities, the degree of vertical integration of business firms and, in the case of the Cambridge economists, individual preferences and expectations. It was further assumed that these factors would change only slowly over time and, hence, that the velocity of circulation of these money balances would remain quite stable even over long time periods. Thus, the Classical Theory in its rigid form left no room for the interest rate to influence money holdings. Ignoring any possible real balance effects, Say's Law and the Quantity Theory together assured the in dependence of the real variables of the economy— output, employment, interest rates— from the variables of the mone tary sector and led to the familiar conclusions about the 38 ineffectiveness of monetary and fiscal policy. Only during one of Fisher's "transition periods," or some similar pe riod representing a temporary divergence from equilibrium, could there be any interaction between the "real" and the "monetary" variables of the economy. Even then, however, this interaction could bring about no lasting change in the real sphere and could cause no lasting effect upon the com parative static full employment equilibrium towards which the economy was tending. Hence, with this analysis as a basis, the classical economists reached the familiar con clusions about the effects of monetary changes upon the equilibrium level of prices and the inability of government fiscal operations to affect the overall level of real ac tivity in the economy. The Quantity Theory remains an important tool today 18 primarily in the work of Milton Friedman. In his view, the income-money balance relation, as reformulated in his work, is the most stable of all macroeconomic relationships and, hence, the one which should form the basis of our analysis for policy decisions. Friedman's empirical work in this field centers around his own theoretical construc tion of the velocity function. His version of the equation l ^ M i l t o n Friedman, "The Quantity Theory of Money— a Restatement," Studies in the Quantity Theory of Money, ed. Milton Friedman (Chicago: University of Chicago Press, 1956). 39 of exchange is a more sophisticated one than the simple classical formulation since, in his view, the velocity of circulation need be neither constant nor even slow to change over time. Rather, he postulates a stable velocity function containing several interest rates, the rate of price variation, income, and wealth as arguments. As we shall see below, however, his empirical results lead him to deny the significance of any interest rates in the deter mination of desired money balances. Thus, the major con clusions of the Classical Quantity Theory are maintained in his work. The Liquidity Preference Theory. In the Classical view, the emphasis is on money as a medium of exchange and as a mechanism useful for smoothing out the discrepancies between receipts and expenditures. We have Keynes to thank primarily for the present emphasis on money as a store of value, i.e., as an asset alternative to other assets, in cluding income earning assets, which we may desire to hold. While accepting the precautionary and transactionary mo tives for holding money as delineated by the classical and neoclassical economists, Keynes insists that money be treated as an asset which people may quite rationally hold as a store of value even though it yields no nominal return. In the Classical system, the time preference of individuals was summed up in the psychological propensity 40 to save. Within that system, the interest rate functions as a balancing mechanism which equates the demand for in vestment funds with the supply of saving as determined by the community's propensity to save. However, the possi bility of holding money itself as a store of value indi cates that "... the psychological time preferences of an individual require two distinct sets of decisions to carry 1 Q them out completely." The first decision, embodied in the psychological propensity to consume, determines how much of his income an individual will save ". . . in some 20 form of command over future consumption." This immedi ately implies a second decision: namely, what specific form will this "command over future consumption" take. As Keynes states: Does he (the individual) want to hold it in the form of immediate, liquid command (i.e., money or its equivalent)? Or is he prepared to part with immediate command for a specified or indefinite pe riod leaving it to future market conditions to determine on what terms he can, if necessary, con vert deferred command over specific goods into immediate command over goods in general? In other words, what is the degree of his liquidity prefer ence— where an individual's liquidity preference is given by a schedule of the amounts of his re sources, valued in terms of money or wage units, John M. Keynes, The General Theory of Employment, Interest, and Money (New York: Harcourt, Brace and World, Inc. , m e n P~ 166. 20Ibid. 41 which he will wish to retain in the form of money in different sets of circumstances.21 In Keynes' view, then, the total demand for money is the result of a transactions and precautionary motive determined primarily by the level of income and general economic activity, and a speculative motive which "... usually shows a continuous response to gradual changes in 22 the rate of interest." Thus, he specifically writes these components of total money demand as separate additive components in a money demand function: M = (Y) + M2 (r), where M^ is the amount of money demanded for transactionary and precautionary purposes and M2 is the amount demanded to satisfy the desire for speculative balances; Y is the nomi nal level of income and r is the rate of interest. This specification has recently been criticized by Boris Pesek and Thomas Saving. While in substantial agree ment with Keynes' discussion of the determinants of the demand for money, they note that "... the demand for money equation reproduced above (M = M^(Y) + M2<r)) has little relation to his verbal analysis of the demand for money. whereas Keynes writes an additive function dis playing the transactions demand as determined by the level 21Ibid. 22Ibid., p. 197. ^Boris P. Pesek and Thomas R. Saving, Money, Wealth and Economic Theory (New York: The Macmillan Company, 1 5 3 7 ), p. 325. 42 of income, and the speculative demand as determined by the rate of interest, he presents a very different theory. For, in his discussion, he notes explicitly that the trans actions demand will depend upon income and "... the effective cost of holding idle cash." Likewise, in dis cussing the speculative demand he notes that "... uncer tainty as to the future course of the rate of interest is the sole intelligible e x p l a n a t i o n."2^ Hence, he should have written his function as M = M^(Y, r) + M2<X), where X is an expectational function which, of course, may depend upon the current interest rate and other factors. Three results of the Liquidity Preference Theory, as compared to the Quantity Theory outlined above, should be noted specifically. First, the money demand function specified is interest sensitive— perhaps highly interest elastic under certain conditions. Second, the determina tion of the interest rate by the supply and demand for funds to be held for speculative purposes destroys the in dependence of the real sphere variables from monetary in fluences. Third, the conclusions of the Quantity Theory noted above concerning monetary and fiscal policy must be modified so as to show positive effects for both these mechanisms in modifying the real and monetary equilibrium of the economy. 2*Keynes, o£. cit., p. 201. 43 The Inventory Theoretic Approach. The results of empirical tests of one hypothesis often suggest modified hypotheses or new hypotheses to deal with a given phenome non. Disputes concerning the results of specific tests on Keynes' formulation of the Liquidity Preference theory, together with the recognition of the growing importance of a certain group of financial intermediaries not previously of significant importance in the economy, have led to a reformulation of money demand theory using the analytical techniques developed in the field of inventory analysis. This view may take many forms. On the one hand, it may simply be asserted that the transactions component of the demand for cash balances, as well as the speculative compo nent, will be interest elastic at some interest rates. On the other hand, the much stronger assertion may be made that the assets issued by financial intermediaries such as the savings and loan associations which we find in the modern developed economy, as well as the variety of many other kinds of liquid assets available, completely elimi nate the need for holding speculative balances. According to this latter view then, all money balances are transac- tionary balances and they are interest elastic at all rates of interest. This view of the interest elasticity of transac- tionary balances, though incorporated within Keynes' own 44 analysis, was first popularized by Alvin Hansen. The com plete statement of this theory has been explicitly analyzed by William J. Baumol and James Tobin. Specifically, Tobin focuses his analysis on the interest elasticity of the demand for cash at a given volume of transactions. As he states: The failure of receipts and expenditures to be perfectly synchronized certainly creates a need for transaction balances. But it is not obvious that these balances must be cash. By cash I mean gen erally acceptable media of payment. . . . Why not hold transaction balances in assets with higher yields than cash, shifting into cash only at a time an outlay must be m a d e ? 2 5 It follows from this, that the degree to which an individ ual will be willing to switch continuously from money to interest earning assets, that is, the degree to which he will try to conserve on his transactions (cash) balances, depends on costs of switching assets for money (transaction costs) relative to the return on those assets. The consideration of transactions balances in these terms leads to the application of inventory theoretic anal ysis to the holding of cash balances. People desire money to smooth out the irregularities in the payments-receipts process. Businessmen desire an inventory of goods to smooth out the irregularities in the sales-deliveries 25«robin, "The Interest Elasticity of the Trans actions Demand for Cash,* o£. cit., p. 241. 45 process. Therefore, just as businessmen try to keep enough inventory on hand to assure they will not be caught short and lose a sale or incur embarrassment, and just as they try to minimize the cost of holding those inventories, (storage costs, tied up capital, etc.), so, too, individ uals will try to adjust their monetary balances to a level sufficient to meet their expected transaction needs at the same time that they try to minimize the income foregone from holding this monetary inventory instead of income earning assets. Thus, as Baumol demonstrates, inventory- management principles can be applied to transactions bal ances. Such an application leads to an expression of the optimal level of transaction balances relative to the in terest rate and the level of income. Specifically, under rather restrictive assumptions, these balances can be shown to vary proportionately with the square root of income and in inverse proportion to the square root of the rate of interest. This is analogous to the familiar "square root law” of physical inventory management. Thus, in this view, as in the Keynesian view, mone tary balances are seen to be interest elastic. But as op posed to the strict Keynesian formulation as represented by Keynes' additive money demand relation, it is not so cer tain here that total money balances are actually the sum of two more or less separable components: active transactions 46 balances and inactive speculative balances. The Portfolio Approach. The second significant modification of Keynes' view of the demand for money con cerns the extension of Keynes' own comparison between money and one other asset, bonds, to an even more general view of money as one among all the possible assets which people desire to hold in their portfolios of financial and physi cal wealth. In this view, individuals desire to attain a certain combination of yield and risk through the diversi fication of their portfolio. In this schema, money can be viewed as an idle balance, as one of the assets which indi- vidulas wish to hold as a store of value, or as an active transactions balance, i.e., as the mechanism through which trading in financial and physical assets is carried out. In the former view, the size of money holdings would obvi ously be constrained by the size of the total portfolio; or from an aggregative point of view, the demand for money would be directly related to some measure of total national wealth. In the latter view, the number and value of trans actions among these assets would be related to the size of portfolio and the desired money holdings would depend upon these transactions; thus, portfolio size would again be the ultimate determinant of the size of monetary balances. Total money holdings, therefore, would be a function of wealth, income and a spectrum of yields on the other assets 47 held in the portfolio. The separation of the effects of income and wealth on these money holdings is a very diffi cult empirical task, however, and remains one of the more stubborn problems in money demand analysis. Empirical Investigations of MoneyDemand The multiplication of such diverse theories as those summarized above has stimulated attempts by many authors to submit one or more of these theories to empiri cal testing. The questions proposed for testing may be conveniently summarized under three familiar headings: 1. The definition of money appropriate for such investigation. 2. The arguments which should be included in the demand for money or velocity function; more specifically, the determination of the statis tical significance of income, interest rates, and wealth in empirical money demand functions. 3. The stability of the money demand or velocity function. These are convenient heuristic categories rather than des ignations of specific questions which can be treated sepa rately. The stability of a particular demand for money function is certainly dependent upon the arguments which one includes in that function. Likewise, the variables 48 chosen to be included as explanatory variables in the func tion will depend upon the particular definition of money which the investigator employs. The definition of "money." Some of these questions proposed in the literature seem closer to satisfactory settlement than others. For example, most investigators have agreed that the relevant definition of money to be used in these empirical studies is "currency plus demand 2 6 deposits adjusted." The strongest voice of dissent in this matter comes from Milton Friedman. Friedman believes that the near perfect substitutability between demand and time deposits as "temporary abodes" of purchasing power requires the addition of time deposits to the above defini tion of money. He feels that if time deposits are included within the concept of total money balances, less error will be introduced into our studies and into the measurement of historical monetary statistics than would be the case if they were not included. This is most certainly true within the framework of the very long run studies upon which Friedman concentrates, for it is impossible to get any reliable data on what we now refer to as "demand deposits" ^Allan H. Meltzer, "The Demand for Money: The Evidence from the Time Series," Journal of Political Econ omy, LXXI, No. 3 (June, 1963), 2J T ~ . 49 for the period prior to the 1930's. It is not clear, how ever, why this concept of money should lead him to draw the line at commercial bank time deposits to the exclusion of savings accounts, holdings of U.S. government securities, and the various other highly liquid, interest earning as sets. This definitional dispute has important implications which must be considered when comparing the results of Friedman's work with the results obtained through other empirical investigations. This is particularly true when comparing the validity of conflicting conclusions concern ing the significance of various arguments in explaining the variation observed in actual monetary balances. The determinants of the demand for money. The ma jor disputes over the specification of the arguments which should appear in any empirical money demand or velocity function have centered around the interest rate, the defi nition of income, and the relevant wealth concept. We may review these in succession. The interest elasticity of the demand for money.— The importance of finding empirical evidence of the role of the interest rate in the money demand or velocity function stems from the contrast between the Quantity Theory which, in its most rigid form, assigns no monetary role at all to the interest rate, and the Liquidity Preference Theory 50 which assigns it a crucial role. In Friedman's restate ment of the Quantity Theory, the interest rate appears in the velocity function. In his empirical work, however, Friedman claims to have found no need for employing inter est rates to derive what he considers to be a satisfactory velocity function. As he states it: In our secular analysis, we have found that the yield on corporate bonds is correlated with the real stock of money and velocity in the expected direction. . . . Bond yields, however, play nothing like so important and regularly consistent a role in accounting for changes in velocity as does real income. The short term interest rate was even less highly correlated with velocity than the yield on corporate bonds.27 This result contrasts strongly with the results ob tained by Tobin, Latane, Bronfenbrenner and Mayer, Christ and others.2® In all of these studies, both those that follow Tobin in using the somewhat questionable technique of separating "active" and "idle" balances and those that 2^Milton Friedman, "The Demand for Money: Some Theoretical and Empirical Results," Journal of Political Economy, LXVII, No. 4 (August, 1959)345. 2®Tobin, "Liquidity Preference and Monetary Policy," loc. cit.; Henry Latang, "Income Velocity and Interest Rates— A Pragmatic Approach," Review of Economics and Sta tistics, XLII (November, 1960), 445-447; Martin Bronfen brenner and Thomas Mayer, "Liquidity Functions in the Amer ican Economy," Econometrica, XXVIII, No. 4 (October, 1960), 810-834; and Carl Christ, rInterest Rates and 'Portfolio Selection' Among Liquid Assets in the U.S.,” Measurement in Economics, eds., Christ et al. (Stanford: Stanford Univer sity Press, 1963), pp. 2$T-7T8. 51 consider total money balances (as we have defined them) as the dependent variable, the interest elasticity of the de mand for money balances was found to be statistically sig nificant. Likewise, an important role for the interest rate in determining money balances has been demonstrated in various studies for both long term and short term rates. Estimates of the elasticity figure range from a low of -0.33 in an equation estimated by Bronfenbrenner and Mayer where total money balances were regressed against the short term interest rate, real national wealth, and gross na tional product less government purchases of goods and ser vices, to a high of -1.16 derived in the same study in an equation where "idle" balances were regressed against the short term interest rate, and real national wealth (all variables were measured in logarithms in both equations).^9 Even in studies which have given Friedman the bene fit of defining money in his own terms, there has been found a significant role for the interest rate. Meltzer, for example, compares money demand functions, in which money is defined as demand deposits plus currency, with other functions, in which money is defined as inclusive of time deposits and/or savings deposits. Two of his conclu sions apply directly to our discussion. As he states it: ^Bronfenbrenner and Mayer, loc. cit. 52 . . . the theory and the evidence support the view that the long run demand function is consistent with the Quantity Theory of money and contains two principle arguments of almost equal explanatory power: interest rates and non-human wealth. . . . The evidence does not suggest any compelling reason for broadening the definition of money to include time deposits at commercial banks or liabilities of financial intermediaries.30 In still another study, Brunner and Meltzer actu ally demonstrate that the predictive performance of Fried man's money demand function is substantially improved by the inclusion of an interest rate measure as an argument in the function. This disagreement between Friedman and most of the other investigators in the field can be explained to a very large extent by Friedman's techniques of estimating his postulated relations. First of all, his use of a defini tion of money which includes time deposits most likely obscures some of the interest responsiveness of demand de posits. One of the things people are likely to do when in terest rates rise if they are conscious of foregone inter est as a cost of holding currency and demand deposits, is to switch some of their holdings into time deposits. If time deposits are included with demand deposits in the definition of money, however, the substitution effect 30fteltzer, 0£. cit., p. 227. 53 induced by interest rate changes will be partially hidden within the composition of money. As Brunner and Meltzer note: "More inclusive definitions of money appear to mix the effects of general and relative changes in interest rates and to obscure part of the wealth adjustment pro- cess."Likewise, Friedman's statistical techniques bias his results against finding a significant role for interest rates. He first regresses money balances (including time deposits) on income. Then he regresses the residuals of this equation against the interest rate. Not surprisingly, no significant relation is found to exist between money balances and the interest rate. But it should be clear that as long as any close relation exists between income and interest rates, this method is necessarily biased against finding a significant role for interest rates in determining the variation in money balances. Hence, few people are willing to accept Friedman's results and are rather willing to admit that a significant relation between money demand or velocity and interest rates in fact exists. 3^-Karl Brunner and Allan H. Meltzer, "Predicting Velocity: Implications for Theory and Policy," Journal of Finance, XVIII, No. 2 (May, 1963), 350. 54 Wealth as a constraint in money demand relations.— Interest elasticity of the money-demand function is consis tent with some version of each of the four major theories reviewed above, including Friedman's own reformulation of the Quantity Theory. Thus, we must consider the further problem of what other variables should appear as arguments in the empirical money demand function along with interest rates. The Crude Quantity Theory and the Liquidity Pref erence Theory as stated by Keynes imply that some measure of national income is the other important factor determin ing money demand. Friedman's statement of the Quantity Theory and the modified approaches to the Keynesian theory including most importantly, the portfolio approach, suggest some measure of wealth as the other constraint on monetary holdings. The difficulty of separating out the empirical ef fects of income, interest rates and wealth are well known; yet both theory and recent empirical work seem to suggest wealth as the more important constraint on money balances. One of the earliest references to wealth as a de terminant of the demand for monetary balances is in Marshall's Money, Credit and Commerce: . . . It us suppose that the inhabitants of a country . . . find it just worth their while to keep by them on the average ready pruchasing power to the extent of a tenth part of their annual in come together with a fiftieth part of their prop erty, then the aggregate value of the currency in 55 the country will tend to be equal to the sum of these amounts.32 A more modern view goes further in its emphasis on wealth as an ultimate determinant of money balances by showing that income itself is simply a return derived from the stock of wealth. In this view, money balances held for liquidity purposes within the individual's portfolio are determined by the size of the portfolio and the spectrum of returns on the other assets available to this individual, while money balances held to affect transactions depend on the size of the portfolio and the level of income derived from the individual's wealth— both human and non-human. Hence, wealth is the ultimate determinant of the size of both transactions and asset balances. As Meltzer argues, "The wealth constraint emphasizes the role of money as a productive asset and focuses attention on the equilibrium of the balance sheet, the allocation of assets, and the services that money provides." Further, ''. . . effecting a 33 volume of transactions is but one of these services. Meltzer's conclusions on the importance of wealth derive from his empirical studies. He has shown that when both real income and wealth are included in his money 32alfred Marshall, Money, Credit, and Commerce (London: Macmillan and Company, Ltd., 1923}, pi TTl ^^Meltzer, oja. cit., p. 232. 56 demand equation, the income variable fails to show statis tical significance. As he notes: Real income has no significant effect on the demand for real money balances when real non-human wealth appears in the equation. Interpretation of these findings is difficult owing to substantial multi- collinearity due to high correlation between income and real wealth. However, we note that the interest rate and real wealth coefficients are generally quite similar to those estimated earlier, while those for the real income coefficient are quite dif ferent. From this it appears that the addition of real income to the money demand equation adds little additional information. His general conclusion, then, is that "... the demand function for money is more stable when the function is for mulated in terms of a wealth constraint rather than an in come constraint. These results derived from time series studies are given additional credence by the fact that similar conclu sions have been reached on the basis of cross section studies. In an analysis of different income and asset classes in Great Britain, for example, Lydall presents a strong empirical case for the significance of the wealth constraint.35 The conclusions which one should derive from the liquidity function estimated by Bronfenbrenner and Mayer, 34Ibid., p. 233, 35H. F. Lydall, "Income, Assets, and the Demand for Money," Review of Economics and Statistics, XL (February, 1958) , 1^1T. 57 which include wealth as an independent variable, are not immediately clear. In their estimates of liquidity func tions which take "idle" balances (a la Tobin) as the depen dent variable, they find that the stock of wealth does have a significant influence on their estimates. In their esti mates of liquidity functions using total money balances as the dependent variable, however, no significant role is found for the wealth variable and, in fact, the sign of the estimated wealth coefficient is opposite to that suggested by economic theory. A serious criticism of these results is raised by Meltzer, however. He notes that the definition of wealth which Bronfenbrenner and Mayer employ is inappropriate for 3 f i a proper test of a wealth model. This has, in fact, been conceded by Bronfenbrenner and Mayer who acknowledge in debtedness to Meltzer for pointing out how their measure of wealth led to their "anomolous results."^ A more delicate problem exists in determining the bearing that Friedman's work in money demand, which employs "^Bronfenbrenner and Mayer employ Goldsmith's series on total national wealth in 1929 prices. Govern ment-owned wealth was not excluded but rather used as a proxy for the government securities omitted from the wealth of the private sector; for Critique see Meltzer, 0£. cit., p. 230. 3?Martin Bronfenbrenner and Thomas Mayer, "Rejoin der to Professor Eisner," Econometrics, XXXI, No. 3 (July, 1963), 539. 58 his permanent income concept, should have on a wealth model. "Permanent income," he claims, "can be regarded as a con cept closely allied to wealth and, indeed, as an index of wealth, provided that we count both human and non-human sources of income as components of total w e a l t h . " ^ 8 While he is perfectly right in making this statement about the theoretical concept, "permanent income," it is still not clear how we should interpret his empirical results based on his constructed measure of this variable. Specifically, his use of the permanent income concept in the sense of a wealth proxy presents at least two basic problems. First, his calculation of the per capita income series through the use of a weighted average of past levels of income has the statistical effect of combining components of wealth, in terest rates, population, and lagged income within a single variable. Hence it is impossible to separate out the ef fects of each of these individual factors in his empirical money demand or velocity function. Second, Friedman de fines his concept of permanent income as the yield on total wealth: Y = rW, where r is the rate of discount and W is P the stock of total wealth (including human resources), so that Yp is the expected income stream. He measures perma nent income, however, as an exponentially weighted average ^®Friedman, "The Demand for Money: Some Theoretical and Empirical Results," ojs. cit. , p. 349. 59 of past income. As noted by many authors, then, even as suming that Friedman's measure is in fact Y^, he must come up with a stable r in order for to be an index of W. On the level of empirical testing, the evidence seems to indicate that a more precise measure of non-human wealth, such as that used by Meltzer, yields a money demand function which is just as stable as Friedman's, explains at least as much of the variation in the money stock as Fried man's estimate, but which has the added advantage of more clearly separating the interest rate and wealth effects. Thus, these considerations throw doubt on Fried man's conclusions that there is ". . .no close connection between changes in velocity from cycle to cycle and any number of interest rates"-*9 and that the demand for real money balances is highly elastic with respect to permanent real income, i.e., that money is a luxury. As Meltzer's evidence indicates Friedman's conclusion that money is a luxury . . . is largely a result of the definition of money that he employs and the process of deflating by population which raises the wealth and permanent income elasticities when money is defined as Mo (currency + demand deposits + time deposits).40 Likewise, on interest elasticity, ^9Ibid. ^^Meltzer, op. cit., p. 239. 60 . . . the evidence from one variant of the perma nent income hypothesis itself . . . shows that when interest rates are used along with per capita permanent income, interest rates enter signifi cantly into the money demand relation.41 Conclusions and implications for our study. The above review and critique of single equation studies of money demand relations leads us to the following conclu sions. First, the appropriate definition of money to be used in empirical analysis is "currency + demand deposits adjusted." The exclusion of time deposits seems warranted by the fact that only by excluding all interest earning assets can we hope to distinguish clearly the substitution effects between money and other assets caused by interest rate movements. Conversely, the arguments for including time deposits seem extremely weak and arbitrary since they could just as well be used to argue for the inclusion of savings and loan shares, holdings of U.S. securities, etc. Second, the case for a significant interest elasticity of the demand for money seems extremely strong from the tests carried out thus far. Hence, interest rates will be in cluded within our own analysis. Third, the results on the importance of wealth as a constraint on money demand, while still uncertain, seem strong enough to warrant the specifi- 41lbid., p. 236. 61 cation of a wealth model to explain individual and aggre gate money holdings. The problems of the "proper" concept of wealth to be used in such a model will be considered in detail in a later section. III. THE SUPPLY OF MONEY Review of the Theory of Money Supply Determination Actual specification and testing of functional supply of money relationships is of quite recent origin. There are only a few important works upon which we can base our own analysis, notably those of Polak and White, Teigen, Brunner, and de Leeuw. Studies done in the United States previous to these works concentrated primarily on the work ings of the deposit expansion mechanism in a multi-bank fractional reserve system (specifically, a system with legal minimum reserve requirements) and on the development and specification of the "reserve position" doctrine. More recently, theoretical and empirical works criticizing the original formulations of the "reserve position" theory and the policies which derive from it have contributed much to our understanding of at least some of the more important factors influencing money supply. The deposit expansion mechanism. The first com plete treatment of the deposit expansion process was pre- 62 sented by Phillips^ in 1920. In addition to the deriva tion of the simple deposit and loan expansion coefficients specifying the amount of new lending which can be supported by a given inflow of new reserves, Phillips carefully dis tinguished between the response mechanism of a single bank and that of the banking system as a whole to cash acquisi tion. Phillips states the now familiar loan and deposit expansion formula for a system composed of only a single bank as 1 — (c - sc) 6 where c = new cash deposits and 6 = the required reserve ratio. He then shows how the behavior of a single bank in a multi-bank system in creating loans and deposits on the basis of its own excess reserves can be generalized into an analysis of the entire system. Under relatively modest assumptions, the above formula, derived for the monopoly bank, is then demonstrated to be valid as a description of the response mechanism of the multi-bank system. More complete statements of the precise mechanism involved in deposit expansion have been forthcoming both from the Federal Reserve and from academic writers. A. Phillips, Barnk Credit (New York: The Macmillan Co., 1920). 63 Specifically, demand deposit expansion coefficients have been derived which consider not only reserve requirement ratios but also other factors which can affect the total money supply, such as the relative desire of the public for currency, time deposits and demand deposits, and banks' desire to hold excess reserves. These formulas are usually derived on the basis of an assumption of constant currency and time deposit to demand deposit or money supply ratios rather than upon functional currency and time deposit de mand relations. In all these cases the expansion coeffi cients are derived from static, deterministic models of bank behavior. Only recently have some studies indicated the alternatives to assuming constant ratios or constant levels of currency, time deposits, and the other reserve absorbing factors.^ ^ The modifications caused by the introduction of un certainty into the system have been indicated in some re cent studies by Orr and M e l l o n . ^4 They demonstrate how the presence of uncertainty in the model modifies the expected volume of new deposit liabilities which will be created on the basis of new reserves. 4^Karl Brunner, "A Schema for the Supply Theory of Money," International Economic Review, II, No. 1 (January, 1961), 79-169. ^Daniel Orr and W. G. Mellon, "Stochastic Reserve Losses and Expansion of Bank Credit," American Economic Re view, LI, No. 4 (September, 1961), 617. 64 "Reserve Position" Theory. The focus of the major ity of these studies which have been concerned with money supply determination, has been on the process by which a given stock of reserves or a given change in that stock of reserves is related to the stock of demand deposits or the money supply via the deposit expansion mechanism. A closely related problem has been the determination of the stock of bank reserves itself. Thus, a body of literature has de veloped which is concerned primarily with the behavior of commercial banks as it relates to their desired holdings of excess reserves and borrowings. This literature has come to be known under the title of "Reserve Position" Theory. This theory derives originally from an attempt to explain the observed response of commercial banks to at tempts by the Federal Reserve in 1922 and 1923 to build up its portfolio of earning assets. It was soon discovered that the purchase of securities by the Federal Reserve which injected reserves into the banking system did not have the expected effect on total bank reserves. Various observations indicated that the purchase or sale of securi ties by the Federal Reserve led the commercial banks to modify their borrowed reserve position. Specifically, it was found that open market purchases tended to decrease the volume of outstanding loans to commercial banks, and sales forced the banks to borrow to adjust for the initial loss 65 of reserves. Consequently, these results cast serious doubt on the ability of the discount rate to regulate mem ber bank borrowing. Rather, it appeared that borrowing was in fact independent of the discount rate and dependent on the rate of open market sales and purchases. For, since excess reserves tended to be negligible during this period, variation in bank borrowing tended to offset the effects of open market operations. Thus, since these operations by the Federal Reserve had very little net effect on total reserves (borrowed and unborrowed), some other mechanism had to be found for determining their impact as a policy tool. The alternative control mechanism which was in volved was first described by W. Riefler in his Money Rates and Money Markets in the United States, published in 1930. Riefler made bank indebtedness the most important factor in the determination of the money supply and of general credit conditions. He offers two possible hypotheses to explain this indebtedness. The first, a profit theory, views banks as above-all profit maximizers who borrow when market rates are sufficiently above discount rates to assure a net return on borrowing and lending. The second hypothesis, the "needs and reluctance" theory, holds that "member banks borrow at Reserve banks only in the case of 66 necessity and endeavor to repay their borrowing as soon as possible."45 Riefler submits the implications of each of these theories to empirical tests. Specifically, he postulates that if the profit theory was indeed a better explanation of actual bank behavior, this behavior would cause market rates to maintain a close correspondence with the discount rate; for, any time the discount rate fell substantially below market rates, banks would borrow sufficient funds to cause the market rate to decline to the discount rate, and any time the discount rate rose above the market rates, borrowing would cease, deposit and loan expansion would slow down or contract, and market rates would rise. The evidence on market rates and discount rates fail to support this thesis and, thus, Riefler decides in favor of the "needs and reluctance" theory. As he notes: . . . it is impossible to explain the movements of money rates in the open market and the levels which they have occupied during recent years by the move ments and levels of discount rates at the Reserve Banks alone. . . . The functioning of the Reserve Banks in the money markets must, therefore, be con sidered from the point of view of the theory that changes in the volume of member bank borrowing exert a more important influence on rates than do changes in discount rates.46 4^w. W. Riefler, Money Rates and Money Markets in the United States (New York: Harper and Brothers, 19367T pp. 19-20. 46lbid., p. 25. 67 The primary chain of causation which arises from Riefler's analysis, then, is as follows. Since the "needs and reluctance" theory predominates as an explanation of bank borrowing behavior, banks borrow primarily when open market operations reduce their reserves, and they repay these funds when open market operations increase their re serves. Hence, Federal Reserve open market operations control bank borrowing. But, bank indebtedness is the most important element in the determination of market interest rates, and since market rates are the prime determinants of the public's supply of earning assets to the banks, through open market operations, the Federal Reserve can control bank credit, the money supply, and yields on credit markets. This view was applauded and extended by W. Randolph Burgess in 1936. He accepted completely Riefler's formula tion of the open market mechanism but added a more critical role for the discount rate. Burgess emphasized the dis count rate as the cost of bank borrowing, a factor which must be taken into consideration in a complete appraisal of the response of bank borrowing to open market operations. The discount rate was the connecting link between the abso lute level of bank indebtedness and market interest rates. Other things equal, the banks would be willing to borrow a greater amount from the Federal Reserve before raising 68 market rates, the lower the discount rate. Discount rate changes, therefore, were an important supplement to open market policy. Likewise, open market policy could effec tively be used to prepare for discount rate changes and to assure their effectiveness. This position was accepted and extended in the works of many other writers. Goldenweiser, for example, restated the Riefler-Burgess thesis, adding only a discus sion of the important psychological "announcemnt effect" of discount rate changes and explicit consideration of the effect of excess reserves on the policy mechanism.4® As follows from the initial Riefler statement of the theory, excess reserves must be kept negligible in order for the Federal Reserve to maintain control over bank borrowing. The existence of excess reserves would break the causal chain and sterilize open market operations. Hence, Golden weiser explains the doubling of reserve requirements by the Federal Reserve in 1936-37 as an attempt to wipe out excess reserves and restore the link between effective open market operations and bank behavior. 4?R. Burgess, The Reserve Banks and the Money Mar ket (New York: Harper and Brothers^ IU36). 4®E. Goldenw«iser, "Instruments of Federal Reserve Policy," Banking Studies, Board of Governors of the Federal Reserve (Washington, D.C., 1941). 69 Free reserves and the "Policy Target" debate. The most important single development along the lines suggested by these theories in recent years has been the replacement of the measure of borrowed reserves as the prime variable in the analysis by the concept of net free reserves, which includes both borrowed reserves and excess reserves. It has been recognized for some time now that banks may at times desire to hold positive excess reserves as a pre caution against various contingencies, and that these re serves do not simply represent a break in the policy chain. Indeed, the free reserves measure (excess reserves minus borrowed reserves) has become the prime target variable of Federal Reserve policy and is widely used by the financial community as a guideline by which to measure the ease or tightness of Federal Reserve monetary policy. Statements made in Federal Reserve publications confirm this position. For example, they state, "The general level of free re serves prevailing over a period of time may be viewed as an indicator of the degree of restraint or ease that exists in the money market. The use of this variable, both as a policy target ^Board Qf Governors of the Federal Reserve System, "Processes and Procedures in the Formulation and Execution of Monetary Policy, " Readings in Money, National Income and Stabilization Policy, editors, Warren L. Smith and Ronald Teigen (Homewood, 111.: Irwin, Inc., 1965), p. 195. 70 and as an indicator of credit market conditions, has come under fire in recent years, however. Specifically, critics point out that the level of free reserves which banks main tain would be a useful and accurate guide to the character of monetary policy at any one time, only if banks always sought to maintain some constant level of such reserves. If the desired level of free reserves should change suffi ciently over time, the same target level of free reserves maintained at any two different points in time could have completely different effects on the ease or tightness felt in credit markets. This is the position assumed by James Meigs. As he explains: The principle hypothesis . . . is that banks seek to maintain certain desired ratios of excess re serves and borrowings (or free reserves) to total deposits and that these desired ratios are func tionally related to market interest rates and the discount rate. . . . An . . . objective of this study is to demonstrate the hazards of using the level of member bank free reserves as an indicator of the tightness or ease of monetary policy. . . . For, according to the hypothesis of this study, it is not the absolute level of free reserves that is significant but the difference between actual free reserves and the volume of free reserves desired by banks.50 Using multiple regression analysis and quarterly data for the period 1947-1958 and various subperiods, Meigs 50A. J. Meigs, Free Reserves and the Money Supply (Chicago: University of Chicago Press, 1962), pp. 3-4. 71 demonstrates that a significant linear relationship does indeed exist between the variables postulated by his hy pothesis. As he states: The evidence considered here indicates that the desired free reserve ratio of the member banks is functionally related to market interest rates. The scatter diagrams with annual data and all the regressions with monthly data suggest that market interest rates have a strong influence on the free reserve ratio.51 Meigs anticipates the criticism that such evidence derived from regressions is not sufficient to distinguish between his hypothesis, on the one hand, which makes the free reserve ratio a function of interest rates, and the "reserve position" thesis, on the other hand, which makes market interest rates a function of the banks' reserve position. High correlation between the variables involved is not sufficient to justify a unique judgment on the di rection of causation (or any causation at all, for that matter). He responds to this critique as follows. First, he notes that a proper test could be performed by viewing the effect which a lag in interest rates would have on the correlation. However, the data available do not permit such a test since various studies by Horwich and others have indicated "... that the responses of banks to changes in their stock of reserves ususally occur within less than 53-ibid. , p. 82. 72 one month,"52 yet, at present, we have only monthly data available for the necessary reserve and market rate meas ures. Second, he notes that furhter evidence indicates that open market operations seem to have exerted little in fluence on the free reserve ratio over the period covered by the data. Hence, he notes that "the evidence that the influence of open market operations upon the free reserve ratio was small is consistent with the hypothesis of this study but tends to contradict a key hypothesis of the 're serve position' doctrine."^3 And so, Meigs concludes that his hypothesis ex plains the overall evidence available on the free reserve behavior of commercial banks better than the reserve posi tion doctrine. From this he infers that the practice of using free reserves as a policy target and as an indicator of the degree of ease or tightness of Federal Reserve pol icy is dangerous and misleading. "The Principle conclusion of this study is that what really matters is the difference between the actual free reserves of the banks and their desired free reserves."^ Thus, he suggests that since the Federal Reserve can control the rate of change of unbor rowed reserves through open market operations, if the 5^Ibid. 54ibid., p. 87. ^Ibid. , p. 83. 73 behavior of bank reserve ratios is indeed predictable, as this study indicates, a complete theory of money supply and credit control can be developed on the basis of the use of total reserves rather than free reserves as the policy target. These conclusions are supported by the results of an analysis presented by DeWald in 1963. Using a Hicks- Hansen commodity market-money market equilibrium type of analysis, DeWald shows that the use of a free reserve tar get makes it impossible to distinguish between tight and contractionary policies or between easy and expansionary policies on the part of the Federal Reserve. Shifts in the commodity market equilibrium curve, for example, cause the Federal Reserve, in using a free reserve target, to simply respond to changes in the real sphere automatically. As he notes, Given the relevant behavioral relation and policy determined magnitudes, maintaining a free reserve target in the face of an increased desire to spend, prevents using interest fTftes for dampening in creased spending at all." Specification of Empirical Money SupplyReTationships The results of all the previous works reviewed, 55William DeWald, "Free Reserves, Total Reserves and the Money Supply," Journal of Political Economy, LXXI, No. 2 (April, 1963), 14T. both those which were concerned primarily with the strict mechanics of the deposit expansion mechanism in a multi bank fractional reserve system and those concerned with be havioral patterns and functional relations of the response mechanism of banks to Federal Reserve policy action, have formed the basis upon which recent attempts to specify functional money supply equations have proceeded. The most important studies in this field have been carried on by Polak and White, Teigen, and Brunner. The study by Polak and White. The analysis pre sented by Polak and White represents one of the first at tempts in the literature to demonstrate that a stable func tional money supply relationship could be derived from certain simple assumptions about bank behavior. The prob lem and hypothesis presented by Polak and White are most concisely stated by the authors themselves. The desire of the public for more money and the wish of banks to contract the money supply cannot be reconciled without bringing in another element. The two tendencies can be reconciled as soon as both the demand for money and the supply of money are considered in the schedule sense, and a price, in this case the rate of interest, is brought into play as the equilibrating factor.*® Concerning the money supply relationship itself, they state 5®J. J. Polak and W. H. White, "The Effects of In come Expansion on the Quantity of Money," International Monetary Fund Staff Papers, IV (August, 1955), 401. 75 It has been shown that the public changes its cash reserve ratio . . . in light of the rate of inter est. It is plausible to assume that banks operate in a similar manner. Like the public, they will want to balance the convenience of a high reserve ratio against a low rate of interest, the inconve nience and risk o rate of interest. To formulate a complete hypothesis, Polak and White postulate that since excess reserves are desired as a cushion between variations in actual reserves relative to required reserves, the need and desire for such reserves should be considered as proportional to the total of de posit liabilities. Thus, they postulate a functional rela tionship between the ratio of net excess reserves to de posit liabilities and the cost of holding these reserves— the market interest rate. Scatter diagrams of the reserve/ deposit ratio and the logarithm of the treasury bill rate indicate the existence of a good linear relationship be tween the specified forms of these variables. This indi cates that a given proportional change in the short term interest rate tends to affect the desired net excess re serve/deposit ratio by the same absolute amount whatever the value of the initial interest rate. The important conclusion to be derived from this study is that Polak and White have demonstrated the possi- a lower ratio against a higher 57Ibid., p. 422. 