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A Dynamic Model For Predicting The Effects Of Fiscal Policy Measures

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A Dynamic Model For Predicting The Effects Of Fiscal Policy Measures

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Content This dissertation has been microfilmed exactly as received 6 7 -1 0 ,7 7 9 WHITE, Hubert Dale, 1930- A DYNAMIC MODEL FOR PREDICTING THE EFFECTS OF FISCAL POLICY MEASURES. University of Southern California, Ph.D., 1967 Economics, theory University Microfilms, Inc., Ann Arbor, Michigan A DYNAMIC MODEL FOR PREDICTING THE EFFECTS OF FISCAL POLICY MEASURES by Hubert Dale White A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Economics) June 1967 TH E GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 9 0 0 0 7 This dissertation, written by HUBERT DALE WHITE under the direction of h.XS...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 Dean Date........................... DISSERTATION COMMITTEE .. I / ( IChairman f ....... TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION.................................... 1 The Problem ................................ 1 Significance of the Problem ............... 2 The Objective of This S t u d y ............... 3 The Contributions of This P a p e r ........... 5 Limitations and Scope ..................... 5 Preliminary Problems Relating to Method . . . 7 Selection of the Time Period............... 7 Development of a Model ..................... 9 Choice of the Time Increment............... 11 Testing the M o d e l .......................... 12 Organization of the Dissertation ............. 13 II. REVIEW OF THE THEORY............................ 15 The Theory of Fiscal Policy................. 15 Fiscal Policy as a Concept................. 16 Basic Elements of the Theory............... 19 Dynamic Aspects of the Theory............. 23 A General Theory of Fiscal Policy ........ 25 The Formation of Fiscal Policy ............. 27 Institutional Considerations ............... 28 ii i ii CHAPTER PAGE Demand Models .............................. 29 The Contributions of Klein........ 30 The Brookings Quarterly Model ........... 32 The Structure of the Brookings Model . . . 34 Simple vs. Complex Models ............... 35 Causal Chain Models ..................... 36 Some Notes on Other Related Studies . . . 37 Conclusions.......................... 42 III. PRESENTATION OF THE M O D E L ............. 44 Initial Considerations ..................... 44 Autonomous Variables ..................... 44 Initial Conditions ........................ 49 Capital Formation and Capital Consumption 49 The Simultaneous Block ..................... 50 Investment.......................... 51 Investment in the Brookings Model .... 53 Investment and the Money Market ........ 56 Disposable Wage Income ................... 58 Private Consumption Expenditure ........ 59 Gross National Product ................. 60 Distribution of the National Product .... 60 Indirect Business Taxes ................. 61 National Income Shares ................... 61 Personal Income .......................... 62 iv CHAPTER PAGE Tax Payments and Disposable Income .... 64 The Money Market.......................... 65 Summary of the Model to be Tested........ 69 Definitions of Symbols ................... 71 Summary of the F o r m .................... . 73 IV. ESTIMATION OF THE PARAMETERS................. 75 Method of Estimation..................... . . 75 Estimating a Causal Chain System ........ 75 The Simultaneous Block ................... 78 The Kinds of Errors..................... 80 First Differences........................ 81 The Simultaneous Block ..................... 82 Estimation of the Reduced Forms ........ 82 Interpretation of the Results........... 87 Testing the Hypothesis ................... 91 An Alternative Formulation ............... 95 Second Stage Estimates ................... 95 The Recursive Equations ................... 99 A Preliminary Study of the Distribution of Income.............................. 99 The Capital Consumption Function ........ 102 Estimating with First Differences .... 103 Corporate and Personal Taxes ............. 106 Conclusions................................ -T-06 CHAPTER PAGE V. ADDITIONAL TESTS OP THE M O D E L ............... 110 Testing the System.......................... 110 Recession and Recovery from 1954 through 1956............................ 110 The Tax Cut of 1964 118 Conclusions................................ 120 VI. A FISCAL POLICY CRITIQUE ..................... 121 Estimated Impacts .......................... 121 Tax Policy................................ 121 Government Spending Policy............ * ■ . 123 Policy Critique ............................ 124 General Economic Characteristics of the Period.................................. 124 The Background of 1953 ................... 125 The Recession of 1953-54 ................. 126 Expansion and Recession in 1955 to 1958 . 