76 bility of deriving a stable functional money supply rela tion. For, if the reserve/deposit ratio-interest rate relation is stable, it is easy to derive the effect of any change in the interest rate on the banks' supply of de posits and— assuming that currency in circulation varies proportionally with deposits— on the total money supply. Ronald Teigen's use of the "potential money stock" concept. The money supply relationship specified by Teigen for inclusion in his simultaneous equation model is similar in spirit to the Polak-White formulation. As was shown above (in Part I) Teigen constructs a ratio between the observed money supply and the total potential money stock which could be created on the basis of exogenously supplied (unborrowed) reserves. The size of the numerator will, of course, depend upon the banks' demand for free reserves. In Teigen's formulation, this is determined by the differ ence between the return from lending and the cost of bor rowing, i.e., by the divergence between the market loan rate and the Federal Reserve discount rat .. Like Polak and White, Teigen attempts to explain the variations in the willingness of banks to supply deposit liabilities through an investigation of bank desired reserve relations. The most important weakness of Teigen's method, however, is that his specification of a "maximum potential money stock" assumes as constants certain factors which are probably 77 themselves functionally related to the same influences which affect bank reserve behavior. Specifically, his assumption that the proportions of the total money stock held in the form of currency and in the form of demand de posits at non-member banks may be represented as constants is a rather rough approximation to the actual relations indicated by the data over the period covered by his model. The money supply "Schema" of Karl Brunner. Only in the work of Karl Brunner do we find a relatively com plete analytical statement of the mechanics of money supply determination in the United States commercial banking sys tem. This work supplies an explicit integration of the major institutional characteristics of our banking system such as the unequal reserve requirements on time and demand deposits, the special treatment afforded interbank deposits, and the reserve effects caused by flows between member and non-member banks. In "A Schema for the Supply Theory of Money," Brunner takes specific note of the uncultivated state of money supply theory and complains that "... most of the literature presents us with an accumulation of analytical fragments which form at best only building blocks of an empirically significant theory."^® ^Brunner, 0£. cit. , p. 79. 78 Brunner's own purpose is to extend the existing analysis and ". . .to construct a schema which can be used to for mulate an empirical macro supply function for money within the institutional framework of the American banking sys tem."59 The basic premise of Brunner's analysis is that the existence of "surplus" reserves in the banking system gen erates a change in banks' desired asset portfolios. With this behavioral postulate as a basis, a supply function for new bank funds can be derived from a consideration of the portfolio adjustments which are induced by the exis tence of these reserves. Surplus reserves are defined in terms of available (excess) reserves and a demand function for cash assets. Specifically, they represent cash assets in excess of required reserves and desired excess reserves. Brunner first develops a supply function of funds for a single bank. This involves the specification of a loss coefficient which measures the drain in surplus re serves which occurs as a result of a one dollar expansion of earning assets. The reciprocal of this measure repre sents the bank's expansion coefficient which, when multi plied by the dollar amount of surplus reserves available. 59lbid., p. 80. 79 determines the total supply of bank funds which will become available through the adjustment of the bank's portfolio to the new desired level. In deriving this loss coefficient, Brunner follows closely the work described above which flows from the initial attempts by Phillips and the con tinued efforts in the texts on money and banking to specify all the drains which can affect a bank's reserve position as it expands its holdings of earning assets. But Brunner sees this as only half the problem. The other half, which has received no complete analysis in the literature, is the need for a detailed description of the sources which can generate the initial surplus reserves which induce the actual asset expansion. Brunner classi fies the "events and magnitudes" which generate these re serves into eight categories: 1. Currency flows independent of changes in port folio and deposits. 2. Conversions between demand and time deposit holdings by the public. 3. Net clearing balances for a single bank. 4. Bank transactions with the Federal Reserve, such as bank borrowing, transfers of tax and loan accounts, and open market operations in volving the public. 5 . Changes in reserve requirements. 80 6. Changes in the bank's allocation of its cash assets between bankers' balances, deposits at the Federal Reserve and vault cash. 7. Reallocations of other banks' holdings of de sired reserves which cause an inflow of Federal Reserve funds to the given bank. 8. Changes in the bank's own desired level of excess reserves. These eight factors, when appropriately specified, com pletely determine the generation of surplus reserves, s. This figure, together with the loss coefficient, describes the response of a single bank to surplus reserves ". . . in the form of a demand for earning assets designed to absorb s."60 Starting with the assumption that all surplus re serves in our multi-bank system are initially located in a single bank within that system, the framework specified by this relationship allows Brunner to derive an aggregate expansion (or loss) coefficient for the entire system ". . .as the limit of a series whose terms describe a single bank's adjustment to its surplus reserves. It remains then, only to specify a macro relation corresponding to the micro formula describing the genera- 60Ibid., p. 88. ^Ibid., p. 89. 81 tion of surplus reserves for a single bank. This aggrega tion proceeds simply by summing over the factors listed above which generate reserves for individual banks and by canceling out certain inter-bank flows. This expression, together with the system expansion coefficient derived above, describes a formal relationship for the rate of growth of the total money stock. This is a formal con struct expressed in terms of the monetary multiplier, sur plus reserves, and a component to account for changes in the money stock which occur independent of portfolio ad justments. A total money supply function can then be de rived by integration of this growth rate expression. As Brunner then notes, The money supply function explains the observable behavior of the money stock in terms of a specified combination of magnitudes. Such a function, ex pressing a confirmable hypothesis is obtained from the schema with the assignment of semantic rules to the variables and definite values to the coeffi cients . 62 This function is specified as follows: M = a - m^cQ + n»2tQ + mQ (B + L3) + m4e0 + mQ (vQ - wQ) where the variables are defined as follows: M = total money supply cQ = a function of a vector of variables expressing the public's demand for currency 62Ibid., p. 95. 82 tQ = a function of a vector of variables expressing the public's demand for time deposits (B + L3) = the monetary base adjusted for changes in re serve requirements eQ = a factor to account for the generation of re serves resulting from variations in the systems inter-bank deposit structure (vQ - wQ) = a factor representing the banks' demand compo nent for Federal Reserve money in excess of required reserves (The coefficient of the measure of the adjusted monetary base, mo, is the same as the coefficient of the last term in the equation because of certain a priori restrictions placed on the variables by Brunner in the course of the derivation of his final model.) No extensive empirical investigations are presented in this paper, but Brunner does give us some evidence in the form of correlations which result from a simple hypoth esis which uses only the unadjusted monetary base as a determinant of M, and from extended hypotheses which in clude the effect of cQ, tQ, and on M. The most impor tant results of these preliminary tests are that "... the sample estimates . . . establish that the neglect of cQ, t0, and L results in a hypothesis with poor and unreliable 6 3 predictive power." Further tests on the estimation of the monetary multiplier show that stable results can be ob tained only if currency demand, time deposit demand, and 63ibid., p. 98. 83 the cumulative effects of changes in the reserve require ments are included in the explanation of M. In other study, Brunner, together with Allan Meltzer, tests more completely the money supply relation postulated here (and hereafter referred to as the linear hypothesis) and compares the results obtained with those derived from a non-linear hypothesis.®^ The specific lin ear equation tested is the same as that derived above con taining cQ, t0, and (B + L^) as arguments. The alternative- hypothesis is developed on the basis of an investigation of the supply and demand relations in the credit markets in which banks operate. This theory leads to a non-linear money supply relation which includes interest rates and a linear combination of the relevant policy controlled vari ables, such as reserve requirement ratios and the size of the exogenous monetary base, as arguments. The tests carried out in this paper include one stage and two stage least square estimates of the two basic models. The first model contains the linear money supply equation derived from the analysis presented in the "Schema" and a linearized version of a demand for money function 64Rarl Brunner and Allan H. Meltzer, "Some Further Investigations of Demand and Supply Functions for Money," Journal of Finance, XIX, No. 2 (May, 1964), 242. 84 derived by Brunner and Meltzer in an earlier study, which postulates wealth and interest rates as arguments in the demand relation. The second model includes the non-linear money supply equation explained above and stated in loga rithms together with the logarithmic form of the authors' money demand function. All tests are carried out using both the inclusive and the exclusive concepts of money as dependent variables. Most of the tests are carried out with annual data from 1929-1959, though one set of tests is made on annual first differences of quarterly data from 1/1949 to IV/1958. The latter tests are performed to give more explicit con sideration to the short run variations in the public's currency and time deposit behavior. No tests are specified or performed in this paper which would enable us to ap praise one of these hypotheses relative to the other. In the tests performed, all coefficients are sta tistically significant at the usual levels and the coeffi cients of determination of the equations indicate that the hypotheses specified are capable of explaining 98-99 per cent of the variation in the dependent variable. In only a few cases, however, does the Durbin-Watson statistic indi cate a non-significant level of autocorrelation. But this is to be expected with the type of data which the authors employ. The use of long term annual data, likewise, throws 85 some doubt on the degree of confidence which one can place in the multiple correlation coefficients. In all, however, the tests do indicate that Brunner and Meltzer have prob ably specified more of the important factors affecting the money stock than have any of the other investigators work ing in this field. CHAPTER III FORMULATION OF A MODEL OF THE MONETARY SECTOR The first task one faces in the specification of money supply and money demand relationships is the neces sary explication of exactly what behavioral assumptions will be employed in explaining the interaction between the three agents of our monetary sector— the Federal Reserve Authorities, the commercial banks, and the non-bank public. This specification is necessary to develop an analytical framework within which we may relate the relevant supply and demand functions. On the a priori level, we can derive no unique specification of such a framework since our in stitutional structure allows for a variety of differing assumptions. For example, in determining such things as which variables are truly exogenous in the policy con trolled sense, we have only the pronouncements of the mone tary authorities and the works of previous investigators to guide us. But these sources are by no means unanimous in their judgments. These are essentially empirical questions and different specifications can only be judged in light of the final power of the model to perform its implicit func tions of explaining the empirical data. Our own procedure, 86 87 then, shall be to lay out in some detail the assumptions which determine the ultimate structure of our model, and to reserve judgment on the relevance and success of this par ticular framework in explaining the workings of our mone tary system until we have estimated the resulting equations. Thus, we have the following task to perform in this chapter. First, we shall examine the various items of the "bank reserve equation" in order to determine which factors represent the most important constraints upon commercial bank behavior. Second, we shall examine in detail those factors which interpose themselves between the determina tion of the supply of reserves and the determination of the actual money stock outstanding. Last, on the basis of this specification of a complete accounting framework, we shall construct a testable model of money supply determination. This will involve a complete specification of all the be havioral demand relationships derived from the above frame work. I. MONEY SUPPLY Development of the Accounting Framework The accounting frameworks of most of the studies done to date are basically all alike— some of them more or less complete than others. The one major exception in this 88 group of studies in the "Schema" presented by Karl Brunner. As we have seen, he develops a rather complete structure explaining the generation and loss of surplus reserves for a single bank and then aggregates to derive relations for an entire system. The more usual procedure has been to deal with aggregates right from the start. The benefit of specifying a complete accounting framework is that this procedure clarifies the necessary relationships involved, the precise restraints on commer cial bank behavior, and the exact way in which technical and non-monetary factors such as float and demand deposits of the federal government work to diminish or increase the money stock. Hence, we proceed in a rather detailed manner with the development of our own framework. The bank reserve equation. The bank reserve equa tion may be expressed as follows: I. Positive Items A. The gold stock B. Federal reserve credit 1. U.S. government securities 2. Discounts and advances 3. Float 4. Treasury currency outstanding II. Negative Items A. Currency in circulation and in banks 89 B. Treasury cash holdings C. Treasury deposits at Federal Reserve Banks D. Foreign and other deposits at the Federal Reserve E. Other Federal Reserve accounts (A) - (B) = total member bank reserve deposits at the Federal Reserve. An empirical examination of the above listed items reveals that all factors except "currency in circulation and in banks," "commercial bank borrowing," and "Federal Reserve holdings of U.S. government securities" are either relatively small, directly under the control of the govern ment, or primarily technical factors. Whatever the case, most of these "secondary" accounts are relatively stable and changes in them are fairly easily offset by Federal Reserve action. Often, in fact, the monetary authorities have advance warning of the necessity for such offsetting action, as, for example, when treasury deposits are to be changed by substantial amounts. Within the reserve equation, then, we focus on three specific items— each of which we consider to be under the primary control of one of our financial agents. These items are currency holdings of the public, commercial bank borrowing, and Federal Reserve holdings of U.S. government securities. The determinants of commercial bank borrowing and their effect upon the stock of money outstanding will 90 be discussed in detail below. We turn first to a discus sion of the behavioral assumptions which determine our treatment of the other two factors. Currency holdings of the public and government security holdings of the Federal Reserve are discussed to gether since it is still an unsettled question as to just how these two measures together relate to the policy ac tions of the Federal Reserve. It is not clear from theory, nor from recent empirical work, nor even from a study of the policy pronouncements of the Federal Reserve Board, which particular measure or combination of measures from the reserve equation can be considered to be exogenously determined by the monetary authorities. Some models, such as de Leeuw's model of the financial sector, take as the exogenous variable the sum of currency plus unborrowed re serves. But, as de Leeuw himself notes, "Alternative forms would define total reserves, total reserves plus currency, or free reserves as exogenous."^ Only the final perfor mance of the model can throw any light on the difference between these alternative open market targets. Hence, we postulate the following framework. We define "total exogenous high powered money" (HM), ^■Frank de Leeuw, "A Model of the Financial Sector," The Brookings Quarterly Econometric Model of the United States, editors, James S. Duesenberry et aTT (Amsterdam: North Holland Publishing Company, 1965TT p. 524. 91 as the sum of currency outside banks plus the unborrowed reserves supplied to the commercial banks by the Federal Reserve authorities, i.e., HM = Curr + RU. (We shall here after refer to this measure simply as high powered money.) The institutional arrangements of our financial sector are such that the public may hold any amount of currency it desires up to the total amount of high powered money sup plied by the authorities. This implies two specific as sumptions. First of all, we assume that people always hold the exact amount of currency they desire. This is a com pletely reasonable assumption since switching between cur rency and the various types of deposit liabilities offered by commercial banks is an extremely simple process. Also, the implied rapid speed of adjustment has ample precedent in the literature. Secondly, we assume that the monetary authorities exogenously determine only the total stock of high powered money, but that they have no direct influence on its form. Thus, whether any dollar of this stock of high powered money is held by the public in the form of currency or held by banks in the form of reserves is com pletely determined by the desired currency holdings of the public. Therefore, we view actual currency holdings of the public as completely determined by the public's demand— within the rather broad limits imposed by the monetary 92 authorities' determination of the stock of high powered money. Hence, though the monetary authorities and commer cial banks are often said to determine or influence the stock of money directly, more correctly, they determine only the supply of demand deposits— that part of the money stock which can be created on the basis of the stock of high powered money left to the banks after the public has determined its desired currency holdings. (As we shall see below, the public's time deposit holdings must be consid ered as an additional constraint on bank behavior.) Of course, there are elements of indirect control over the desired currency stock which operate through the influence which the monetary authorities have over the variables which enter as arguments in the currency (and time deposit) demand functions. However, we assume that the authorities do not try to control currency holdings through the direct manipulation of these factors. Within our model, then, we view the alteration of the stock of high powered money (HM) , through open market operations as the only portfolio adjustment originated by the monetary authorities which is important to the money supply process. Such variation in this level is taken to be an exogenous policy decision. Currency holdings by the public are assumed to be determined strictly by the banks' totally passive and perfectly elastic response to such de- 93 mand. We will return to the specification of the currency demand function below. Intermediate influences between reserves and the money stock. Full explanation of bank borrowing, currency demand, and the exogenously determined supply of unborrowed reserves is far from sufficient to explain the outstanding money stock, however. For, interposed between the determi nation of total member bank reserves from the bank reserve equation and the actual volume of money in circulation are a great many factors under the influence and control of several different economic agents. We may summarize these factors under three headings: (1) reserve utilization fac tors, (2) expansion ratio factors, and (3) other components of the money stock. Under reserve utilization factors, we include all the various non-monetary uses which may absorb reserves and therefore cut down on the potential volume of "money" which a given stock of reserves may support. These include com mercial bank holdings of excess reserves and reserves re quired to be held against commercial bank time deposits, federal government demand deposits (which are not included in the usual definitions of money) and net interbank de posits. Expansion ratio factors which may influence the volume of money outstanding, given a fixed stock of re serves, include the legal reserve requirements set by the 94 Federal Reserve against both demand and time deposits and the distribution of these deposits among the various classes of banks with different legal reserve requirements. Lastly, in addition to member bank demand deposits and cur rency held by the public, all definitions of money include net demand deposits at non-member banks. Since we have thus far been concerned only with the Federal Reserve structure and member bank operation and control, we must take consideration of this additional component in order to derive a complete measure of the nation's money stock. The treatment of each of the above listed factors shall be noted explicitly in the following accounting structure. Formalization of the derived accounting structure. The money stock, M, is traditionally defined as follows: M s * DDadj + Curr where DDadj = total demand deposits at all commercial banks Curr = total currency in circulation outside banks and where "barred" variables refer to nominal values Recognizing that within our monetary system not all commer cial banks are members of the Federal Reserve System and that even within the system, there are several distinct classes among member banks, we may express the money stock as follows: 95 « - E<DDadj>i + DD^dj + CURR where (DDadj)^ = demand deposits adjusted at the ith class of member banks DDa^j = demand deposits adjusted at non-member banks Thus the demand deposit component of the money supply held at member banks, DD^Jdj, may be expressed as folows: 5SJdj - E(ra5adj)i = M - SURR - DDadj We may investigate the factors determining this measure by analyzing the sources and uses of member bank reserves. As can be seen from our interpretation of the bank reserve equation, total member bank reserves may be considered to originate from two sources, borrowings from the Federal Reserve, RB, and reserves supplied exogenously by the monetary authorities, RU. On the other hand, total reserves are either required against time and demand de posits, RR, or they are held in excess of these require ment, RE. Thus RE + RR = RB + RU. Within our system, member commercial banks are legally required to hold reserves against time deposits, TDadj' and "net demand deposits," DDnet (gross demand de posits less deposits due from banks, DFB, and cash items in the process of collection, CPC). Thus, required reserves are not calculated against the usual measure of demand de 96 posits included within the money stock, i.e., they are not calculated against DDa£j. In order to include within our model a measure of required reserves which is consistent with our definition of the money stock, therefore, we must modify the required reserve measure published by the Federal Reserve. We have two alternative approaches open to us. First, we may employ the published measure directly and adjust it to correspond to our money stock measure by sub tracting out reserves required against net interbank de posits, demand deposits of the federal government, and float. This would necessitate the inclusion of these minor items as exogenous variables within our model. The alter native is to calculate a measure of reserves required against the specific demand deposit and time deposit meas ures which we employ in our model. The former method of adjusting the required reserves measure involves an unnec essary introduction of several new exogenous variables into what shall become a rather large model. Consequently, we shall employ the second technique. This will undoubtedly introduce some inexactness into our data. However, as a glance at the data appendix will show, the comparison be tween our calculated value and the actual values of re quired reserves indicates that this inexactness should be of a minor order. In calculating this measure, to assure consistency with the final deposit measure which we employ, we must take explicit consideration of deposits at non-member banks and of the differing reserve requirement ratios on deposits at different classes of member banks. Thus, reserves re quired at member banks, RR, shall be calculated as follows: RRi = SiDD I(DDadj)i] + S.TD RR = ? RRi 1 1 where RR^ = reserves required at the i^*1 class of bank. fiiDD = legal reserve requirement on demand deposits for banks of class i. <siTD = legal reserve requirement on time deposits for banks of class i. TDadj = total time deposits less deposits due to other commercial banks and the U.S. government For simplicity, we may assume that the reserve re quirement ratios on demand and time deposits at the various classes of banks may be weighted by the distribution of these deposits, respectively, among the member banks. Thus, the average daily required reserve ratio on demand deposits at member banks shall be calculated on the basis of legal reserve ratios multiplied by the proportions of total de mand deposits subject to reserves at each class of bank. The same procedure shall be used in calculating an average reserve requirement on time deposits. Thus: , DO ,J .55 « , . , TD , E (SiK , , 98 DD where 5 = the average required reserve ratio on demand T deposits at member banks at time T TD o , j , = the average required reserve ratio on time deposits at member banks at time T. But since z (DD . and ? (TD ) do not i ad} i x adj i include non-member bank deposits, we shall employ an exog enously determined but variable ratio of member bank de posits to total commercial bank deposits in calculating the required reserve figure on the basis of total deposits liabilities at member and non-member banks. Thus: DD __ TD __ RR = 6 (DD ..) * + < 5 (TD ..) d , T ad] DD t adj' VTD „ mem , DD where < p = ------- = the ratio of member bank demand DD DDtQtai deposits at all commercial banks TDmem TDtotal >rn = =------- = the ratio of total member bank time « * ■ w deposits to total time deposits at 2 all commercial banks. 2This specific approach is necessitated by the lack of data on adjusted deposits at member banks. Though we desire to calculate 6DD*DD§8^ and $TD*TDa§^' data limita tions force us to employ the ratios of total demand and time deposits at member banks to total demand and time de posits at all commercial banks in our calculation of This approach contrasts with that of de Leeuw and others who have assumed in their own studies that the pro portion of member bank demand and time deposits in total commercial bank demand and time deposits have remained con stant over the period of the study at .84 and .82 respec tively. Our own approach may provide greater flexibility and a smaller degree of error in our estimates than could be achieved by the alternative method. Substituting our derived relation into the reserve identity, we derive: RU + RB = RE + RR Solving this for demand deposits adjusted at all commercial banks: To relate these measures to our exogenously determined stock of high powered money, we define a concept Havailable reserves," RA, equal to the total exogenous stock of high powered money less currency holdings of the public and re serves required against time deposits. This may be viewed as a measure of unborrowed reserves available to support demand deposit liabilities. RU + RB 1 DD adj Z (RU + RB - RE 6dd DD 100 Thus: RA = HM - CURR - 6TD <TDadj) ^ 1 (RA + RB - RE) • *DD Specification of a testable form for our model. The above equation, derived from our accounting framework, may be put into a form suitable for regression analysis in several ways. The usual procedure has been to focus upon the one particular element in that framework which the analyst considers to be influenced by commercial bank be havior and to specify the theory behind this behavior. The measure most frequently separated out for such analysis is free reserves, defined as the difference between excess and borrowed reserves. The usual reason given for focusing on such a measure is that, as we have seen above, the Federal Reserve itself claims to use it as a guide to its open mar ket policy and the financial community is said to interpret movements in its level as indicative of the general trend of monetary policy. However, no other a priori reasons exist for this special emphasis. Yet there are certain reasons which rest upon both a priori and empirical grounds for doubting the wisdom of focusing on this combined meas ure of free reserves. First of all, this additive form depends upon the assumption that the relationships express 101 ing desired excess reserves and desired borrowing as func tions of other variables are linear in form. For example, in the usual case (Teigen), defining rQ as the discount rate and rm as the market interest rate, the following relationships are postulated: Therefore, the implied free reserve relation is RF = (a-d) + (b-e)rD + (c-j)rm However, in such a framework, where the two basic measures are functionally and linearly related to common arguments, clear interpretation of the results of a regression of free reserves against these arguments will be impossible, since the relative effects of the coefficients in the estimated equation will be unknown. Secondly, the empirical evidence available, notably Meigs' study of Free Reserves and the Money Supply clearly shows the dangers of focusing on free 3 reserves as a Federal Reserve policy target. Hence, as Friedman has remarked, RE a + br_ + cr D i m (Chicago: 3A. J. Meigs, Free Reserves and the Money Supply : University of Chicago Press, 1962), pp. 87-9^ 102 Now that he (Meigs) has demonstrated that this emphasis is misdirected, his techniques of analy sis can be used to develop a more satisfactory understanding of the relation between Federal Reserve actions and the stock of money.4 Friedman goes on to suggest that we start such an analysis from the finding that "there is a close relation between changes in (1) unborrowed reserves corrected for altered reserve requirements and (2) member bank deposits." He suggests, then that there are two specific analytical prob lems in the final determination of the money stock. The first analysis may proceed by working backward from changes in unborrowed reserves, RU, to the origins of those changes. The second proceeds by working forward "to explore the links between changes in (1) and (2), with special emphasis on a separate analysis of excess reserves and of borrow ings ." ^ We shall not be concerned with the first problem in this study. Consequently, we have assumed unborrowed re serves, RU, to be exogenously determined. We will concen trate solely on the second problem. Within our accounting framework, then, we will focus upon the determination of "available reserves," RA, borrowed reserves, RB, and excess 4Milton Friedman, "Foreword," Free Reserves and the Money Supyly (Chicago: University of Chicago Press, 1962), pp. vii-vm. 5Ibid. 103 reserves, RE, as the behavioral determinants of the money supply. We may interpret this treatment as a partitioning of the demand deposit supply equation into two components: (1) an outside, imposed constraint on the commercial bank ing system, available reserves, equal to ^HM - Curr - 6TD(TDa(jj) • dependent upon the Federal Reserve's exogenous supply of high powered money and the public's demand for currency and time deposits and (2) two behav ioral relations embodying the bank's demand for excess reserves and for borrowing. In this schema, then, the sup ply of demand deposits depends upon the public's demand for other components of the total money stock which absorb a portion of the exogenously supplied stock of high powered money, and upon the banks' willingness to borrow and hold excess reserves.** fiLyle Gramley and Samuel Chase have criticized this type of formulation of a money supply hypothesis. "Con structs of this nature," they hold, "... are devoid of postulates regarding the willingness of any economic unit to supply either of the two components of the money stock— currency and demand deposits." This critique does not apply to the current formu lation, however, since we shall, in fact., specify behav ioral supply and demand relations for all major factors which absorb bank reserves. Within our schema, the supply of currency and the supply of time deposits shall be as sumed to be perfectly elastic at exogenously established rates and, hence, the quantity outstanding at any time will be determined by the demand of the public for these assets. The stock of demand deposits, on the other hand, is deter mined by the interaction of the public's demand for such deposits and the banks' willingness to supply these deposits as reflected in their desired excess reserve and borrowing relations. For, after all, the decision to hold excess 104 Thus we view all three elements, RA, RB, and RE, as endogenously determined behavioral variables. Our pro cedure, then, will be to specify and estimate separate structural demand equations for currency and time deposits which enter the determination of RA, and for borrowed re serves and bank holdings of excess reserves. These esti mates will then be used with the calculated value of ( 6^), the average reserve requirement as determined by the dis tribution of member bank demand deposits, in order to esti mate the demand deposit supply function. The specification of a demand for demand deposits equation will complete our financial model. Commercial Bank Holdings of Excess Reserves The first behavioral relation which we consider explicitly is the demand for excess reserves by member com mercial banks. We might note that throughout our analysis reserves is simply the reverse of a decision to supply de posits up to the limit of available unborrowed reserves. Likewise, the borrowing decision is simply a decision on the part of the banks to expand deposits beyond the limits set by the stock of exogenously supplied reserves and the legal reserve requirements. The interaction between these relations will become more obvious when we present a sum mary of the entire model in Chapter V below. See Lyle E. Gramley and Samuel B. Chase, Jr., "Time Deposits in Monetary Analysis," Federal Reserve Bul letin, October, 1965, pp. 1380-1406. 105 we assume that the level of excess reserves actually held by commercial banks is roughly equal to the level which they desire to hold. We point this out simply to emphasize the contrast of current thought on bank behavior with the theories which were held as recently as World War II. For, as noted in Chapter II, the interpretation which was cur rent in the late thirties, which formed the basis for the reserve requirement increases in 1936-37, was that "the ac cumulation of usable reserves results from the temporary unavailability of earning assets banks are willing to pur- 7 chase." From this it was concluded that an increase in reserve requirements would have no effect upon the total reserves which banks desire to hold. Although in recent years bank holdings of excess reserves have been at relatively low levels, economists have not reverted back to assuming that the desired level is generally zero. Rather, the desire for relatively small holdings is explained by two factors. First, the banks have confidence that the Federal Reserve will lend suffi cient reserves to avert any serious unforeseen liquidity crises. This confidence is based in part upon the fact that the Federal Reserve banks have continuously had the ^Phillip Cagan, Determinants and Effects of Changes in the Stock of Money, 1875-1950 (New YorEl N.B.ETR., dis tributed by CoTumbia University Press, 1965), p. 194. 106 means to make such loans since their holdings of gold have been significantly above their statutory reserve require ments. Second, the deposit insurance provided by the F.D.I.C. has been extremely successful in striking at the heart of the need for large reserves--financial panics and their resulting liquidity crises. However, though bank holdings of excess reserves have been relatively small, averaging 650 million dollars over the period covered by our data, they represent the power of the commercial banks to choose whether or not to make deposits available on the basis of reserves supplied by the authorities. Thus, regardless of the target level employed by the Federal Reserve in the operation of its monetary policy and, particularly, its open market policy, its effectiveness will depend to a significant degree upon the existence of predictably stable excess reserve posi tions so that commercial banks act as reliable intermedi aries in the transmission of monetary changes to the rest of the economy. Hence, complete explanation of the deter minants of these holdings is absolutely necessary in any model which purports to explain the money supply. Excess reserves and vault cash. We begin our anal ysis by representing the balance sheet of a commercial bank (and the consolidated balance sheet of all member commercial 107 banks in the Federal Reserve System) as composed of the following accounts: Assets Liabilities I. Vault cash I. Demand deposits II. Time and savings deposits II. Reserve balances with the Federal Reserve A. required reserves III. Borrowed reserves B. reserves in excess of requirements IV. Other III. Federal government securities IV. Private loans and in vestments V. Other Due to certain changes in the regulations governing the calculation of reserves which occurred during the period covered by our data, we must make perfectly explicit the basis upon which excess reserves are calculated. Before December 1, 1959, i.e., before the revision of Regulation D, which allows the inclusion of vault cash in determining legal reserves, item (2b), "reserve deposits in excess of requirements," was identical with total excess reserves (RE). Since November 24, 1960, excess reserves (RE) are represented by the sum of vault cash plus (minus) reserve 108 Q deposits in excess of (below) requirements. The revision of the rules specifying what may and may not be counted as reserves by commercial banks may be expected to have changed the attitude of bankers towards holding certain assets. These changes may be expected to have one of the following effects on desired holdings of excess reserves: (1) perhaps they bring about no change, (2) since holdings of vault cash now provide the dual func tion of supplying both ready currency and legal reserves, we may expect larger holdings of this asset with no change in the total volume of excess reserves, or (3) banks may now desire larger holdings of excess reserves. As Friedman has noted, since any decline in vault cash now means a de cline in reserves, banks which previously considered only factors such as clearinghouse drains in calculating the buffer of free reserves they desired to hold must now con sider vault cash as well. Since fluctuations in two random Between these dates, vault cash was absorbed into reserves in the following steps: effective Dec. 1, 1959, country banks having vault cash in excess of 4 per cent of their demand deposits were permitted to count that excess as part of their legal reserves; effective Dec. 3, 1959, reserve city and central reserve city banks were permitted to count vault cash in excess of 2 per cent of their net demand deposits; effective Auguest 25, 1960, for country banks and September 1, for reserve city and central reserve city banks, these limits were reduced respectively to 2.5 per cent and 1 per cent; effective November 24, 1960, all vault cash became eligible as legal reserves for all member banks. 109 variables are likely to have a wider range than fluctua tions in one alone, Friedman concludes that banks will hold Q additional free reserves. If this last possibility de scribes the bankers' actual reaction to the revision of Regulation D, so that this modification has caused a change in the desired level of excess reserves as defined above, this will affect our structural estimates and our reserve requirement identity and must be considered explicitly. The evidence brought to bear on this problem thus far is inconclusive. Friedman himself does not test his own hypothesis. But this task has been attempted by others. Jack C. Rothwell, for example, has conducted a survey of non-money market banks in the third Federal Reserve dis trict. He asked a random sample of bankers if they now hold more excess reserves as a precaution against a possible * 1 # * • * ^ . wider range of reserve fluctuations now that vault cash counts as reserves. Twenty-five out of twenty-five of the bankers answered in the negative.^-® Though such a test is subject to all the very serious criticisms which may be raised against such survey techniques, it possibly provides some evidence against Friedman's postulates. However, ^Milton Friedman, "Vault Cash and Free Reserves," Journal of Political Economy, LXIX, No. 4 (August, 1961), 181-I1T2. ^■®Jack C. Rothwell, "Vault Cash and Free Reserves: Some Evidence," Journal of Political Economy LXX, No. 2 (April, 1962), lFT 110 another test carried out by Dr. G. Basevi, using the format presented by Meigs in his study of free reserves, concludes that Friedman is correct.^-1 Basevi argues that since banks must hold vault cash in any event, allowing them to count this asset as part of their reserves is equivalent to a de crease in reserve requirements. Using Meigs' data and ex tending it to cover the relevant period, Basevi finds a definite shift in the relation at the time of the vault cash regulation changes. Actual "free reserves" are con sistently above the values predicted by Meigs' equation after December, 1959, when the gradual absorption of vault cash began. Since there is no reason to expect that these changes had any effect on borrowing, the level of desired excess reserves seems to have shifted up at the time when vault cash became eligible as legal reserves. This conflicting evidence indicates that at this time no final judgment seems possible on the effect of this institutional change. Since at least one important piece of evidence seems to support the idea that this change has caused a structural shift in the banks' desired level of excess reserves, we shall include a dummy variable in our regression equation as a test of the presence of this shift. H-G. Basevi, "Vault Cash and the Shift in the De sired Level of Free Reserves," Journal of Political Economy, LXXI, No. 4 (August, 1963), 408-412. Ill The use of such variables to represent the temporal effects of such structural shifts is quite familiar. We shall test our empirical excess reserve equation with the dummy vari able included and we shall compare these results with the free structural form of the equation estimated without the use of the dummy variable. Constraints on commercial bank portfolio manage ment. With these questions of measurement and institu tionally induces structural shifts aside, what factors must we consider explicitly to determine commercial banks' de sired holdings of excess reserves? We start with a consideration of certain character istics specific to commercial bank portfolios. First, we may assume that the commercial banker attempts to manage his portfolio according to the same general principles which guide the organization of any other portfolio. He has certain goals to achieve, most notably the maximization of expected profit, and he is subject to certain con straints which impinge upon his ability to reach these goals, namely, the need to maintain liquidity and avoid undue risk. Thus, he faces the basic problem of balancing the marginal return from an investment (in any form) against the marginal loss of liquidity and the marginal in crease in overall risk. Specific characteristics of the accounts in which 112 banks deal, however, impose special constraints upon their investment possibilities— constraints not generally faced by any sector of the non-bank public. These constraints arise from the legal requirement that commercial banks hold specific proportions of t heir various deposit liabilities in the form of "legal reserves" and from the institutional characteristic of having a very large fraction of their liabilities due "on demand." The latter of these factors implies that banks must be concerned with the general liq uidity of their asset portfolios in a very special way. Yet, the former requirement that they hold a portion of their assets in a legally approved form of reserves ( a form which yields no income) is really of little help in satisfying this liquidity need. For fractional required reserves, being required by law, are not really available as liquidity reserves. Thus, banks can only count on their other cash assets for buffer purposes. This is commonly noted in monetary texts where it is emphasized that the purpose of legal reserves in a fractional reserve system is control rather than liquidity. Hence, the banks are left to arrange their portfolios, after the provision of legal reserves, in whatever way they think best to serve the conflicting purposes of liquidity and profit. By tradition and because of certain additional legal restrictions which specify certain classes of financial assets as forbidden to commercial banks, we find that banks generally satisfy their liquidity needs by hold ing some combination of three specific assets: vault cash, reserve deposits at the Federal Reserve in excess of re quirements, and short term government securities. In de termining the banks' desired level of excess reserves, therefore, we must answer two questions. First, what will determine their general desired level of liquidity as meas ured by their total holdings of the above noted "cash as sets" and, second, what determines the allocation of that total among the specific classes available. Since vault cash has typically been a rather minor item held primarily for the purpose of providing convenience in meeting cur rency demand and sicne it is presently counted within banks' total reserves and has been so accounted for above, we may neglect this item. Thus, we focus on commercial bank hold ings of excess reserves and government bills and seek to determine the forces influencing their absolute and rela tive levels. The determinants of desired excess reserve holdings. On a priori grounds, general portfolio analysis leads us to expect that the most important determinants of commercial banks' desired holdings of excess reserves will be among the following: the size and composition of both total 114 deposit liabilities and interest earning asset accounts; the alternative cost of holding these non-interest bearing reserves; the penalty for falling short on reserve require ments when unexpected cash drains draw reserves below the legal minimum; the rate of change of unborrowed reserves supplied by the Federal Reserve; and the demand for loans by regular depositors. By far, the predominant liabilities of commercial banks are their demand and time deposits outstanding. Be cause of the differing characteristics of these two ac counts, they are likely to affect desired excess reserve holdings in different ways. The larger the proportion of highly active and/or erratic deposits in the total of com mercial bank liabilities, the larger will be those desired holdings. For example, since demand deposits may be with drawn at any time without notice, the commercial bank must hold a relatively large stock of liquid assets to insure its ability to meet the net drains which they can expect to occur in a random process such as check clearing. Time deposits, on the other hand, generally represent a more secure and stable source of funds to the bank both because of the purposes for they they are employed by depositors and the fact that, legally, the depositor can be required to present thirty days' notice of his intention to withdraw funds from such an account. 115 Consequently, we would expect a bank's holdings of liquid assets to be related to the composition of its lia bility accounts as measured by, say, the ratio of its time deposit liabilities to its total deposits. However, two factors may weaken this influence. First, since the legal reserve requirement on time deposits is significantly lower than the requirement on demand deposits, a one-dollar with drawal of funds from a time account frees fewer required reserves than the same withdrawal from a demand account. This may induce banks to hold a slightly greater amount of reserves against time deposit withdrawals than they would if equal requirements were applied to all accounts. This would reduce the empirical effects of the differences in these accounts on bank behavior. Second, in fact, banks do not require time depositors to give prior notice of with drawal, but generally honor withdrawals upon demand. This undoubtedly increases the need to hold liquid assets against time deposits over what it would be if the legal thirty days* notice requirement was generally enforced. Hence, though we would expect desired holdings of excess reserves to vary inversely with the specified ratio, the above influences may so weaken this relation as to make it imperceptible from the data. We will test for these ef fects by including the ratio of time deposits to total deposit liabilities in our excess reserved demand equation. 116 Similar considerations based on portfolio theory would lead us to expect to find that the composition of a bank's earning assets account will be of significance in determining that bank's desired reserve holdings. Speci fically/ the greater the degree of "frozenness" and the longer the maturity of its "loan account," the greater the need to maintain a high degree of liquidity among its other accounts. The lower the ratio of government securities (of all maturities) to private loans, for example, the more reliance must be placed upon excess reserves as a source of liquidity. Once again, however, the existence of very strong cross effects makes the empirical untangling of this influence extremely difficult. For the factors which cause the government securities/loan ratio to be relatively low are the very same factors which will cause a low level of desired reserves. These include such factors as generally high loan rates, high levels of employment, profit and general business activity which make loan applications look more secure and the interest rate look more attractive (due to a lower imputed risk differential), and the growing con fidence of banks that the Federal Reserve will meet any unexpected liquidity needs in times of shortage. Thus, what little relationship is evident from the data between this ratio and holdings of excess reserves seems to be positive in contrast to the negative relation we would 117 expect to observe in the absence of these common factors. One way in which we may attempt to account for this entire combination of forces is to take explicit considera tion of those forces which will both increase customer loan demand and also decrease bankers' risk estimates. One rather crude way in which this may be done is to associate both bankers' confidence and aggregate loan demand with the general state of the economy— not necessarily its level of performance but, rather, the change in that level over recent quarters. Hence, we will include in our regression a measure of the rate of change of national income over the past quarter. While certainly not a perfect measure of what we seek, this variable should sufficiently reflect the forces which increase loan demand and cause bankers to be more bullish in their estimates of risk on loan accounts. Turning to factors external to the size and compo sition of a bank's portfolio, we would expect the alterna tive cost of holding excess reserves to be one of the most important determinants of their desired level. We may con sider short term government securities— government bills maturing in ninety days or less, for example— as the closest income-yielding substitute for excess reserves. Given the transactions cost of switching back and forth from securities to cash, the higher the return on these securities, the greater the net return foregone by holding 118 excess reserves. Thus, the higher the return on government bills, the more it will be worthwhile to conserve on their holdings of vault cash and excess reserves which do not yield a return. Tighter and tighter control over excess reserve holdings, however, leads inevitably to higher and higher probabilities that the banker will find himself short of reserves to meet requirements. Indeed, it is specifically this measure of probability which controls the liquidity decisions and excess reserve holdings of the commercial bank. The banker will be willing to risk the higher prob abilities of falling below the level of legally required reserves only if he is compensated by a higher return on funds invested in alternative assets. Thus, the relation between excess reserves and the alternative cost of holding these reserves as represented by the bill rate, for ex ample, is directly influenced by the attitude of the banker towards accepting the higher probabilities of a short fall. This attitude, in turn, is dependent upon the means avail able to the banker of covering this shortage. Basically, he has three alternatives: he can sell assets, usually very short term government treasury bills which have stable market values; he can borrow in the federal funds market; 119 12 or, he can borrow from the Federal Reserve. Rather than a simple relation between reserve holdings and market in terest rates, we are dealing here with a more complex set of arguments. The basic reserve-alternative cost relation ship must be modified to take account of the fact that the banker has available to him various methods by which he can cover his "shortages." He is not compelled simply to sell securities. Rather, his decision will depend upon a com parison of costs, a comparison which centers on the bill rate as the interest foregone if securities are sold, and the discount rate as the cost incurred if the banker bor rows the needed funds. Thus, the bill rate is the basic determinant of the relative relation between the degree of management of excess reserves and the expected probability of a short fall. But since the expected cost of that short fall is determined by the way in which it is covered, the discount rate enters as an argument in the full specifica tion of this relation. The precise empirical form by which this return- cost relation should be represented is not at all clear ^The individual banker also has available to him the possibility of calling in loans or using correspondent balances at other banks to meet unexpected shortages. The former of these possibilities, however, is not a very use ful short term solution and the latter possibility is no solution at all for the banking system as a whole, since it simply shifts the burden of adjustment between banks. 120 from a priori considerations alone. Meigs, for example, in dealing with this problem in his own study of commercial bank free reserves, makes no theoretical judgment on the appropriate form of this relation other than that of lin earity. He makes the final choice of exact specification of his equation dependent upon his empirical results. A similar approach is taken to this problem by de Leeuw. The basic choice of form, within the constraint of linearity imposed on our model, must be made among the ratio of the bill rate to the discount rate, the arithmetic difference between these rates or the level of each of these rates entered separately. Each of these forms im plies different assumptions about the way in which bankers take consideration of the relation between these rates. We will reserve judgment on these matters and, like Meigs and de Leeuw, let the results of our tests indicate the best form for inclusion within our final model. The last factor which we consider to be of signifi cant importance in the determination of commercial bank holdings of excess reserves is the change in the level of exogenously supplied unborrowed reserves corrected for re serve requirement changes. We employ this adjusted measure in order to eliminate the effects brought about by simulta neous changes in the supply of unborrowed reserves and re serve requirements. Simultaneous and offsetting increases 121 or decreases in the supply of unborrowed reserves and re serve requirements can be expected to have little or no effect upon a bank's desired level of excess reserves. We are concerned only with the effects of net changes in banks' excess reserve positions. Thus, we require a meas ure which reflects only exogenously determined changes in "surplus" reserves. There are two ways in which this measure may pos sibly affect actual excess reserve levels. On the one hand, if we postulate that the basic equilibrium level of desired excess reserves is primarily explained by interest rates and the other factors previously discussed, the rate of change of unborrowed reserves would be a short term dis turbance pushing the banks away from that equilibrium level and necessitating some sort of readjustment. In this case, we would expect to find a positive relation between actual excess reserves and the change in unborrowed reserves. On the other hand, bankers may come to formulate their own expectations concerning the behavior of the Federal Reserve in supplying such reserves and may incorporate these expec tations into their calculations of a desired excess reserve level. An attempt has been made to sort out the effects of both these possibilities by including not only the cur rent change in unborrowed reserves in our equation, but, also, the changes experienced in the recent past upon which 122 bankers may be assumed to have formulated their expecta tions about the near future. Our preliminary tests indi cate that it is the current change in the stock of unbor rowed reserves which was the most influence in the determi nation of excess reserve levels. Therefore we specify this current value in our excess reserve equation. the total deposit liabilities of commercial banks, then, full consideration of all the above factors leads to the specification of the following linear form for our prelimi nary test of the demand for excess reserves: With the inclusion of a scale factor represented by ( a Y) + a-, . (rn-r„) 14 D B t + a15(nT) + a16(DD + TD) where all variables are defined as above and A 5 + (TDadj) • < f > TD A6 ] = change in unborrowed reserves corrected for reserve re quirement changes, and a "barred” variable, such as DD, represents the nominal value of a variable. 123 Member Bank Borrowing The second structural relation in our model of money supply determination is the demand for borrowed re serves by member commercial banks. Over the period covered by our study, the average level of these reserves was 423 million dollars as compared to average holdings of excess reserves of 650 million dollars. The variation in commer- cail bank borrowings was much greater than the variation in those holdings of excess reserves, however. Whereas excess reserves ranged from a low of 422 million dollars to a high of 964 million dollars from 1948 to 1962, borrowed reserves were as low as 52 million dollars in the third quarter of 1961 and as high as 1.391 billion dollars in the fourth quarter of 1952. Commercial bank borrowing and free reserves. In Chapter II, we reviewed in some detail the various theories which have been presented over the past several decades to explain commercial bank borrowing and banks1 holdings of excess reserves. Prior to World War II, when it was gener ally assumed that commercial banks would not willingly hold excess reserves for any extended periods of time, analytical attention was focused on borrowed reserves. In postwar writings, with recognition of the fact that banks may at 124 times reasonably desire to hold a positive level of excess reserves in their portfolios, the emphasis of most analyses of the money supply mechanism, both within the Federal Re serve and in academic and financial circles, focused upon the newly defined measure: free reserves. Thus, we have shown that in the financial press and in much analytic work as well, we have come full cycle from a rigid assumption of zero excess reserves to an inflexible emphasis on a rigid level of free reserves. We are perhaps just now experi encing a peak in this emphasis on the free reserve measure, for, although it is still used both by the Federal Reserve and by the financial community, the basis of that focus is slowly being destroyed by the many empirical studies re cently presented on the subject. Thanks to the work of Meigs, DeWald and others, which have clearly demonstrated the danger of a constant free reserve policy target, there has been a reemphasis on the possibility of analyzing bor rowed reserves and excess reserves separately rather than in the combined measure of free reserves. With the focus on free reserves* however, direct attention was diverted away from bank borrowing and the arguments over the various theories dealing with this as pect of bank behavior seemed to have faded into the back ground. They were still there, of course, but it was easy to talk of the new measure without getting involved in the 125 old disputes. However, our separation of free reserves into its components once again brings these questions to the fore. And well it is that we do this, for there still remain many unsettled questions. A synthesis of theories of the determination of bank borrowing. It is profitable to begin by looking at commercial bank borrowing from both sides of the discount window. The policies governing discounting at district Reserve Banks are summed up in Regulation A of the Reserve Board. In part, this reads as follows: Federal Reserve credit is generally extended on a short term basis to a member bank in order to en able it to adjust its asset position when necessary because of developments such as a sudden withdrawal of deposits or seasonal requirements for credit beyond those which can reasonably be met by use of the bank's own resources. . . . Un3er ordinary con ditions, the continuous use of Federal Reserve credit by a member bank over a considerable period of time is not regarded as appropriate. . . . It (the district Reserve Bank) considers whether the bank is borrowing principally for the purpose of obtaining a tax advantage or profiting from rate differentials and whether the bank is extending an undue amount of credit for the speculative carrying of or trading in securities, real estate, or com modities, or otherwise . . .13 As is obvious from this statement, the Federal Re serve does not intend to be in the business of lending l^Board of Governors of the Federal Reserve System, The Federal Reserve System: Purposes and Functions Tw£sKing£on, D.C. , 1 « 3) , p. ------------------- reserves to member banks at a rate of interest below the market rate simply to provide these banks with an opportu nity to profit from the differential. However, at the same time, the authorities do not attempt to discourage such borrowing simply by making it very expensive. For, as the data show, the discount rate, while usually above the trea sury bill rate, has almost invariably been below the rate on corporate securities— a rate which represents a fair approximation to the bank loan rate. This is to be ex pected, however, since the Federal Reserve does not rely solely upon the discount rate to control the flow of bor rowing. As is indicated by Regulation A, and as is evident from an examination of the operation of the discount window, at least some reliance is placed upon administrative "moral suasion" and the power of the loan officer to refuse loans on an individual evaluation basis. Yet, though the mone tary authorities personally discourage the banks from bor rowing strictly for profit purposes, neither this fact nor the existence of a differential between the discount rate and market loan rates represent conclusive evidence that banks do not still use the discount facilities at some times and in some places solely for such purposes. This issue is further clouded when we view borrow ing from the commercial bank's side of the discount window. Many depositors, especially larger business and financial 127 depositors are "critical of bank borrowing since, in case of insolvency, creditors' claims take precedence over the claims of depositors."^4 Thus, a bank with large and con tinuous balances due to the Federal Reserve runs the risk of alienating some of its more conservative depositors. In addition, since the Federal Reserve is in the position of performing certain services for the commercial banks, the rather personal way in which the discount window is admin istered will insure that the banker understands the author ities' policy on discounts and that he avoids abuse of his discount rights so as not to jeopardize the availability of those services. Thus, in addition to the nominal discount rate to be paid on borrowings, there are other real costs to the banker of having large borrowings outstanding with the Federal Reserve. Even if we know that the discount rate is below the market loan rate, if the "needs and re luctance" theory has any validity at all, the non-monetary costs incurred by the bank in borrowing reserves make it impossible to judge whether the total real cost of that borrowing is actually above or below the market loan rate. The discount rate by itself, then, is probably best viewed as a measure of the variation in the total cost of borrow ing rather than as a complete measure of the real cost of 14Ibid., p. 44. such action. What, then, is the true role of the discounting mechanism? Basically, we feel that the evidence supports the "needs and reluctance" thesis. Yet, we also feel that a rational banker will use the mechanism to the extent possible within the framework specified by the attitudes of the Federal Reserve authorities to increase his profit or decrease his cost. While basically reluctant to use the discount privilege for outright profiteering for fear of incurring reprisals from the authorities or from his own customers, the commercial banker will freely borrow when this is the cheapest way of covering a shortage (consider ing all real cost involved). He may even remain in debt for some time rather than repay the advances immediately at the cost of giving up the chance to make a profitable loan. Though reluctance prevents the banker from borrowing from the Federal Reserve every time a profit opportunity pre sents itself and thus prevents the equality between the discount rate and the market loan rate which such action would imply, we do not believe that this prevents the banker from "selective" use of the discount mechanism for profit purposes. A similar view of the discount process which com bines the "needs and reluctance" theory with the "profit" theory of borrowing has recently been presented by Murray 129 Polakoff. Polakoff tries to separate two specific ques tions. First, what is the basic motive behind commercial bank borrowing? Second, what are the determinants of the extent of that borrowing? He postulates that commercial banks attempt to balance the utility of borrowing "to save the least cost spread," by which the treasury bill rate exceeds the discount rate, against the disutility of bor rowing "viewed as an activity engaged in reluctantly to meet temporary needs."15 Through the use of scatter dia grams, Polakoff shows that a strong positive relation ex ists between the spread in interest rates and bank borrow ing. Further, in several of the scatter diagrams, there is an observed tendency for those borrowings to abate in the upper reaches of the least cost spread. This decline Polakoff attributes to the declining marginal utility of profit and the increasing disutility of the socially dis- approved-of practice of borrowing. In a comment on this work, Donald Hodgman criti cizes Polakoff's use of the bill rate and proposes that the proper measure of profitability would be the market loan rate. Polakoff defends himself, however, by noting that he has no concern whatever for the ends of bank borrowing, but ^Murray Polakoff, "Reluctance Elasticity, Least Cost and Member Bank Borrowing," Journal of Finance, XV, No. 1 (March, 1960), 1-18. 130 is concerned only with the means. Hence, he concentrates on the alternative cost measures rather than on cost- revenue measures. This criticism aside, Hodgman substan tially agrees with this combined theory. He would only emphasize the role of Federal Reserve administration some what more strongly. For he feels that although "... com mercial banks borrow because of the profit motive broadly interpreted . . . the limits of borrowing are primarily those enforced informally by the attitude of Federal Re serve Officials."16 From the point of view of an analysis of commercial bank behavior, however, there is little dif ference in these propositions; for, as we noted above, the attitude of the monetary authorities is one of the very important factors in the determination of the banks* own reluctance to borrow. Specification of the demand for borrowed reserves equation. The above considerations indicate that in the specification of our bank borrowing equation we need to investigate two related sets of factors: the determinants of the relative cost or relative profitability of bank borrowing, and the influences which affect and modify the l ^ D o n a l d d. Hodgman, "Member Bank Borrowing: A Comment," Journal of Finance, XVI, No. 1 (March, 1961), 93. 131 basic reluctance of bankers to borrow. As is noted in The Federal Reserve System; Purposes and Functions, "Continu ing pressures on the reserve positions and other special developments may, at times, weaken the reluctance to borrow, but it nonetheless persists as a factor affecting member bank borrowing.what specific measures, then, may we use to represent the kind of pressures which would weaken the banks' "reluctance to borrow"? If we look at the bal ance sheet presented above, we may categorize certain ac counts as "liquid assets." These would include vault cash, excess reserve holdings with the Federal Reserve, and the government securities account. If we postulate that it is basically pressure on these liquid assets which breaks down the banks' reluctance to borrow, we may formulate a vari able measuring the change in the other accounts which would affect bank holdings of these assets. Under the assumption that changes in the private securities and loan account are substantially under the control of the banks themselves, exogenous changes in the banks' liquid assets accounts can arise from the non-bank puclic's movement of funds into or out of time and demand deposit accounts, from the Federal Reserve1s increase or decrease in the supply of unborrowed reserves or from changes in reserve requirements, and l^Board of Governors of the Federal Reserve System, op. cit., p. 44. 132 certain other minor items. Since borrowing to cover short ages or to restore liquid asset positions to desired levels after an unexpected change caused by one of the above fac tors is a legitimate use of the discount mechanism, we would expect that a commercial bank, though generally re luctant to borrow, would not hesitate to employ this means to meet such a need. Thus we specify two separate measures of such changes, one of which focuses on the Federal Re serve's action and the other of which focuses on flows de termined by the non-bank public. The first of these meas ures we represent by the change in Federal Reserve supplied unborrowed reserves. As used above, we correct this meas ure for reserve requirement changes. DD __ TD n = ARU — t(DDa(jj) ’ A 6 + *^TD ^ The second measure, the change in deposit liabilities net of loan creation or destruction and corrected for changes in required reserves, we define as follows: A (DD . ■ + fD _ . - PL - RR) * AO aa} adj where all variables are as defined above and PL = the pri vate loans and securities held by banks. Through the pressures created on liquidity posi tions and the effects which these pressures have on bank reluctance to borrow, we would expect changes in these 133 measures to have potential effects on commercial bank hold ings of borrowed reserves. The degree to which this poten tial will be realized, however, depends upon the cost and profit characteristics of all the alternatives facing the bank. While an unexpected shift from time deposits to demand deposits, for example, would increase required re serves, decrease excess reserves, and thereby lead to a shortage of liquid assets which would weaken the reluctance to borrow, we cannot assign any automaticity to the borrow ing decision. For, the possibility of meeting shortages and restoring liquidity positions through the sale of in terest earning assets such as short term government securi ties will force the profit maximizing banker to compare the costs of borrowing with these and any other alternative. Hence, the basic relation stated above is not complete. It must be modified so as to include these alternative cost factors. Again, however, though we specify the comparison to be between the Treasury bill rate and the discount rate charged by the Federal Reserve, it remains an open question as to what exact form of this relation best represents the banker's response to these alternatives. Although Polakoff, Hodgman, and others couch their analyses in terms of the arithmetic difference between these measures, there is little a priori basis for this emphasis. Hence, as in the case of our excess reserves relation, we shall test various 134 possible ways in which these rates may enter the demand for borrowed reserves equation and we shall choose that form which performs "best” for inclusion in our final model. As in the case of the demand for excess reserve holdings, we shall also include within our borrowed re serves equation as a crude measure of loan demand, the change in the level of national product, and a scale factor represented by total deposit liabilities. Hence, we spec ify the following structural demand for borrowed reserves: (RB)t = a2i + a22<AY)+ a23 ( Ae) + a24(nT) + a25( rfi-rD)T + a26(DD + TD)t or (RB)t = a21 + a22(AY) +a23( aq ) + a24(nT) + a25(rD/rB)T + a26(DD + TD)t II. THE DEMAND FOR MONEY The studies on money demand which were reviewed in detail in Chapter II suggest that the appropriate defini tion of money for use in a model such as this is that de fined to include currency held by the public and demand deposits (adjusted) at commercial banks. As already noted, however, the structure of our model necessitates the divi sion of this concept of money into its component parts in 135 order to satisfy the specification requirements of the money supply relations. Hence, we consider, in turn, the demand for demand deposits by the public and their demand to hold currency. We conclude with a brief investigation of the determinants of the public's demand for time de posits . The Demand for Demand Deposits Our review of the work which has been carried out in an attempt to test the explanatory and predictive power of the various theories of money demand suggests three main conclusions which will be helpful to us in the formulation of a deposit demand function. First of all, almost all the works reviewed indicate that time and demand deposits are held for substantially different reasons and should be con sidered in separate equations. We will follow this proce dure here. Second, the evidence presented overwhelmingly favors the view that the demand to hold money balances shows a significant response to interest rate variations within the range of recent experience. Third, the wealth constraint suggested by the portfolio balance theory of money demand seems to yield the best results for predicting the public's behavior with regard to their monetary hold ings. Viewing demand deposits as one asset among the many 136 assets in an individual's portfolio, these initial consid erations lead to the following specification for the demand deposit relation: DD = DD( r, W) where r and W represent the rate of interest and the pub lic's wealth, respectively. However, so stated, this hy pothesis lacks empirical content. In order to derive a testable formulation from this hypothesis, we must answer four questions. First, what is an appropriate empirical measure of the theoretical yield variable which acts as a constraint on the public's demand for demand deposits? Second, what theoretical considerations are relevant to our judgment of a proper empirical measure of the wealth con straint included in our relation? Third, what is the spe cific form of this functional relation? And, fourth, what modifications in the basic relation are suggested by the short run focus of our model? We will consider each of these questions in turn. Questions on the empirical measure of the interest rate. We first consider the problem of determining which particular measure of the interest rate from the entire term structure of rates is most relevant as a measure of the actual figure which acts as the constraint on the pub lic's money demand. The general view of money demand as 137 part of the theory of portfolio balance and asset choice indicates that all assets in the balance sheet are substi- tutes for all other assets. Wealth is held in the form of demand deposit balances strictly for the services these balances yield relative to the return foregone by not hold ing positive interest yielding assets. This indicates, however, that any particular yield measure chosen will be somewhat arbitrary and will perform merely as a proxy for the spectrum of returns which alternative wealth forms afford their owners. At bottom, then, this is an empirical question. Turning to the literature for guidance in this matter is of little help. Very many different forms have been used in the works already surveyed; yet, none of them presents a strong enough case to weaken the position of any of the others. In fact, none of these studies have really faced up to the question of which rate seems to perform best. In the studies by Brunner and Meltzer,^-® for example Durand's series of the yields on twenty-year corporate bonds is used in the empirical tests. Teigen^ employs l®Karl Brunner and Allan H. Meltzer, "Some Further Investigations of Demand and Supply Functions for Money," Journal of Finance, XIX, No. 2 (May, 1964), 240-283. L. Teigen, "Demand and Supply Functions for Money in the U.S.: Some Structural Estimates," Econo- metrica, XXXII, No. 4 (Oct., 1964), 476-509; R. L. Teigen, "An Aggregated Quarterly Model of the U.S. Monetary Sector: 1953-1964" (Paper presented to the Conference on Targets and Indicators of Monetary Policy, University of California at Los Angeles, April 29, 1966). (Mimeographed.) 138 the rate on four-to-six month commercial paper in his money demand estimates. This measure is also used by Bronfen- 2 A brenner and Mayer# although their estimates are made from annual data whereas Teigen employed postwar quarterly figures. In the Brookings model# de Leeuw employs two rates in his demand for demand deposits equation--the yield on private securities# and the rate of return on time de posits. Friedman^l tries both short term and long term rates on government securities before he dismisses the interest rate as a significant argument in his velocity function. This lack of agreement over which rate to use in dicates our current lack of knowledge of the effect of the term structure of rates on the behavior of economic units. Yet it also lends support to the idea expressed above that whatever rate is used will be merely a proxy for the whole spectrum of rates. Therefore# if the term structure of rates remains relatively stable over the period of time covered by our data# the choice of different rates will involve merely a change in the scale of the independent 20j4artin Bronfenbrenner and Thomas Mayer, "Liquid ity Functions in the American Economy," Econometrica# XXVIII# No. 4 (October, 1960), 810-834. ^Milton Friedman, "The Demand for Money: Some Theoretical and Empirical Results," Journal of Political Economy, LXVII, No. 4 (August# 1959). 139 variable. We know that this will not generally be the case, however, since it is quite clear from even casual observa tion that short term rates are usually much more variable than long term rates. It is precisely this extra degree of sensitivity of the short rate which is often given as the reason for employing it in empirical work. For example, as Bronfenbrenner and Mayer state, "Besides being readily available, the rate (four-to-six-month commercial paper rate) is nearly free of risk and appreciation factors and it is also more sensitive to economic changes than are longer term rates."22 Hence, we determine our use of interest rates on the following basis. Since a time deposit demand equation will be considered explicitly within the framework of our model, it will be possible for us to focus upon the sub stitution effects between demand and time deposits in the public's portfolio. Thus, as a measure of this effect, we shall test the rate on time deposits as an argument in our equation. We shall also test to see whether or not demand deposit holdings are sensitive to the rather sharp move ments in the short term rates. We will employ the interest rate on three-month treasury bills as a measure of the short rate and include it within our regression on demand 22Bronfenbrenner and Mayer, 0£. cit., p. 196. 140 deposits. This will allow us to judge the sensitivity of the public's response mechanism to changing yield condi tions. Hence, our final specification will be the result of empirical tests carried out on the measures suggested above. This appears to be the best we can do at present with our limited knowledge of the true response mechanism which determines the public's portfolio behavior. Considerations on the empirical measure of the wealth constraint. We now turn to the question of which specific measure of wealth should be included in our empir ical tests as the relevant constraint on the public's be havior in determining their monetary holdings. Since wealth will again appear as a constraint in the consumption function, we will consider the relevant issues for both de cisions at this time. Though quite a lot has been written in connection with the Pigou and Patinkin analyses concerning the role of the government's liabilities in the public's wealth stock, very little has been written about the other problems which the actual measurement of the appropriate constraint in volves. We have here only the suggestions and tests made by Allan Meltzer to guide us. Meltzer lists three specific questions which imme diately suggest themselves concerning the measurement of 141 the wealth constraint. We may quote him directly: First, should human wealth be treated along with non-human wealth as a constraint in the determina tion of asset equilibrium? . . . Second, should non human wealth be consolidated or combined? That is, do we consider each economic entity (individual or firm) to be constrained by its gross wealth and the aggregate constrained by the unconsolidated sum? Such an approach involves substantial double count ing but may nontheless more closely approximate the behavior of economic units. Third, how do we treat the assets and liabilities of the government?23 Meltzer concludes that "at heart, the issue is em pirical," and suggests that we submit several different definitions of wealth to specific tests geared to throwing some light on the above questions. In his own tests, Meltzer uses four alternative wealth concepts. His results indicate that when money is defined as M^, currency plus demand deposits adjusted, increases in aggregate wealth as defined by three of the four measures employed "have roughly the same effect on the demand for money." Specifi cally, the elasticity measures for these wealth variables were as follows: IMi.w = 1.01; SMl>A = .997; ^ = 1.08.24 The most interesting part of these results is that ^Allan h . Meltzer, "The Demand for Money: The Evidence from the Time Series," Journal of Political Econ omy, LXXI, No. 3 (June, 1963), 25TI ibid. The four wealth concepts employed by Meltzer are as follows: 1. W = total wealth from Goldsmith's table W - 1 plus monetary and non-monetary debt of the gov. ernment (all levels) minus government assets. This measure is referred to as "consolidated 142 these similarities were displayed only by those measures of wealth which include the government debt as an asset of the public. This result lends support to and is in turn explained by the recent theoretical presentation of Pesek and Saving in which they demonstrate that the existence of different discount rates on the taxes imposed on human and non-human wealth "assures that government debt will repre sent a positive component of w e a l t h . "25 And, as Meltzer goes on to note, when wealth is defined as "net wealth," G, a measure obtained by consolidating the balance sheets of all sectors, "We get a result that is much less satisfactory than those obtained when total assets and net worth were used as the measure of wealth or when government assets net non-human wealth of the public." 2. A s unconsolidated total assets of households, business, and governments. This series was constructed by Meltzer from the figures given by Goldsmith in his balance sheets W - 9 through W - 16 for the benchmark years from 1900-1949. 3. N = aggregate net worth of households and busi ness. Meltzer employed a similar process of interpolation based on figures given by Gold smith for the benchmark years 1900-1949 in con structing this series. 4. G * consolidated wealth of households, business, government and the rest of the worlds This is Goldsmith's series (W - 1) unadjusted. It should be noted that both series A and series N involve substantial double counting. For example, in these measures both equity ownership of households and business plant and equipment are included. ^Boris pesek and Thomas Saving, Money, Wealth and Economic Theory- (New York: The Macmillan Company^ I75’ 7J ~ , p^ 282. 143 were subtracted and government liabilities added . . ."26 Specifically, there appears to be no effect of the net wealth measure on the demand for money. The elasticity of with respect to "net wealth," G, is zMl.G = ”0*02. This result is all the more interesting since it explains the results obtained in tests by Bronfenbrenner and Mayer in which they failed to find a consistently significant role for the wealth variable in the demand for money func tion. They employed a definition of wealth similar to the "net wealth" concept used by Meltzer and they regressed it against total money balances. Meltzer*s tests seem to in dicate that their results are due to an incorrect specifi cation of the wealth constraint. Meltzer makes one further test to throw some light on the questions originally posed. He calculates a rather crude measure of human wealth and adds it to his non-human wealth measures and reestimates his equations. He finds that, again, real money balances are approximately unit elastic with respect to this broader measure. What do all these tests indicate for us? First of all, they show that government liabilities should be in cluded in whatever measure of wealth we employ. Secondly, they indicate that, on the average, money is as much a 26Meltzer, 0£. cit., p. 230. 144 substitute for real assets as it is for other financial assets. Thirdly, they seem to suggest that we may choose whichever of the three successful measures employed in Meltzer's tests is most consistent with our aims in esti mating our simultaneous equation model. And lastly, these results indicate that the exclusion of human wealth from our empirical measure will not in any way seriously bias our estimates. Two specific considerations, then, will determine our final choice of a wealth measure. First, the first measure employed by Meltzer, consolidated net non-human wealth of the public, W, is the only series taken directly from Goldsmith's figures. The other series he employs are annual interpolations from benchmark dates. Hence, the ready accessibility of the (W) series and the fact that we will have to interpolate to a quarterly basis and, thus, do not wish to further bias our estimates by using a series which has already been interpolated once, suggests the use of this measure over the other two. Second, since a priori considerations on the proper constraint to employ do not seem to point unequivocally to any one of the three wealth measures under review, we seem justified in using the most convenient and least biased measure— consolidated net non human wealth of the public. 145 The form of the functional relation. We will spec ify our demand for demand deposits equation as a linear relation— linear in the levels of the variables. As in the case of interest rate measures, the precedent in the liter ature is confused on this point and yields no firm conclu sion favoring any specific formulation. Though the theory initially presented by Meltzer, for example, suggests a log linear form for his hypothesis, he tests separate equations which are linear in both levels of the variables and in the logarithms of the variables. Likewise, Teigen tests both linear and log linear specifications. Thus, again, the considerations of how best to fit this particular equation into our model shall determine our final form. Specifi cally, since we shall want to compare single equation esti mates with the estimates derived from two stage least squares applied to the entire model, we will specify the function as linear in the levels of the variables. The influences of short run factors on our model. The above considerations lead to the following formulation of the demand for demand deposits equation: (DDadj)T = a31 + a32(wealth)T-1 + a33(rB)T + a34(rtime)T where (wealth)T_^ = end-of-previous-period stock of wealth 146 This particular formulation derives primarily from the con sideration of money as one among the very many assets which individuals and firms may hold. It therefore focuses on the size of the asset portfolio in which those money bal ances will be held and the relative rates of return on the alternative forms in which that wealth may be stored. One of the primary services performed by money in our portfolio is that of facilitating transactions. In a short period of time, there may be fairly wide variations in the need for these services. Therefore, in a model such as this one, with a specifically short run focus, we need to include a measure of this rate of change of transactions needs. We will do this by including a measure of the rate of change of income (GNP) in our equation. The inclusion of the level of income may lead to certain estimation and interpretation problems because of the theoretical rela tion, Y = r*W. There should be little correlation, however, between the rate of change of income, (AY), and (rW). We will also test our model for the sensitivity of the pub lic's demand for money to expected changes in the price level. This shall be done by including the rate of change of prices, (aP)/P, in our preliminary regressions. Hence, we postulate the following demand for demand deposits equation: 147 (DD , .) = a + a (wealth) + a (r, ...) + a,.(r.. ) ad] t 31 32 T-l 33 bill 34 time'T + a35(AY),p + a^gtAP/P)^, The Public's Demand for Currency The behavioral assumptions of our model as postu lated above are such that we view the total stock of high powered money to be exogenously determined by the Federal Reserve authorities, and the stock of currency outstanding to be determined by the demand of the public and the per fectly passive response of commercial banks and the Federal Reserve to that demand. The supply of unborrowed reserves made available to commercial banks, (RU), is the result of the interaction of these two forces— one exogenous to our model and the other endogenous, i.e., RU » HM— CURR. Within this framework, then fluctuations in currency hold ings given the stock of high powered money, will have a significant influence on the supply of money. This view is supported by Phillip Cagan's study, Determinants and Ef fects of Changes in the Stock of Money. His empirical in vestigation leads him to conclude that: . . . the currency ratio is the chief contributor to specific cycles in the rate of change of the money stock, equalizing the contributions of the other two determinants (the reserve ratio and the 148 stock of high powered money) combined.27 Hence, a complete explanation of the forces determining the money stock outstanding necessitates an examination of the determinants of the public's desired currency holdings. The motives for holding currency. In textbook dis cussions and in most of the theoretical literature, cur rency holdings are usually explained under two headings: convenience and safety. Currency is generally referred to as the "convenience" money component of the total money stock. Likewise, it is generally postulated that the value of these holdings possess a certain amount of safety which is not shared by bank money. On a priori grounds, however, there seems to be little validity to the arguments favoring currency holdings over demand deposits because of the safety factor. In a developed economy such as the postwar United States, for example, people have an extremely high degree of trust in the banking system because of the ex tremely low rate of bank failures in the last two decades, and because of the various guarantee mechanisms which pro tect depositors against loss. Thus, people do employ checking accounts, both to facilitate virtually all large transfers, and a great many of the smaller payments which 27Cagan, 0£. cit., -. 42. 149 recur on a regular basis, and to serve as a store of value for their wealth, with seemingly no worry whatsoever about the safety of these deposits. On the contrary, protection against theft, for example, dictates the use of demand de posits rather than currency, both to facilitate transac tions and to store wealth. Likewise, the value of demand deposits in providing accounting services and of cancelled checks in providing proof of payment far outweigh any pos sibility of real loss which the public may feel. The arguments are all too familiar to require repetition here. These considerations lead us to expect that cur rency will be held primarily to facilitate relatively small day-to-day, hand-to-hand transactions and little else. These conclusions are supported to a degree by the steady decline in large denomination currency outstanding since the second world war: 2 8 Number of Bills Outstanding 1945 1966 $500 Bills 454 239 $1,000 Bills 801 283 $5,000 Bills 7 3 $10,000 Bills 24 4 However, it seems impossible to justify the total amount of 28pederal Reserve Bulletin (December, 1966), p. 1791. 150 currency by the "convenience money" arguments presented above. In December, 1964, for example, the figure stood at 33.5 billion dollars. This is a per capita figure of $175.00 for every man, woman, and child in this country. At a time when the average weekly earnings of production workers in manufacturing in the United States’was $102.97, this seems like an unduly high currency figure to be ex plained simply by arguments about "convenience money." Phillip Cagan has discussed this question in some detail. Cagan feels that, besides the usual reasons for holding a very large stock of currency during "panics," the large secular holdings can only be explained if we consider such factors as the desire to use currency as a store of wealth, and also such considerations as the use of currency in illegal transactions and as a tool for facilitating income tax evasion. Now, to explain the public’s demand for currency in the postwar period, both the transactions function and the store of wealth role of such balances shall be taken into account. As Cagan notes: To explain changes in the amount demanded, two sets of variables are involved, one for the transactions demand and one for the store of wealth demand. Two important variables in the first set might be the volume of consumer expenditures and cost of a checking account; in the second set, they might be 151 total private wealth and the return on savings deposits.29 Thus, Cagan is postulating the following functional rela tion : CURR = f(C, X, W, r.. ) ' time where C is the total volume of consumer expenditures, X is the cost of checking accounts, and the other variables are as defined above. Cagan himself goes no further in speci fying the exact relations involved, nor does he perform a regression analysis to test his hypothesis. The determinants of the public1s demand for cur rency. We view the separation of the functions which cur rency holdings perform as analytically useful. However, we do not agree completely with Cagan's formulation. First of all, the cost of a checking account is a very nebulous thing, since it is collected in very different ways at dif ferent banks. Some banks charge a fixed amount per check, some charge monthly service fees, some simply require that a minimum balance be maintained, while others use various combinations of these charges. Likewise, while this par ticular factor or some other general measure of the "quality” of checking accounts may be important in explain ing the very long-run use in demand deposits, and the 20 Cagan, 0£. cit., p. 119. 152 corresponding decline in currency holdings, our observa tions indicate that these factors, having remained rela tively stable in the postwar period, are unimportant in our analysis. Therefore, we drop this factor as a potential argument in the currency demand equation. Much more important as a determinant of the trans actions need for currency is the actual volume of transac tions carried out in this medium. Any measure of national income or gross national product would likely be a poor estimate of such a measure. Cagan suggests the total vol ume of consumer expenditures as the appropriate variable. This too, however, is not likely to be the best measure available. Rather, consumer expenditures on non-durable goods and services is likely to be a fair approximation to the measure we desire. Certainly, the elimination of ex penditures on consumer durable goods, which include pri marily relatively large expenditures which are likely to be paid for by check or purchased on credit, can only improve this approximation. However, no clear reasons exist for using any less aggregative measure. Thus, we postulate that it is the volume of expenditures on non-durables and services as a measure of the value of currency transactions carried out which determines the public's currency holdings. Like the transactions component of the total de mand deposits, it is reasonable to expect that currency 153 holdings will be sensitive to interest rate movements since people will conserve on such holdings in direct proportion to the interest foregone by holding such balances. For this reason, and also because any holdings of currency held solely as a store of wealth are likely to be responsive to the alternative costs involved, total currency holdings should exhibit fairly strong interest elasticity. Cagan suggests the rate paid on time deposits as the proper meas ure to test the effect. Certainly this is reasonable since, besides demand deposits, time deposits (or savings and loan shares) are likely to be the closest substitutes available for currency holdings. Hence, we shall include this measure in our currency demand function. However, as discussed in detail above, interest effects can, at the present time, only be determined on an empirical basis. Thus, we shall also test to see if currency holdings are responsive to the rates paid on other alternative short term assets. Specifically, we shall include the three- month Treasury Bill rate in our regressions. As in the case of demand deposit holdings, since the bill rate is much more sensitive to short run changes in the economic climate than are time deposit rates, this test will serve as an indication of the speed of adjustment of the public's currency holdings to changes in economic conditions. Lastly, we have to consider the role played by 154 wealth in the determination of currency holdings. There is a strong possibility of getting mixed results from includ ing a wealth variable in the currency demand equation. It is quite possibly true that currency holdings are used as a store of wealth and, in fact, strong evidence of such behavior on the part of the public does exist. We would expect that as wealth increased, so would these currency holdings. We would expect, therefore, that a positive coefficient will be attached to our wealth variable in our empirical estimate. However, as development theory would indicate, the wealth variable is also quite likely to be highly correlated with the degree of urbanization in the economy, the level of financial sophistication of the gen eral public, the acceptance of the banking system by the laboring class, and other variables which have been shown to have a depressing influence on the public's desire for currency. If this is truly the case, and if these negative effects together outweigh the wealth effect, the estimated coefficient of the wealth variable from the regression will have a negative sign. There seems to be no simple way to separate these effects, and so we shall interpret the re sults of our regressions as reflecting the net effect of all these factors as summarized within the wealth variables. As in the case of demand deposits, we shall include the rate of change of prices in our regressions as a test 155 of the sensitivity of the public's holdings of fixed value assets to changes in their real value. Thus, we postulate the following linear currency demand function: (CURR)T - a41 + a42(wealth)T_x + a43<rtime)T + a44<rbill)T + a45(CNDS)T + a46(aP/p)T The Demand for Time Deposits at Commercial-Banks Our specification of the money supply framework in section one demonstrates the importance of an explicit con sideration of commercial bank time deposits within any study which purports to investigate the links between re serve creation and the money stock. Likewise, the very high rate of growth of the stock of time deposits over the period covered by our study increases the importance of such an analysis. For, between 1948 and 1964, a period during which GNP increased almost two and one-half time and the public1s consolidated stock of wealth increased by slightly over 100 per cent, the volume of time deposits at commercial banks increased more than three and one-half fold from 35.6 billion dollars to 126.6 billion dollars. This increase was at an average rate of just under three billion dollars a year up to 1960. Since that time, the rate of increase has jumped to over eleven billion dollars 156 per year. Time deposits within our money supply framework. Our definition of "available reserves" as high powered money less currency and reserves held against time deposits, (HM - CURR - TD • 6 * 6TD) points out the technical TD influence of these changes upon the money supply process. An increase (decrease) in time deposit liabilities absorbs (releases) reserves and thereby diminishes (increases) the stock available to support demand deposit liabilities. Repeating the formulas given above, if RA = HM - CURR - TDadj * 6TD • 4 >TD = RU - TDadj • 6TD . *TD we may consider the maximum volume of demand deposits which banks can create on the basis of a fixed stock of unbor rowed reserves (given the current constraints imposed by the public and neglecting commercial bank borrowing), as determined by: 1 i _ TD ~ E 5 ■ (RA> - -7DB <RU - TDadj • *TD • « > - r a w o 0 The rate at which this figure changes as the public changes its holdings of time deposits is then given by 3 DDmax td = --5---- < 0 3TDadj jDD 157 Thus, the effect of fluctuating time deposit holdings is seen to depend upon the relative rates at which time de posits and demand deposits absorb bank reserves. Lyle Gramley and Samuel Chase, in a recent article in the Federal Reserve Bulletin, have criticized this view of the money creation process. They hold that the treat ment of time deposits as a leakage in the money supply pro cess is totally arbitrary in that "it would be equally justifiable analytically to regard the money stock as a leakage in the process of time deposit creation or destruc tion."