128 From 1958 to 1 9 6 1 ........................ 134 1961 Through 1963 136 Conclusions................................ 137 VII. CONCLUSIONS................................... 139 Evaluation of Results ...................... 139 The Form of the M o d e l ................... 139 The Estimation Process................... 140 The Distribution of Income............... 142 vi CHAPTER PAGE The Accuracy of the Predictions..... 143 Relevance of the Study................. 144 Value Judgments...................... 144 Relevance Beyond the Period of the Study . 146 Further Limitations ..................... 147 Usefulness of the Results........... 148 Capital Formation as a Key Factor .... 151 Fiscal Policy in the Period Under Review . 154 BIBLIOGRAPHY ......................................... 158 LIST OF TABLES TABLE PAGE I. Net Exports, Total Transfer Payments, and Gross National Product for 1953 through 1965 in Billions of Current Dollars .... 47 II. Regression Coefficients for A an ' A c , and A yw Against A k , A E t-1, A s t_i, and A h ......................................... 83 III. Regression Coefficients for Ai, A v and Ata Against Ak, A E t-1, Ab^-^ and A h ......................................... 84 IV. Regression Coefficients for A ir A v and Ata Against Ak, AEt_-j_, A Bt-l' and A g ........................................... 88 V. Regression Coefficients for A v Ac, and Against A k , AEt_x, A B t_lf and A g ......................................... 89 VI. Regression Coefficients of A yw on A K, AEt_lf Ab^-j^, and A d ................... 92 VII. Regression Coefficients for Ai, Ac, and Ayw Against Ak, AE-t-ir and A d ......... 93 VIII. Regression Coefficients for Ai, Ac, and vii viii TABLE PAGE A* Against A k , AEt_]_, and A ® t_1 • • • 94 IX. Regression Coefficients for 1^1, Aa^, and A ta Against Ak, A e^-_1' anc^ Ag .... 96 X. Regression Coefficients for A a^, A c , and A yw Against A K, A Et_1, and A g .... 97 XI. Regression Coefficients for Non-Wage Dis tributive Components of National Income, as Functions of Gross National Product . . 101 XII. Coefficients of the Depreciation Function . 103 XIII. Regression Coefficients of First Differences of Non-Wage Components of National Income 105 XIV. Components of Non-Wage Personal Income in Billions of Current Dollars ............. 107 XV. Personal Income Taxes and Corporate Profits Taxes in Billions of Current Dollars . . . 108 XVI. Exogenous Policy Variables in Billions of Current Dollars .......................... 113 XVII. Predicted vs. Actual Changes in Income Variables for 1954 ........................ 114 XVIII. Predicted vs. Actual Changes in Income Variables for 1955 and 1956 115 XIX. Predicted Changes of Income Variables for 1954 through 1956 Showing the Effect of the Reduced Government Spending ......... 117 ix TABLE PAGE XX. Actual and Predicted Income Data for 1964 119 XXI. Calculated GNP (In Constant 1958 Dollars) with G Assumed Unchanged through 1956 but with Actual Changes for 1957 and 1958 131 XXII. Predicted and Actual Changes in Investment, Consumption, and GNP for 1960 and 1961 . . 135 LIST OF FIGURES FIGURE PAGE 1. Actual and Predicted GNP in Constant 1958 Dollars for 1954 through 1956 ................ 112 2. Calculated GNP (in Constant 1958 Dollars) with G Assumed Unchanged through 1956 but with Actual Changes for 1957 and 1958 .... 133 x CHAPTER I INTRODUCTION The usefulness of economic theory as a tool for the implementation of national policy has been greatly enhanced by the development of econometric methods. "Econometrics presently stands at the intersection of theory and experi ence ..." writes Edwin Kuh.^ This paper will apply certain econometric methods to the study of fiscal policy measures. Chapter I states the problem, describes briefly the method of analysis, and introduces the content of the remainder of the paper. I. THE PROBLEM Much of the available literature on fiscal policy is theoretical rather than empirical, and it is hampered by a theoretical framework that is static in its analysis of a rapidly changing economy. The problem to be considered by this dissertation will be that of structuring a dynamic model which will be specifically designed for the study of ^Edwin Kuh, "Econometric Models: Is a New Age Dawning?" American Economic Review, LV, No. 2 (May, 1965), 363. 1 fiscal policy measures. This model will then be applied to the study of appropriate empirical data from a recent time period in order to perform a critique of fiscal policy measures during the period. Finally, conclusions will be drawn regarding the general usefulness of this model as a fiscal policy tool. Significance of the Problem It is accepted today that the government can influ ence the level of the aggregate economy through its actions of spending, taxing, and debt management; and through mani pulations of the money supply, interest rate, and credit conditions. Whether the government should attempt such a policy of economic control on a regular basis is still open to dispute. The majority of economists would argue that it should attempt to do so, but a very competent minority con- 2 tend that small fluctuations are a healthful phenomenon. Government action in the event of severe fluctuation would no doubt be brought about by political considerations. With the realization that government purchases of ; 2 Milton Friedman, A Program for Monetary Stabilxty (New York: Fordham University Press, 1960), pp. 4-23; W. J. Baumol, "Pitfalls in Contracycle Policies: Some Tools and Results," The Review of Economics and Statistics, XLIII (Feb., 1961); A. W. Phillips, "Stabilization Policy in a Closed Economy," Economic Journal, XLIV (June, 1954); D. J. Smyth, "Can Automatic Stabilizers be Destabilizing," Public Finance (1963). goods and services represent a significant portion of the national product, even the non-economist is aware that the government therefore has the power to influence the aggre gate economy through its spending and taxing policies. The general recognition of this power and the increasing will ingness to use the power make it rather frightening that we know so little about the quantitative effects of various measures that can be adopted. The Objective of This Study The objective of this paper will be to perform a quantitative study of the effect of changes in the level of government spending and taxing on the level of the national output under the conditions existing during a specific time period. A dynamic predictive model will be the basic tool of the study, and the development of an appropriate model is therefore an important requirement. The model must be formulated, estimated, tested, demonstrated, and its use for studying the effects of fiscal control measures evalu ated. The model which is developed is of the general type •^The federal government currently purchases about one-fifth of the gross national product of the United States. that has become associated with the name of L. R. Klein,^ but it differs from that of Klein in a number of important aspects. The model is tailored specifically to the purpose of determining the effects of fiscal policy on the aggre gate economy. The model is therefore more aggregate in its concept than the models of Klein which attempt to disaggre gate the consumption and investment sector, and to show the interrelation of different sub-sectors, such as agricul tural and non-agricultural. Another major difference is that the model presented in this paper is recursive in structure; that is, it is defined as a series of steps or blocks, each of which takes as its inputs the outputs of previous steps or blocks, with the policy variables as ex ogenous variables. From a single set of initial conditions, it is therefore possible to use this recursive feature to predict the results of alternative measures for a period of several years. Klein's models do not have this as an ob jective, but use exogenous variables such as the average work week and the liquid assets at the beginning of a time period. . R. Klein and A. S. Goldberger, Econometric Model of the United States, 1929-1952 (Amsterdam: North Holland Publishing Co., 1957); Laurence R. Klein, et al., An Econometric Model of the United Kingdom (Oxford: Oxford University Press, 1961); Duesenberry, Fromm, Klein, Kuh, The Brookings Quarterly Econometric Model of the United States (Chicago: Rand McNally & Company, 1965). The Brookings quarterly model which has been devel oped by Klein and others may ultimately be adapted to this kind of study because recursivity is one of its objectives. Such an elaborate model is not really comparable to the much simpler one presented in this paper, but pertinent aspects of the Brookings model are nevertheless discussed in Chapter II. The Contributions of This Paper The general implications of the study which this paper describes are discussed in the last chapter. At this point it may be useful to briefly summarize the contribu tions as follows: 1. Conclusions are drawn from empirical data re garding the quantitative effects of certain kinds of fiscal policy measures. This is the major objective of the study. 2. A dynamic model for the evaluation of fiscal policy measures is constructed and evaluated. 