^® With the stress in this sentence put heavily on the word "analytically," they are correct. However, the generally accepted theory of commercial bank behavior cer tainly does not support their view. On the contrary, the view of the commercial banker as primarily an investor, who purchases loans and securities through the mechanism of demand deposit creation, implies an active role for such a banker in the determination of his total stock of demand deposit liabilities and a rather passive role in the market for time deposits. This is not to say that the banker may never solicit time deposits through advertising and other sales promotion techniques. Indeed, he may. But his gen eral behavior is to expand his asset portfolio through the 3®Gramley and Chase, 0£. cit., p. 1381. 158 extension of his demand deposit liabilities within the reserve constraints imposed upon him by his current level of time deposit liabilities. It may be objected here that the people who receive the demand deposits in return for the sale of their own or someone else's I.O.U.'s to a commercial bank, are perfectly free to switch that deposit to a time account, to currency, or to any other asset form they may desire. This is, of course, true; but it does not change our basic conclusions. The banker does not assume anything about the depositor's secondary behavior and hence he still views his time de posit liabilities and the reserves which they absorb as "given" at any one time. In view of the fact that our primary interest and focus in this study is on the money stock as narrowly de fined, our treatment of time deposit liabilities of commer cial banks shall be as follows. We shall assume that the rate of interest paid on time deposits is an exogenous variable. This assumption may be justified on both empiri cal and a priori grounds. On empirical grounds, it can be shown that the announced rate on time deposits held at commercial banks has increased rapidly after each change in the maximum allowable rate as specified by the Federal Reserve Board under Regulation Q. These changes, occurring on January 1, 1957, January 1, 1962, July 17, 1963, and 159 November 24, 1964, have invariably been followed by in creases in the actual rates paid. We may apply two possi ble interpretations to these occurrences. First, it may be thought that this consistency means that the actual rate paid on time deposits is in fact determined by the Federal Reserve's specification of the maximum rate. On theoreeti- cal grounds, however, this would be unreasonable, since it would imply that commercial banks would always maintain the maximum rate even in the face of falling market rates and falling earnings. A more reasonable interpretation is that the equilibrium rate on time deposits, i.e., the rate which would equate free market supply and demand, has been con sistently above the maximum allowable rate set by the mone tary authorities. Thus, commercial banks have willingly raised rates to the maximum allowable limit at every oppor tunity. This interpretation is supported by the fact that rates on savings and loan shares and other assets, which may be considered by the public to be very close substi tutes for time deposits, have consistently yielded a higher return than these deposits. We may infer from this that a freely determined time deposit rate would have been close to these rates, and thus, higher than the maximum rate set by the authorities.^ Thus, accepting the rate paid in commercial bank time deposits as a predetermined variable, we further assume that the supply of such deposit liabilities is per fectly elastic at the announced rate. The theory of com mercial bank behavior stated above, which postulates pas sivity of the commercial banker is the ’ ’creation" of time deposits certainly supports this view. Likewise, if our contention that the equilibrium rate on time deposits has concistently been above the maximum rate set by Regulation Q is correct, the perfect elasticity of the supply of time deposits over the relevant range of interest follows imme diately. For, as we demonstrate in the figure below, if Dtd represents the public's demand for time deposits and STD represents the supply schedule, and rmax is the maximum rate set by the authorities, then our contention implies that DrpD must intersect S«td above rmax. Since banks may not legally pay a rate above rmax, rmax • A • STD will be the actual supply curve. The level of demand together with the price ceiling r^jj, will determine the volume of time ^It must be noted that the rate paid on commercial bank certificates of deposits has been more variable than the rate paid on passbook accounts and has, in fact, ap peared to respond to fluctuations in the bill rate. How ever, it, too, has been treated in the same manner as the time deposit rate. 161 deposits outstanding at the point of intersection of the demand curve with the perfectly elastic segment of the supply curve. TO T D It thus appears reasonable that, as in the case of currency holdings, we assume the stock of time deposits outstanding to be determined by the public's demand and the commercial bankers' perfectly elastic and perfectly passive supply. Thus, the quantity of reserves absorbed by time deposits is determined by factors external to the commer cial banks, i.e., by the public's demand for time deposits and the legally set reserve requirements. The determinants of the public's demand for time deposits. Our general portfolio balance approach suggest wealth and the relative rates of return on alternative asset holdings as the critical determinants of the public's desired stock of time deposits. We would expect that, with 162 a given term structure of interest rates, the public's holdings of time deposits would vary directly with the size of their portfolio. On a priori grounds, we would not expect any of the influences which cloud the effects of wealth on currency holdings to affect the public's desired level of time deposits. In this case, then, we postulate a direct relationship between our measure of the public's wealth stock and their holdings of time deposits. In his 1966 model, Teigen attempted to test the wealth effects which determine time deposits holdings. As an alternative to his income constraint hypothesis, he in cludes household net worth (a series supplied to him by Albert Ando) as an argument in his time deposit equation. He concludes from his empirical estimates that "the net wealth and income hypotheses appear to be roughly of equal quality in terms of the regression criteria. ..." How ever, "... because the data on net worth are somewhat less reliable than the income data used," he chooses "in- 3 2 come" as the preferred constraint in his final model.It is obvious that more work needs to be done along thse lines. Therefore, we will test our measure of wealth (which is different than that employed by Teigen) against a measure of income in the time deposit equation and compare our own ■^Teigen, 1966 manuscript, 0£. cit., p. 12. results with Dr. Teigen's. Unlike currency and demand deposits, time deposits held at commercial banks yield a nominal return which is greater than zero. In investigating the effects of rela tive asset yields on the public's holdings of time deposits, we must take consideration of this non-zero return as well as the return yielded by other assets. To determine how we may best treat these relative rates of return, we first note the various important characteristics of time deposits. First of all, before the growth in popularity of commercial bank certificates of deposit (CD's) in the early sixties, time deposits were primarily held in small accounts by de positors with fairly small asset holdings. This class of savers was attracted to these holdings for several reasons. First, the various guarantee mechanisms surrounding these deposits, sponsored by the Federal Deposit Insurance Corpo ration and other agencies, insured low risk. Second, the fact that commercial banks very seldom invoke the technical requirement of making the depositor wait thirty days for payment after notification of a desired withdrawal has resulted in a very high degree of liquidity for these hold ings. And last, the extremely low level of financial knowledge required to make deposits and withdrawals on such accounts makes them attractive to people who take little interest in such matters. 164 These factors help determine the alternative rates of return which are probably most relevant in determining the demand for time deposits, for they indicate the char acteristics which other asset forms must possess for them to be considered by the public as close substitutes for time deposits. These characteristics include a very low degree of risk, very high liquidity, and simplicity in transaction. We may consider the alternatives to be postal savings accounts, savings and loan shares, credit union shares, and similar assets which possess these character istics. The most important of these in recent years has been share-deposits at savings and loan institutions. Con sequently, we would like to include the rate of return on these holdings as an alternative cost in our demand func tion. However, as de Leeuw notes in his own study of time deposit demand, such data is not available on a quarterly basis. However, the work done by Gramley and Chase based upon de Leeuw*s results indicates that a quite satisfactory alternative approach exists. They have shown that securi ties with the low risk-high liquidity characteristics of commercial bank time deposits appear to be quite close substitutes for these deposits. As they note, N. . . in vestors seem to have become increasingly willing to sub stitute time deposits for other financial assets, especially open market securities, in response to changes in yield." 165 The development of CD's and the spreading of financial knowledge among the general population would, in fact, lead us to expect this. Thus, we may take the rate on these open market securities as representative of the alterna tives available to time deposit holders. On the basis of these results, we shall include an interest rate representative of the yield on open market securities within our time deposit equation. Specifically, we shall employ the short term market rate as measured in our model by the three-month Treasury bill rate. This particular measure is chosen for two reasons. First, the estimates derived on the basis of the bill rate are more likely to demonstrate the true effects of relative changes in alternative costs on the public's holdings of time de posits. For, in the recent past, the public has reacted fairly quickly to changes in the security rate, while the time rate itself, because of its policy-oriented character, and for other reasons, has adjusted more slowly. Second, the use of the relatively volatile short term rate will help to avoid some of the more serious problems of multi- collinearity present in the term structure of interest rates. We shall also test the substitutability between the stock of time deposits and expenditures on consumer durables. We expect a negative relation between these two / 165 measures for two reasons. First, time deposits are used to store funds for the purchase of durables. Hence, the stock decreases when the actual purchase is made. Second, the purchase of a durable goods reduces funds available to be saved from current income. Including the rate of change of prices within our equation in order to test the sensi tivity of the public's holdings of fixed value time de posits to movements in the level of average prices, we specify the following linear form for inclusion within our model: <TDadj) = a51 + a52(wealth)T_1 + a53(rtime)T + a54<rbill)T + a55(AP/P)T + a56(CDUR)T CHAPTER IV FORMULATION OF A MODEL OF THE REAL SPHERE The specification of the monetary relationships in Chapter III represents an investigation of some of the most important factors which create or absorb bank reserves and thereby affect the willingness and ability of commercial banks to supply demand deposits. Our stated purpose is to integrate this analysis into a model of income determina tion which includes a specification of the aggregate ex penditure relations of the real sphere. In this chapter, we shall derive specific structural relations to explain the bulk of real consumption and investment expenditures in the economy. Also, since both long term and short term interest rates appear in our model, we shall specify a term structure equation for inclusion in our final model. We shall conclude with an analysis of the determinants of price movements and a specification of various test. We shall perform in order to determine a suitable price ad justment equation for inclusion in our model. We turn first to an examination of the theory of consumer behavior. The Consumption Function We start our analysis of consumer expenditures with 167 168 the basic proposition that consumer spending decisions are motivated and constrained by consumer wealth or net worth as well as by disposable income. The evidence on the spe cific form of this hypothesis has been growing steadily over the past few years. The inclusion of a wealth or net worth variable in the consumption function is usually de rived from one of two possible theoretical models. In the first, maximization of a utility function subject to a budget constraint which includes both income and wealth leads to the consideration of "beginning of period" wealth or net worth as an argument in the consumption function. In the second, a stock adjustment view of saving as a pro cess of bringing the actual stock of wealth into line with some desired level likewise leads to a consumption (saving) function with the current stock of wealth as an independent variable. Actually, when formulating an operational consump tion function for statistical testing, these two theories yield substantially similar formulations. For if we view wealth as a simple "constraint," we must always remember that, at the lower limit, the constraint can be modified by dis-saving in the form of borrowing. Wealth in this sense, then, at least among those who hold a relatively small stock, may be a proxy for the amount of credit available to the individual. Likewise, a strong desire to adjust 169 one's stock of wealth to some desired level can be just as strong a constraint on present consumption as the actual stock (as well as to other factors such as expected income or age) in some relatively simple manner, perhaps linearly, then the present stock of wealth will appear in the con sumption function in the same form as it would have ap peared had we considered it merely as a constraint in the budget equation. These theories, expressed in more or less rigorous form, have led to the inclusion of wealth, or some proxy for wealth, in many empirical studies of consumer behavior. We will review briefly the treatment given to this view in the studies by Klein-Goldberger in their 1929-1952 econo metric model, by Modigliani, Brumberg and Ando in their "life cycle" studies, by Friedman in his "Theory of the Consumption Function," and by John Arena in his extension of the Modigliani-Brumberg theory. The role of liquid assets in the consumption func tion. Klein and Goldberger refer to their inclusion of a wealth variable into the consumption function of their 1929-1952 Econometric Model of the United States as a "basic modification of the Keynesian Theory."^- The explicit ^-Lawrence R. Klein and Arthur S. Goldberger, An Econometric Model of the United States, 1929-1952 (Amster dam! The North Holland Publishing Company, 1955), p. 8. 170 variable which they include, however, is only a proxy for wealth in the form of "beginning of period liquid assets held by households." Three considerations are listed by the authors in justification of this particular formula tion. First, they note that liquid assets are a strategic form of wealth as far as consumer behavior is concerned since they are readily spendable. Second, liquid assets are highly correlated with overall consumer wealth, and thus serve as a good wealth indicator. Third, they note that statistics on consumer wealth are not generally of high accuracy.2 While these points all contain a certain degree of validity, we do not view them as sufficient any longer to justify the use of a liquid asset proxy for wealth. First of all, since this model was estimated by Klein and Gold berger in 1955, the pioneering Study of Saving in the United States has been published by Raymond Goldsmith.^ From this source, we now have available to us a great vari ety of wealth and net worth statistics which are recognized as being of fairly high accuracy. The lack of good and easily accessible statistics is no longer a valid reason to 2Ibid. ^R. Goldsmith, A Study of Saving in the United States (Princeton, New Jersey: Princeton University Press, i m y : 171 avoid the use of explicit wealth figures in the testing of consumption functions. Secondly, the use of liquid assets clouds the true causal relations which are active in de termining consumer behavior. A high correlation between liquid asset holdings and consumer expenditures may well result from the fact that consumers build up their stock of such assets previous to the purchase of certain goods spe cifically to facilitate those desired purchases. Thus, the high correlation results from the fact that the desire to purchase some good leads to the accumulation of liquid assets and not from the converse hypothesis that the hold ing of the stock of spendable liquid assets somehow stimu lated the purchase of the good. Lastly, the interpretation of the liquid asset variable as a wealth proxy is weakened by the fact that another variable in the Klein-Goldberger function may also be interpreted as a wealth proxy. This is the non-labor or property income variable. This vari able results from a disaggregation of total income into functional components to account for certain non-lineari ties in observed consumption behavior. But, as Ando and Modigliani note, property income, interpreted as the return from wealth, may merely be a proxy for wealth itself. Their own tests indicate that the inclusion of non-property income and wealth in the consumption function "explains" 172 the data better than the formulation which is used by Klein and Goldberger.* Other workers in this field have also included liquid assets in their consumption equations as a test of the so-called Pigou effect. In essence, the Pigou hypoth esis states that . . . like consumption, the real value of liquid assets is subject to diminishing marginal utility. When, therefore, the stock of real purchasing power held in liquid form reaches a proper propor tion to real income, the motive for further accu mulation is removed or diminished, and the level of consumption expenditure should rise.5 However, this view arises from an incomplete analysis of consumer portfolio behavior. Rather, we view the consumer as faced with two basic decisions similar to the two deci sions originally emphasized by Keynes. The consumer does not decide simply whether to consume or to save; rather, he must also decide in what form to hold that part of his income which he does not consume. The consumer must try to maintain an optimum distribution between the resources which he devotes to building up his stock of wealth and those which he devotes to the flow of consumption goods. *Albert Ando and Frano Modigliani, "The Life Cycle Hypothesis of Saving: Aggregate Implications and Tests," American Economic Review, LIII, No. 1 (March, 1963). ^Daniel B. Suits, "The Determination of Consumer Expenditure: A Review of Present Knowledge," Impacts of Monetary Policy (Commission on Money and Credit, Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1963), p. 14. 173 This "optimization” requires further that, in determining his consumption pattern, the consumer must allocate his purchases so as to maximize his utility from that flow of goods; moreover, in arranging his portfolio, he must divide his wealth between all the categories of liquid assets, non-liquid assets, and real assets available so as to maxi mize his return subject to his own preference for risk aversion. An undesired build-up of liquid assets or an increase i** the real value of liquid assets due to price movements need not necessitate an immediate spillover into consumption expenditures. Rather, there is also the very real possibility of a reallocation of the increase within one's portfolio with very little increase in consumer spending. This point is referred to by Pesek and Saving when they discuss the relative effects of price and inter est rate changes on commodity and money markets. A possibly more accurate explanation of the effect which liquid assets have on consumer behavior is contained in the work done by Suits and Sparks for the Brookings model. As Suits notes, the existence of liquid assets per mits the maintenance of a given level of consumption in the face of a short run decline in income. It is the influence of these asset holdings, therefore, which could explain the divergence between the short run and long run marginal pro pensities to consume. In the consumption sector of the 174 Brookings model, the stock of liquid assets held by hous- holds appears in the equations for non-durable goods, ser vices, and durable goods other than automobiles. In this quarterly model, then, these assets are included as ele ments which affect short run behavior. The absence of a wealth variable, however, makes the separation of short run "ratchet" effects due to the liquid asset stock and more truly long run wealth effects impossible. A similar role is attributed to the stock of liquid assets by John Arena. As he notes from his empirical work, "Consumption out of liquid assets tends to be an insignificant factor upon con sumption in the long run, but in the short run, may enable consumers to temporarily adhere to old, higher consumption patterns We may conclude that in a short run study, the stock of liquid assets held by households should be in cluded as a measure of a possible Duesenberry-type ratchet effect. This effect may well be significant even though, in the long run, these assets seem to have little or no effect of their own and may appear significant only insofar as they may be interpreted as a proxy for consumer wealth. Wealth and the "life cycle" hypothesis. One of ®John Arena, "The Wealth Effects and Consumption: A Statistical Inquiry," Yale Economic Essays (Fall, 1963), 281. 175 the most important of the studies which consider the wealth constraint explicitly is an empirical study by Ando and Modigliani based on the theoretical model developed by Franco Modigliani and Richard Brumberg— the so-called "Life Cycle Hypothesis of Saving."7 In the original model as presented by Modigliani and Brumberg, the utility function of any individual consumer depends upon his total consump tion in current and future periods. The consumer maximizes his total utility subject to the resources at his disposal. These resources include "the sum of current and discounted future earnings over his lifetime and his current net worth."® The authors carry out this maximization under the simplifying assumption that the individual wishes to ex haust all his resources over his lifetime, i.e., that "the individual neither expects to receive nor desires to leave any inheritance."^ "As a result of this maximization, the current con sumption of the individual can be expressed as a function of his resources and the rate of return on capital with parameters depending on age."^° Community consumption 7Franco Modigliani and Richard Brumberg, "Utility Analysis and the Consumption Function: An Interpretation of Cross Section Data," Post Keynesian Economics, ed., K. Kurihara (New Jersey: Rutgers University Press, 1954). ®Ando and Modigliani, o£. cit., p. 399. ®Ibid., p. 400. 10Ibid., p. 399. 176 functions are then derived by aggregation over those indi vidual consumption functions. The final form of the theo retical function specified by Modigliani and Brumberg makes aggregate consumption expenditures dependent upon the ac tual level of aggregate non-property income, Y.j, the ex pected level of annual non-property income, Y®, ^ and net worth, A ^ ^ , i.e., CT = a^YT + a2 YT + a3 ^Vr-l Ando and Modigliani make this theory operational by postulating certain relations to measure "expected" non property income. One hypothesis is derived on the assump tion that "expected non-property income is the same as actual current income except for a possible scale factor,"^2 i.e., Y^ = SY^, Therefore CT = ( yt + “3 ^-1 The second hypothesis is derived by assuming different ex pectations as to future income on the part of the employed and the unemployed. This leads to a modification of the above formula via an employment ratio: ^Ibid. , p. 401. 12Ibid., p. 403. 177 where L<p is the size of the total labor force, and ET is the number of persons engaged in production. Ando and Modigliani test various specific formula tions of these two hypotheses using different specific measures of the variables based on annual, current dollar figures. Their most important results for our purposes are that "all the tests seem, by and large, to support the basic hypothesis advanced in this paper, and, in particular, the importance of net worth as a determinant of consump tion . An extension of the basic Modigliani-Brumberg model has been carried out in a doctoral dissertation written at Yale University by John Arena. In his work, Arena modifies the original model presented above in two strategic ways. First of all, he explicitly allows for the possibility that an individual may derive satisfaction from "bequeathing a fortune." Hence, he includes in the utility function a measure of the desired level of final wealth which the in dividual wishes to pass on to future generations. Secondly, he extends the concept of the budget restraint used by Modigliani and Brumberg to include a capital gains compo nent. Specifically, he considers changes in the value of net worth because of changes in the price of capital assets l^Ibid.f p. 415. J 7 8 and the value of liquid assets relative to the price of consumer goods. This particular formulation allows the author to study a very broad concept of the Pigou effect. He notes, as we did above, that the Pigou effect has typi cally been interpreted as restricted to the "monetary por tion of asset holdings.However, he quotes Patinkin to show that this interpretation grows out of the specific characteristics of the models with which Pigou and Patinkin himself were working— models in which there was no possi bility of a wealth effect deriving from price movements of capital assets. But Arena notes that a comprehensive definition of the Pigou effect may include both types of wealth changes due to price movements. He defines the wealth effect resulting from an increase in the price of capital assets as "the same as the Pigou effect only car ried over to the capital stock."15 Arena's statistical results bring evidence to bear on the importance of several factors which have been thought to affect aggregate consumer spending patterns. First of all, like Ando and Modigliani, he finds that net worth has a significant influence on consumption spending and that its inclusion in the consumption function tends to l^Arena, 0£. cit., p. 251. 15Ibid., p. 252. 179 lower the estimated marginal propensity to consume out of income. Second, he finds no clear role emerging for the flow of capital gains. However, he notes that since this flow becomes part of the stock of initial wealth for the next period, and since this stock is positively and signi ficantly related to consumption, the capital gains flow affects consumption period after period once it has been capitalized into net worth. Third, he concludes that liq uid assets are significant only as a proxy for net worth. For when net worth is included in the function, both the sign and significance of the liquid asset variable fall. We would anticipate this result in a very long run model such as this from the considerations discussed above. Last, he finds that age and income distribution variables which change substantially over long time periods, can have a definite impact on aggregate consumption. Our own pre liminary tests, however, indicate that these latter factors play no substantial role in fluctuations in consumer expen ditures over relatively short periods of time. Professor Friedman1s permanent income hypothesis. A different approach to this problem, but one which em bodies the same basic premises as the above studies, namely, that consumers have a fairly long time horizon and that wealth is an important constraint in the determination of 18 0 consumer behavior, has been taken by Professor Milton Friedman. The importance of wealth in his pure theory of consumer behavior as presented in his Theory of the Con sumption Function is quite familiar by now and needs little explanation. We shall simply indicate briefly the relation between his formulation of the basic consumption relation and the formulation which we shall employ. Friedman demonstrates at the outset how a period analysis of consumer behavior leads to an explicit relation between consumer expenditures and wealth. He notes that what we call income, and what we measure as income for statistical convenience, is simply an approximation to a one-period return on the human and non-human components of our wealth stock. The importance of this fact becomes abundantly clear if we view the behavior of the consumer for more than a single time period. Friedman's own two- period analysis (which is easily extendable to the con sumer's lifetime) postulates that consumer expenditures in period one ". . .do not directly depend on (expected receipts in year one) at all.''^ Rather, these receipts affect consumption only insofar as they affect wealth, WT, defined as the present capitalized value of future income streams. (Using Professor Friedman's terminology, 16Friedman, oj>. cit. , p. 10. 181 W1 = where equals the expected return in period j, and r is the appropriate discount rate.) This conclusion is derived from the assumption that the consumer must allocate his purchases over several time periods, as well as among the goods available in any one time period, if he is to truly maximize his inter-temporal satisfaction. Thus, a change in receipts (income) in any one period could very possibly have no effect at all on consumer expendi tures if an appropriate opposite change was expected in the receipts of succeeding periods. The total effect of these changes can only be accounted for by explicit consideration of the wealth figure, W«j«. This analysis leads Friedman to formulate the fol lowing functional relation: C = f(WT, r) When the relevant concepts of "permanent income," Yp, and "permanent consumption," Cp, are introduced and defined, the form of the function is modified to read: Yp cp = f<-F' r) = g<Yp, r> = g(rw, r) However, the identical theoretical relationship between the Y interest rate, r, wealth, WT, and income, Y, i.e., W = —, allows us to specify any particular form of this function which best serves the purpose of our analysis. This 182 formulation is substantially the same as the Ando-Modigliani and Arena formulations which postulate the level of income and wealth as the relevant determinants of consumption spending. It is only on the basis of his particular as sumptions about consumer responses and the homogeneity of the consumption function with respect to "permanent income" that Friedman can finally write his function in a form which emphasizes the proportionality relation between per manent consumption, Cp, and permanent income, Yp, i.e., Cp = k(r, u) • Yp In this function, r is the interest rate and u represents those factors which determine the slope of the individual's indifference curves (age, family composition, etc.). Thus, in his formulation, k does not depend upon the absolute level of wealth or permanent income, but only on the inter est rate and utility factors. (Ultimately, when he intro duces another factor as a measure of the stimulus to save under uncertainty, the ratio of non-human wealth to per manent income, W /Yn, is also included as an independent N & variable.) The relation between Friedman1s hypothesis and our own study. Our own purpose in specifying a testable con sumption function, however, is not the same as Professor 18 3 Friedman's. His specific formulation is not particularly useful to us. He was primarily concerned with developing a theory which would explain the phenomena first made ob vious in Kuznet's^7 data on aggregate savings: the fact that over very long periods of time the proportion of in come saved remains almost constant. This relationship contradicted one of Keynes' suggested hypotheses (a hypoth esis which was not necessary to any of his analytical con clusions) that as income increased, the average propensity to consume would decrease. To focus on this specific postulate, Friedman formulated his relation so as to give maximum attention to the long run phenomena in consumer spending patterns. Our own purpose, however, is to explain the level of consumption and, more specifically, the variations in that level over somewhat shorter periods of time, and to specify a function which is compatible with the rest of our model. We find it of no use, therefore, to transform our measured variables into figures representing the perma nent elements of consumption spending or income. Rather, we will focus on the relatively short run adjustments which people make in the level of their expenditures in response 17Simon Kuznets, "Proportion of Capital Formation to National Product," American Economic Review, XLIZ, No. 2 (May, 1952), 507-526. i 84 to changes in the levels of their wealth and current in come. Implicit in this formulation will be a denial of Friedman's assumption of zero correlation between the tran sitory components of consumption and income. We will be able to make some judgment on this matter from the results presented below. The specification of the consumption function. The general conclusion of the work done in the above studies indicates that on both theoretical and empirical grounds, there is a very strong basis for including both wealth and income as arguments in the consumption function. There is fairly wide agreement in the literature on the specific formulation of community consumption functions which in clude at least these two factors as independent variables. Less agreement exists, however, over the exact empirical measures of these variables which would serve as accurate 18Friedman assumed that all transitory income (un expected windfall gains) would be saved. This is not as strong a statement as it first appears to be, since Fried man includes expenditures on durable consumption goods in his measure of "saving." However, this assumption is con tradicted by the results obtained by Bodkin in analyzing the effect of the National Service Life Insurance dividends paid in 1950. His results indicate that windfalls tend to increase the level of consumption expenditues and that this increase is not confined to durable goods. See Ronald Bodkin, "Windfall Income and Consumption," American Eco nomic Review, XLIX (September, 1959), 602-614. 185 reflections of the true constraints which influence con sumer spending patterns. A sample of the literature reviewed above indicates almost complete agreement on the use of a "disposable" con cept of income as the relevant constraint to be included in the consumption function. We shall follow this practice initially. However, since disposable income appears in no other equations of our model, its inclusion here would re quire the introduction of several new exogenous variables in what will already be an overly large model. We shall therefore test the measures which we employ for (YGNP) and for (YDISP) to see if a sufficiently stable proportional relation exists between these variables to allow us to sub stitute the (YGNP) measure for (YDISP). If the results of this test indicate that the tax parameter, t, in (YDISP) = (1-t)(YGNP) has remained relatively stable over the period covered by our data, we shall substitute the (YGNP) measure for the disposable income measure in our consumption func tions, thereby eliminating the exogenous variables which would necessarily have to be included in the definition of (YDISP). Regardless of which measure we finally employ, we shall formulate our model so as to specify the change in the level of the income variable as the argument in the consumption function. We do this for two reasons. First, 186 in a wealth constraint model, the change in the level of income may serve as a measure of expectations which the consumer holds for the future and as a measure of the ef fects of "transitory income" on current consumption. Sec ond, the use of the change in the level of income will reduce the probability of incurring serious problems of multicollinearity between the wealth and income measures. The precedent supplied by work which appears in the literature is much less helpful in indicating a potentially successful wealth measure to include in our model. The measures actually employed in empirical studies range from Friedman's concept of "permanent income," which he suggests is a proxy measure for real wealth, to Klein-Goldberger's use of liquid assets held by households, to Ando-Modig- liani's measure of net worth. The theoretical discussions in the literature on this point generally center around questions concerning the role of government liabilities in the public's measure of net wealth. These arguments are usually highly abstract and most often turn on the author's assumption concerning the ability of the public to discount the expected future taxes which the interest payments on the public debt will require. For example, Harry Johnson, in his review of monetary theory for the American Economic 187 Review,^9 asserts that there is a very real possibility that the positive wealth represented by bonds will be pre cisely offset by the capitalized value of the taxes imposed on non-human wealth to pay the interest on those same bonds. However, Pesek and Saving, in their recent work, note that if these taxes are imposed on human wealth, the difference in the discount rates on human as opposed to non-human wealth will insure that the government debt "will 2 0 represent a positive component of wealth." These discussions, however, are really of little help to us in trying to make an a priori judgment on what is in essence an empirical question. We shall fall back upon our discussion of Allan Meltzer's results, which we presented above, and restate our decision to employ the original concept utilized in his tests, namely: consoli dated net non-human wealth of the public. However, our treatment of the wealth constraint will be somewhat differ ent in the consumption function than it was in the money demand equations. We shall include two specific measures to represent the total constraint which wealth imposes on consumer behavior: non-human, non-monetary wealth, the l9Harry G. Johnson, "Monetary Theory and Policy," American Economic Review, LII, No. 3 (June, 1962). 20Boris P. Pesek and Thomas R. Saving, Money, Wealth and Economic Theory (New York: The Macmillan Co., 1967) , pT"2S7:------------ 188 variable specified in the money demand function, and real monetary wealth. We do this for the following reason. The conclusions reached above concerning the role of liquid assets in consumer spending indicate to us that some meas ure of the real value of monetary assets should be included in a model which has a specifically short run focus. The inclusion of these assets will allow us to separate out some of the short run "ratchet" effect caused by the modi fication of income variability which the holding of these assets is purported to accomplish. Thus, the inclusion of both monetary and non-monetary components of wealth will give us a proxy measure for liquid assets which will allow us to test the above assertions. Further considerations of the nature of consumer spending (along with a desire to reconcile our definition of consumption expenditures with that used by John Arena and others indicates that the factors affecting total spending on bulky and expensive durable goods, such as ap pliances and automobiles, are not likely to be the same factors which determine the level of expenditures on non durable consumer goods and services. Likewise, although both durable and non-durable goods are grouped together in most measures of "total consumption," actually there is a significant characteristic difference between the expendi tures on these goods. It is quite likely that expenditures 189 on non-durable goods and services and the value of those goods consumed in any one period will be about equal. But for durable goods, which are consumed over several periods, there may be a very large divergence between the level of expenditures on these goods in any one period and the ac tual value of the goods consumed (depreciated) in that period. Thus, we will specify two separate functions: one for expenditures on non-durable goods and services, and one for total expenditures on consumer durables. We hope that this separation will permit us better interpretation of our results. For example, such disaggregation will allow us to include specific measures of lagged values of the dependent variables. The separation of these variables is imperative in order to be able to distinguish what are likely to be opposite effects. For it has been shown that although a variable measuring lagged expenditures for total consump tion in a single aggregate consumption function usually has a low and insignificant coefficient; this may well be due to aggregation. The work of Zellner,21 for example, indi cates that large expenditures on durable goods (like auto mobiles) , this period, may be expected to have a depressing effect on expenditures next period, while a high level of ^Arnold Zellner, "The Short Run Consumption Func tion," Econometrica, XXV (October, 1957), pp. 552-567. 190 consumption expenditures on non-durable goods (because of the characteristics distinguished above) is more likely to be continued as a trend next period and thereafter. Thus, we would expect 3(CDUR)T 3(CNDS)T ------------ < 0 and — > 0 3(CDUR)T_1 3(CNDS)T-l This effect is quite likely to be disguised in an aggre gated function. One last result of this disaggregation is that it will allow us to test the effects of credit conditions, short run movements in the level of income, and fluctua tions in the aggregate price level on the separate compo nents of total consumption expenditures. To test these effects accurately, some kind of disaggregation appears imperative since consumer survey data and previous analyses using regression techniques indicate that these factors will have different, sometimes opposite, effects on differ ent kinds of consumption expenditures. Thus for testing purposes, we specify the follow ing relations in linear form: (1) CDUR = a61 + a62 (Wealth) T.x + a63<DDadj + CURR) T + a64 (CDUR) T-1 + a65 (rB> T + a66(AY)T + 191 + ag^(AP/P)T (2) CNDS = a?1 + a?2(Wealth)T-1 + a?3(DDadj + CURR)T + a74(CNDS)T_! + a75(rB)T + a?6 (aY)T + a7?(AP/P)T where we define the variables as follows: CDUR ~ real consumption expenditures on durable goods CNDS = real consumption expenditures on non durable goods and services Y = some concept of income in real terms (Wealth)= real consolidated net non-human wealth stock of the public at the end of the previous period (DDadj + CURR) = real money balances-average during period T r_ = the short term interest rate D The Determinants of Investment Expenditures One of the most striking characteristics of the wide ranging body of research on investment expenditures which has appeared in the literature is the failure of much 192 of the empirical work to support some of the most funda mental and most widely stated theoretical propositions. Most significantly, there has been a highly disconcerting inability on the part of empirical researchers to produce strong evidence in support of the very important position given to the interest rate in almost all theoretical dis cussions of investment behavior. Most of the evidence pro duced to date fails to find the significant relationship between interest rates and investment spending as postu lated in both classical and Keynesian models. One explanation, deriving from Keynes' "General Theory,” which is often put forth to rationalize these results, emphasizes the fact that the psychological and expectational factors affecting the stability of the in vestment demand function are probably of such overwhelming importance that they "swamp" any effects which interest movements could produce on aggregate investment spending. If this were indeed the true explanation, it would be ex tremely unlikely that we would ever find stable relation ships with which to construct income-expenditure models, which could be used for predictive or forecasting purposes. The great variety of empirical hypotheses which have been supported by the tests presented in the litera ture have been hypotheses which did not postulate a central role for the interest rate in the determination of invest 193 22 ment expenditures. These theories run the entire gamut from those which stress factors which are external to the firm and almost totally exogenous to the economy— such as Schumpeter's innovation theory— to those which stress totally internal factors such as recent profit levels or the present stock of liquid assets. Between these come all the various formulations of the acceleration hypothesis with its view of the firm as consciously responding to its sales and production levels in an effort to maintain a given proportional relation between its stock of capital and its output or sales level. These results are particularly discouraging to us in the construction of the present model. For, if no sig nificant role can be found for some interest rate in the investment demand function, one of the strongest potential theoretical ties between the real and the monetary forces in the economy will be discredited. However, work done by Frederick Hammer in a recent doctoral dissertation written at Carnegie Institute of Technology23 indicates that the failure to find significant 22Robert Eisner and Robert H. Strotz,"Determinants of Business Investment," Impacts of Monetary Policy (Com mission on Money and Credit, Englewood Cliffs, N.J.: Pren tice Hall, Inc., 1963), pp. 60-338. 23Frederick S. Hammer, "The Demand for Physical Capital: Application of a Wealth Model" (unpublished Doc toral dissertation, Carnegie Institute of Technology, Pittsburgh, 1963). 194 interest elasticity for the investment demand function may be due to a failure on the part of the investigators to correctly specify the true constraint which ultimately af fects investment decisions. Specifically, he develops a portfolio-balance theory of the firm in which a criterion function, which defines an optimal portfolio as the one which maximizes the difference between the return from the stock of assets and the stream of liabilities held by the firm, is constrained by the wealth of the firm. This wealth is determined by the market value of the original portfolio. By employing such a model, Hammer shows that the time series of past investment expenditures can be quite satisfactorily explained by a derived equation which includes wealth, expected yields, and the interest rate as independent variables. We will base our own analysis on Mr. Hammer's theo retical construction. In so doing, however, we will modify his basic model so that it more accurately reflects those factors which are judged important for the actual timing of investment expenditure. This short run focus will neces sitate a certain degree of disaggregation of gross invest ment expenditures into more homogeneous categories. Eco nomic theory indicates that the factors which influence the various components of what is usually defined as "gross 195 private domestic investment"^ are so diverse and so lack ing in homogeneity that to group all these expenditures together is totally unsatisfactory when the end in view is a structural wStimate of the behavioral relations involved. For example, those specific influences which determine business expenditure on plant and equipment are not likely to be the same precise factors which determine residential construction activity. We will consider three separate categories of investment expenditure: non-agricultural gross business expenditure on plant and equipment, total inventory investment, and expenditures on non-business con struction. We will consider the possibility of formulating a structural equation for each of these components in turn. Gross non-agricultural business expenditures on plant and equipment — a wealth model. As noted above, we follow closely the work of Frederick Hammer in deriving our structural equation to explain business expenditures on plant and equipment. Dr. Hammer's own work proceeds as follows. He develops a model of a "representative firm" 24The Department of Commerce defines "Gross Private Domestic Investment" as "the net acquisitions of fixed cap ital goods by private business and non-profit institutions and the value of the change in the inventories held by them. It covers all private new dwellings, including those acquired by owner occupants.” See Dept, of Commerce, Office of Business Statistics, Biennial Supplement to the Survey of Current Business: Business Statistics, 1?%5 (Washington, D.C.: Government Printing Office, 1965). 196 which shows the firm as striving to achieve an optimal portfolio balance so as to maximize its profits. This specific conception of the firm differs from that of tradi tional theory in several important respects. First of all, the emphasis is on stocks— primarily the stock of assets (A) and the stock of liabilities (L). Flow variables are introduced specifically in the form of rates of change of stocks or as returns on stocks. Secondly, the search for profits by this "representative firm" shows itself not in a continuous and direct adjustment of output levels to equate marginal costs of production with the marginal revenue from sales; rather "the motivational assumption upon which the model is founded is that the firm behaves so as to 2 c achieve an optimal portfolio of assets and liabilities." This "optimal" portfolio is that balance between assets and liabilities which yields maximum profit. Thus the profit equation serves as the criterion function in the model. Profit in this model is defined as the difference between the return from the stock of assets (r= • A) and a the payments on the liabilities of the firm (ri • L).2® 2^Hammer, o£. cit., p. 164. 2 6 In Hammer's model, total costs are composed of two components: (1) Cq— costs per period incurred in pro ducing the output of the firm exclusive of interest payments on the firm's outstanding liabilities. These costs are assumed to be a function of output levels: Cq - Cq(Q); (2) C— debt costs represented by the payments on the firm's 197 Two specific assumptions must be made in order to derive an equation for the desired stock of assets (from which we can determine the desired stock of capital). The first assump tion is that the cost of liabilities (i.e., the interest rate) is an increasing function of the firm's debt-equity ratio. The second is that the marginal yield on assets is a non-increasing function of the stock of assets. The for mer assumption realistically implies that the coupon rate at which a firm can issue bonds is an increasing function of the ratio between the value of the firm's liabilities and its wealth (a measure of risk for the bond purchaser). The latter assumption is an implication shown to result from horizontal or downward sloping demand curves in the market in which the firm sells its output. At this point, Hammer specifies his crucial postu late: "The constraint within which portfolio adjustment decisions are assumed to be made is that wealth (equity) of the firm is determined by the market value of the original portfolio."27 It is wealth, (WBUS), which imposes an ultimate limit on size, since growth beyond that point liabilities: C = ri . L Therefore, Ctotal = Cg + C = Cq(Q) + r^ • L Net revenues (R) are defined as gross revenues of the firm R - less the costs of production Cq: R = Rq - Cq = ra • A Thus, profits ( ) are stated as * R - C = ra *A - r^ • L 27Hammer, o£. cit., p. 165. 193 where marginal returns and payments are equal will be un profitable and, therefore, avoided by the firm. From the above considerations, a Lagrangian expres sion is formulated in which the profit equation (ra • A - ri * L) serves as the criterion function and original port folio wealth (WBUS) as the constraint. The first order equilibrium conditions derived fro a maximization of this Lagrangian expression form a set of equations from which it is possible to derive a formula for the desired stock of assets at the beginning of a period. On the basis of the assumptions made in this model, it is then demonstrated that this derived formula may be taken to hold for a given asset, such as physical capital, as well as for the stock o of assets as a whole. Thus, Hammer shows that the desired stock of physical capital, KD, depends upon wealth, (WBUS), and the difference between the expected yield on capital, and the cost of liabilities, i.e., the interest rate, r. K§ = a' (WBUS) T + t{ pk)t - (r)T] On the assumption that construction lags and high trans actions costs for physical capital imply a relatively long period of adjustment to bring the actual capital stock into line with the desired level, the author derives an invest ment demand equation for the firm. (Investment is viewed here as the process which equates the actual capital stock 199 to the desired stock, i.e., 1^, = X (Kt - KT) . Depreciation is absorbed into the equation by assuming that deteriora tion in period T is proportional to the stock of capital at the beginning of the period, i.e., Dip = wK^,. The final investment demand equation for the firm is IT = a (WBUS) ip + B [( PK)T “ (r) T] - X (1 - m)Kt Hammer then demonstrates that by valid aggregation tech niques a linear aggregate investment demand equation for the economy may be derived.28 A IT = a81 + a82(WBUS)T + a83[( pR)T - <r)TJ + a85(K)T Various statistical tests are performed on this equation using the following annual data measured in constant dol lars, 1915-1961. Irp = gross non-agricultural business expenditures on plant and equipment (WBUS)t = the net worth of the firm given by the market value of its common stock A p K = expected yield on assets— a proxy for the ex pected yield on physical capital rip = average rate of interest paid on the outstanding bonds of corporations 28Ibid., pp. 77-82 200 K,p = a measure of capital stock hammer's statistical results provide extremely impressive evidence for the ability of his derived investment demand function to explain the fluctuations in investment expendi tures. Two of his results are especially significant for us in modifying the original formulation of the equation for inclusion within our own model. First of all, he finds that the elimination of the capital stock variable from the regression equation leads to no loss in explanatory power 29 for the relation. Secondly, his tests indicate that, as his model had implied, the coefficient of the yield vari- able ( p k )t has the same order of magnitude as, but is op posite in sign to, the coefficient of the interest rate. Hence, we may rewrite his equation as: A XT = a81 + a82(WBUS)T + a83< + a84(r)T The focus of Dr. Hammer's model is specifically on the long run. Certain short run factors which take explicit consideration of the timing of expenditures are going to have to be introduced into his model to make it satisfac tory as an explanation of short run movements in investment. The author himself attempts to consider certain of these factors in order to reduce the variation in the residuals 29lbid., p. 115. 201 of the regressions run on the basic model as reviewed above. In an effort to take explicit notice of partially completed plans, he includes a lagged value of the depen dent variable. In a further effort to allow for the ef fect of short term cyclical movements in the general level of economic activity, a measure of the National Bureau's diffusion index is also included.30 These modifications are shown to have a fairly significant effect in expanding the explanatory power of the model, while at the same time having little effect on the original values of the coeffi cients of the independent variables in the basic model. Further a priori considerations along these lines lead us to the following tentative conclusions concerning short run influences on the investment decision. First of all, the actual specification of time lags becomes most important in a quarterly model. However, there is little theoretical basis for deciding on lags of any particular length. The choice involved is almost totally an empirical one, with the final decision to be determined by the per formance of each lag tried in the actual estimation. 30Hammer tries several possible variables in an attempt to explain the variation in the residuals of the basic model: (1) Friedman's index of transitory aggregate income as defined in the Theory of the Consumption Function, (2) a measure of the level of unemployment, and (T) the National Bureau of Economic Research diffusion index. The last measure performs best in reducing residual variation in the series. 202 Planning periods, decision delays, and other factors which cause lags between the points at which a project is pro posed, acted upon, approved, and undertaken indicate that perhaps investment decisions involve long time periods and are directly influenced by factors which occurred several quarters or even years past. But the fact that a "stop order” can be issued at little expense any time up to the actual start of construction or fabrication suggests that shorter lags may be more accurate in describing the finan cial influences involved. Our own preliminary tests indi cate that current investment expenditures on plant and equipment are primarily determined by events and factors influencing decisions made from three to nine months pre viously. Within this range, two quarter lags on both in terest rates and the aggregate net value of corporate stock seem to be the crucial determinants of current expenditures. Thus, we specify the following equation for inclu sion in the model: (IPandE) t = agl + a82(WBUS)T_2 + a83( + a84(rc)T.1 + ags(Oif)T + ag6(IPandE)T-1 where the variables are defined as above and IPand E = gross non-agricultural expenditures on plant and equipment 203 (WBUS)t_2 = business wealth stock Dif = NBER diffusion index The presence of an expectational variable, ( pR), in this equation requires the explication of specific assumptions to derive a measure suitable for use in our empirical tests. In our regressions we shall employ calculations based upon the recently developed Almon technique in order to derive a measure of expected yield from the past profit ex perience of businessmen. This technique shall be described in detail below and the specific derivation of the expected value measure will be explained in the data Appendix A. Hence we shall test (IPandE)T = agl + a82(WBUS)T_2 + a83<rc>T_2 + a84(Dif)T + a85(IPandE)T , + Z b.(YALM.) 1 x i=0 1 where YALM^ * ■ the i ^ Almon variable calculated from the past values of ( Inventory investment expenditures. By absolute measures, expenditures on investment in inventories are quite small relative to total expenditures in the economy. However, their volatility makes them extremely important, particularly in a short run model. As Darling and Lovell note in their article for the Brookings Quarterly model, 204 . . . shifts from investment to disinvestment in business inventories accounted for 60% of the shrink age in aggregate demand for goods output during the four recessions 1948-49, 1953-54, 1957-58, and 1960- 61; during the first year of the four periods of business expansion, on the other hand, shifts from disinvestment to investment in stocks accounted for 58% of the increase in total demand for g o o d s .31 The first question which we must consider is whether we should treat total inventory investment expendi tures as a single dependent variable or if we should disag gregate the total measure into two or more component parts. Two specific considerations will lead us to choose the aggregated measure as the appropriate variable to explain. First of all, a detailed study of the theoretical factors which may lead to a suitable disaggregation of these expen ditures and of the tests which such disaggregation would necessitate is beyond the scope of this study. Secondly, in a recent empirical study Michael Lovell produces some evidence on the value of disaggregation in the estimation of inventory relations. Lovell specifies and tests both aggregated and disaggregated inventory investment equations. Specifically, he estimated an inventory change equation for 31paul G. Darling and Michael C. Lovell, "Factors Influencing Investment in Inventories," The Brookings Quar terly Econometric Model of the United States'^ editors, James S ~ . Duesenberry et aT. (Chicago: Rand McNally and Co., 1965), p. 131. 205 purchased goods and goods in process and one for finished goods inventories. He then estimated a "total" inventory investment equation by two different methods: once by direct least squares regression and once by adding the estimates of the component equations. A comparison of these two estimates leads him to the following conclusion: "Only the coefficient of the rate of change in prices of purchased materials and goods in process shows a marked senstitivity to the level of aggregation."32 His results, therefore, show that the coefficients of all the other variables in the equations remain highly stable when the jump is made from the disaggregated formulation to the "total" inventory investment equation. Therefore, on this basis, we have decided to consider total inventory change as the variable to be explained in a behavioral relation in our model. As in the case of consumer spending and business expenditures on plant and equipment, our model of inventory investment behavior will be based upon the stock adjustment concept. Specifically, we consider a flexible accelerator model to explain the adjustment of the actual level of in ventories to some desired level. In this development, we -^Michael c. Lovell, "Manufacturer*s Inventories, Sales Expectations, and the Acceleration Principle," Econo- metrica, XXIX (July, 1961), 293-314. 206 follow the general outlines of such a model as presented by Darling and Lovell in their work on the Brookings model and in much of their previous w o r k . 33 We view the actual level of inventory investment to be composed of two components: the desired change in the level of inventories, and an unexpected build up or drawing down of those inventories because of a discrepancy between the expected and the actual level of incomes (sales). Therefore we state (DINV)t = a'I(INVD)t - (INVJt.!] + b'(YT - YT) (1) where (INV)rp = total level of inventories at time t (INV)jjJ = desired level of inventories at time t (Yt _ Yt) = the discrepancy between expected and actual sales or income level To make this hypothesis operational, we must spec ify relations explaining the desired level of inventories and the expected level of income in terms of observable 33Darling and Lovell, loc. cit.; Lovell, loc. cit.; Paul G. Darling, "Surrogative Measurements of Expectations: An Example in Estimating the Liquidity Influence on Invest ment," Review of Economics and Statistics, XXXVIII (Novem ber, 1956), 413-426; and Lawrence Klein, "Economic Fluctua tions in the United States, 1929-1941" (Cowles Commission Monograph No. 2, New York: John Wiley and Sons, Inc., 1950). 20 7 variables. Following Lovell's formulation, we postulate that the desired level of inventories is a linear function of the actual level of income, the recent change in income, and the level of unfilled orders. This last variable is a proxy measure for the degree of market tightness. This has been shown to have a significant influence on the desired level of inventory since it strongly influences the ex pected delivery lags and bottlenecks which lead business men to build up inventories in the face of possible short ages . Further theoretical considerations indicate that a measure of the alternative cost of tieing up capital in stocks of goods for inventory purposes should be included as a determinant of the desired level of inventories. On the assumption that the marginal returns from holding an inventory decline as those inventory stocks increase, we would expect the entrepreneur to conserve on those stocks as the cost in terms of the interest rate on tied up capi tal increases. Some evidence for this position is pre sented in the study of inventory investment by the "trade sector" of the economy done by Lovell for the Brookings model. Lovell also includes a change of price variable in •*4Darling and Lovell, oj>. cit. , p. 151. 2 08 his specific formulation. This is included in an attempt to discover what effects price movements have upon the holding of inventories. It is often asserted that one of the motives for holding inventories is the so-called specu lative motive— the hope of earning a capital gain from fluctuations in the prices of goods in stock. Tests on this variable in the inventory demand are performed in the hope of separating this effect from the other motives for holding inventories. Lovell's own empirical tests indi cated that this factor played a significant role in the determination of inventory investment in retail durable goods.35 Consequently, we will try to test for the influ ence of this factor within the framework of our own model. These considerations lead us to specify the follow ing relation for the desired level of inventories: (INV°)t = a^ + a^ (YGNP) t + a^YGHP) + a^ (UNFIL) rp +a5<rc)T + ag(AP/P)T where UNFIL = the level of unfilled manufacturers' orders rc = the long term interest rate It is extremely difficult to devise a truly useful 35ibid., p. 153. 20 9 measure for the level of expected income. Under present conditions, the only test of validity possible for such a measure is its actual performance in the estimate. Hence, we assume the following: people responsible for determin ing inventory levels are highly sensitive to the general level of economic activity and probably have a relatively short but intense time horizon, Thus, we will assume that they expect last period’s rate of growth in the level of income to be repeated this period. Thus, YT-i - Yt_2 Yt_x 2 YT = YT_X + ---- • Yt_l =------- it-2 *t-2 The level of income is expected to grow (or decline) at the same rate this period as it grew (or declined) last period. Substituting these relations in equation (1), we derive the following final relation for inventory invest ment expenditures: (DINV)t = a*[a^ + a2(YGNP)T + a^(AYGNP)T + a^(UNFIL)T + a5(rC}T + a6(AP/P)T " CUnOT-ll + b'[YT - (YGNP) ^ Combining terms, (DINV)t - a91 + a92(YGNP)T + a93(aYGNP)t + a94(rc)T + agst P/P)^, + a9g(INV)»r_i + ag^ (UNFIL) + a9g(Y)T 210 The treatment of non-business construction expen ditures . The volatility of non-business construction ex penditures evident in the data covering the years to be included in our estimates indicates that the important com ponent of gross national product must be included as an endogenous element in any model which hopes to explain short run fluctuations in the level of economic activity. With the inclusion of a satisfactory behavioral equation for this sector within the framework of our simultaneous equation model, we can hope for two results. First of all, if the degree of explanation afforded by the estimated equation is relatively high and its ability to forecast future expenditures relatively accurate, we can make cer tain judgments on the basis of this equation about the actual structure of this market. Second, economic theory tells us that financial factors, such as interest rates, are probably quite important in the determination of housing expenditures. Hence, a correctly specified struc tural equation for this sector may provide another link in the model between the "real" and "monetary" spheres. A fairly broad review of the literature on this subject indicates that the specialists in this field have not yet been able to produce any particularly convincing evidence about the actual structure of this very important market. Hence, investigators constructing simultaneous 211 equation models like the present one do not yet possess the necessary basis upon which to make the appropriate judg ments about how this sector should be integrated with the rest of the model. This is not stated as a criticism of the kind of work being done by analysts in this field. Rather, it is said in sympathy with the fact that those people have to be content with what is probably the worst sectoral data on expenditures in the United States. For example, an investigation by the War Production Board found little or no relationship between Bureau of Labor Statis tics reports of starts and actual net additions to the housing stock. Using 1935-1939 = 100, the BLS index varied only between 26 and 143 during the 1930's. The W.P.B. estimate of additions to the stock varied only between 55 and 115. The lows and peaks were in different years and the actual direction of change differed in four of the nine years.3® These kinds of considerations lead Grebler and Maisel, in their review of the work done in this field, to state that "Until data re improved and made available for more periods, or until less rigorous procedures are devel- 36Leo Grebler and Sherman J. Maisel, "Determinants of Residential Construction: A Review of Present Knowl edge," Impacts of Monetary Policy (Commission on Money and Credit, EnglewoocT Cliffs’ , N.J. s Prentice-Hall, Inc., 1963), p. 551. 212 oped to deal with existing data, it appears unlikely that equations suitable for use in current analysis or predic tions can be worked out."37 This is not to say that there is no data available. In fact, Maisel himself, in his work for the Brookings 38 Quarterly model, has estimated much of the necessary data on a quarterly basis. However, it is extremely difficult to judge the value of this data. As Maisel notes, the only possibly accurate figures are the decennial census figures. His quarterly figures are interpolations from these decade benchmarks. His article in the Brookings work is replete with warnings about the incredibly poor state of the data. The indications of the work already done in this field by Converse, Teigen, Maisel and Grebler, and others are that in order to achieve a fairly high degree of ex planation of the time series of expenditures on residential construction, several explantory variables not already in cluded within our model would have to be introduced. All of these studies specify rental indices, family formation measures, vacancy rates, down payment requirement and other such factors in their structural equation. The cost of 37lbid. 3®Sherman j. Maisel, "Nonbusiness Construction," The Brookings Quarterly Econometric Model of the United States, editors, James S~ Duesenberry et aXT (Chicago: Rand McNally and Co., 1965), pp. 178-2(JT. 213 including a model of this sector which would be fairly certain to yield satisfactory results seems unduly high in terms of the expansion of our reduced forms and the loss of degrees of freedom. As the previous works indicate, at least three or four additional exogenous terms would have to be specified. In addition, the extremely poor state of the data which are available on these measures may easily cause serious errors which would weaken any good results derived from their introduction. Since our prime interest is in the monetary sector of our model and not the real sphere, we do not feel it worthwhile to enlarge the size of our model to include this sector. In view of these circumstances, we choose an al ternative approach. We shall experiment empirically with a very simple model in an attempt to provide a rough ex planation of housing expenditures using as arguments the variables already included within our structure. Employing non-human wealth of the public as a constraint in the be havioral equation, we shall test the sensitivity of housing expenditures, HE, to recent changes in the level of income, to price movements, and to general credit conditions. If an acceptable degree of explanation for the level of these expenditures can be achieved from this very simple model we shall include this factor as an endogenous variable within our model. We specify the following linear form for our pre liminary tests: (RC)t = «12>1 + ai2>2 (Wealth)^ + a12 .3<aY)t + a12-4 <ap/p>T + The results of our tests shall be presented in Chapter VI. The Term Structure of Interest Rates Both the long term interest rate as represented in this model by Moody's composite yield on corporate bonds and the short term rate as measured by the market rate on three-month Treasury bills have appeared in one or more of the equations in our model. We wish, therefore, to de scribe the relation which exists between these rates. Thus, we shall include an equation which will attempt to explain the term to maturity structure of interest rates. On the theoretical level we have available to us several hypotheses explaining the phenomena exhibited by historical yield curves. These explanations are tradi tionally listed under three familiar headings: the *fexpec- tations" hypothesis, the liquidity preference theories, and the market-segmentation hypothesis. Recently some 215 important modifications of these basic theories have ap peared. These include the combined expectations— liquidity preference model of Reuben Kessel and the "Preferred Habi tat Theory" of Franco Modigliani and Richard Sutch. On the level of empirical testing, there have been two approaches taken to the investigation of the term structure of interest rates in the literature. On the one hand, there is the work of Culbertson, Meiselman, Kessel and others who have been primarily interested in testing the implications of the above theories. Specifically, they have sought to discover whether or not the market actually does try to predict interest rates and, if so, whether these predictions are biased or unbiased estimates of the future expected rates. On the other hand, there are the works of Klein-Goldberger, de Leeuw, Modigliani and Sutch, and others in which the authors have attempted to express within a single regression equation the process through which expectations of short term rates determine the long term rate. In this section, we are specifically interested in the approach taken in this second group of studies. How ever, we will first review the basic theories and the em pirical work surrounding them, since they form the basis of all the studies cited thus far. Traditional explanations of the term structure of 216 interest rates. We will discuss, in turn, the expectations hypothesis, the liquidity preference theory, and the mar- ket-segmentations hypothesis. The expectations hypothesis.— The expectations hy pothesis, developed within a model which postulates both certainty and rational behavior, assumes that the returns from holding securities of varying maturities during the same period of time should be identical (abstracting from default risks). Thus, this theory postulates that the forward rates, (r^), implicit in the term to maturity structure of market interest rates, are equal to the ex pected short term (spot) rates and are unbiased estimates of those rates. We may illustrate this as follows. If Rn is the current market rate on an n period loan and r^ are the implicit forward rates, these implicit rates may be calculated as follows: (1 + R^) = 1 + r^ (1 + R2) = ^/(l + rx)(1 + r2) (1 + V = n/ d + rx(l + r2) ...(1 + rn) Thus, the implicit forward rate is simply the "mar ginal cost of extending a one year term to maturity for an 217 additional year."^ If the yield on two period securities is 3 per cent and the current rate on one period securities is 2 per cent, the forward rate on a one period loan in the second period is 4 per cent. This, however, is tautology. The economics of the theory is introduced only by the spec ific postulate that the forward rates implicit in the cur rent term structure of rates are, in fact, unbiased esti mates of future short term rates.40 This formulation of the pure expectations hypoth esis has been subjected to rigorous empirical testing by David Meiselman. He proposes and carries out a test of the ^^Reuben A. Kessel, The Cyclical Behavior of the Term Structure of Interest Rates (NBER Occasional Paper 91, New York: The Columbia University Press, 1965), p. 6. 40It should be noted that an implication of this "pure expectations" hypothesis is that short and long term securities are perfect substitutes for each other (again, default risks aside). Because of this, many writers have been willing to dismiss this hypothesis simply on the basis of the observed behavior of the participators in financial markets. It is pointed out that most individuals and in stitutions in the market do, in fact, specialize in securi ties of specific maturities. The implication, then, is that since such specialization takes place, securities are obviously not perfect substitutes for each other in the eyes of the purchasers. This, however, is not evidence against the expectations hypothesis. For as Kessel has shown, "As long as some ranges of maturities are considered as alternative by individual participants in this market, and in the aggregate these ranges cover the entire spec trum, the market will act as though bills and bonds are alternatives. Yet every participant in this market may deal in a highly circumscribed maturity spectrum." Kessel, op. cit., p. 11. 218 model which involves the use of actual forecasting errors as a guide to revision of market rates. Specifically, at the beginning of any year T, one can look back at the mar ket rates prevailing one year earlier. From these, he can infer the rate which was expected to prevail (the forward rate) at the beinning of time T. A comparison of this rate with the currently prevailing rate on one year loans at time T, defines the forecasting error. His hypothesis, then, is that if actual rates are higher than had been anticipated, the market may systematically revise upward expectations of what short term rates in the future are likely to be— and conversely. Hence, he is potulating a primarily extrapolative expectations thesis. Then, "Be cause a long term rate is an average of current and forward short term rates, we also have a substantive hypothesis that unanticipated changes in the long rate are also based on errors made in forecasting the short term rate."4^ - Thus, in linear form: At RnT = a + b Et (2) where AT RnT is the change in the rate on n period securi ties, and is the forecasting error. 4^David Meiselman, The Term Structure of Interest Rates (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1962), pT“2ff. 219 Meiselman’s primary evidence in support of the ex pectations hypothesis is derived from regression analysis. Using time series data presented by Durand, he shows that for many different periods and different maturities, re gressions on the above equations yield a constant term which is very small and not significantly different from zero. For example, for thirty-year securities from 1901 to 1954 :42 AmRorvm = . 03 + • 25 Em R = . 87 ' 3Ui (.07) (.03) 1 Likewise, he shows that the regression coefficient declines as the term to maturity increases and that, at the same time, the correlation coefficient declines but at a much slower rate. Meiselman interprets the zero order constant term as evidence in favor of the pure expectations hypothe sis indicating that he would expect a bias in the estimates of future short term rates to show up as a significant positive constant term in the regressions. The inverse re lation between the regression coefficient and the term to maturity M. . .is consistent with behavior of forward rates as they become more distant."4- * The liquidity preference theory.— The basic postu- 42Ibid., p. 40. 4-*Ibid., p. 28. 220 late of the theory and tests presented above is the asser tion that forward rates are unbiased estimates of expected short term rates. In contrast to this is the liquidity preference hypothesis. This theory holds that since in vestors in general prefer to avoid the risks of illiquidity, and since this risk becomes greater the longer the term to maturity of a security, a positive cost is involved in ac quiring the service of speculators to hold the longer term securities. The implication of this theory is that forward rates will be biased estimates of expected short rates since the implicit forward rates will contain a risk pre mium which is greater than zero, i.e., r^ = the expected short rate (R^ip) + L, where L is the liquidity premium. As noted above, Meiselman interpreted the constant term in his regression equations as a "reflection" of this liquidity premium. His conclusion, therefore, was that no such premium was evident in his results. Reuben Kessel, however, disputes this interpretation. He points out that if the forward rate is interpreted as equal to the expected short rate plus a liquidity premium, the resulting hypoth esis comparable to the equation tested by Meiselman con tains a constant term which is the sum of two separate components— the liquidity premium on securities last period and the change in the premium over the past period. Thus the "a" in Meiselman*s equation (2) above equals (Lqj-i” AL). 221 With this interpretation, an observed zero term in the re gression does not uniquely imply L = 0; it is also consis tent with I*T_1 = AL.44 Furthermore, the key element in Meiselman's tests is his interpretation of the difference between forward and subsequently observed spot rates as the forecasting error of the market. Kessel questions this interpretation since "it is unreasonable to expect the mar ket to err asymmetrically. The mean error in a long series of observations should be zero."45 He notes that this is not the case with Meiselman's series. He concludes, there fore, that the liquidity preference theory remains untested in Meiselman's work. Kessel's own interpretation of Meiselman's work and of the further evidence which he himself presents is that both the expectations hypothesis and the liquidity prefer ence theory have a role to play in explaining the term structure of interest rates. Specifically, he interprets the positive mean value of Meiselman's series of forecast ing errors to be a reflection of the positive liquidity premium present in the implicit forward rates. The actual market forecasting error, therefore, is much smaller. Kessel's own results are derived from a long run averaging 44Kessel, 0£. cit., p. 17. 45Ibid., p. 96. 222 of the Durand data on rates by term to maturity to derive a single upward sloping yield curve for the entire 1900- 1954 period,46 and from a detailed analysis of the struc ture of rates over the 1958-61 cycle. These results lead him to conclude that "forward rates are biased and high estimates of future short rates."47 Thus, these forward rates are not simply predictions of the market but rather predictions plus liquidity premiums. In contrast to the arguments of Meiselman and others, Kessel presents the view that "the greater liquidity yield of short maturities leads to a persistent pecuniary yield differential in favor of long maturities. . . . Therefore, the expected value of holding period yields (with 'yield' defined as total, as distinguished from pecuniary only), is equal for all terms to maturity.4 ® The market-segmentation hypothesis.— The third the ory presented as an explanation of the term structure of interest rates is the so-called market-segmentation theory. This thesis holds that the market for default free securi 46The upward sloping yield curve is especially convincing evidence of the bias contained in forward rates since, if anything, this was a period during which interest rates were tending downward. 47Kessel, 0£. cit., p. 25. 48Ibid., p. 97. 223 ties is a segmented one in the sense that it is composed of buyers and sellers who generally specialize in certain maturities and hence engage in little or no switching among securities of varying maturity. The implication here is that what happens in one market, the bill market for ex ample, has little or no effect on other markets, such as the long term government bond market. Rather, the yields on maturities of varying length are determined primarily by the supply and demand for that particular maturity within its own market. Therefore, the method proposed for the analysis of the term structure of rates involves partial equilibrium analysis of the separate markets for securities as defined by the current institutional structure. The evidence for this hypothesis in its strictest form comes from two primary sources. The first is the institutional material presented to show that buyers in se curities markets (such as life insurance companies) do, in fact, specialize in narrowly circumscribed ranges of the yield spectrum. As noted by Kessel, however, this is no evidence of market segmentation as long as the circum scribed ranges overlap. The second bit of evidence is that presented by investigators who failed to find support for the other two hypotheses. In 1957, for example, Culbertson attempted to investigate predictions made by speculators in the government securities market as a test of the expecta- 224 tions hypothesis. His results indicated that the partici pants predicted so badly that he rejected the idea that they try to predict at all. He rejected the possibility that "expectations" lay at the heart of the explanation of the term structure of rates. The data and analyses of both Meiselman and Kessel, however, indicate that Culbertson's method of analysis had much to do with his specific results. These three theories seem to have different degrees of appeal on different levels of abstraction. Most ana lysts agree that in a world of certainty and rational be havior, since all securities would have to yield identical returns, the expectations hypothesis would have a great deal of a priori appeal. Very many argue, however, that this is not even a close approximation to the real world— particularly to financial markets. These people are gener ally those who feel that the Hicks-Keynes-Kessel variant of the expectations hypothesis— the view that forward rates are estimates of future short rates plus a liquidity pre mium which varies directly with the term to maturity--is the minimum necessary to explain the actual term to matu rity structure.Lastly, the institutional factors of our 4 Q *John M. Keynes, A Treatise on Money, Vol. II (London: Harcourt, Brace and Co., T97^) ] and J. R. Hicks, Value and Capital (London: Oxford University Press, 1939), ppTT3S^T40. 225 society argue loudly, though superficially, for the market segmentation theory. Each of these theories, then, has a great deal of a priori appeal and most probably contains an element of truth. In fact, it is possible to combine them into a single theory. This has been done by Franco Modig liani and Richard Sutch. The ’ ’Preferred Habitat" Theory. The basic assump tions of the Modigliani-Sutch model are as follows. First, ". . . the yield structure is basically controlled by the principle of the equality of expected returns, but modified by the risk premiums." Second, ". . . different trans actors are likely to have different habitats," i.e., pref erences for securities of fairly specific maturity.50 Thus, if a person has money to invest in bonds for n peri ods, he has an n period habitat. According to Modigliani and Sutch, it is not at all certain that an individual with an n period habitat, when n > 1, will prefer a one period securities to an n period security simply because of liq uidity consideration. These considerations may easily be outweighed by the transactions costs of transferring funds successively through one period securities for n periods. 50pranco Modigliani and Richard Sutch, "Innovations in Interest Rate Policy," American Economic Review (Papers and Proceedings, May, 1966T7 178-19TT 226 Thus, if an individual is a risk avoider, "he will prefer to stay long unless the average of the expected short rates exceeds the long rate by an amount sufficient to cover extra transaction costs and to compensate him for the risk of going short" (i.e., the risk that short rates will de cline).51 Likewise, the risk of investing in a bond of longer than n periods involves estimating the sale price of a not-yet-matured security. This may well lead the in vestor to remain in his own habitat. Thus, as Modigliani and Sutch note, Under this model the rate for a given maturity, n, could differ from the rate implied by the pure ex pectations hypothesis by a positive or negative "risk premium," reflecting the extent to which the supply of funds with habitat n differs from the aggregate demand for n period loans forthcoming at that rate.52 Given the fact that the maturity preference "ranges" dis cussed by Kessel coincide with Modigliani and Sutch's "habitat" and probably overlap among themselves signifi cantly, these liquidity premium differences should cause shifts in funds between different maturity markets. Modigliani and Sutch summarize their presentation as follows. The expected return on an n period bond = R(n,T) + expected capital gain = R(1,T) + FT, where R(1,T) is the short rate and FT "stands for the net effect of ^Ibid. , p. 184. 52Ibid. 227 53 relative supply factors." The expected capital gain is then approximated by the expected change in the long rate. Thus, R(n,T) = R(1,T) - expected capital gain + FT (2) = R(1,T) + BAR (nfT) + Ft The specification of the term structure equation. We turn now to the work which has been done in employing these theories in the formulation of specific term struc ture equations. In their econometric model of the U.S., Klein and Goldberger employed a very simple linear term sturcture equation in which the long term rate was re gressed on the short term rate lagged three and five peri ods. This particular formulation was the result of experi mentation and had no particular a priori justification ex cept the vague notion that past levels of short rates could be employed as proxies for expected short rates— the deter minants of the long rate. In more recent work, Frank de Leeuw, in his model of the financial sector, develops his term structure equa tion from primarily a priori reasoning. Specifically, he derives his equation from considerations of the separate 53ibid., p. 185. 22 8 demands for short and long term securities. His model re sults in an equation in which the spread between the long rate and the short rate depends upon expected capital gains, the amounts of U.S. debt outstanding in different maturity classes and on the changes in the amounts of these securities outstanding. However, he is forced into empiri cal experimentation to find a suitable measure to represent his estimate of "expected capital gains." Being restricted to the usual regression techniques, he experiments with different lag structures. His results are somewhat disap pointing. His 's are in the range of .55 to .65 and the standard errors of the estimates are rather high { > .34 54 bsis points). In view of our previous discussion, how ever, his results do have one particularly interesting as pect. Under a Modigliani-Sutch formulation, the variables other than "expected capital gains" which appear in de Leeuw's equation would be interpreted as representing the supply factor, FT. These factors turn out to be signifi cant in de Leeuw's estimates. We can avoid the necessity of this empirical exper imentation, however, for we have available to us a much 54prank de Leeuw, "A Model of Financial Behavior," The Brookings Quarterly Econometric Model of the United States, editors, James S~ Duesenberry et aXT (Chicago: Rand McNally and Co., 1965), pp. 465-537. 229 more powerful and more flexible estimation technique than that employed by de Leeuw. This is the method developed by Mr. Shirley Almon55 in her analysis of capital expendi tures and used by Modigliani and Sutch in the estimation of their own term structure equation. We will follow the Modigliani-Sutch formulation very closely and employ this technique in our own estimation below. However, a comparison of the results obtained by Modigliani and Sutch with the results obtained by many of the investigators noted above leads us to modify their ap proach just slightly. For example, in comparing their re sults with de Leeuw's, one particularly important point stands out. As noted above, several of the variables in de Leeuw's equation can be interpreted as representing the supply factors in the Modigliani-Sutch model. Yet, when this same model is estimated by the more powerful "Almon" technique, these factors no longer play a significant role. Regressing the spread between the long rate and the short rates, we can explain over 97 per cent of the variation in the dependent variable and reduce the standard error to less than one-third of what it was in de Leeuw's estimates 55Shirley Almon, "The Distributed Lag Between Capi tal Appropriations and Expenditures," Econometrica, XXX, No. 1 (January, 1965), 178 ff. 2 30 When additional supply factors corresponding to (F^) are added to this regression equation, none of these additional variables appear significant and none of them improve the correlation to a significant degree. This seems to indi cate two things: first, the results obtained by de Leeuw were spurious and the result of the particular lag struc ture imposed on his independent variable; second, the mar ket segmentation component of the Modigliani and Sutch model lacks support from the evidence. Modigliani and Sutch themselves do not conclude that they failed to sup port the "Habitat Theory," but in view of these results and those of Meiselman and Kessel noted above, it seems likely that we may safely drop the maturity preference component of the preferred habitat model and view it as a liquidity preference-expectations theory. This has the effect of simply dropping the FT variable in the Modigliani-Sutch formulation presented in equation (2) above. Hence our equation to be estimated is as follows: (rC> T = aio.l + a10-2*rB*T + B^^B^T-i where (rc) is the composite bond yield and (rfi) is the rate on three-month Treasury bills. Specification of the weight pattern and description of the "Almon" technique. Like Modigliani and Sutch, we 231 assume that there are both extrapolative and regressive elements in investors' expectations concerning future mar ket rates.This has also been pointed out by de Leeuw. This implies that no simple geometric pattern can be used to formulate the weights by which past short rates affect expectations and, thereby current long rates. However, the development by Mrs. Almon of a method for estimating an unknown lag structure through the use of Lagrangian inter polation polynomials means that we now have available a technique to estimate these more complex geometric pat terns. We need only restrict our structure to one which can be approximated by a polynomial. In this particular instance, consideration of the relative strength of the regressive and interpolative elements in the estimation of 5®The Hicks-Keynes theory of "normal backwardation" indicates that people have some notion of a "normal" rate of interest and if the actual rate does not conform to the normal rate, investors will expect a return (at some un specified rate) to this normal level. This theory implies that there are likely to be regressive elements in inves tors' expectations. Duesenberry, on the other hand, has indicated that there are likely to be extrapolative ele ments in the expectations in the sense that if interest rates are rising (falling), it is quite likely that this will lead investors to expect a further rise (fall) in those rates. Since both of these theories may well contain elements of truth (de Leeuw), the actual lag structure will represent a summation of two more basic structures. Our a priori analysis of the relative importance of these two elements in the recent past leads us to conclude that the lag structure represented by our polynomial should rise to a single peak and then decline. This is by no means unique or necessary. 232 future rates indicates that our weight pattern should rise to a single peak and thereafter decline to zero. The work of Modigliani and Sutch indicates that this can be quite satisfactorily approximated by a fourth degree polynomial. Hence, our estimation will proceed by the following method as described by Mrs. Almon. We assume that the weights B(i) are the values at X = l...n of a polynomial, W(X), of degree (q + 1). Mrs. Almon has shown that once (q + 2) points on a curve repre senting a polynomial of degree (q + 1) are known, W(Xq) = bQ...W(Xq+1) = bq+^, the other W(i) can be calculated as linear combinations of these values by q+1 (i) = Z bj i = 1 n (4) j = 0 J J The (q + 2) values Xj may be chosen arbitrarily. The for mulas for the calculation of the (i), the Lagrangian interpolation polynomials, are given by Mrs. Almon. If we substitute formula (4) for our weights into our basic hy pothesis, we derive the following: (rc)T = a10 * 1 + ^ o ^ ^ T + 2 3 (i) (rB) T_i i=l n q+1 = a10*l + a10*2^rB^T + 2 2 (rB*T-i i=l j=0 J This may be rewritten as 233 “ a10*l + a10• 2 a10.1 + a10•2 where the (q + 2)(ALMj)T's are referred to as "Almon Vari- the use of the Lagrangian interpolation polynomials, the bj's can be estimated by direct regression. In our own case, we follow Modigliani and Sutch in estimating a fourth degree polynomial with a sixteen quar ter lag. Hence, n = 16. We impose only one restriction on our fourth degree polynomial. We assume that the value of the weight becomes zero in thi first period beyond our lag structure, i.e., W(n + 1) = W(17) = 0 and bq+^ = b4 = 0. Therefore, we need calculate only four Almon variables: n ables." Once the (ALMj)T's have been calculated through J = 0,1,2,3 Thus we estimate <rd T = al0.1 + a10*2*rB*T + + bi<ALMl)T + b2(ALM2)T + b3(ALM3)T The Price Adjustment Equation While there is a substantial measure of agreement 234 over the list of factors which various economic theories postulate as influencing the movement of the price level in the economy, there is much less accord over the exact em pirical specifications given to "price adjustment" equa tions which are derived from these theories. Even less agreement exists among the interpreters of these theories over the exact explanation to be given to actual price changes evident in our statistics. (We shall not consider here the very real dispute over the interpretation to be given to specific price indices and the reliability of those indices in depicting actual price movements. We shall assume that the price index employed in our study is an accurate reflection of the actual movement of the "gen eral price level" in the economy.) The various empirical analyses carried out to test these diverse postulates have as yet produced no results which allow us to make a strong judgment on the relative explanatory power of the theories from which these postu lates were derived. Consequently, in present circumstances, our own approach shall be one of experimentation with vari ous linear combinations of the variables suggested by several theories as crucial to the determination of price changes. The price level in classical analysis. The theo ries which have been proposed to explain price movements in 235 the economy range from the hypotheses presented by the ad herents of the crude Quantity Theory of Money to the recent views proposed by the so-called "structuralists" in the United States. In the classical system, under the assump tion of complete wage and price flexibility, the marriage of Say's Law and the Quantity Theory of Money produces a theoretical system in which changes in the stock of money are transmitted directly to the price level. With the stability of the velocity of circulation assumed and with full employment and the independence of the real and mone tary variables of the economy assured by the analysis, the equation of exchange, MV = PT, indicates that any change in the nominal money stock, M, leads to an equiproportionate change in prices. Though Fisher's discussion of the tran sition period^ gave evidence that the movement from one equilibrium level to another may not be a perfectly smooth process and may cause some interaction between "real" and "monetary variables, the comparative static equilibrium described in the classical system remained intact. This dichotomy between monetary factors and the price level on one hand and the real variables on the other has since been 5?Irving Fisher, The Purchasing Power of Money (New York: The Macmillan Company, 1911). 23 6 criticized by Patinkin58 and others. The specification of a "real balance effect" destroys this dichotomy through the introduction of real money balances into the expenditure functions of the public. The modification which this re quires in the conclusions of the empirical effects in a classical model, however, is still open to question.5® The price level in Keynesian analysis. In most ex positions of the basic Keynesian system, a different kind of dichotomy is assumed. This one concerns the response of real production and prices to changes in aggregate demand. In the analysis of an economy at less than full employment, it is generally assumed . . . (1) that all unemployed resources are homoge neous and interchangeable in their efficiency to produce what is wanted, and (2) the factors of production entering into marginal cost are content with the same marginal wage so long as there is a surplus of them unemployed.60 Under these conditions, prices remain perfectly inelastic up to the absolute level of full employment while real out put is perfectly elastic and absorbs the total effect of 5 8 Don Patinkin, Money, Interest, and Prices, (2d ed.; New York: Harper & Row, 1565). SOThomas Mayer, "The Empirical Significance of the Real Balance Effect," Quarterly Journal of Economics, LXXIII (May, 1959), 275-251 ^°John M. Keynes, The General Theory of Employment, Interest and Money (New York: Harcourt, Brace, and World, 1' 936), p.-T55~---- 237 any increase in aggregate demand. Beyond full employment the conditions are reversed and prices become perfectly elastic with the level of real output perfectly constant at its full employment level. The conclusions on the re sults of a change in the money stock within this system are the same as the conclusions derived from a classical system which postulates downward wage and price rigidity. Though different mechanisms are operative in these two models, below full employment an increase in the nominal money stock leads to an increase in real output and employment. Though Keynes himself sometimes spoke in these same terms, in his own exposition he recognized the com plicating factors likely to be present in the economy which would weaken this dichotomy. After listing five complicat ing factors which "will in fact influence events," Keynes specifically notes that . . . we must . . . consider the effects of changes in the quantity of money on the quantity of effec tive demand; and the increase in effective demand will, generally speaking, spend itself partly in increasing the quantity of employment and partly in raising the level of prices. Thus instead of con stant prices in conditions of unemployment and of rising prices in proportion to the quantity of money in conditions of full employment, we have in fact a condition of prices rising gradually as em ployment increases.61 Keynes indicates further that he not only expects to find 61Ibid., p. 296. 