3. The model is used for a study and critique of fiscal policy during the decade from 1954 to 1963. Alter native fiscal policy measures are suggested, and their re sults predicted. Limitations and Scope This paper will be limited primarily to a discus- sion of the aggregate effects of fiscal policy; it will not be directly concerned with the interrelation of the sectors of the economy. The effects of fiscal policy on such in terrelations between sectors will be regarded as a related topic, but a separate one. There are of course certain ex ceptions, and these include a discussion of the distribu tion of income as a factor in determining the aggregate de mand for consumption goods, and a consideration of the af fect on investment plans of the contributions of individual sectors to loanable funds. This study will attempt to separate fiscal policy from monetary policy, and will be directly concerned with only the former. It must of course be recognized that ef fective fiscal and monetary policies must support each other, but a division can be imposed between them which is useful for purposes of research and study. At the same time, in concentrating on fiscal policy it would be incor rect to completely ignore the interrelationship between fiscal and monetary phenomena, and possible ways of com bining the two are explored. The model will concentrate on the demand side of the aggregate domestic market. During the period of the study, the availability of unemployed resources implied that the aggregate output was free to expand in response to increasing demand, and adequate mobility of resources is assumed in this regard. The scope of the paper will include the effect of taxation and government spending on the aggregate level of the economy. The effects of debt management, though part of fiscal theory, are not included in the discussion. II. PRELIMINARY PROBLEMS RELATING TO METHOD The method of analysis will be in general economet ric. The purpose of this section will be to explore cer tain initial problems which relate to the method of study. Selection of the Time Period The question is posed by Kuznets as to whether we would be justified in extending a single study over a long period of time— say over the past four hundred years in America. This leaves us with the possibility of comparing the economy of the sixteenth century Indians with that of twentieth century United States. Kuznets points out that the answer is not as obvious as it may seem, for in both economies we are dealing "with human beings who belong to the same species and have the same elemental needs, in stincts, and aspirations." Yet the social organization, institutions, and technology of the two groups are so ^Simon Kuznets, Capital in the American Economy (Princeton, N.J.: Princeton University Press, 1961). different that we are not justified in considering them as two different points on the same line. In contrast to this, those who study trends will contend that there are no large discontinuities which would naturally separate a study of the 1870's from the 1950's. A study such as that which is undertaken in this paper must seek a period of time which is homogeneous in a still much finer sense than the time period which is con sidered in a study of trends for it is concerned with the short-term effects of changes of certain of the parameters of the model. In order to do this effectively, it is ne cessary to estimate the parameters over a time interval which is homogeneous in the sense that certain other para meters remain reasonably stable. Kuznets points out that it is important to distin guish between the concept of a long-term trend and a short term change. Long-term trends are consistent components of change over time. In their cumulative effect they usually dwarf the short-term variations. The two kinds of changes may be caused by different factors, and the problem of the researcher is to identify these factors. In the study of short-term changes, it is desirable to select a period in which the long-term trends can easily be recognized, and in which the short-term changes are few enough in number that they may be identified as to cause. 9 In our argument we are implicitly following Kuznet's assumption (which is not fully provable) that long-term movements are distinct from short-term changes, and that the causes of the two kinds of changes are distinct and separable. Fortunately, there was a recent period with charac teristics of homogeneity which were very satisfactory for the present study; this period was the decade from 1954 to 1963. During this period the tax code of 1954 remained in effect, the administration of the federal government re mained conservative with only minor efforts to employ any elements of fiscal policy, and the business outlook re mained reasonably constant. In 1954, at the beginning of the period, there was a reduction in government expendi tures which may conveniently be used as a test of conclu sions; while after the end of the period in 1964 there was a change in the tax code, and this provides another con venient test. The period from 1954 to 1963 was therefore used to estimate the parameters of a predictive model. Development of a Model The objectives of the study demand that the model be dynamic in method. It was desired to be able to fore cast for several time periods in advance, and to predict 10 the effects of given fiscal policy measures during those periods. It was for this reason that the model was pre pared in the form of a block recursive system of equations which employs the "causal chain" principle of Wold.