238 that the dichotomized relation does not exist in any actual circumstances but also that the actual degree of response of prices and real output to changes in aggregate demand cannot be predicted by any simple relation, as for example, between the elasticity of price changes and the level of unemployment. Rather, he emphasizes that psychological and political factors influencing both employers and labor unions can be expected to cause discontinuity in the rise of prices at a series of "semi-critical points" on the path to full employment. The wisdom of this view has been sup ported by the inability of empirical investigators to find such simple relations in their several attempts to estimate Phillips curves for various countries. The Keynesian system, then, suggests that any of the factors which may change aggregate demand, such as changes in the money stock, changes in the psychological propensities to consume and to invest, or changes in gov ernment spending and tax policy, will influence the move ment of prices. The degree to which prices are affected, however, depends on the elasticities involved. These, in turn, depend upon psychological and political factors and technical restraints. Since measures of very many of these factors are not available, we shall have to content our selves with testing various plausible empirical proxy variables. 239 Specification of empirical tests on factors influ encing the movement of prices. 1. Real factors. The degree to which employees are willing to press for wage increases and the necessity for management to grant such increases depends to a large extent on the level of employment. This is not likely to be a smooth and stable relation since so many other intrac table factors, such as expectations, are involved. In the hope of accounting for some of these influences, however, we shall include a measure of the level of unemployment in our preliminary tests. In a very rough way, this measure of the unemployment of the human labor force will serve as an index of the level of employment of all factors of pro duction and as a measure of the degree of restraint imposed on the expansion of real output by the current use of pro ductive capacity. The level of employment of capacity, however, is not the sole factor influencing the ability of real produc tion to absorb increases in aggregate demand. Among the other important factors, it is likely that the rate at which demand is increasing or, more specifically, the rate at which producers are trying to expand output to meet those increases in demand, will have a significant influ ence on the degree of restraint imposed on that expansion by bottlenecks and other technical restraints. The need 24 0 for rationing by price increase will depend on these same factors. Therefore, we shall also include a measure of the change in the level of real output within our tests as a proxy for a measure of the pressure existing to expand production. There is another rationale for including this meas ure in our equation. Several economists ’ have pointed out that certain "structural shifts" in an economy may lead to price increases under specific conditions. Charles Schultze,®2 for example, postulates that in a dynamic, growing economy, characterized by fairly long term contrac tual wage agreements and a general inflexibility of wages and prices in a downward direction, you can expect to have some inflation even at a relatively high level of unemploy ment. These price increases, which may be expected to be fairly mild and never the cause of runaway inflation, re sult from the fact that expanding industries will be in duced to raise wages and prices to attract the labor (usu ally, skilled labor) necessary to continue its desired rate of growth. In an economy characterized by downward price rigidity, this will lead to a net increase in the price 62charles L. Schultze, "Recent Inflation in the United States," Study Paper No. 1, Study of Employment, Growth, and Price Levels. Joint Economic Committee, 86 Cong.^ Tst sess~ 15)59 (Washington: Government Print ing Office, 1959), pp. 4-10. 241 level since the increase in the expanding markets will not be offset by corresponding decreases in prices and wates in the declining markets. The change in the level of in come included in our equation will pick up some of these effects since it serves as a measure of the expansion of industry. 2. "Monetary" factors. One of the most important tests we shall perform wil be to estimate the effects of changes in various monetary factors on the level of prices. The most obvious measure to employ is, of course, the change in the money stock itself. Our use of a "mixed mode" in our estimates permits us to include the change in the nominal level of money balances within our tests in the same equation with the real income variable. This should assure that the monetary influences are picked up by the monetary variable itself and not absorbed by the price level changes in the income variable. These price level effects in the income variable will hopefully have been removed by our process of deflation. We know that the sep aration of these empirical effects will not be complete but we hope we have succeeded in separating them to a fairly large extent. What little knowledge we already have on the mecha nism by which monetary changes affect the price level indi cates that lagged monetary changes rather than current 242 changes will be the determining factor in current price movements. We shall experiment with several lagged values of the change in the money stock and choose our final model strictly on the basis of our empirical results. In addition to the change in the level of nominal money balances, we shall test certain money related meas ures in our equation. Specifically, we shall substitute the policy variable introduced above, the adjusted change in unborrowed reserves, to test the direct effects of Federal Reserve action on the price level. Lastly, we shall test the effects of past price in creases upon movements in the current period. We do this for two reasons. First, on the assumption that expected price increases can lead to actual price increases because of the behavior they induce— panic spending, speculation, etc.— we include the lagged value of price changes in the economy. This variable here serves as an expectational variable under the assumption that current expectations are formed on the basis of extrapolation of recent experience. Second, there are cumulative effects to price increases. This is postulated on the grounds that on-going inflation weakens the resistance to further inflation because people get used to tailoring their expenditures and investments to an inflation economy. Likewise, large wage and price in creases in one important sector of the economy will cause 243 similar inflationary contract demands by labor unions in other sectors and corresponding anticipatory or consequent price increases by the producers in those sectors. Specification of the dependent variable. Similar considerations based on the special characteristics of a highly developed industrial economy and the realization of the severe inadequacy of our knowledge about the precise lags involved in the pricing mechanism, leads us to take a "longer view" in this equation than in the rest of our model. Rather than focus on quarterly changes in the level of prices, we shall specify the annual rate of change in the price level as our dependent variable. Thus, ~ ^T-4 <AP/P) = A pT-4 Our explanatory variable shall have to be measured in a similar fashion. Thus, <ay)t = (yt - yt_4) 4 r (UNEMP) i*0 q T-i (UNEMP)T = ---------------- (AM) T-i - (^.i - M^.^) The lags specified on our dependent variable when it is specified as an explanatory variable wil be quarterly lags. Hence, we test the following equation: <&P/P>T = an .1 + a11.2*aP^P*T-l + all-3*iY*T + a ! ^ . 4 (aM)t_i + aii>5<miEMP)T We present the results of our empirical test on various forms of the price adjustment equation in Chapter CHAPTER V REVIEW OF THE MODEL AND METHODOLOGICAL PROBLEMS INCURRED IN ITS ESTIMATION The Complete Model The aim of Chapter III was to investigate the be havior of various economic agents in determining their desired stocks of the several money related variables which either provide or absorb commercial bank reserves. This analysis included the specification of demand relations for currency, demand deposits and time deposits on the part of the public, demand relations for excess reserves and bor rowings on the part of commercial banks, a presentation of a consistent accounting framework relating all these vari ous measures, and a review of the implications involved in our decision to assume unborrowed reserves supplied by the Federal Reserve to be exogenously determined. In Chapter IV, we turned to a specification of the behavioral rela tions which determine aggregate expenditures and interest rates and a technical relation describing the movement of prices in the economy. For both the "stock" demand rela tions of the monetary sector and the "flow" demand rela tions explaining expenditures in the real sphere, portfolio 24 5 245 adjustment theory and the conception of sector wealth as a major constraint on behavior formed the basis of our anal ysis. We consider each relation postulated to include the most important factors in the economy which influence the dependent variable. We do not consider these relations to be exact specifications of the observed facts of reality, however. Since the variables which we can actually measure will never be precise representations of our theoretical constructs and since we must admit the existence of a myr iad of unspecified factors which influence the determina tion of each of our endogenous variables (hopefully, in some minor way), we substitute for the models derived above, models which include stochastic error terms to represent these unspecified influences. In this way, we take spe cific account in our assumptions of the fact that the fac tors determining our dependent variables are partly unknown to us. Data employed in our estimates. In our estimation process, we employ seasonally adjusted quarterly figures for our variables. Our data extends from 1948-III to 1962-IV. The use of annual first differences of some of our variables restricts our final estimates to the period from 194 9-III to 1962-IV. Hence, we employ fifty-four observations in our final regressions. 24 7 Though the use of quarterly data provides four times as many observations as annual data, it does not actually increase the number of degrees of freedom by the same amount. This results from the fact that trends and seasonal patterns present in the data reduce the extra amount of new information which quarterly figures actually provide. The seasonal adjustment of our data also consumes several degrees of freedom, though we cannot be certain ex actly how many are lost in this process. We have chosen seasonally adjusted data to use in our regressions in order to free ourselves of the burden of estimating seasonal parameters. We shall already have a great many parameters to estimate in our rather large model and the additional effort involved in estimating seasonal patterns does not seem worthwhile. We chose 194 8 as the starting point for our series as the earliest possible date which may be employed without running an undue risk of including postwar reconversion effects and other such war induced factors in our estimates. Our series stops at 1962-IV because of limitations imposed by the wealth data. Goldsmith's basic figures, upon which our own estimates are constructed, extend only as far as 1958. de Leeuw has taken some of these series up to 1962. In the absence of further extensions of this data, 1962-IV is the last date which we can employ in our estimates. 243 Although several major disturbances, such as the Korean War and the steel strike of 1959 occurred during the period covered by our data, we have made no systematic attempt to correct for these effects. The only structural change which we do attempt to investigate through the use of a dummy variable is the change in the definition of "legal reserves" which occurred in 1959-60. The "flow" variables of our model are measured as quarterly totals at annual rates. Some "stock" variables, (Wealth) and (WBUS), are measured as of the end of the current period; e.g., (Wealth)T is the measure of consoli dated net non-human wealth as of the end of period t. The money and money-related "stock" variables (reserves, de posits, currency) are measured as quarterly averages of daily figures. Interest rates (the bill rate, the rate paid on time deposits, the composite bond yield, and the discount rate) are computed as the mean values of monthly averates of daily figures. All dollar valued variables are measured in bil lions of dollars. Real values are derived by deflating nominal figures by the implicit GNP deflator (1957-59 = 100). Interest rates, unemployment, and the rate of change of prices are measured as percentages. The basic measure employed in our estimates is the "level" of the variable. The use of such a measure runs 24 9 the risk of introducing serious trend problems and problems of multicollinearity. We have tried some experiments with first differences, but we found the results quite sensitive to the timing of certain variables (first month of quarter, average over the quarter, etc.). Hence, we dropped the estimation of our model in this form as a goal of the pres ent study. The introduction of lag values in many of our equations has the effect of absorbing most of the trend in the level of the dependent variable. This does not, how ever, in any way reduce the problem of multicollinearity. Summary of the model. We now present the complete structure derived from the general relations postulated above. (1) (RE) rp = alx + a12(TD/TD + DD)T + a13(AY) + ai4(rD)T + a15<rB*T + a16 ) t + a17(DD + TD) T + Ux (2) (RB)(p = a2^ + a22 (fiY)^ + ^23^©)^, + a24(n)rp + a25<rD>T + a26<rB>T + a27<D& + TD) T + U2 <3> <DDadj>T = a31 + a32<Wealth>T-l + a33<rTime>T + a34 + a35 (AP/P) T + a36(rB)T + U3 250 (4) (CURR)t = a41 + a42(Wealth)T_1 + a43(rTime)T + a44(rB)T + a45(CNDS)T + a46(AP/P)T + U4 (5) (TDa(jj).j. = a ^ + a52 (Wealth) + a53 (?<ji^me) <p + a54(rB)T + a55(Ap/p)T + U5 (6) (CDUR)T = a61 + a62(Wealth)T_1 + a63(DDadj + CURR)T + a64(CDUR)T_1 + a65(rB)T + a6(J(AY) + a67(AP/P)T + U6 (7) (CNDS)t = a71 + a?2 (Wealth) (p_1 + a73<DDadj + CURR) T + a74(CNDS)T_1 + a75(r3^ T + a76^AY^T + a77(Ap/P)ip + U7 (8) (IPandE)T _ agl + ag2(WBUS)T_2 + a83*rC*T-2 + a84*Dif*T 4 + a85(IPandE)T_1 + z ag.i+4(YALM)^ + Ug 251 (9) <DINV)t = a91 + a92(Y)T + a93(AY)T + ag4(AP/P) + a95(rc)T + a g g d N V ) ^ . . ! + a97(UNFIL) + a98 t " * * Ug 4 (10) *rc*T = a10*l + a10*2^rB^T + Z a1 0 * i + 2 i + uio i=l (11) (aP/P)t — ^ . 2 ^ T-i all. 3 ( aY) + a11(4[ (DD + CURR) ] T + a11#5( UNEMP) T+ U n (12) (RC) ip — a12*l ^12 * 2 j-i ^ ap2 . 3 ( AY) + a12•4 ^ AP/P)t + ai2.5 trC^ T + U12 (13) (Y)T = (CDUR)T + (CNDS)t + (IPandE)T + (DINV)T + (RC)T + (EXOG)t (14) (YDISP)t = (Y)t - (TAX) t£ TD (15) (RA)t = (HM)T - (CURR)T - f i T . (TDadj)T • * TQ (17) (DDadj)T = (DDadj)T • (P)T The endogenous and exogenous variables may be defined as follows: Endogenous Variables CDUR: real expenditures on consumer durable goods CNDS: real expenditures on consumer non-durable goods and services IPandE: real gross investment in plant and equipment DINV: real inventory investment Y: real gross national product YDISP: real disposable income rc: Moody's composite rate on industrial bonds (AP/P): the annual rate of change in the price level DDadj: real demand deposits adjusted CURR: real currency holdings of the public TDadj: real time deposits at all commercial banks RE: nominal level of excess reserves held by commer cial banks RB: nominal borrowings of commercial banks from the Federal Reserve RA: reserves available to support demand deposit liabilities B the Treasury bill rate 253 DD: nominal level of demand deposits Exogenous Variables (Wealth): consolidated net non-human wealth of the public the value of corporate stock outstanding diffusion index of industrial production beginning of period level of inventory real exogenous income components of YGNP (WBUS): Dif: (INV) : EXOG: TAX: UNEMP (UNFIL) r. TIME TD TD+DD -1 rD * n : A0: A Y: (ALM) i : (YALM)±: real exogenous tax and other itemsin the defi nition of YDISP a four quarter moving average of the level of civilian unemployment in the economy real level of manufacturers' unfilled orders the rate of interest paid on commercial bank time deposits the ratio of commercial bank time deposit liabilities to total deposit liabilities New York Federal Reserve bank discount rate the rate of change of unborrowed reserves cor rected for reserve requirement changes net inflow of funds to commercial banks expected level of YGNP Almon variables calculated from past levels of short term interest rates Almon variables calculated from past values of the yield on business assets A complete description of all data sources and special cal culations appears in the Data Appendix on page 351. 254 Least Squares Estimates and the Specification of the Error Terms The complete "definition" of our model requires the characterization of the distribution of the error terms, u^, in order to derive meaningful results from our statis tical tests. Likewise, a listing of the specific assump tions which must be made to employ the method of ordinary least squares (OLS) will aid us in interpreting our own estimates, will demonstrate the danger of using this tech nique on interdependent relations such as those specified above, and will provide us with a basis upon which to judge the best method of estimation to employ in our model. Spe cifically, least squares regression will yield the best linear unbiased estimates of the parameters of a model only if four particular assumptions are satisfied by the dis tribution of the random term, u^, in each equation.^ These assumptions are as follows: 1. The observations on the independent variables in the regression equation are either fixed numbers (non-stochastic constants) or random variables dis tributed independently of the error terms. 2. The error term (ut) is distributed indepen dently with zero expectation, i.e., E(ut) « 0 3. The distribution of the error term has a con stant finite variance (homoscedasticity) and suc cessive values of this term are pairwise uncorre lated, i.e., E(uu') = < j2 ir where I is the unit matrix. ^E. Malinvaud, Statistical Methods of Econometrics (Chicago: Rand McNally & Company, 1§66), pp. 75-78. 255 4. The matrix of observations on the independent variables, Z, has rank K < N, where N is the number of observation. This final assumption means that the number of observations exceeds the number of parameters to be estimated and no exact linear re lations exists between any of these independent variables. In short, there is no problem of multicollinearity. The inclusion of the error term with our model and the specification of these assumptions about the distribution of that term, defines a distribution of each of our endoge nous variables corresponding to each set of values of the exogenous variables. Simultaneity and Least Squares Estimates In the light of these assumptions, it is obvious that the single equation least squares technique is inap propriate for the estimation of our model and would not yield the best linear unbiased estimates of our parameters. For, even if the other assumptions listed above were satis fied, the consideration of our relations within the frame work of a simultaneous equation system violates assumption number one. That is, some of the explanatory variables in our model are not distributed independently of the error terms in the equations in which they appear. It can be shown, for example, that the disturbance term and the ex planatory variable, YT, in the inventory investment equa tion are correlated with each other and a single equation 256 least squares regression will not yield unbiased estimates of the parameters involved. Estimation by Simultaneous Equation Techniques To minimize the bias in our estimates, therefore, we must employ an estimating technique which takes explicit consideration of the simultaneous nature of the relations included within our model. One such technique which cor rects for the interaction of the explanatory variables and the error term in each equation and which, in effect, "purges" these endogenous explanatory variables of the stochastic component associated with the disturbance term, is the method of "two stage least squares."^ This is not the only possible method open to us by which we may try to solve the problems caused by the simultaneous nature of our relations, but it does appear at the present time to be the most practical. Each of the alternative methods available have some serious drawbacks connected with them which make their use less desirable than the use of two stage least squares. For example, the method of indirect least squares is made impossible by the over-identified nature of our equations, while the "full information maximum likelihood" ^J. Johnston, Econometric Methods (New York: McGraw-Hill Book Co. , Inc., 1$63) , p. 2"3"6. 257 technique is too costly and complicated a method to be of much practical use. Likewise, a high degree of dependency of the optimal properties of full information maximum like lihood estimates upon the correctness of the a priori spe cification of the complete model has been demonstrated by several authors using Monte Carlo techniques.-* Thus, just as our assumption of linearity was based in part upon a lack of precise knowledge about the exact specification of our relations, so too, the very real possibility of speci fication error in our model leads us to reject the full information maximum likelihood method as a practical means of deriving the estimates of our parameters. The only method of estimation which presents a real alternative to us is the method of limited information maximum likelihood. But here too, questions of computa tional simplicity and a comparison of the small sample properties of this technique with the properties of two stage least squares estimators leads us to favor the latter method for our purposes. Though mathematical intractabil ity has prevented the derivation of very many general re sults on the small sample properties of these simultaneous equation estimators, the use of Monte Carlo techniques has 3Ibid., p. 293; and Daniel B. Suits, The Theory and Application of Econometric Models (Athens: Center of Economic ResearcK", 1963) . 258 permitted a certain amount of conjecture on these proper ties. A rather complete review of some of the most impor tant Monte Carlo studies done to date appears in J. John ston's Econometric Methods. The results of these studies are not completely consistent and do not allow a unique judgment on the choice of a particular estimator. However, they do indicate a slight superiority of two stage least squares over limited information techniques for the estima tion of both the structural parameters and the reduced form equations. In the studies presented, this superiority is maintained for models constructed both with and without specification error. Using as criterion the "root mean square deviation," a measure which takes account of both the bias and the standard deviation of the estimate, the two stage least squares estimates presented in studies by both Basmann and Summers were invariably "better" than the estimates derived from limited information methods.* Thus, as Johnston notes in his summary of these results, though exception can easily be found, "the choice among the . . . 4R. L. Basmann, "An Experimental Investigation of Some Small Sample Properties of GCL Estimators of Struc tural Equations: Some Preliminary Results" (General Elec tric Company, Handford Laboratories, Richland, Washington, November, 1958). (Mimeographed.); and R. Summers, "A Capital Intensive Approach to the Small Sample Properties of Various Simultaneous Equation Estimators" (unpublished paper, 1962). These studies are reviewed in Johnston, op. cit., pp. 278-295. 259 methods would appear to be two stage least squares first and limited information maximum likelihood second . . . These results and the arguments based on computa tional simplicity and convenience have led us to choose two stage least squares as our estimating technique. In judg ing the estimates derived from this method, we shall employ the usual statistical criterion. These include the coeffi cient of multiple correlation, R, the standard error of the regression coefficients and the standard error of the esti mates, S.E., and the Durbin-Watson statistic, D.W. Other Methodological Problems By estimating our model using a technique which takes explicit consideration of the interdependence in our postulated relations, we hope to correct for the lack of independence between some of our explanatory variables and the error terms. If all the other assumptions listed above were satisfied, we could expect to derive consistent esti mates of the parameters of our model through the use of this technique. However, we still have to face the prob lems posed by possible violations of the other assumptions. Multicollinearity. One of the most serious of ^Johnston, oj3. cit. , p. 294. 26 0 these problems which appears frequently in studies employ ing time series of the "levels" of variables is that of multicollinearity. This problem arises when some or all of the explanatory variables in an equation are so highly cor related with one another that it becomes very difficult to disentangle their separate influences and to obtain a rea sonably precise estimate of their relative effects. Though it becomes impossible to identify the effects of one of the variables alone in this situation, the estimates of the standard error of the total equation and thus, of the mul- £ tiple correlation coefficient, remain unaffected. Thus, this problem will result in some uncertainty in the inter pretation of certain elasticity measures, but it will not affect our interpretation of the explanatory power of en tire equations. Autocorrelation. Our second assumption above requires that the off-diagonal terms of the variance- covariance matrix of the error terms are all zero. If this assumption is not satisfied, we may expect three specific results. First, though the estimates will remain unbiased, the least squares technique will no longer assure that a ^Trygve Haavelmo, "Remarks on Frisch's Confluence Analysis and Its Use in Econometrics," Chapter 5 in T. J. Koopmans, ed., Statistical Inference in Dynamic Economic Models (New YorJT: John Wiley and Sons, 1950) . 261 minimum sampling variance will be attached to the esti mates. Second, the application of the usual least squares formulas for the sampling variances of the regression coef ficients is likely to yield a serious underestimate of these variances. Third, our predictions will be ineffi cient, that is, they will contain needlessly large sampling variances.' Tests for the presence of autocorrelated distur bances shall be made through the use of the Durbin-Watson statistic. Though exact significance levels are not avail able , tables have been prepared which give the upper and lower bounds of the statistic for several levels of signi ficance, given the number of observations (N) and the num ber of independent variables (k). For example, for various figures relevant to our study, the upper and lower bounds at the 5 per cent level of significance are given as follows:® k = 3 k = 4 k = 5 dL du dL du dL du N 55 1.45 1.68 1.41 1.72 1.38 1.77 60 1.48 1.69 1.44 1.73 1.41 1.77 ^Johnston, oja. cit. , p. 294. ®J. Durbin and G. S. Watson, "Testing for Serial Correlation in Least Squares Regression," Biometrika (Dec., 1950 and June, 1959). See June 195l"i pp. 173-175. 262 We shall present the results of our calculations of this statistic with our regression results in Chapter VI. Methodological problems introduced by the use of a "Mixed Mode." One last methodological problem remains to be discussed before we turn to the actual results of the estimation of our model. As we have noted above in Chapter I, we shall attempt to more faithfully portray the re sponses postulated by economic theory by estimating the commerical bank behavioral relations of our model in nomi nal terms and all the other structural relations in real terms. Thus, we assume that no "money illusion" exists in the relations determining expenditures in the real sphere or in the relations explaining the public's desire for money and time deposits. This is precisely the framework used by Pesek and Saving in their exposition of the basic Keynesian model. As they note, In the money market, equilibrium requires that the demand for real money for transactions purposes . . . plus thedemand for money for asset purposes . . . be equal to the real money supply, ms. This real money supply is definitionally equal to the nominal money supply, Ms, deflated by the price level P.9 In our own model, this has been formulated as follows: ^Boris P. Pesek and Thomas R. Saving, Money, Wealth and Economic Theory (New York: The Macmillan Company, 19677") 3T DDadj = DD[Wealth, r, (ap/p ), ay] CURR = h[Wealth, r, CNDS, (aP/P)3 CURR = CURR • P DD = g(RA, RB, RE) = DDadj * p where "barred" variables represent nominal values. This particular formulation of our model in a mixed mode could conceivably make the effective transforma tion of the structural equations of the model into reduced forms impossible. For, since the price level enters the system as an endogenous variable, it cannot be used to de flate current valued exogenous variables which appear in the reduced forms. This would involve including an endoge nous variable in the reduced form system and would defeat the purpose of using the reduced forms to eliminate the stochastic component from the endogenous variables which appear as arguments in the structural equations. A glance at the list of exogenous variables pre sented above indicates that this will cause no praticular problem in our case, however. For, of all the dollar valued variables which appear in that list, only the "TAX" measure and the "EXOG" measure could possibly lead to dif ficulties. All the other variables which appear either enter as lagged values directly, such as (Wealth)and 264 (WBUS)t_i, or are calculated on the basis of lagged values, A such as (y )t * We can dispose of the problem posed by the presence of the "TAX" variable by eliminating it from our final model. Since (YDISP)T = (YGNP)T - (TAX)T, a stable proportional relationship between the level of taxes and the level of gross national product will allow us to sub stitute (Y)t for (YDISP) i j i in our consumption functions. That is, if (YDISP)T = (YGNP)t - (TAX)t and (TAX)t = T (YGNP)T then (YDISP)T = (YGNP)^ - T(YGNP)T = (1-T) (YGNP)t Empirically we find that although tax rates have changed several times over the period covered by our data, these changes have been such that a fairly stalbe proportionate relation has in fact been maintained between total tax collections and the level of gross national product. This result appears to indicate that we may safely substitute (Y) for (YDISP) in our consumption functions and thereby drop equation fourteen, the definition of (YDISP), from our model and the (TAX) variable from our reduced forms. Thus, the only current period exogenous variable which appears in the reduced forms in deflated terms is 265 "EXOG," the exogenous expenditure component of YGNP. How ever, we hope to show that this presents no difficulty, for the largest single component of income expenditures defined within this exogenous term in our model is real government expenditure (GOV/P)^,. But it can be argued that the gov ernment does in fact determine real expenditures in its budget and not nominal expenditures. That is, in most cases, short period price fluctuations do not affect the proposed purchases of the government. This implies that the actual decision variable for the government is (GOV/P)T, the deflated term, not (GOV)T, the nominal term. The real value of government expenditures is thus independent of short period fluctuations in the price level, P. A small increase in p will lead to a similar increase in nominal government expenditures, (GOV)T, rather than to a cancella tion of expenditures. Consequently, real government expen ditures (GOV/P)t remain unaffected by the change in the price level. The validity of this assumption seems quite reasonable in a short period (quarterly) model such as this one. On the basis of this reasoning, we include the deflated value of government expenditures within "EXOG" in our model with few misgivings and expect that this will cause little, if any, bias in our final estimates.10 10See the treatment of this problem by Gerhard Tintner and B. von Hohenbalken in their "Econometric Models of the OEEC Countries, the United States and Canada and Their Application to Economic Policy," Weltwirtschaftliches Archiv, LXXXIX (1962), 29 ff. CHAPTER VI A PRESENTATION OF OUR RESULTS Before presenting our final empirical results, we must mention certain modifications which were made in the structure of our model on the basis of preliminary tests. The most basic changes made in our initial structure affect the specification of the plant and equipment expenditures equation. In both single equation regressions and in ex periments within the simultaneous equation framework, when the current measure of the long term interest rate is in cluded in an equation of the form originally specified, the coefficient of this term lies in the range from -.240 to -.270. These values are consistently less than one-half the values of their respective standard errors. When this measure is lagged two quarters, however, the coefficient is always at least three times the size of its standard error. Similar results are found in experiments with the "busi ness wealth" measure. Consequently, we have specified the lagged values of these variables in this equation in our final model. We have also decided to drop the "diffusion index" as an explanatory variable. Our tests indicate that this factor play an insignificant role in the determination of expenditures on plant and equipment. Its elimination 267 268 from our model leads to only very small changes in the coefficients of the other arguments in the equation and no significant change in any of the criterion statistics. The total effect of these changes has been to make business expenditures on plant and equipment a function of solely exogenous and predetermined variables. Consequently, the specified equation becomes a reduced form in our final model. While this change destroys one of the current links between our "real" and "monetary" sectors, it has the de sirable property of greatly simplifying the reduced form structure of our simultaneous system. Our second modification concerns the inventory in vestment equation. Our original specification of this equation included a calculated measure for the expected A level of income (Y) and a measure of manufacturer's un filled orders. Our tests indicate that the measure we con structed to represent the expected level of income (derived on the assumption that businessmen expect the same growth rate in the level of income this period as occurred last quarter) shows little relation to inventory investment. This is not to say that expectations are not important in the determination of inventory investment. Rather, our proxy measure for income expectations is not sufficient to represent these expectations. In our regressions, when we include this measure along with the actual level of income, 269 its coefficient is negative and insignificant. When it is included in the equation in place of the actual level of income, the coefficient is positive but insignificant and the coefficient of determination is substantially lower than when (Y)T is included by itself. In all these cases, A the introduction of (Y) seems to absorb some of the effects otherwise attributed to the price change variable which itself appears to be a more important factor influencing expectations relevant to inventory decisions. The high A degree of correlation between (Y) and (Y) also leads to certain problems of multicollinearity. Since we have little basis upon which to place confidence in the assump tions governing the calculation of (Y), these results indi cate that our specific measure has failed to represent the true effects of business expectations and is best dropped from our final model. We also drop the measure of unfilled orders from our final model. Like the "diffusion index" in the plant and equipment expenditures equation, this measure should be treated as endogenous to our complete system if we wish to avoid excessive bias in our results. But since little explanatory power is lost by eliminating it, we shall drop it as an argument in the inventory investment equation. Thus, our final model specifies real income, the change in the level of real income, price changes, the long term 270 interest rate and the lagged inventory stock as arguments in our inventory investment equation. These modifications do not significantly affect the theoretical interpretation presented in Chapter IV. Our preliminary tests on the third element of gross investment expenditures, residential construction, indicate that although our results are rather poor, they are good enough to warrant the inclusion of this sector within our final model as an endogenous factor. We had previously de cided that the expansion of our model by the introduction of the great many exogenous factors seemingly necessary to achieve results in this sector comparable to the results derived from the specifications of the other sectors of our model was not warranted by the gain derived from ex plaining these expenditures. However, we have achieved moderately successful results by specifying an equation for this sector which includes as arguments only variables which already appear in other equations within our simul taneous system. We include in the final two stage least squares model an equation which postulates non-human wealth, the annual change in the level of income, the long term ■interest rate and the rate of change of prices as arguments in the determination of the level of residential construc tion expenditures. Real monetary wealth, judged on the basis of our preliminary tests to be an insignificant fac- 271 tor in the determination of these expenditures, shall not be included in our final equation. The last preliminary tests which we must report concern the specification of the bank reserve equations. These tests fall into three categories. First, we find no significant role for the composition of commercial bank deposit liabilities in the determination of the desired levels of excess reserves and borrowings. Our results in dicate that any effects which the differing liquidity char acteristics of time and demand deposits may potentially have on bank reserve behavior are either insignificant or already fully compensated for by the differing reserve re quirements imposed by the authorities upon these deposits. We calculated the ratio of time deposits to total deposit liabilities as a measure of the liquidity needs determined by the composition of the liability account and included this measure in our test regressions (single equation) on the bank reserve equations. Almost without exception, the sign of the coefficient of this term was contrary to what economic theory would lead us to expect. In no case was the coefficient as large as its standard error. The elimi nation of this term from these equations has little or no effect on the coefficients of the other terms included in the model. Our second set of empirical tests involved an at 272 tempt to investigate various forms in which the interest rate constraints postulated as determinants of excess re serve holdings and commercial bank borrowing may be speci fied within the basic limitations imposed by our assumption of linearity. These different forms were included in re gressions in which we tried several alternative specifica tions for the other arguments in these equations. These alternatives were tried in order to test the sensitivity of the interest rate constraints to the specification of these other factors. Regardless of what other arguments were included within these equations, the results on the inter est rate terms were always substantially the same. The results of these regressions on equations which contain all the arguments included within our final model are pre sented in Table I. The very different coefficients attached to the discount rate term and the bill rate measure in equation two in this table (and confirmed by equation one) indicate several things. First of all, these terms should probably not be combined into a single measure since they appear to exert very different degrees of influence on excess reserve holdings. Second, it is the "bill rate" which appears to be the more important factor influencing bank decisions on excess reserves. In all the cases tested, the coefficient of the discount rate was definitely insignificant and in TABLE I TWO STAGE LEAST SQUARE ESTIMATES ON VARIOUS FORMS OF THE INTEREST RATE CONSTRAINTS ON COMMERCIAL BANK HOLDINGS OF EXCESS RESERVES AND BORROWINGS (n ) t (A ©) (DD+TD) Dummy (1) (RE)T * 1.33 - .079(rBill) - .024(l/rDi )T (.027) 1 (.179) + .031 (.032) + .007 (.003) -.0034 (.0005) + .101 (.033) R = .942 SE = .041 (2) (RE) * 1.32 - .074(rBiU)T + .004(rDis_)T 1 (.028) (.033) + .035 (.033) + .008 (.004) -.0036 (.0005) + .103 (.024) R = .941 SE = .042 (3) (RE)tp = 1.58 - .223(rBill/rDi ) (.055) U1SC + .041 (.035) + .016 (.005) -.0048 (.0004) + .102 (.29) R = .927 SE = 0.46 (4) (RE)ip = 1.39 + • 090(rBisc_rBi 11) (.031) T ** +.050 +.017 -.0050 +.091 (.038) (.005) (.0005) (.030) TABLE I (Continued) (h)t (DD+TD) • £ Dummy (RB) (5) (RB)T = -.815 + .190(rRill)T + .879(l/rDisc)m (.076) Bl11 T (.550) DlSC T -.225 (.105) +.0014 (.0018) -.182 +.660 (.085) (.094) R = .917 SE = .141 (6) (RB)T = .175 + .376(rDisc)T - .395(rDisc)T (.082) U1SC T (.098) T -.177 (.093) +.0010 -.056 +.665 (.001) (.083) (.078) R = .935 SE = .125 (7) (RB)T = -.594 + .906(rBill/rDisc); (.107) T -.161 (.086) +.0003 -.150 +.571 (.001) (.067) (.062) R = .941 SE = .119 (8) (RB)T = 192 - .377(rDi - rBin) (.081) U1SC 1 ** -.172 (.091) +.0006 (.001) -.065 (.077) + .648 (.061) R = .935 SE = .126 ♦This is the measure employed by Meigs in his study of "free reserves. **Teigen employes (rBj^ - rD;£SC) in both his 1964 and 1966 models. t s ) - v l .u 275 some single equation estimations (see equation 6.1.11)^ the sign of the coefficient was opposite to that expected from theory. Seemingly, the alternative cost of holding excess reserves which the banks consider most important is the rate on short term government securities. This appears as the overriding constraint on excess reserve holdings. The discount rate appears to be an insignificant factor in these decisions. To keep these influences separate, we shall employ equation two in our final model. A very different result is achieved in our tests on commercial bank borrowing. In this case, the coefficients estimated in equations six and eight of Table I indicate that the bill rate and the discount rate are of roughly equal significance in the determination of bank borrowing. These rates, both when entered separately and when combined into a single measure, yield coefficients which are of the expected sign and significant at the 5 per cent level. For the sake of consistency with the excess reserve equation ^Stephen F. GoIdfeld, Commercial Bank Behavior and Economic Activity (Amsterdam: North Holland Publishing Company, 1966), p. 137. This work of Stephen Goldfeld, which has not been previously mentioned in this study, did not come to my attention until I had started to write up these results in Chapter VI. Consequently, it was of no benefit to me in the formulation or testing of my own models. Many of Dr. Goldfeld's results confirm our own findings. In later sections of this chapter, we present the elasticities derived from his model to indicate in a very sketchy way how his results compare with those derived in this study. 276 and in order to facilitate the calculation of elasticity measures for the supply of demand deposits, we shall employ equation six in our final model. Lastly, we included a proxy variable as a measure of the loan demand from banks. We tested a measure of the change in the level of income as representing general business activity in an attempt to isolate the effects of the strength of loan demand by bank customers on reserve holdings. The results of these tests seem to indicate that this proxy measure is not sufficient to characterize these effects. Hence, we drop this measure from our final estimates. I. ESTIMATES ON THE FINAL FORM OF OUR MODEL We turn now to a presentation of the empirical re sults of the estimation of the structural equations of our model. As already noted, very little is as yet known about the small sample properties of two stage least squares estimators. This presents certain problems in hypothesis testing with respect to individual coefficients or equa tions. The familiar t test of significance is particularly suspect. Goldfeld recently cited some evidence which sug gests that the usual t values calculated from TSLS esti mates tend to be somewhat conservative and to understate the significance of particular coefficients. In the ab sence of a more certain criterion, we shall place strong 277 emphasis on the a priori specification of the model (the signs of the coefficients, in particular) and we shall somewhat arbitrarily designate a coefficient value of at least twice its standard error as the "significance level" for the purposes of our discussion. By the usual test, with thirty degrees of freedom (a rough and conservative estimate for our model) the t statistic is 2.042 at the 5 per cent level of significance. If the evidence cited above is correct, our procedure will tend to understate the significance of our coefficients by an unknown amount. (The theoretically expected sign shall be noted above each coefficient when presenting our results.) In the following pages, we present the results of two least squares estimates on the structural equations of our model. The single equation estimates are designated by "primed" identifying numbers. (A table of the reduced form coefficients is available from the author upon request.) The Consumption Functions (6.1.1) (+) (+) (CDUR)t = -28.68 + .012(Wealth)T.i + .171(DD+CURR) T (.003) (.081) (-) (+) (-) -.394(aP/P)t + .063(aY)„ + .614(CDUR)T_, (.130) (.017 (.091) R2 = .932 SE = 1.55 D-W - 2.25 278 (6.1.1)' (CDUR)t = -27.10 + .012(Wealth)T_i + .159(DD+CURR)T (.003) (.080) -. 335 ( aP/P) rp + .063(aY)„ + . 609 (CDUR) T i (.124) 1 (.016) 1 (.090) R2 = .931 SE = 1.56 DW * 2.32 (6.1.2) (+) (+) (CNDS)t = -18.46 + .025(Wealth)T-1 + .077(DD+CURR)T (.012) (.064) (-) (+) (+) -. 260 (rB) + . 026 (aY) T + . 866 (CNDS) (.341) r (.014) 1 (.079) 1 ■ L R2 = .998 SE =1.32 DW = 2.15 (6.1.2)• (CNDS)t = -19.53 + .025(Wealth)T_i + .084(DD+CURR)T (.012) (.064) -.296(rB) + .026(AY)t + .868(CNDS)T_X R2 = .998 SE = 1.31 DW = 2.09 With the exception of the coefficient of (CDUR)T_^, all co efficients in both consumption expenditure equations have the expected signs. The highly significant positive coef ficient of (CDUR)T_^ contradicts our hypothesis that a high level of expenditures on consumer durables in one quarter acts as a drag on such expenditures in subsequent 279 periods. All coefficients in equation (6.1.1) and (6.1.1)' are significant and the Durbin-Watson coefficient indicates that the residuals are not autocorrelated. In the (CNDS) equation only the coefficients of (Wealth), (CNDS)T_1 are significant. The coefficient of (AY) is almost twice the size of its standard error. The Durbin-Watson test again indicates the absence of autocorrelation. Though the co efficient of the bill rate is not significant, we left it in our final model because it had the a priori expected sign. However, not even these weak interest rate effects could be found in various estimates of the (CDUR) equation. When the bill rate is added to this equation as it now stands and a regression is run on this form, the coeffi cient of (rB)T is +.315 with a standard error of .415. In this form, all other coefficients remain almost identical to what they are in the above relation. This elusiveness of the effects of credit conditions on consumer expendi tures is well documented in the empirical literature. We dropped the price adjustment variable from the non-durable and services equation. The results of the tests on this variable were as expected. In the (CDUR) equation, the coefficient of the price change variable is negative and highly significant. This corresponds to re sults obtained in survey studies of consumer buying habits. Though we may expect that in an economy with downward 280 price rigidity, when consumers saw prices rising they would rush to purchase durables before a further rise, this is not in fact the way consumers tell us they behave. In studies by Katona and Mueller, it was found that among those who expected prices to decrease, . . . only a slightly larger percentage thought that it was a bad time to buy than among those expecting price increases (53 per cent vs. 45 per cent). While there is some differential impact of price expectations, it is striking that people can simul taneously (a) expect prices to increase, yet (b) think it is a bad time to b u y .2 Since price expectations are formed on the basis of current experience, our results tend to support the results of these surveys. Another possible explanation for this negative co efficient in the (CDUR) equation is the fact that the price variable itself may reflect part of the impact of the real balance effect. The price increase leads to a de crease in purchases of consumer durables via its effect on real balances. However, this causes the price movements themselves to be highly (inversely) correlated with such expenditures. This view is confirmed to some extent by the fact that the coefficients of both the price variable and real balances are significant in equation (6.1.1) and 2 Gardner Ackley, Macroeconomic Theory (New York: The Macmillan Company, 1961), p. 292, citing G. Katona and E. Mueller, Consumer Attitudes and Demand, 1950-52 (Sur vey Research Center, Michigan State University, 1953), p. 25. 281 insignificant in equation (6.1.2). In the (CNDS) equation when the price variable is added, its coefficient is nega tive but always less than its standard error. This result reflects the fact that people generally have less discre tion over their total purchases of non-durables and ser vices than over expenditures on durable goods. In large measure, the former expenditures are for necessities or near necessities which are by nature less sensitive to price changes and the value of real money balances. In both consumption functions, non-human, non monetary wealth is seen to be a significant constraint upon consumption expenditures. Real money balances, again, are significant only in the (CDUR) equation. The importance of dividing wealth into its monetary and non-monetary compo nents and of disaggregating total consumption expenditures is seen in these results. The wealth elasticities, pre sented in the table below, differ significantly in these equations. These effects would be clouded if we had used aggregated measures. These strikingly different elasticity measures have some interesting implications. As we would expect, expen ditures on consumer durables are by far the more sensitive to the real value of money balances. Our figures indicate that a 10 per cent increase in the price level would de crease expenditures on consumer durables by 2.1 billion 282 TABLE II SHORT RUN ELASTICITIES* OF THE ON THE LEFT WITH RESPECT (DD+CURR) AND (WEALTH) VARIABLES TO (DD+CURR) (Wealth) CNDS .046 .176 CDUR .622 .505 ♦Calculated at the means of the variables. dollars this period as a result of its effect on the value of real money balances. This represents a decrease of more than 5 per cent in the level of expenditures. An addi tional decrease of nearly four billion dollars is indicated by the coefficient of the price change variable. How much of this effect is due to expectational factors and there fore of (possibly) short duration and how much is due to the effect of price changes on real balances is impossible to tell. The coefficient of the lag term in the (CDUR) equation indicates that the long run effects of these changes will be even greater than the short run elastici ties presented above would suggest. These effects will also be magnified by the changes in the level of income caused by the initial change in expenditures. These re sults imply a crucial role for real money balances and fluctuations therein in the determination of expenditures 283 on consumer durables. The Inventory Investment Equation (6.1.3) ( = ) (+) < + ) (DINV)T = 1.41 + .048(Y) + .199 (&Y)m + 1.181 (AP/P)T (.024) 1 (.038) (.216) (-) (-) ’ 1 *124(rcomp^ t ' -243(INV)t_1 (1.17) P T (.135) R2 = .807 SE = 2.23 DW = 2.12 (6.1.3)’ (DINV)t * 1.09 + .048(Y)t + .202(AY)T + 1.055(AP/P)T (.025) 1 (.032) (.188) 1 • 197 (r^omp) m — . 230 (INV) m_]_ (1.06) * 1 (.119) R2 = .819 SE = 2.16 DW = 2.26 In our estimates of the inventory investment equa tion, all parameters have the expected signs. The Durbin- Watson statistic indicates that we may reject the hypothe sis of positive autocorrelation in the residuals. One of the most interesting results in this equa tion is the highly significant coefficient of the endoge nous variable measuring the annual rate of change of prices. The capital gains potential of a steady rise in prices sig nificantly increases the inventory stock which businessmen 284 are willing to hold. Our figures indicate that an increase in the price level of about 1 per cent per year, such as occurred in the early 1960's in the United States, will increase the level of inventory investment by over one billion dollars per year. This sensitivity to price move ments and price expectations goes a long way in explaining the volatility of inventory investment expenditures. The other variables in our equations show varying degrees of significance. General business conditions as roughly indicated by the change in the level of income ap pear quite crucial to inventory investment decisions. On the other hand, the coefficients of the long term interest rate and the lagged inventory stock are insignificant, though the latter is just barely so. In other tests on this equation, when the bill rate was substituted for the long term rate, it too failed to show significance. Our results seem to show that potential capital gains reaped from price increases on goods in stock are a more important consideration in the determination of inventory investment than the cost of tied up capital. There appears to be a large element of speculation in inventory investment be havior. 285 Residential Construction Expenditures (6.1.4) (+) (+) (RC)m = 6.50 + .013(Wealth)„ . + . 095(aY)t (.003) 1 (.015) (-) (-) - . 238 (^P/P)T _ 2.109( r ) (.119) (.966) F T (6.1.4)’ (RC)t = 6.02 + .013 (Wealth) T + . 089(AY)T (.003) (.014) - .165( a P/P)T - 2.285(rc ) (.114) (.934) F T R2 = .59 SE = 1.52 DW = .62 In our residential construction expenditures equa tion, all coefficients are at least twice their standard errors and all signs attached to them are as postulated by our theory. Through the use of solely endogenous factors specified within the framework of the rest of our model, we have explained almost 60 per cent of the variation in the level of expenditures on residential construction. The Durbin-Watson statistic, however, indicates a very high degree of autocorrelation in the residuals and thus weakens the above results. These results appear to be the best we can do without expanding our reduced form structure to include several more exogenous variables. 286 Business conditions and "transitory income," as represented by (AY), appear quite important in the deter mination of housing expenditures. The effects of price movements and credit conditions provide an important link between these expenditures and the monetary factors in our model. The coefficients of the wealth and income change variables show almost no change in the two stage estimates from the single equation results. The coefficient of the price change variable increased (in absolute value) sub stantially and the interest rate coefficient declined by almost 10 per cent. These results are similar to those found in the consumption and inventory investment equa tions. There, too, price effects became stronger and in terest rate coefficients decreased when the equation was estimated as part of the simultaneous system. Business Investment in Plant and Equipment (6.1.5) ' (+) (-) (IPandE)T = 5.29 + .0159(WBUS)T_2 - 1 * 659(rCOmp>T_2 (+) + .857(IPandE)T_i + .022(YALM I)T (.017) - .029(YALM II)T + .010(YALM III)T (.014) (.014) + .001(YALM IV)T (.019) 287 R2 = .953 SE = .827 DW = 1.40 In our reduced form equation explaining expendi tures on business plant and equipment, the coefficients of the measures of business wealth, the long term interest rate and the lagged value of the dependent variable are all highly significant and have the theoretically expected signs. The Durbin-Watson statistic is in the indeterminate range indicating the possible presence of serial correla tion. The most interesting aspect of these results is that they demonstrate that a significantly negative coefficient for the interest rate term can be isolated in a properly specified equation. The results indicate that interest rate levels two quarters previous are crucial in the de termination of this quarter's investment in plant and equipment. We may compare these results with those presented by Hammer. Using annual data, 1915-1940, 1946-1961, he derived the following estimate:J ^Frederick Hammer, "The Demand for Physical Capital: Application of a Wealth Model" (unpublished Doctoral dis sertation, Carnegie Institute of Technology, Pittsburgh, 1963), p. 133. (iPand E)t = -1.43 + .0417(WBUS)T + .881 p — 1.165 ^ + . 417 (IPandE) R2 = .985 DW = 1.24 In his equation, p is his measure for the "expected” yield on assets. All his coefficients are statistically signifi cant, but the Durbin-Watson statistic suggests positive autocorrelation. In comparing these results with our own, we see that the use of quarterly data increases the coeffi cient of the lag term and decreases the coefficient of (WBUS). This is quite probably the result of the higher correlation between the dependent variable and its lag term in a quarterly than in an annual time series. Our use of the lagged value of the interest rate (the same measure employed by Hammer) has increased the coefficient of this term. This results from the fact that his annual data is less sensitive to the fairly wide changes which can occur in the level of interest rates over a period as long as a year. His estimate combines the more significant effects of lagged rates with the insignificant effects of current rates. In the table which follows we present a comparison of the short run and steady state elasticities derived from these two models. Our results generally confirm the results derived by Hammer. The much wider range evident in the short run 289 and steady state elasticities derived from our study re sults from the very high coefficient of the lag term in our equation. TABLE III INTEREST ELASTICITIES* OF BUSINESS ON PLANT AND EQUIPMENT EXPENDITURES Study Short Run Steady State Hammer -.422 -.726 Boorman -.196 -1.37 ♦Calculated at the means of the data employed in each study. Our results from the use of "Almon" variables cal culated on the basis of past values of the yield on busi ness assets are rather disappointing. Only one of the four coefficients of these variables is significant. One of them is clearly insignificant. This may result rom the restricted way in which we calculated these variables and the assumptions which we made concerning the lag structure (see the data appendix). These assumptions were made on the basis of certain suggestions derived by Dr. Hammer from his results, but they have little a priori justification. However, since no experimentation was done to test various forms of these variables in our model, it is quite likely that substantial improvement could be achieved with some change in these assumptions and in the form in which the lag structure is specified. The Term Structure Equation (6.1.6) <rcomp>T = 1'71 + (;o38) (,:b)T + .081(ALM II)T (.006) + .026(ALM (V)T (.005) R2 = 976 SE = (6.1.6) (+) ^rcomp)t = *294 (rg)^ (.034) + .081(ALM II)T + (.006) + .026(ALM IV)T (.005) R2 = .979 SE = + .047(ALM I)T (.026) .067 (ALM XXI) m (.005) 109 DW = .783 + .045(ALM I)T (.024) . 069 (AIjM 111) T .005) 102 DW = .599 With the exception of the presence of autocorrela tion indicated by the Durbin-Watson statistic, our results in estimating the term structure of interest rates equation 291 are highly successful. Four out of five of the coeffi cients are significant. The fifth coefficient is almost twice its standard error. The results of the single equa tion least squares estimation are almost identical to the estimates derived from the two stage least squares model. The very excellent fit of our estimate, as indi cated by our criterion statistics, seems to be directly attributable to the use of "Almon variables" in the estima tion of the lag structure. de Leeuw's work on the Brookings model contains one of the most successful attempts to estimate a term struc ture equation prior to the presentation of the Almon tech nique. A comparison of our results with those presented by de Leeuw indicates the power of this new technique. Esti mating his model with quarterly data for the period 1952- I960, de Leeuw's method yields an equation with an R = .55 and a standard error of .376. This compares with our sta tistics: = .976 and SE = .109. de Leeuw's method is essentially one of empirical experimentation to find a suitable lag structure to represent the formation of expec tations. The Almon technique assures the estimation of the "best" lag structure given only the degree of the polyno mial assumed to represent this structure. The flexibility of this technique provides a much wider range of experimen tation than was previously available. The superiority of its estimates is evidenced in our results. Our estimate is very similar to those presented by Teigen (1966) and Modigliani and Sutch who employ the same technique. Their tests with the Durbin-Watson statistic, however, indicate no autocorrelation. The only difference between our model and theirs is in the choice of the time period and the measure used to represent the long term rate of interest. An investigation of these differing interest rate measures and the form in which they are employed in the equations suggests that the choice of this variable could not have led to such divergent results. Hence, this difference must be due to the choice of the time period. When we investigate the residual pattern derived from our results, we find that our estimates seriously understate the actual value of the long rate in the period from 1949-11 to 1952-1. This was the period when the rates on govern ment securities were pegged by action of the Federal Re serve at very low levels. It may well be that in the for mation of their expectations about future interest rates investors made adjustment for what they knew to be arti ficially low short term rates which could not be maintained under normal circumstances. We tested this postulate by reestimating our equa tion over a period which clearly excludes the effects of the support program of the Federal Reserve: 1953-1 to 293 1962-IV. Our results confirm our hypothesis. (rcomp>T " 1-48 +/*^?,(rB)T + *°fO(ALM I)T + 087 (ALM II)T * (.021) (.015) (.004) + .075(ALM III)T + .034(ALM IV)T R2 = .990 SE = .060 DW = 1.77 The Durbin-Watson statistic indicates that the autocorrelation in our original equation is due to the in clusion of the pre-accord period in our time series. The effects of this result on our estimates of the interest rate elasticities of inventory investment and residential construction are difficult to assess. The very high corre lation between the estimates of the long rate derived from our original structural equation and those derived from the equation reestimated for the 1953-1962 period, indicates that any bias introduced by these effects should be of a fairly small order of magnitude. The Price Adjustment Equation (6.1.7) (+) (-) (AP/P)t = .97 + .611(AP/P),p t - .058 ( aY) t (.097) 1 x (.023) (-) (+) - .04 7(Unemp)T + .285(DINV)T (.117) (.071) R2 = .802 SE = .855 DW = 1.61 294 (6.1.7)• (AP/P) = .39 + .740(AP/P)T_i - .019(AY)T (.089) (.017) 1 - .005(Unemp) + .134(DINV)T (.124) T (.055) R2 = .879 SE * .914 DW = 1.69 The results of our attempt to estimate a price ad justment equation indicate the need for further work along these lines. The signs of all coefficients except that of the change in income variable were as postulated above. The latter parameter was significant, but negative in sign. The Durbin-Watson statistic is very near the upper boundary of the range of indeterminacy, indicating the slight possi bility of autocorrelated residuals. Looking at specific parameters in the equations, we see that although the coefficient of the unemployment meas ure has a negative sign as expected, it is less than one- half the size of its standard error. This result was re peated in most of the tests which we performed on this equation. The negative coefficient of the income variable indicates that the more rapidly GNP increases, the lower will be the price increases (or the larger the decreasel). We had anticipated a positive coefficient for this term on the assumption that the change in the level of income would represent a proxy for the bottlenecks and technical 295 restraints incurred in trying to expand output. It seems, however, that this variable has picked up some of the ef fects of the level of unemployment. The level of GNP can expand most rapidly when unemployment is high; this is when prices remain most stable. It is more difficult to expand output when unemployment is low; this is when prices in crease most rapidly. Consequently, we find that the change in the level of income and the movement of prices are his torically inversely correlated. In another attempt to isolate the "real" influences on the movement of prices, we included the inventory in vestment measure in our equation. The interpretation of our results is somewhat difficult. While it may be postu lated that rapid inventory investment puts pressure on price sensitive wholesalers and other such groups, indi cating a cause-effect relation between these terms, it is just as likely that the same factors which lead to high in ventory lead to price increases and that the inventory in vestment measure simply serves as a proxy for these factors. This relation is further clouded by the fact that price anticipations formed on the basis of recent price movement experience influences the level of (DINV). The separation of these effects demands further investigation of this equation. One of the most disappointing results of our analy- 296 sis was the failure of our estimates to indicate any role for the nominal monetary factors of our model in the deter mination of the price level. The change in the nominal money stock, for example, invariably had an insignificant negative coefficient in our tests. So, too, with our meas ure of the adjusted change in unborrowed reserves. These results are doubly disappointing, for it was hoped that the estimation of our model in a "mixed mode" would allow the separation of these monetary effects from the real factors influencing price movements. These effects, however, have eluded us just as they have eluded most other investigators in this field. The great difficulty appears to be the specification of the actual lags involved in the monetary transmission mechanism. Some of the work done by Friedman along these lines has indicated that these lags may be of extremely long and unstable duration. None of his results, however, are particularly useful to us in our model. Hence, the actual effects of monetary movements on the price level remains an unanswered challenge in our work. In the presentation of some further results below, we shall have more to say about the price adjustment ef fects in our model. Money and Time Deposit Demand Equations 297 (6.1.8) (+) (-) <DDad^T = 7*32 + *0045 (Wealth)_ . - 1.116(r. . )_ ad3 T (.002) T_;L (.789) txme T (-) (-) (+) - .644 (r ) - ,149(AP/P) + .898(DDadj)„ , (.194) B T (.062) 1 (.048) J (+) + .012(AY)T (.007) R2 = .937 SE = .700 DW = 1.27 (6.1.8)' <DDad-i>m “ 7*88 + .0050 (Wealth) T_i - 1. 305 (rtime) T J T (.002) (.749) - .583(rB)T - .181(AP/P)T + .889(DDadj)T-l (.183) (.056) (.047) + .014(AY)m (007) R2 = .941 SE = .679 DW = 1.21 (6.1.9) (+) (+) (TDad j) t ~ —2.63 + .0037 (Wealth) + 1 • 18 0 ( «p (.002) (.989 (-) (-) (+) - . 719 ( ) _, - .054 (AP/P) T + 1.007(TDadj)T-1 (.252) " (.074) (.053) (-) - .090(CDUR)T (.052) R2 = .996 SE = .788 DW = 2.18 298 (6.1.9)' (TDadi>T = -2.43 + . 0036 (Wealth) _ . + 1.349 (r^-.) T (.002) T_1 (.948) - .753(rB)T - .084(AP/P)T + .992(TDadi)T , (.234) (.068) (.049) - .076(CDUR)T (.045) R2 = .996 SE = .778 DW = 2.16 (6.1.10) (-) (-) (CURR)T = 7.69 - .0010 (Wealth)™-. - . 032 (rf im(J „ (.0008) T 1 (.195) time T (-) (+) - .060(Ap/P)T + .800(CURR)T i (.026) (.084) R2 = .968 SE = .240 DW = 1.14 (6.1.10)• (CURR)t = 8.91 - .0011 (Wealth)., . - .057(rtime)T (.0008) T_± (.185) - .074(AP/P)T + .769(CURR)t_i (.023) (.076) R2 = .971 SE = .229 DW = .96 All variables in the money and time deposit demand equations are measured in real terms. The signs of all the coefficients in each of these equations are as predicted by theory, though not all coefficients are significant. 299 The Durbin-Watson statistic indicates that there is auto correlation in the residuals of both the demand deposit and currency equations. In the demand deposit equation the coefficient of the time rate is insignificant while the coefficient of the bill rate, at more than three times the size of its stand ard error, is highly significant. If we assume that the coefficient of (rt^me) is really equal to zero, this would indicate that short term market instruments, such as gov ernment bills, are closer substitutes for demand deposits than are commercial bank time deposits. The basis for this conclusion is extremely weak, however. The size of the time rate coefficient relative to its standard error, and the arbitrariness with which we must choose significance levels in TSLS estimates, indicate that some substitutabil ity does exist between time and demand deposits. We shall return to this point below. The significance of the wealth and interest rate coefficients and the lack of significance of the coeffi cient of the income variable lends some support to our hy pothesis that portfolio considerations rather than income flows are the primary factors in the determination of the level of demand deposits. The coefficient of the price change variable indicates the significance of the price sensitivity of the public's real holdings of demand 300 deposits. There may be a spurious element in this result since, with a constant nominal stock of demand deposits, a price increase would, by definition, reduce the real stock of such deposits. However, we have tried to reduce this element to a minimum by measuring price changes as the movement over the previous year and demand deposits as the average stock in the current quarter. Our result, there fore, implies that the current desired stock of demand de posits is determined by the public's price experience over at least the past year (experience which probably forms the basis for expectations of future price movements). Looking now at the time deposit demand equation, we see that the wealth coefficient is not quite significant at the 5 per cent level, but it is significant at the 10 per cent level. Both the wealth and interest rate measures appear as important constraints in our equation. Again, this is what we expected from our portfolio analysis. The coefficient of the income-expenditure variable, (CDUR), is not quite twice its standard error and it is actually nega tive in sign as we postulated. It is interesting to note that time deposit demand seems to have similar interest rate responses to demand deposit demand. In the time deposit equation, the bill rate is highly significant while the coefficient of the time deposit rate is just slightly larger than its standard 301 error. These results suggest that perhaps time deposits provide a "residual" outlet for funds. These balances do not seem to be particularly sensitive to their own yield, yet they are very sensitive to the rate paid on other short term debt instruments. We propose a different interpretation of the re sults presented in these equations. First of all, the close substitutability between demand deposits and short term market instruments may be due to the fact that there is always a possibility of gain from holding open market instruments for even a short term. Time deposits, on the other hand, must generally be held for an entire quarter before they yield a return. (It must be remembered that our data does not cover the recent experience with certifi cates of deposit.) Secondly, the failure of the time de posit yield to show significance in the time deposit demand equation is a result of the fact that the dividend rate on saving and loan shares, one of the very closest substitutes for time deposits at commercial banks, is very highly cor related with that yield. Thus, though time deposit hold ings may be very sensitive to the yield paid on those hold ings, the negative substitution effects represented in (rtime)' as a proxy for the rate on savings and loan shares, reduces the significance of the coefficient of this term. This interpretation cannot at present be tested explicitly 302 since quarterly data on rates paid by savings and loan associations and other such institutions are not available. The negative coefficient attached to the measure of consumer durable purchases in the time deposit demand equa tion is as we postulated. The purchase of an expensive durable good by a consumer not only reduces the income available to be saved in deposit form, but probably drains funds from previously accumulated deposits. It is well recognized that these deposits are in fact used by the middle income group as "temporary abodes" in which funds may earn some return while being "saved" for a specific purchase. The actual purchase of the good then diminishes these deposits. In the demand for currency equation, the coeffi cient of the wealth measure is negative, but only slightly larger than its standard error. This result was expected since the wealth variable serves as an excellent proxy for urbanization, financial sophistication and other such fac tors which tend to diminish the need for and the use of currency in the economy. The coefficient of the rate of interest paid on time deposits is negative, as it should be, but is highly insignificant. This same result is de rived when the long term rate, represented by the composite bond yield, is substituted for the time deposit yield. Cur rency holdings, it appears, are not sensitive to interest 303 rate movements. These results lend some additional support to the results already presented by Cagan. It will be noted that we have dropped the level of expenditures on consumer non-durables and services as an argument in our currency demand equations and substituted for it the lag term, (CURR)T_^. When the consumer expendi tures variable is included in the equation without the lag term, its coefficient is positive and significant. When the lag term is then included in this equation, the coeffi cient of the lag term takes on these characteristics while the coefficient of (CNDS)i j i declines to an insignificant level. The introduction of the lag term also reduces the standard error of the estimate by almost 100 per cent and raises the Durbin-Watson statistic from .25 to something greater than unity. The removal of the expenditures vari able then leaves these statistics, as well as all other coefficients, virtually unchanged. The price adjustment effects evidenced in our esti mates require some comment. The sensitivity of currency holdings to price movements is as postulated. It is at first surprising, however, that of the two deposit measures, only demand deposits appear significantly responsive to fluctuations in the price level. The different sensitivi ties of these deposit stocks to price movements may be due to the differing characteristics of the owners of the bulk 3 04 of these deposits. In general, time deposits are held predominantly by idnividuals of the middle income bracket. The bulk of demand deposits, on the other hand, are held by corporations and very wealthy individuals. In 1964, for example, 0.2 per cent of the demand balances, held in ac count of one hundred thousand dollars or more, held 35.1 per cent of all dollars owned by all individuals, partner ships and corporations. To some extent, then, we may ex pect that these demand balances are more carefully managed and are therefore more sensitive to price movements. The Bank Reserve Equations In order to facilitate the comparisons to be made among a fairly large number of parameters, we have listed the results of our estimation of the bank reserve equations in Table IV. We continue to designate the single equation estimates by a "primed" number. Below each of the single equation and two stage least square estimated in this table, we present another estimate which is identical to the one above it in every way except for the exclusion of the dummy variable. In the TSLS estimate of the excess reserve equation, (6.1.11), only the coefficient of the nominal stock of liabilities is contrary to our expectations. All other parameters, including the coefficient of the dummy variable. TABLE IV BANK RESERVE EQUATIONS Constant (rB^ t (rDJT (n) t (A©) T_x (DDtTD) T Dummy (6.1.11) (RE)t 1.32 -.074 (.027) +.0043 +.035 (.033) (.032) R2 = .885 SE = + .008 (.004) .042 DW = -.0036 (.0005) 1.90 + .103 (.026) (re)t 1.15 -.131 (.033) +.068 +.027 (.026) (.037) R2 = .847 SE = + .007 (.005) .048 DW = -.0025 (.0005) 1.30 (6.1.11)' (re)t 1.32 -.068 (.025) -.0025 +.038 (.031) (.032) R2 = .883 SE = + .008 (.005) .042 DW = -.0036 (.0005) 2.02 + .105 (.025) (RE)t 1.14 -.118 (.025) +.054 +.034 (.031) (.037) R2 = .841 SE = + .007 (.005) .049 DW = -.0025 (.0005) 1.45 u> o U1 TABLE IV (Continued) Constant (rB)T (rD)T (n) t (dd+td)t tRB)T-l Dummy (6.1.12) (rb)t .175 + .376 (.082) -.395 -.177 (.098) (.083) R2 = .874 SE = +.0010 (.001) .126 DW = + .665 (.078 1.51 -.056 (.083) (RB)t .189 + .391 (.079) -.426 -.169 (.083) (.080) R2 = .867 SE = +.0008 (.001) .128 DW = + .687 (.074) 1.47 (6.1.12)• (rb)t .107 + .303 (.077) -.320 -.208 (.095) (.096) R2 = .863 SE = +.0013 (.001) .131 DW = + .674 (.081) 1.54 -.089 (.085) (RB)t .224 + .335 (.071) -.372 -.196 (.081) (.095) R2 = .859 SE = +.0007 (.001) .133 DW = + .707 (.075) 1.51 w o C T i 307 are as postulated. The coefficient of determination indi cates that we have explained almost 90 per cent of the variation in bank holdings of excess reserves and the Durbin-Watson statistic is significant at the 5 per cent level. In the borrowed reserve equation (6.1.12), all signs are as expected from theory though the coefficients of the nominal stock of liabilities and the dummy variable are not significant. The Durbin-Watson statistic is in the indeterminate range indicating the possibility of autocor related residuals. Let us first look at our experiments with the dummy variable. We introduced this variable to test the hypothe sis that the inclusion of vault cash in legal reserves at the end of 1959 caused a structural shift in bank behavior leading to larger desired holdings of excess reserves. In the excess reserves equation, both in single equation and simultaneous form, estimation without the dummy variable leads to a highly autocorrelated residual pattern due to the serious understatement of excess reserve holdings in the 1959-1962 period. The introduction of the dummy vari able not only eliminates this autocorrelation, it also de creases the standard error and increases the coefficient of determination. This appears to be very strong evidence in favor of a structural shift. There is one complicating factor in the equation, however. This concerns the effect which the dummy variable has upon the discount rate coeffi cient in our tests. The introduction of the dummy variable reduces this coefficient to a highly insignificant level. The behavior of the criterion statistics, however, and a failure to find any evidence of a shift in discount rate policy or in bankers' attitudes toward borrowing in the 1959-1960 period when the vault cash change occurred, leads us to conclude that the significant coefficient attached to the discount rate variable in the regressions without the dummy variable is a spurious result. We conclude, therefore, that a structural shoft did occur, that the re gression with the dummy variable more accurately portrays bank excess reserve behavior, and that the discount rate has little or no influence upon commercial bank holdings of excess reserves. The results of our regressions in the borrowed re serve equation tend to support these conclusions. The in troduction of the dummy variable into this equation has only a very small influence on the coefficients of the other items in the equation and on the criterion statis tics. The relative stability of the discount rate coeffi cient and the low value of the coefficient of the dummy variable in these regressions is evidence that no signifi cant change in bank borrowing behavior occurred over this period. This supports our contention that the significance 309 of the discount rate in the excess reserve equation without the dummy variable is a spurious result. The size and sign of the coefficient of the dummy variable in the borrowed reserve equation indicates that the larger holdings of excess reserves stimulated by the inclusion of vault cash in legal reserves may have had a slight effect of reducing the need and desire for borrowing. In the discussion that follows# we shall employ the equations which include this dummy variable as the basis for our analysis. The parameter estimates related to the interest rate terms in our equations have some interesting implica tions both for theory and policy. First of all, the very close similarity between the coefficients of the bill rate and the discount rate in the borrowed reserves equation indicates the sensitivity of bankers to the relative values of these rates. In all borrowed reserve equations the coefficient of rD is just slightly larger than the coeffi cient of rB. This seems to indicate that whenever the bill rate (the market rate) exceeds the discount rate by a cer tain small margin, bankers will borrow from the Federal Reserve. This result presents strong support for the hy pothesis that bankers are sensitive to the profit potential of borrowing when market rates are higher than the discount rate. The similarity of these coefficients also lends sup port to the practice of combining these rates into a single 310 measure (such as a ratio or a difference) and using this measure in the regression equation on the theory that it is the relative value rather than the absolute size of these rates which determines bank borrowing. These results do not support a naive profit theory of borrowing, however. The significant negative term at tached to the variable measuring the adjusted change in unborrowed reserves indicates some support for the reluc tance theory. For it indicates that bankers will always use some proceeds from an increase in net unborrowed re serves to reduce their debt. The low value of this coeffi cient, however, and the relatively high value of the coef ficient of the lag term indicates that a strong profit potential caused by a divergence of the bill rate and the discount rate can overcome the basic reluctance of bankers to borrowing and may induce banks to remain in debt for some time, even in the face of an increasing stock of un borrowed reserves. These coefficients indicate that bankers change their borrowed reserve positions moderately slowly and do not rush to decrease debt as soon as unbor rowed reserves become available. There seems no doubt, then, that the profit motive must be included in any valid analysis of borrowing decisions. The parameter estimates of the interest rate terms in the excess reserve equation present a very different 311 picture. These results do not support the practice of com bining the bill rate and the discount rate into a single measure, since the discount rate appears to have little or no influence on excess reserve holdings in this equation. Rather, we may surmise that bankers consider the bill rate as the real alternative cost of holding excess reserves. There is also the possibility that the development of the federal funds market throughout the 1950's has influenced these results. The rate on federal funds has been closely related to the bill rate over this period. Our bill rate measure may well have picked up some of the effects of movements in the federal funds market and our estimated coefficient may thus be biased downward. It is impossible to perform a test on this hypothesis since the Federal Reserve has been collecting data on the federal funds mar ket only since 1959. In any case, our results seem to in dicate that the discount rate mechanism works primarily through its relation to bank borrowing and has little ef fect on the level of excess reserves. The coefficient of the variable measuring the net change in unborrowed reserves is positive as expected but is quite small and insignificant. This result seems to indicate that bankers do not use their excess reserve hold ings as the primary buffer against open market changes by the authorities. Rather, a comparison with the results of 312 this parameter estimate in the borrowed reserves equation indicates that it is borrowings and not excess reserves through which the bulk of adjustment to changes in unbor rowed reserves takes place. Our equations seem to indicate that the practice of combining the excess and borrowed reserves measures into the single category, "free reserves," will cloud and ob scure many of the basic relations involved in the analysis of bank behavior. In particular, combining our measures into a single regression equation would totally obscure the basic responses to bill rate and discount rate movements and make it impossible for the analyst to make unequivocal statements on the mechanism through which certain policy variables have their effect. For the same free reserve value results when banks hold 600 million dollars in excess reserves and 500 million dollars in borrowed reserves as when they hold 100 million dollars in excess reserves and no borrowings. Our results indicate that bank responses under these two very different circumstances would them selves be quite different. This could not be demonstrated through the use of the "free reserve" measure. The significant positive coefficient of the lagged value of the net inflow of funds to banks in the excess reserves equation indicates that banks are fairly sensitive to the rate at which the deposit and loan accounts change. 313 Holdings of excess reserves appear to serve as a buffer against short run changes in the rates at which deposits move in and loans move out. Since it is specifically the lagged value which appears as the determining factor in bank behavior, we may attribute a certain expectational character to this variable. Under these conditions, banks determine their need for excess reserves on the basis of recent experience with the flow of funds into and out of the bank. Our results are marred by the negative significant coefficient of the stock of deposit liabilities in the ex cess reserves equation. We combined time and demand de posits into a single measure since we had found that the composition of deposit liabilities had no visible effect on reserve holdings. We have not tested this equation with separate measures of the stock of time and demand deposits. A complete judgment on the structure of this equation should await this test. II. EVIDENCE ON SOME DISPUTED POINTS The money supply relation. Assuming unborrowed reserves to be exogenously determined, we can construct a demand deposit supply relation on the basis of our behav ioral reserve equations and the reserve identities. 314 (6.2.1) 1 1 <DE>adj) = (RA + RB - RE) A o DD where RA = (RU TD __ (RU - 5 •TD* * ) TD TD We shall concentrate only on demand deposits at member banks and so we drop < | > DD* the ratio of member to non-mem ber bank deposit liabilities, from our relation. We calcu late this relation at the mean values of reserve require ments on time and demand deposits over the period of our study. Thus: mean and „TD <5„ TD TD 5 mean These relations simplify our calculations. Since TD DD 0, n T = <ARU)t Ad + Ad Thus we substitute RUt = (RU)t_x + (ARU)T = rut_x + (n) T and (6.2.2) TD __ RA = (RUt_x + (n)T - 5 • TD • *TD) 315 At mean values, RA = 14.755 + n- Substituting equations (6.1.11) and (6.1.12) and our figure for RA into (6.2.1) we derive: (6.2.3) (DDadj)T = 83.29 + e.758(rB)T - 2.442(rdisc)T + 4 . 822 (n) T + .028(TD)T - .049 (4©),^ + 4.070(RB)t_1 - .973(Dummy) This represents the demand deposit supply relation derived from the two stage least square estimates of the bank re serve equations. The same relation derived from single equation estimates is: (6.2.4) (5Sadj>T = 83*03 + 2.266(rB)T - 1.950(rdisc)T + 4.623(n)T + .030(TD)T - .049(A©)T_1 + 4.133(RB)T-1 - 1.190(Dummy)T The short run elasticities of the supply member commercial bank demand deposits with respect to the bill rate and the discount rate are presented in the following table. These 316 results shall be compared with those of other investigators and with other results of our own work in the sections below. TABLE V SHORT RUN ELASTICITIES OF (DDadj) WITH RESPECT TO (rB) AND (rdisc7 (rB) (rdisc) structural .055 -.055 single equation .045 -.044 The similarity of these elasticities is most surprising and results primarily from the dominant role played by the in terest rate coefficients in the borrowed reserves equation in the calculation of the demand deposits supply relation. The coefficients attached to the lagged borrowing term and the term measuring the net change in unborrowed reserves are most reasonable in the light of results of other work carried out in this field and their similarity gives us confidence in the validity of our results. The interest elasticity of money demand. The re sults of the estimation of our wealth constraint model pre sent some interesting evidence relevant to one aspect of the dispute in the literature over the interest elasticity 317 of the demand for money balances. In both the demand de posit and time deposit demand equations, the short term interest rate represented by the rate on three month Treasury bills appears as a significant argument. This result contrasts sharply with the results presented by Professor Friedman and it adds another bit of evidence in favor of those who argue that the money demand function (regardless of the definition of money employed) is inter est elastic. The insignificance of the interest rate term in the currency demand equation does not invalidate this evidence nor our conclusions flowing from it. Rather, it simply indicates that the public views currency and demand deposits as different types of assets which perform dif ferent types of services. Hence, they determine their de sired stock of these assets on different bases. It is striking to note that if we combine the time and demand deposit variables into a single measure and add to their respective equations, the coefficient of the bill rate will be -1.36. This is highly significant. The rate of interest paid on time deposits, on the other hand, will drop out of the final equation since the coefficients of this term in the two component equations are roughly equal in size and opposite in sign. The near equality of these coefficients in these equations is very strong evidence that the practice of combining time and demand deposit 318 balances into a single measure, such as is done by Friedman and others, neutralizes much of the interest elasticity of these measures and eliminates any hope of analyzing the substitution effects which may exist between them. These results lend credence to the contention of his critics who claim that Professor Friedman*s failure to find a signifi cant role for the rate of interest in the determination of the demand for money is due not only to the statistical techniques which he employs but is also strongly affected by the basic measure he employs as his dependent variable. Simultaneous equation estimates vs. single equation results. We have attempted to reduce the bias in our em pirical estimates to a minimum by structuring our relations within a simultaneous system of equations which takes ex plicit account of the interaction of our endogenous vari ables. We have estimated each of our structural relations both within this simultaneous framework by the method of two stage least squares and as separate models by the method of ordinary single equation least squares. These estimates have been presented above. It is instructive to compare the results of these different estimation tech niques. We find that in both the real sphere expenditure relations and the money and time deposit demand functions of the monetary sphere, there is very little change in the 319 coefficients of the wealth variables, the income and expen diture variables, or the money stock variables between the, two stage least square estimates and the estimates derived from the ordinary least square regressions. The parameters which appear most sensitive to the estimation procedure employed are the interest rate coefficients and the coeffi cients attached to the price change variable. In Table VI, we have calculated the absolute change in the size of these several coefficients in each equation and the percentage change in those coefficients (and, therefore, in the elas ticities) between the single equations and the two stage least squares estimates. In moving from the ordinary least squares to the two stage least squares estimates, we notice three basic changes. First of all, the price sensitivity of the depen dent variable in the money and time deposit demand equa tions decreases, while the price sensitivity of all the expenditure variables increases. Second, with the single exception of the bill rate coefficient in the demand de posit equation, the coefficients of all the interest rate variables in the money and time deposit demand equations and in the expenditure relations are smaller (in absolute value) in the simultaneous model than they are in the same equations estimated by ordinary least squares. Third, there is a strikingly uniform increase in the coefficients 320 TABLE VI THE PER CENT CHANGE IN THE ELASTICITIES OF THE ENDOGENOUS VARIABLES WITH RESPECT TO VARIABLES LISTED FROM THE SINGLE EQUATION TO THE SIMULTANEOUS EQUATION ESTIMATES Endogenous Variable (AP/P)* <rBill)* (r . ) * v Time' ^rComp^ * ^rDisc^* CDUR +15.0 (.059) CNDS -3.8 (.010) DINV +10.7 (.127) - 6.5 (.073) RC +30.7 (.073) -8.3 (.176) DD -21.5 (.032) +9.5 (.061) -7.9 (-.189) TD -55.6 (.030) -4.7 (.034) -14.2 (.168) CURR -21.7 (.013) -78.1 (.025) RE** +18.9 (.014) RB** +19.4 (.073) +18.9 (.075) *The figure in parenthesis is the absolute change in the coefficient. **Calculated on equations which include the dummy variable. 321 of the interest rate terms in the bank reserve equations. The consistency of these results suggest the pres ence of some systematic factor which has brought about these changes. Though no specific judgments seem possible on the basis of this presentation, these results seem to support the contention that single equation least squares techniques may yield seriously biased estimates of the parameters of a regression equation. III. ESTIMATES OF SECTORAL SUBMODELS One of the major goals of this study has been the estimation of certain important monetary relations of the economy within the framework of a simultaneous equation model which includes expenditure relations of the "real sphere." This project was inspired by the suggestions that the neglect of the real sphere in a structural model of the monetary sector or, conversely, the neglect of monetary relations in a structural model of the real sphere, will lead to specification bias in the estimates of the struc tural coefficients. Our model presents us with an opportu nity to test the effects of such neglect. We have divided our model into two separate components, "real sphere" and "monetary sphere" submodels. The results of estimating each of these submodels as separate simultaneous systems are presented below. 322 The real sector. (6.3.1) (CDUR)t = -22.45 + .Oil(Wealth)™ . + .135(DD+CURR)T (.003) (.079) . 468 ( aP/P) T + . 059 (AY) T + .643(CDUR)ip , (.131) (.017) (.090) A_X R2 = .934 SE = 1.52 DW = 2.43 (6.3.2) (CNDS)t = -19.55 + .027(Wealth)T_i + .079(DD+CURR)T (.012) (.062) .333 (xrB) T + .032(AY) + . 853 (CNDS) t-1 (.329) (.015) 1 (.077) R2 = .998 SE = 1.29 DW = 2.16 (6.3.3) (DINV)t = .893 + . 033 (Y) + .219(AY)T + 1.138(AP/P)T (.028) (.039) (.227) - -617(r ) - .181(INV)_i (1.172) COmp T (.139) T 1 R2 = 1788 SE = 2.34 DW = 1.89 (6.3.4) (RC)t = 6.15 + .014 (Wealth) mi + .092 (AY) (.003) (.015) — 2.395(rcomp)m — .308 (aP/P)t (.928) * (.122) R2 = .583 SE = 1.51 DW = .567 323 (6.3.5) (r™ J T - 1.71 + . 294 (r ) + .04 5 (ALM I) + .081(ALM II) P (.034) B T (.024) (.006) + .069(ALM III) + .026(ALM IV) (.005) (.005) R2 = .979 SE = .102 DW = .599 (6.3.6) ( P/P)T = 1.98 + .395(aP/P)t_i - .133{AY)T (.110) (.029) .105(Unemp) + .544(DINV)T (.109) (.104) R2 = .832 SE = .788 DW = 1.25 The monetary sector, (6.3.7) <DDsd-i>m * 6.880 + .0049 (Wealth) T_! - 1.175 (rtime) Sd3 T (.0024) (.725) time T - .719(rB)T - .172(AP/P)T + .898(DDad^)T_, (.189) B T (.054) T (.045) ad3 T 1 + . 014(AY)m (.007) R2 = .945 SE * .654 DW = 1.30 324 (6.3.8) <TDadjJT = (6.3.9) (CURR)t = (6.3.10) (RE)T = (6.3.11) (RB) T = -2.298 + .0037(Wealth)T_, + 1.575 (r. . )„ (.002) (.948) time 1 .879(r ) - .084(AP/P)T = .978(TD_di) (.249 B T (.067) (.050) 3 .066(CDUR)T (.045) R2 = .996 SE = .765 DW = 2.09 8.913 - .0011(Wealth)T_^ - .057(rtime)T (.0008) (.185) .074(A P/P)m + .769(CURR)t_1 (.023) (.078) R2 = .971 SE = .229 DW = .961 1.333 - . 064 (r ) _ - .0060(1:^. )m + .040(n)„ (.038) B T (.044) disc T (.036) T + .0080(Ae)T_i + .108(Dummy)T - .0036(DD+TD) (.005) (.030) (.0005) R2 = .874 SE = .044 DW = 2.06 .081 + .277(rB)T - .295(rdlfic)m - ,219(n)T (.122) B T (.137) dlSC T (.111) 325 - .101(Dummy)T + .0014(DD+TD)t + .678(RB) - (.101) (.0017) (.089) T“1 R2 * .837 SE = .143 DW = 1.60 All variables in the real sphere submodel are measured in real (deflated) terms. The "mixed mode" is maintained in the monetary sector submodel. The real and nominal values in this submodel are related through the price level which is now treated as exogenous to the monetary sector. The data employed in these submodel estimates are exactly the same as that employed in the estimation of the complete model. Interest rates and real money balances are now exogenous in the real sphere expenditure relations; the price adjustment term and the income-expenditure variables are exogenous to the behavior relations of the monetary sphere. It is interesting to investigate the effects which the destruction of these intersectoral links has upon the coefficients and the elasticities of these various measures. In none of the equations do we find a singificant change in any of the coefficients of the wealth or income- expenditure variables. With the exception of real money balances in the consumer durables expenditure equation, all significant changes occur in the interest rate and price adjustment variables. The decline in the coefficient of (DD+CURR) in the consumption relation in the real sphere 326 submodel to a value less than twice its standard error presents a possible explanation of why some investigators have failed to find a significant role for this measure in models which postulate money balances as an exogenous vari able. A glance at Table VII will show that in comparing the results of the submodel estimates with those of the complete model, there is a slight increase in the interest elasticities of the deposit demand equations and rather sizeable decreases in the interest elasticity of the bank reserve measures. The expenditure variables show mixed results. For example, all elasticities of the inventory investment measure decline while those of the residential construction increase. There is a striking change in the size of the co efficients of the interest rate paid on time deposits in several of the equations in which it appears. In the de mand deposit equation, this coefficient increases very slightly from the complete model to the submodel. In the time deposit equation, however, it increases by almost 50 per cent and in the currency demand equation it almost doubles. In all these equations it remains less than twice the value of its standard error. These results indicate that the effects of the interest rate paid on time deposits may be overstated in the monetary submodel and that some 327 TABLE VII COMPARISON OF THE RESULTS OF SUBMODEL AND COMPLETE MODEL ESTIMATES Short Run Elasticities Model Complete: Short Run Submodel: Short Run Complete: Steady State Submodel: Steady State (DDadj) rB rT w -.012 -.018 .067 -.014 -.108 .073 -.119 -.172 .660 -.133 -.186 .715 <TDadj) rB rT W -.026 .036 .107 -.032 .046 .107 -.243 .332 . 989 -.266 .384 .885 (RE) rB rD -.242 .016* -.212 .022* (RB) rB rD 1.76 -2.09 1.30 -1.56 5.24 -6.23 4.04 -4.85 (DINV) rc Y -1.296 6.39 -.712 4.40 (RC) rC W -.386 1.053 -.438 1.134 ♦Highly insignificant. 328 of the substitution effects that would be attributed to fluctuations in this rate may in fact be due to income flows, expenditure decisions and price movements. The most drastic change in all our estimates be tween the complete model and the submodels occurs in the price adjustment equation. Though all signs remain un changed, the coefficients of the income, unemployment and inventory investment terms almost double, while the coeffi cient of the lag term declines by 35 per cent. We note also that the Durbin-Watson statistic declines to a level which indicates the definite presence of serial correlated residuals. These changes are reflected in the significant alterations which occur in the coefficients of the price change term in the other equations in which it appears as an explanatory variable. In all these cases, this coeffi cient increases (in absolute value) from the complete model estimates to those of the submodels. One possible interpretation of the substantial changes which occur within the price adjustment equation, may be that although we could find no specific structural relation between the monetary factors and changes in the level of prices, these factors had a very strong influence on price movements and influenced our estimates substan tially through the reduced forms. The elimination of the monetary influences from the reduced forms of the real 329 sphere submodel eliminates these influences. It may be noted, for example, that in the reduced form structure, the coefficients of RU, the stock of unborrowed reserves, and n, the adjusted change in those reserves, are both positive and significant in the price adjustment equation. A comparison of the estimates derived from the com plete model with those derived from the isolated submodels, and a comparison of each of these with the single equation estimates turns up no specific patterns upon which we may generalize these results. Though the existence of bias seems evident in these parameters, it is not easy to cate gorize it as to direction or causation. Hence, we must conclude that, although our results are instructive in demonstrating the sharp differences which can result in the values of parameters derived from different estimation pro cedures on the same structural forms, we cannot at this time isolate the precise character of that bias. IV. A COMPARISON OF RESULTS We conclude this chapter with a comparison of the results of our own study and the results of several other studies which have focused on related issues. To facili tate this comparison, in Table VIII we present some of the more important elasticity measures derived from the esti mates presented in these studies. We have included figures Study TABLE VIII— PART A ELASTICITIES3 "Mode" Data Definition of X Klein-Goldberger de Leuw (Brookings) Teigen, 1966 Teigen, 1964 Steady State Teigen, 1964 Short Run Teigen, 1964 Steady State Goldfeld Real Assumes homogeniety of dollar values Nominal Nominal Nominal Nominal Annual 1928-1941, 1945-1952 Quarterly 1949-1962 Quarterly 1953-1964 Annual 1924-1941 Quarterly 1946 IV-1959 IV Quarterly 1946 IV-1959 IV Quarterly 1950 III-1962 II Household liquid assets; business liquid assets <DDadj> (DDadj) ( D D a d j + C U R R ) ( D D a d j + C U R R ) ( D D a d j + C U R R ) (DDact> 330 TABLE VIII--PART A (Continued) Study "Mode" Data Definition of X Boorman Complete Model Short Run Mixed Quarterly 1949 11-1962 IV ( D I W Boorman Complete Model Steady State Mixed Quarterly 1949 11-1962 IV «®adj> Boorman Submodels Short Run Real in expendi ture model; mixed in monetary Quarterly 1949 11-1962 IV <DDadj> Boorman Submodels Steady State Real in expendi ture model; mixed in monetary Quarterly 1949 11-1962 IV <DDadj> Boorman Income Model Short Run Real in expendi ture model; mixed in monetary Quarterly 1949 11-1962 IV ( D I W TABLE VIII— PART B ELASTICITIES Study Demand for X Demand for Time Deposits Supply of Money* rBill rTime Y W rBill rTime Y W rBill rDisc Klein- Goldberger -.