^ This technique leads to certain simplifications in a large model because it invites the use of single-equation methods of 7 estimation for portions of the system. The use of this method leads to an obvious problem; this problem is that some of the variables are, in effect, mutually determined within the time increment chosen. For example, the total wage share of the gross national product can be determined only after the gross national product has been determined; but one of the largest components of the gross national product is private consumption, and this is dependent on the take-home pay of wage earners. This vio lates the causal chain principle, because this principle implies a one-way causal relationship without such feedback. The problem is solved by means of a simultaneous block within the recursive system. ^Herman 0. A. Wold, Econometric Model Building (Amsterdam: North Holland Publishing Co., 1964), p. 12. 7 See Laurence R. Klein, "Single Equation vs. Equa tion System Methods of Estimation in Econometrics," Econometrica, XXVIII (October, 1960), 866-71. Choice of the Time Increment 11 A yearly model was decided upon because of the ob jectives in dealing with fiscal policy and taxation. While many taxes are now paid quarterly and government expendi tures are made continuously throughout the year, neverthe less both are based on a fiscal budget which is drawn up annually, and taxes are calculated on the basis of yearly income. Selection of the yearly time period also serves to eliminate such factors as seasonal variation, and it re duces the problem of serial correlation in the data. A different pattern of time lags must be considered in constructing models with different time increments. The problem of time lags is different in different equations and can be a complicated matter. Most of these complica tions are eliminated by using a yearly model. An alterna tive problem is however realized in that the smaller number of data points reduces the number of degrees of freedom and thereby limits the number of independent variables in the equations.^ 8This problem cannot necessarily be solved by taking observations at more frequent intervals unless this actually increases the available information, and matters may be made worse by voiding some of the assumptions on which the model is based. An example is discussed in Chap ter III, Section II in relation to the Brookings Model. Testing the Model Several methods are used for testing the model. The t-test is used to test the individual coefficients. The hypothesis that the coefficients are significantly dif ferent from zero is tested at the 5 per cent level. The individual regression equations are tested by calculating the coefficients of determination; the coefficients of de termination are normalized for the number of degrees of freedom as described in Chapter IV. Finally, the model as a whole is tested by using it to predict events which took place in years which were not used in the estimation of the equations. First the model is used to predict the effects of the tax revision of 1964. Estimates are made for 1964 using functions representing both the old and the new tax codes in order to compare both estimates with the actual data. Then the model is used to predict the effect of the cut in government spending in 1954. This latter test is not as good as the former since 1954 data were used in the estimation of the model; however, 1953 data were not included. We may therefore use 1953 data as initial conditions to attempt to predict the reces sion of 1954, and with the recursive feature attempt to predict the recovery of 1955 and 1956. These tests will give confidence that the equation system as a whole is reasonably correct. 13 III. ORGANIZATION OF THE DISSERTATION The organization of the dissertation will be as follows. Chapter II will discuss pertinent aspects of the theory of fiscal policy, and will serve as a review of the literature on this subject. Chapter III will be a development of the basic model which is used for the ensuing study. This develop ment will emphasize underlying assumptions, hypotheses, and definitions which are consistent with each other. There will be a brief discussion of the economic theory on which the relations are based. Chapter IV discusses the estimation and related testing. Certain supporting studies were performed during the estimation, and these studies with their implications are discussed briefly. Chapter V performs additional tests of the model by first testing individual functions and then testing the model as a whole. It is demonstrated in this chapter that the model predicts to within an accuracy that is very sat isfactory for the given limitations of the present study. Chapter VI uses the model as the basis of a cri tique of fiscal policy during the period between the Korean and Vietnamese wars. Alternative policy measures are 14 suggested and evaluated on the basis of predictions made by the model. Chapter VII draws general conclusions regarding the use of this kind of model as a tool for fiscal policy studies. CHAPTER