°7 -1.06 .174 de Leeuw -.35" -.17 -•37* .68 .25° -. 35c Teigen, '66 -.10 0.43 1.11 -2.82° 3.76 2.09 .14 -.10 Teigen, '64 -.196 .934 2.59 -1.16 Teigen, '64 -.017 .161 Teigen, '64 -.054 .51 .195 -.169 Goldfeld -.03 -.10 .86 -1.62 .37 .65 .22 -.08 Boorman -.012 -.018 .067 -.026 .036 . 107 .055 -.055 Boorman -.119 -.172 .660 -.243* .332* .989* .146 -.164 Boorman -.014 -.018 .073 -.032 .046 .107 .042 -.040 Boorman -.133 -.176 .715 -.266* .384* .885* .113 -.126 Boorman -.012 -.019 .066 -.029 .038 .166 aAll elasticities are derived from structural TSLS estimates— calculated at mean values. ^With respect to yield on private securities. u> Calculated at 1962 mean values. ^ ^Yield on long term government securities. eAll elasticities of supply presented for the current model are calculated from equations of the form (6.2.3). Th^ basic structural equations for RB and RE, i.e., those which include the dummy variable, were used in these calculations. ^The steady state elasticities in the TD equations are calculated to include only a two year adjustment period. The usual method of calculation leads to ex tremely high elasticities because of the size of the lag term in these equations. When calculated in this way, we derive figures very similar to those presented by Teigen in his 1966 model. 333 334 derived from the studies by Klein-Goldberger, de Leeuw, and Teigen which were reviewed in detail in Chapter II. We also include figures presented in the recent study by Stephen Goldfeld. From our own work, we have calculated elasticity figures for both the short run and the long run (steady state) from the complete model and from the mone tary submodel. We have also included elasticity measures calculated from an "income constraint" model which we have estimated. This last simultaneous equation model is iden tical in almost every respect to our "complete” model. Our only modification has been to substitute current real in come for the wealth variable in each of the behavioral relations which postulates non-human wealth as an argument. We hope that the results derived from this last model will help to clarify the basic relation between our wealth con straint model and the income constraint models estimated by Teigen and Goldfeld. It can be seen from Table VIII that except for the results on time deposit elasticities, our own results are quite similar to those derived by Teigen in both his 1964 and 1966 models and by Goldfeld in his recent work. Of these models, the Goldfeld model is structured most like our own. He includes within his framework, however, an explicit consideration of the supply of commercial bank loans. Teigen*s 1964 model which specifies and exogenous 335 "real sphere” is the smallest of these models. His 1966 model, like the Goldfeld model, includes a behavioral rela tion to explain the supply of commercial loans. He also includes within this structure, relations which explicitly treat certain policy variables (such as the discount rate) as endogenous. The major difference between both Teigen models on the one hand and our model and Goldfeld*s model on the other hand is Teigen's specification of a structural relation to describe the supply of money. Goldfeld treats this relation as we have treated it, through the specifica tion of bank reserve equations and reserve identities. The similarity evident in our results despite the use of different time periods and different structural forms speaks well for the stability of the basic interest rate relations which form the basis of all these works. The similarity between the steady state results of Teigen's 1964 model and our complete model, for example, are partic ularly striking. The only structural similarity in these models is our specification of the bill rate and the dis count rate as major constraints in the money supply behav ioral relations. But even here, the form of our empirical constraint differs. Yet, the supply elasticities which we calculated from these models are extremely close (the elasticities with respect to the discount rate do not dif fer significantly). Support for our thesis is also pro vided by the results of Teigen's 1966 model. The most seriously divergent results involve the supply elasticities derived from the estimation of Teigen's 1964 model on annual data. The very long period covered by those estimates undoubtedly contains several serious structural changes. In light of the evidence presented by all the other results, we need not concern ourselves too seriously with this one exception. CHAPTER VII SUMMARY AND CONCLUSIONS Our purpose in this study, as stated in Chapter I, has been to develop and test a macroeconomic model of in come determination which includes certain basic monetary relations of the economy as endogenous elements and which postulates "wealth" as a major constraint on expenditure and stock demand decisions. It was hoped that this kind of model would throw light on several specific issues. First of all, through the specification of bank reserve equations within the framework of our system we hoped to get some insight into the influence which commercial bank behavior has upon the determination of a given money stock. Second, we hoped to be able to isolate the wealth and real balance effects which influence the levels of expenditures in cer tain sectors. Third, through the integration of the "real" and "monetary" sectors within a single simultaneous equa tion system, we hoped to clarify the mechanism through which monetary changes affect the determination of aggre gate expenditures and the level of income. We estimated our complete model and the "monetary" and "real" sphere submodels derived from the complete model 337 338 by the technique of two stage least squares. We also pre sented results derived by estimating each of our structural equations by ordinary, single equation least squares. We employed real (deflated) data in all the expenditure and stock demand equations and nominal (undeflated) data in the bank reserve equations and the reserve identities. The introduction of this "mixed mode" posed certain problems in the reduced form structure. Through various substitutions, however, we managed to avoid most of these problems. The Bank Reserve Equations The conclusions presented by Meigs and DeWald have clearly pointed out the dangers of focusing upon "free re serves" as a policy target. Though this measure is used by the financial press as a guide to the current "posture" of monetary policy, the combining of two separate commer cial bank balance sheet items, excess reserves and borrow ings, to form the construct "free reserves" is both arbi trary and hazardous. This has been pointed out by Friedman. Consequently, in our own analysis, we have focused upon excess reserve holdings and bank borrowings as separate and distinct portfolio accounts and we have specified separate structural behavioral relations to explain each. Our re sults seem to indicate that these separate measures are indeed influenced by different factors and that, in those 339 cases where they are influenced by the same factors, the degree of influence is very different. Net changes in un borrowed reserves, for example, have a much stronger effect on commercial bank borrowings than they do on holdings of excess reserves. Estimation of a "free reserve" relation in place of the two separate equations which we have em ployed would make the isolation of these effects impossible. We have discovered these same results in investigating the effects of the different interest rate measures on bank portfolios. Through the combined use of our behavioral reserve relations, the definition of required reserves, and the bank reserve identity, we have calculated a money supply relation. This relation represents a money supply schedule which is dependent upon the given stock of unborrowed re serves and the arguments which determine bank borrowings and holdings of excess reserves. The similarity between the elasticities calculated from this derived relation and those calculated from Ronald Teigen's structural money supply equations (1964 and 1966) is most striking. Though our procedure provides a greater amount of information on the actual responses involved in discount rate changes, open market operations and other policy moves, the elas ticity measures calculated from our different relations in dicate approximately the same long run results of changes 340 in interest rates on the money supply (see Table VIII). The results derived by Stephen Goldfeld, who uses a tech nique very much like our own generally support our conclu sions . The Expenditure and Stock Demand Equations We derived the specification of our structural ex penditure and stock demand relations primarily on the basis of work done by other authors in postulating and testing single equation wealth constraint models of various sec toral relations. In our consumption, residential construc tion, and money and time deposit demand equations, we em ployed a measure of non-human, non-monetary wealth similar to that employed by Meltzer in his money demand studies. In the consumption and residential construction expenditure functions, we also included a measure of the public's real money balances. Wealth, then, rather than income serves as the unifying constraint in our income determination model. Our results show this constraint to be significant in all but the currency demand equation. In that relation, the coefficient of the wealth variable is negative, as postu lated, but insignificant. It should be noted explicitly that the tests of significance on our wealth constraint model provide us with a judgment on the performance of this model only relative 341 to the null hypothesis. Though an income constraint model almost identical in form to our wealth model was estimated, no systematic tests were carried out to compare the explan atory power of these two models against each other. The results from these two models were so similar (see Table VIII) that isolation of the effects of these two variables would have been extremely difficult. The similarity of these results seems to be due to several factors: the com mon trend in these two measures; the process by which the wealth series was interpolated to a quarterly basis; and the fact that the removal of one variable (wealth) from our rather large reduced form structure has little effect on our first stage estimates. In our estimates of the consumer durables, consumer non-durables and services, and residential construction equations, it was found that real money balances have a significant effect only in the durable goods relation. This result corresponds exactly to the result presented by Goldfeld. (He claims, however, that the measure of money balances included in his consumption relation is a proxy for the wealth measure.) There was seen to be little role for real money balances in the determination of housing expenditures. Our reduced form model of business investment ex penditures on plant and equipment was based upon the wealth 342 model of the demand for capital originally presented by Hammer. Our estimates have demonstrated a significant neg ative influence for the long term interest rate in the de termination of investment spending. The lag structure in this equation gives an indication of the time lapse in volved in influencing investment expenditures through the use of monetary policy to affect interest rates or of tax and fiscal policy to influence the expected yield on assets. The very high coefficient of the lagged investment term emphasizes the relative slowness with which these expendi tures adjust to current conditions. The results of tests on our disaggregated money de mand functions and our time deposit demand equation pro vided interesting evidence on a number of questions. The portfolio restraints, as summarized in the wealth and in terest rate measures, appear as significant arguments in all but the currency demand equation. Also, both money stock variables, currency and demand deposits, showed a relatively high degree of sensitivity to price fluctuations. This result, however, was not evident in the time deposit demand equation. One interesting result in this sector involves the specific estimates of the coefficients of the interest rate terms included within the time and demand deposit demand equations. Our results provided further evidence that both 343 demand and time deposit balances are responsive to move ments in interest rates. These same results also provided evidence on the mutual substitutability of these deposit balances. The size and significance of the coefficients of the rate of interest paid on time deposits in these equa tions gave some support to those who argue against the practice of combining these deposit balances into a single measure in empirical definitions of money. The relations between these balances seem to be such that this practice would totally obscure the interest rate effects on both of them and could well lead one to conclude that interest rate movements do not have a significant influence on "money” balances. In addition to general support for the portfolio approach to the study of these stock balances, our results further indicate that general business conditions have some slight influence on the demand for demand deposits. It further appears that strong substitution effects cause the level of expenditures on consumer durable goods to affect the public's holdings of time deposits. Monetary Influences in the Determination of Real Sphere Expenditures We may summarize the monetary influences in our model under three headins: interest rate effects, real 344 balance effects, and price level effects. These monetary influences are transmitted through our model in a variety of ways. The reserve demand relations, as determinants of the demand deposit supply relation, together with the de mand and time deposit demand relations, determine the short term market interest rate. This rate enters directly into the consumer non-durable and services equation (insignifi cantly) . Through its influence in the formulation of the long term rate in the term structure equation, it also en ters the residential construction and inventory investment equations. With a lag of two quarters, the long rate also enters the plant and equipment investment equation. Through this mechanism, changes in unborrowed reserves or other changes in the monetary factors influencing any of these relations, affect expenditure decisions and the de termination of the level of income. Real money balances appear to directly affect only consumer expenditures on durable goods. An increase in the real value of monetary holdings either through an increase in nominal balances (stimulated, for example, by a decrease in the discount rate) or through a decrease in the price level, will have the effect of increasing these expendi tures. It cannot be claimed that this is a mere proxy for "wealth" in our model since we have included the wealth measure directly. Consequently, it appears that we have 345 isolate the real balance effect. It is interesting to note that this effect appears as insignificant in the con sumer durables equation in the real sphere submodel which we estimated. This submodel treats monetary factors as exogenous. The mechanism and effect of monetary factors upon movements in the price level is much more subtle. The price change variable, as an expectational variable, ap pears as significant in the determination of expenditures on consumer durables, inventory investment, and residential construction. It is likewise important in the demand de posit and currency stock demand relations. The effect of a given change in this variable is obvious from the coeffi cient values presented above. The actual mechanism which causes price movements, particularly as this mechanism is related to monetary factors, is much less clear. We gain only some slight hints about this mechanism from our model. Most of our information is gleaned from the different esti mates obtained from the complete model and from the real and monetary subsector models. As noted in Chapter VI, though direct monetary influences could not be isolated in the structural price change equation, our overall results seem to indicate that monetary factors had a very strong influence on price movements through the reduced forms. Again, the exact nature of this influence is highly uncer 346 tain. The signs and significance of the monetary factors in the reduced form equation of the complete model on (ap/p)t indicate that reserve increases, whether borrowed or unborrowed, will stimulate price increases. Likewise, the coefficient of the dummy variable, which indicates larger holdings of excess reserves (decreases in the money stock) is negative, indicating a depressing influence on price increases. While these factors are difficult to in terpret directly, they do show that monetary factors, through some indirect mechanism, seem to be exerting a strong influence on price movements. This augurs well for success in further investigations along these lines. Thus, the importance of including these monetary factors in a model which purports to explain income deter mination seems clear. A comparison of the results of our complete model estimates with the estimates derived from our real sphere submodel give some indication of the extent of the bias which may result from ignoring such monetary factors. Suggested Directions for Future Research Certain characteristics of our results suggest some further tests which may be carried out within the basic framework of our model as it is presently specified. For example, the results of our estimates on the term structure 347 equation indicate that the autocorrelation in our initial results was primarily due to certain characteristics of the early years of the period covered by our data. The effects of this bias in our final results are unknown. It would be instructive, therefore, to test these effects. However, the loss of data points at one end of our series can only be made up at the other end of the series if the wealth statistics which are now available are brought up-to-date. The success of our model and the single equation models upon which many of our structural equations are based, cer tainly indicates that such an extension of these data would be worthwhile. It is also likely that significant improvement could be achieved in the plant and equipment investment ex penditure equation through experimentation on more flexible forms of lag structures to represent expectations on yields. This would involve tests on various polynomial forms and the calculation of various "Almon" structures to represent these expectations. Our results also indicate the desirability of fur ther tests on the role of deposit liabilities in the deter mination of excess reserve holdings and borrowings. The most obvious tests would involve a disaggregation of time and demand deposits into separate measures. The results of these initial tests would indicate further directions in 348 which to take this analysis. Lastly, the calculation of "impact multipliers" from our complete model may help to point the directions for future work to more effectively isolate the monetary influences on price movements. Our failure in this sector is one of the greatest weaknesses of the current model. Turning to more significant modifications which future analysis may make on the present structure of our model, we suggest the following. First of all, there are various indications that a fairly high degree of multicol- linearity exists in our model, particularly in the reduced form structure. The very high values of all of our 's xn the reduced form, for example, are particularly suspect. This problem is due in great measure to our use of "levels" of the variables to derive our estimates. Though these effects will not influence the overall explanatory power of any one of our equations, it does throw a certain amount of doubt on the interpretation to be afforded to individual coefficients. This would be particularly serious in the calculation of impact multipliers. Serious thought should be given to removing the trend in our variables through the use of first differences or some other such technique in order to reduce these problems of multicollinearity. Second, extensions of the present model might in clude the introduction of production functions for partic 349 ular sectors and the inclusion of the wage-price relation. This would allow us to resort to higher level hypotheses in the explanation of price movements. A more complete analysis of the commercial bank portfolio may help to clear up some of the weakness in our present structure. Our summary measure of portfolio changes, a©, is certainly only first step in a full exami nation of all the major accounts in the balance sheet. This extension should begin with a specification of behav ioral relations to explain bank holdings of various securi ties and a specification of supply and demand relations for commercial loans by banks. Goldfeld's work provides inter esting first steps along these lines. Lastly, it appears that there is still a great need to investigate the true character of the wealth constraint which actually imposes itself on the public’s expenditure and stock demand decisions. There is a need, therefore, for more theoretical and empirical work to be done to dis cern the true measure of wealth which should be specified in models such as this one. A P P E N D I X 350 APPENDIX All the variables employed in the "real sphere" expenditure equations are in "real" terms deflated as indi cated below to 1958 dollar values. The variables in the demand deposit, time deposit and currency demand equation are likewise measured in constant 1958 dollars. In the structural equations for bank holdings of excess reserves and borrowings, all variables are measured in nominal val ues. All dollar variables are measured in billions of dol lars. Interest rates, price changes, and yield variables are measured as percentages, i.e., r = 4.10. Interest rates and all money and money related measures (RE, RB, TD etc.) are averages of daily figures throughout the quarter; the income variables (CNDS, CDUR, YGNP, YDISP, DINV, IPandE) are measured as flows during the quarter at seanon- ally adjusted annual rates. Data sources which are referred to frequently below will be abbreviated as follows: 1. Business Statistics - the Biennial Supplement to the Survey of Current Business, United States Department of Commerce, Office of Business Economics, Washington, D.C., 1965. Abbreviation: Bus. Stat. 2. Federal Reserve Bulletins, Board of Governors of the Federal Reserve System, Washington, D.C. Abbreviation: F.R.B.— Vol. No., Date 3. Studies in the National Balance Sheet of the United States, Princeton University Press, Princeton, New Jersey, 1963. (Two volumes) Abbreviation: Goldsmith Studies— Vol. No. 4. Frank de Leeuw, Data Appendix to "A Model of Financial Behavior" The Brookings Quarterly Econometric Model of the U.S. (eds.), Duesenbury, et all Amsterdam: NortK Holland Publishing Co., 1965. tHTs appendix was kindly supplied to me through personal correspondence with Dr. de Leeuw, Federal Reserve Board, Washington, D.C. 351 Abbreviation: de Leeuw, Appendix I Frank de Leeuw, Data Appendix to his study of the "Demand for Money," November, 1965. This appendix was supplied through personal correspondence with Dr. de Leeuw. Abbreviation: de Leeuw, Appendix II CDUR: CNDS : C: Durable goods component of Personal Con sumption Expenditures; billions of 1956 dollars, Bus. Stat., p. 4. Consumer non-durable goods and services component of Personal Consumption Expendi tures; billions of 1958 dollars, Bus. Stat., p. 4. Total Personal Consumption Expenditures: C = CDUR + CNDS. Y: P: Gross National Product in constant 1958 dollars, seasonally adjusted quarterly totals at annual rates. Bus. Stat., p. 4. (Derived by the Office of Business Eco nomics by dividing components of the sea sonally adjusted current-dollar gross national product. Implicit Gross National Product Deflator. Derived by dividing the current-dollar figure for gross national product by (Y) as defined above. YDISP Wealth; Disposable Personal Income, total. De rived by dividing current-dollar dispos able income by P, the implicit GNP deflator. Bus. Stat., p. 7. A figure representing "consolidated net non-human wealth of the public." This figure was derived as follows: W« = Total National Wealth of the United States, excluding military assets, current prices. R. M. Goldsmith, The National Wealth of the United States in the Postwar Period, Princeton 353 University Press, Princeton, New Jersey, 1962, p. 112, Table A-l Col. 1. W' is given at annual rates. We subtract figures for government struc tures, inventories, public land and mone tary gold and silver stock from W' since these are not part of the public's private holdings of tangible assets. (See text.) The sources of these figures, on an annual basis, are as follows: (a) government structures - Goldsmith Studies, Vol. II, p. 240, Table IV- a-1, ITnes 6 and 7; p. 240, Table IV-a-2, lines 6 and 7. (b) government inventories - Goldsmith Studies, Vol. II, p. 2i6, Table IV- a-6, ITnes 6 and 7. (c) public land - Goldsmith Studies, Vol. II, p. 242, Table IV-a-3, lines 6 and 7. (d) monetary gold and silver - Goldsmith Studies, Vol. II, p. 254, Table IV- b-Ta, Tine 5a. W' - [(a) + (b) + (c) + <d> J = W" The resulting annual series is interpo lated to a quarterly series (stock) by the rate of gross private domestic investment in the economy. For example: W 1949 “ w"i948 * (rate of yearly investment in 1949-1) + W"ig4g = W"i949_i To this resulting series, we add a measure of the government's monetary and non monetary debt as part of the public's net wealth holdings. This includes (a) total gross debt (including guaranteed issues) of U.S. Government Securities, F.R.B., December issues, 1948-1958. Quarterly figures are averages for three months of quarter. (b) Bonds and notes of state and 354 local governments. Annual totals from Goldsmith Studies, Vol. II, Table IV-c-12, pT 342, rine 6. These annual figures were interpolated to a quarterly basis by the rate of new issue of state and local gov ernment securities. "New Issues of State and Local Government Securities for New Capital," F.R.B., December issues, 1948- 1958. (c) Currency and Demand Deposit Liabilities of the Federal Government, Goldsmith Studies, Vol. II, p. 322, Table IV-c-2, line 7. W-T-i + [(a) + (b) + (c) + (d) = W"'T_i Therefore W"' is a quarterly series of consolidated net non-human wealth of the public in current dollars. W"' is then deflated by the implicit GNP deflator, P. as defined above, to derive Wealth. 8. Wealth-A: This figure represents a slightly modified measure of non-monetary, non-human wealth owned by the public. The original measure, supplied by Frank de Leeuw of the Federal Reserve Research Staff, consisted of (a) tangible assets, (b) U.S. government se curities domestically held outside the federal government and the Federal Reserve System and (c) unborrowed reserves plus currency. We subtracted "currency outside banks” from de Leeuw*s measure and de flated the resulting figure by the implicit GNP deflator, P, to derive the final meas ure employed in this study, de Leeuw, Appendix II. 9. CURR: Currency outside banks. Averages of daily currency liabilities of the Treasury and Federal Reserve Banks minus commercial banks 1 currency holdings. Seasonally ad justed. Series provided by Frank de Leeuw, Appendix I_. This series was deflated by implicit GNP deflator, P. 10. DDa£-i Demand Deposits adjusted (at all commercial banks). Averages of daily demand deposit 355 11. 12. 13. 14. 15. 16. 17. liabilities of commercial banks, less in terbank deposits, U.S. government deposits, cash items in process of collection and Federal Reserve Float. Seasonally ad justed. de Leeuw, Appendix I. Series deflated By implicitGNP deflator, P. M^: Real value of holdings of currency and demand deposits adjusted, = CURR + DD. TDa<^j : Time Deposit holdings (at all commercial banks). Average of daily time deposit liabilities of all commercial banks less interbank time deposits and U.S. govern ment deposits. Seasonally adjusted. F.R.B., Auguest 1962 and de^ Leeuw, Appen dix I. r^: Moody's composite average yields on corpo rate bonds. Average value for midmonth of quarter. Moody's Industrials, 1965, p. a-20. rB : Average market yield during each quarter on three-month U.S. Treasury bills, com puted from monthly averages of daily closing bid prices, de Leeuw, Appendix I_. rTime: Ratio of interest paid on time and saving deposits to the average amount of such deposits outstanding at all insured banks. de Leeuw, Appendix !E. DINVi Change in business inventories, billions of 1958 dollars. Bus. Stat., p. 4. De flated by Dept, of Commerce largely on the basis of B.L.S. Wholesale Price Indexes. A P/P: Percentage change in the implicit GNP price index over the past year. This com putation was selected rather than a quarter to quarter percentage change to take con sideration of the fact that people become aware of price changes only over periods of time somewhat longer than the quarter, and, most probably, the total experience of at least the last four quarters is im portant in formulating their expectations about the future movement of prices. Therefore: 356 AP p P^i — Pip_4 T-4 18. INV -1 19. UNFIL: 2 0. Y_: T 21. Dif: 22. IPandE: 23. WBUS: The level of business inventories lagged one quarter. Bus. Stat., p. 22 - "Inven tories, Book Value, End or Period, Total Manufacturing and Trade." Seasonally ad justed quarterly figures in billions of constant 1958 dollars derived by deflating current-dollar figures for the mid-month of the quarter by the implicit GNP de flator, P. Total level of manufacturer's unfilled orders, end of period. Bus. Stat., p. 35. Seasonally adjusted quarterly totals in billions of constant 1958 dollars derived by deflating first month of quarter fig ures in current dollars by the implicit GNP deflator, P. Expected level of income (GNP) in quarter T. (See text.) Diffusion Index. Geoffrey Moore (ed.). Business Cycle Indicators, Vol. II, National Bureau of Economic Research, Princeton University Press, Princeton, New Jersey, 1961. 1947-1958, Index of Indus trial Production (26 industries), series D15.0, p. 165. 1959-1962, Index of Indus trial Production (25 industries), series D47, p. 37. All figures based on season ally adjusted data, centered on mid-month of quarter. Total new plant and equipment expenditures by all industries. Seasonally adjusted quarterly totals at annual rates in cur rent dollars, Bus. Stat., p. 9. Constant dollar figures derived by deflating cur rent-dollar series by the implicit GNP deflator, P. Market value of all corporate stock out standing. We choose this measure of wealth to represent the net worth of the firm as opposed to some measure of the 357 book value of the enterprise because of its specific market orientation. This seems desirable for two reasons. First economic theory indicates that entrepre neurs should be relatively more respon sive to current market values and prices than to book values. Second, book values represent the result of many different accounting conventions which are often inconsistent among different firms. This quarterly series is interpolated from basic annual statistics: "Corporate Stocks at Market Value" - year end; Flow of Funds Accounts 1945-1962; 1963 supple ment. Board of Governors of the Federal Reserve System, Table 76, p. 2, line 46. The quarterly interpolation is carried out using the current market value of all listed shares on the New York Stock Ex change from Bus. Stat., The Survey of Current Business Supplement, 1955, 1959, 1963, 1965. Example June '49-Mar *49 Dec '49-Dec '48 = fraction of yearly change over second quarter (end '49- end '48) • a + end first quarter figure = end second quarter figure. Final quarterly current dollar figures are deflated by P. A 24. pK: The expected yield on assets. Strictly speaking, the model calls for inclusion of the expected yield on capital stock. However, it is impossible to accurately separate out that part of a firm's total returns which are due to any one asset category. Also, capital stock represents the largest single asset component for al most all firms. Therefore, to approximate the desired measure, we use the return on assets as a proxy for the return on capi tal. in his work, Hammer defines 358 PT = X-. where X™ is the expected re turn on'assets (the sum of before tax corporate profits and interest payments on corporate bonds) and V is the sum of the outstanding stocks and bonds of all corpo rations. (This may be interpreted as the market value of total assets less current liabilities.) Hammer uses empirical ex perimentation to derive a measure for the "expected" return on assets. He then com pares this measure with the actual figure for V to derive his measure of "expected yield." Our own approach has been to estimate pT, the expected yield, directly by the use of "Almon variables." We define pt = Xt/Vt pip = the actual yield in period T Xt = the actual return (defined as above) in period T Vt = the actual value of outstanding stocks and bonds Thus, ^ n PT = i = i e(i) P r _ i where 6(i) repre sents the weight pattern esti mated through the Almon technique. The data employed in these calculations are as follows: XT = before tax corporate profits; Bus. Stat., p. 6 + interest paid on corp. bonds (VB x r^). VT = value of corporate stock out standing (WBUS) plus the market value of corporate bonds out standing, VB* Vq is interpolated from basic annual data from Flow of Funds Accounts 1945-1962, 1963 Supplement, Board 359 25. 26. 27. 28. 29. 30. (YALM) i rn: of Governors of the Federal Re serve System, p. 2, Table 76, line 42 minus line 45. This series is interpolated to a quarterly basis according to the rate of issue of total new corporate bonds (domes tic) for new capital. F.R.B., June 1947 and following*! fKe series is interpolated by the same technique explained in No. 23 for (WBUS). i = 1...4. The "Almon variable" calcu lated from the past values of T. New York Federal Reserve Bank Discount rate. Since the twelve district Federal Reserve Banks have usually maintained the same discount rate (except for short pe riods of time), the New York rate is taken as representative of the average rate throughout the country. This measure is computed as an average of daily rates throughout the quarter, de Leeuw, Appen- dix I. YGNP UNEMPq: UNEMP: EXOG: Gross National Product in current dollars, seasonally adjusted quarterly totals at annual rates. Bus. Stat., p. 1. Rate of unemployment for all civilian workers in the United States. Adjusted for seasonal variation. Quarterly level is an average of the three monthly fig ures for each quarter. Bus. Stat., p. 67. A moving average of the rates of unemploy ment over the past four quarters, derived from figures for UNEMPg (28). Exogenous components of real expenditure in Y. Exog is the sum of (a) government expenditures on goods and services, (b) net foreign investment. This figure was calculated as the difference between (Y) and the sum of the endogenous expenditure components included within the model. 360 31. 32. 33. 34. 35. 36. TAX: 9: A©! (DD+TD) TD DD+TD _i RR: Exogenous items defining the computation of YDISP, i.e., TAX = Y - YDISP. (DD + TD - RR - PL) where RR = required reserves and PL = bank loans and private security holdings. Sources: RR, see be low; PL, de Leeuw. Appendix I_. All vari ables are measured in current dollars (bar indicates current value of variable al ready defined in real terms). Net inflow (or outflow) of funds to (from the commercial banks. Quarterly first differences of seasonally adjusted figures in current dollars. Total deposit liabilities of commercial banks lagged one quarter. All figures are based on current value daily averages, seasonally adjusted. d£ Leeuw, Appendix 1. Ratio of time deposit to total deposit liabilities. All figures are seasonally adjusted quarterly levels based on aver ages of daily figures in current dollars. Legally required reserve balances of all member commercial banks. In order to as sure consistency with our deposit figures, this series is constructed as follows. RRTD = 6TD . +td DD RRDD = 5 * DD TD DD RR = RRTD + RRDD where: .TD. lTD. »DD. daily average required re serve ratio on time deposits proportion of commercial bank time deposits held at member banks daily average required re serve ratio on demand de posits proportion of commercial Year 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 361 bank demand deposits held at member banks TD and DD; de Leeuw, Appendix 1^. and DD; ratios of quarterly averages of "all commercial bank" and "member bank" time deposit and demand deposit liabili- ties respectively. Source F.R.B., January and July issues, 1949-1963, "Principal Assets and Liabilities by Class of Bank." These "calculated" values compare with ac tual figures as follows Actual Calculated (Yearly Average) First First Levels Differences Levels Differences 15.62 14.71 2.92 2.46 18.54 17.17 1.10 . 97 19.64 18.14 -.32 -.19 19.32 17.95 -.82 -.83 18.50 17.12 -.24 -.05 18.26 17.07 .14 .12 18.40 17.19 .10 -1.36 18.50 15.83 -.44 .66 18.06 16.49 .13 .58 18.19 17.07 -.21 -.25 17.98 16.82 .69 .69 18.67 17.51 .69 .71 19.36 18.22 362 37. 38. 39. 40. 41. RE: Legal Reserves held by member commercial banks in excess of requirements. Season ally adjusted quarterly levels are based on monthly averages of the daily differ ence between total reserve balances (plus the amount of vault cash allowed as re serves since December 1959) and required reserve balances, de Leeuw, Appendix I. The required reserve measure employed here is the actual level of RR not our calcu lated figure. Hence, we derive the meas ure of RE as seen by commercial banks— not a calculated figure. RB: Member bank borrowings from the Federal Reserve. Seasonally adjusted quarterly levels are based on monthly averages of daily closing figures, de Leeuw, Appendix I. RU: Unborrowed reserves of commercial banks, RU = RR + RE - RB. All variables season ally adjusted quarterly levels in current dollars, as defined above. This is the result of our calculated figure for RR and the actual recorded figures for RE and RB as defined above. n: Change in unborrowed reserves adjusted for changes in reserve requirements, i.e., n = ARU - [ DDadj . ♦dd(A6DD) + TDadj . < ( . TD • (A6TD) ] where indicates quarterly first differ ences. Dummy: 0 - 1948-3 to 1959-4 1 - 1960-1 to 1962-4 B I B L I O G R A P H Y 363 BIBLIOGRAPHY A . BOOKS Board of Governors of the Federal Reserve System. The Federal Reserve and the Treasury: Answers to Questions from the Commission on Money and Credit. Englewood Cliffs, New Jersey: Prentice Hall“i Inc. , 1963. The Federal Reserve System: Purposes and Func- tions. Washington, D.C., 1963 . Burgess, R. The Reserve Banks and the Money Market. New York: Harper and Brothers, 193FT Cagan, Phillip. Determinants and Effects of Changes in the Stock of Money~~l§75-1966. New York: N.B.E.R., dTs- tributecT by The Columbia University Press, 1965. Fisher, Irving. The Purchasing Power Money. New York: The Macmillan Company, 1911. Friedman, Milton. A Theory of the Consumption Function. Princeton, New Jersey: Princeton University Press, 1957. _. Studies in the Quantity Theory of Money. Chicago University of Chicago Press, 1956. GoIdfeld, Stephen M. Commercial Bank Behavior and Economic Activity. Amsterdam: North Holland Publishing Com- pany, 1966. Goldsmith, Raymond. A Study of Saving in the United States Princeton, New Jersey: Princeton University Press, 1956. _. Studies in the National Balance Sheet of the United States. Princeton, New Jersey: Princeton Uni- versity Press, 1963. Hicks, J. R. Value and Capital. London: Oxford Univer sity Pressj 1939. Johnston, J. Econometric Methods. New York: McGraw-Hill Book Company, 19(53. 365 Kessel, Reuben A. The Cyclical Behavior of the Term Structure of Interest Rates. N.B.E.R. Occasional Paper 91. New York: The Columbia University Press, 1965. Keynes, John M. A Treatise on Money. Vol. II. London: Harcourt, Brace and Co.,—T930. _______ . The General Theory of Employment, Interest and Money. New York: Harcourt, Brace and World, Inc., m rr Klein, Lawrence R., and Arthur S. Goldberger. An Econo metric Model of the United States 1929-1952. Amster dam: NorthHolland Publishing Company, 1955. Marshall, Alfred. Money, Credit and Commerce. London: Macmillan and Company, Ltd., 1923. Meigs, A. J. Free Reserves and the Money Supply. Chicago: University ofChicago Press, 19677 Meiselman, David. The Term Structure of Interest Rates. Englewood Cliffs, New Jersey: Prentice Hall, Inc., 1962. Morgenstern, Oskar. On the Accuracy of Economic Observa tions . Princeton, New Jersey: PrTnceton University Press, 1950. Patinkin, Don. Money, Interest, and Prices. Second edi tion. New York: Harper & Row7 1965. Pesek, Boris P., and Thomas R. Saving. Money, Wealth, and Economic Theory. New York: The Macmillan Company, 19977---------- Phillips, C. A. Bank Credit. New York: The Macmillan Company, 1920. Riefler, W. W. Money Rates and Money Markets in the United States. New York: Harper and Brothers, 1976. Suits, Daniel B. The Theory and Application of Econometric Models. Athens: Center of Economic ResearcK7 1963. Tintner, Gerhard. Econometrics. New York: John Wiley & Sons, Inc., 19577 B. PERIODICALS 366 Almon, Shirley. "The Distributed Lag Between Capital Ap propriations and Expenditures," Econometrica, XXX, No. 1 (January, 1965), 178-196. Ando, Albert, and Franco Modigliani. "The Life Cycle Hy pothesis of Saving: Aggregate Implications and Tests," American Economic Review, LIII (March, 1963), 55-84. Arena, John. "The Wealth Effects and Consumption: A Statistical Inquiry," Yale Economic Essays, III, No. 2 (Fall, 1963), 251-303. Basevi, G. "Vault Cash and the Shift in the Desired Level of Free Reserves," Journal of Political Economy, LXXI, No. 4 (August, 1963) , 408-43T. Baumol, William J. "The Transactions Demand for Cash: An Inventory Theoretic Approach," Quarterly Journal of Economics, LXVI (November, 1952FJ 545-534. Bodkin, Ronald. "Windfall Income and Consumption," Ameri can Economic Review, LXIX (September, 1959), 602-514. Bronfenbrenner, Martin, and Thomas Mayer. "Liquidity Functions in the American Economy," Econometrica, XXVIII, No. 4 (October, 1960), 810-83T: _______ . "Rejoinder to Professor Eisner," Econometrica, XXXI, No. 3 (July, 1963), 39-44. Brunner, Karl. "Schema for the Supply Theory of Money," International Economic Review, II, No. 1 (January, imy, 70-105.--------------- _____ , and Allan H. Meltzer. "Predicting Velocity: Im- plications for Theory and Policy," Journal of Finance, XVIII, No. 2 (May, 1963), 319-354. _______ . "Some Further Investigations of Demand and Supply Functions for Money," Journal of Finance, XIX, No. 2 (May, 1964), 240-283. Culbertson, J. M. "The Term Structure of Interest Rates," Quarterly Journal of Economics, LXXI (November, 1957), 4'85-517.--------------------- 36 7 Darling, Paul G. "Surrogative Measurements of Expecta tions: An Example in Estimating the Liquidity Influ ence on Investment," Review of Economics and Statis- tics, XXXVIII (November, 1956'J , 413-426. DeWald, William. "Free Reserves, Total Reserves and Mone tary Control," Journal of Political Economy, LXXI, No. 2 (April, 1963), 14I-15TI Durbin, J., and G. S. Watson. "Testing for Serial Correla tion in Least Squares Regression," Biometrika (Decem ber, 1950; June, 1951). Federal Reserve Bulletin(s). Washington, D.C.: Board of Governors of the Federal Reserve System. Friedman, Milton. "The Demand for Money: Some Theoretical and Empirical Results," Journal of Political Economy, LXVII, No. 4 (August, 1959) , 327=7517: . "Vault Cash and Free Reserves," Journal of Polit- real Economy, LXIX, No. 4 (August, 1961), 181-HT2. Gramley, Lyle, and Samuel Chase. "Time Deposits in Mone tary Analysis," Federal Reserve Bulletin (October, 1965), 1380-1406” Hodgman, Donald D. "Member Bank Borrowing: A Comment," Journal of Finance, XVI, No. 1 (March, 1961), 90-93, 98. Johnson, Harry G. "Monetary Theory and Policy," American Economic Review, LII, No. 3 (June, 1962), 335-384. Kuznets, Simon. "Proportion of Capital Formation to National Product," American Economic Review, XLII, No. 2 (May, 1952), 507-526. Latan€, Henry. "Income Velocity and Interest Rates— A Pragmatic Approach," Review of Economics and Statis tics, XLII (November, 19(>0) T4!>-449. Lovell, Michael C. "Manufacturer's Inventories, Sales Expectations, and the Acceleration Principle," Econometrica, XXIX (july, 1961), 293-314. Lydall, H. F. "Income, Assets, and the Demand for Money," Review of Economics and Statistics, XL (February, 1958) , ™ ----------------------- 368 Mayer, Thomas. "The Empirical Significance of the Real Balance Effect," Quarterly Journal of Economics, LXXIII (May, 1959), Meltzer, Allan. "The Demand for Money: The Evidence from the Time Series," Journal of Political Economy, LXXI, No. 3 (June, 1963), 219-24^7 Modigliani, Franco, and Richard Sutch. "Innovations in Interest Rate Policy," American Economic Review, LVI, No. 2 (Paper and Proceedings, May^ 1966), 178-197. Orr, Daniel, and W. G. Mellon. "Stochastic Reserve Losses and Expansion of Bank Credit," American Economic Re view, LI, No. 4 (September, 1961) , 614-623. Polak, J. J., and W. H. White. "The Effects of Income Expansion on the Quantity of Money," I.M.F. Staff Papers, IV (August, 1955), 398-433. Polakoff, Murray. "Reluctance Elasticity, Least Cost and Member Bank Borrowing," Journal of Finance, XV, No. 1, (March, 1960), 1-18. Rothwell, Jack C. "Vault Cash and Free Reserves: Some Evidence," Journal of Political Economy, LXX, No. 2 (April, 1962) , 187-158': Teigen, Ronald. "Demand and Supply Functions for Money in the United States: Some Structural Estimates," Econometrica, XXXII, No. 4 (October, 1964), 476-509. Tintner, Gerhard, and B. von Hohenbalken. "Econometric Models of the OEEC Countries, the United States and Canada and Their Application to Economic Policy," Weltwirtschaftliches Archiv, LXXXIX (1962), 29-84. Tobin, James. "Liquidity Preference and Monetary Policy," Review of Economics and Statistics, XXIX (February, 1947) , T74=TTT.--------------------- _______ . "The Interest Elasticity of the Transactions Demand for Cash," Review of Economics and Statistics, xxxvili (August, 1956), 2TT-2TT. Zellner, Arnold. "The Short Run Consumption Function," Econometrica, XXV (October, 1957) , 552-567. 369 C. PUBLICATIONS OF THE GOVERNMENT, LEARNED SOCIETIES, AND OTHER ORGANIZATIONS Department of Commerce, Office of Business Statistics. Biennial Supplement to the Survey of Current Business: Business Statistics,~T96 5. Washington^ D.C.: Govern ment Printing Office, 1965. Schultze, Charles L. "Recent Inflation in the United States," Study Paper No. 1, Study of Employment, Growth, and Price Levels. Joint Economic Committee, 86 Cong.^ Tst session, T959. Washington, D.C.: Gov ernment Printing Office, 1959. D. ESSAYS AND ARTICLES IN COLLECTIONS Bronfenbrenner, Jean. "Sources and Size of Least Squares Bias in a Two-Equation Model," Studies in Econometric Method, William C. Hood and Tjalling C. Koopmans, editors. Cowles Commission Monograph, No. 14. New York: John Wiley & Sons, Inc., 1953. Pp. 221-235. Christ, Carl. "Interest Rates and 'Portfolio Selection' Among Liquid Assets in the U.S.," Measurement in Economics, Christ et al^. , editors. Stanford: Stan ford University Press, 1963. Pp. 201-218. Darling, Paul G., and Michael C. Lovell. "Factors Influ encing Investment in Inventories," The Brookings Quarterly Econometric Model of the United StatesT James S. Duesenberry et al., editors^ CKicago: Rand McNally and Co., 1965. P. 131. de Leeuw, Frank. "A Model of Financial Behavior," The Brookings Quarterly Econometric Model of the United States. James S. Duesenberry et al., ecTitors. Chicago: Rand McNally and Co., 13RT5. Pp. 465-532. _______ . "A Model of the Financial Sector," The Brookings Quarterly Econometric Model of the United States. James S. Duesenberry et al., editors. Amsterdam: North Holland Publishing-Company, 1965. Eisner, Robert, and Robert H. Strotz. "Determinants of Business Investment," Impacts of Monetary Policy. Commission on Money and Credit. Englewood Cliffs, New Jersey: Prentice Hall, Inc., 1963. Pp. 60-338. 370 Friedman, Milton. "Foreword," Free Reserves and the Money Supply. Chicago: University of Chicago Press, 1962. Pp. vii-viii. Fromm, Gary, and Lawrence R. Klein. "The Complete Model: A First Approximation," The Brookings Quarterly Econo metric Model of the United States. James S. Duesen berry et al., editors. Amsterdam: North Holland Publishing Company, 1965. P. 726. Goldenweiser, E. "Instruments of Federal Reserve Policy," Banking Studies. Board of Governors of the Federal Reserve. Washington, D.C.: Government Printing Office, 1941. Grebler, Leo, and Sherman J. Maisel. "Determinants of Residential Construction: A Review of Present Knowl edge ," Impacts of M ‘ ’ Prentice Hall, Inc., 1963. P. 551. Haavelmo, Trygve. "Remarks on Frisch's Confluence Analysis and Its Use in Econometrics," Statistical Inference in Dynamic Economic Models. T. J. Koopmans, editor. Chapter 5. New York: John Wiley and Sons, 1950. Klein, Lawrence R. "A Postwar Quarterly Model: Descrip tion and Application," Studies in Income and Wealth. Princeton, New Jersey: Princeton University Press, 1964. P. 56. ,_.• "Economic Fluctuations in the United States, 1929-1941." Cowles Commission Monograph No. 2. New York: John Wiley and Sons, Inc., 1950. Maisel, Sherman J. "Nonbusiness Construction," The Brook ings Quarterly Econometric Model of the United States. James S. Duesenberry et al., editors. Chicago: Rand McNally and Co., 1965. Fp. 178-201. Modigliani, Franco, and Richard Brumberg. "Utility Analy sis and the Consumption Function: An Interpretation of Cross Section Data," Post Keynesian Economics. K. Kurihara, editor. New Jersey: Rutgers University Press, 1954. Suits, Daniel B. "The Determination of Consumer Expendi ture: A Review of Present Knowledge," Impacts of - — . on j|Qney and Credit. Money and Credit Prentice Hall, Inc., 371 1963. P. 14. Suits, Daniel B. , and G. R. Sparks. "Consumption Regres sions with Quarterly Data," The Brookings Quarterly Econometric Model of the United States. James S. Duesenberry et al., editors. Chicago: Rand McNally and Co., 19637 E. UNPUBLISHED MATERIALS Basmann, R. L. "An Experimental Investigation of Some Small Sample Properties of GCL Estimators of Structural Equations: Some Preliminary Results." General Elec tric Company, Handford Laboratories, Ricnland, Washing ton, November, 1958. (Mimeographed.) de Leeuw, Frank. "Data Appendix" to "A Model of Financial Behavior," The Brookings Quarterly Econometric Model of the United States. James S. Duesenberry et al., editors. Amsterdam: North Holland Publishing Company, 1965. _______ . "Data Appendix" to "The Demand for Money." Paper received through personal correspondence. (Mimeo graphed .) Hammer, Frederick. "The Demand for Physical Capital: Ap plication of a Wealth Model." Unpublished Doctoral dissertation, Carnegie Institute of Technology, Pittsburgh, 1963. Summers, R. "A Capital Intensive Approach to the Small Sample Properties of Various Simultaneous Equation Estimators." Unpublished paper, 1962. Teigen, R. L. "An Aggregated Quarterly Model of the United States Monetary Sector: 1953-1964." Paper presented to the Conference on Targets and Indicators of Monetary Policy, University of California at Los Angeles, April 29, 1966. (Mimeographed.)

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Creator Boorman, John Thomas (author)

Core Title An Econometric Analysis Of The Influence Of Money Supply And And Money Demand Relations In The Determination Of National Income

Degree Doctor of Philosophy

Degree Program Economics

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

Tag Economics, Finance,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-c18-614686

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