II REVIEW OF THE THEORY The purpose of this chapter is to present an intro duction to the theory of fiscal policy as related to the time period of the study. The topic will be divided into two sections: the first will consist of comments relative to the theory of fiscal policy, the second will be a brief review of studies which contributed to the development of demand models as fiscal policy tools. Both of these sec tions are of necessity brief. The technique used in the presentation will be to mention the salient pertinent as pects, and to give references in which the topics are devel oped more fully. I. THE THEORY OF FISCAL POLICY Fiscal economics is the study of the effects of government spending, taxing, and debt management. It in volves the changes in government taxing and spending which affect the aggregate variables, and it involves the govern ment surpluses and deficits that directly cause differences between leakages and insertions and thereby give leverage to fiscal policy actions through the multiplier effect. 15 16 Government spending for goods and services and gov ernment transfer payments affect the aggregate economy by increasing total demand. The mechanism through which taxa tion has its effect on the economy is complex and cannot be completely described due to the uncertainties of shifting and incidence; however, in a general way the fiscal effects of taxation act through their influence on the ability and the willingness of both individuals and businesses to per form such basic economic activities as saving, investing, producing, and consuming. Aggregate demand is generally reduced by an increase in taxes, due to the resulting de crease in disposable income. Fiscal Policy as a Concept The history of fiscal policy as a concept dates back to the mercantilists, when state policy actively en couraged industry and trade. The concept of fiscal policy suffered a sharp setback in England with the downfall of mercantilism, but the theoretical developments of the next hundred years slowly established the foundation of under standing on which the modern concepts are based. The Swedish school was one of the first to work on a modern theory of fiscal policy, but most of their work remained little known due to the problem of language. For example, Knut Wicksell's Lectures on Political Economy were 17 not translated into English until 1935, and his Interest and Prices until 1936 (though the latter was published in German in 1925). The Italian school was also developing a school of public finance during these years.^ The greatest impetus to the consideration of fiscal policy in England and America came from the work of J. M. Keynes, but Keynes' ideas were not as completely original as sometimes supposed and his work was related to that of Wicksell, Viti de Marco, Pigou, and other of his contempo raries. Interest in fiscal policy became widespread in the 1930's due to the immediate effects of the great depression. The concepts behind fiscal policy evolved slowly, with monetary controls being accepted and tried much ear lier than fiscal controls. Some degree of monetary policy had been attempted by the Federal Reserve Board in the 1920's, and monetary controls were tried in England to a very limited extent during the nineteenth century. Public works were tried in an effort to ease the effects of the depression in the early 1930's, but the 1-The most widely read of the Italian contributors was Antonio de Viti de Marco, whose best known work is First Principles of Public Finance (New York: Harcourt, Brace & Co., Inc., 1936). This was translated from the Italian edition which was published in Turin in 1934. 2 John Maynard Keynes, The General Theory of Employ ment Interest and Money (New York: Harcourt, Brace & World, Inc., 1936). 18 government expenditures were not large enough or consistent q enough to have a significant effect. A more sustained effort of compensatory spending was finally begun in 1938, but its effects were obscured by the beginning of World War II. Fiscal policy for growth was tried on a limited scale by President Kennedy, but the results were inconclusive. Several different approaches to fiscal policy have developed. These include: (1) an extreme functional finance concept in which government spending, taxing and borrowing are undertaken primarily for fiscal control pur poses; (2) a more moderate and flexible concept of managed fiscal policy; and (3) an automatic stabilizer concept. The goals of all of these approaches are similar: they would use the coordinated powers of the government^ to ad just the level of national income, support full employment, provide economic (including price) stability, encourage economic growth, secure an equitable distribution of in come, and influence our international balance of payments. The accomplishment of the various goals is made more difficult by the conflict which exists between the q J The e x a c t e f f e c t o f t h e s e e a r l y m e a s u r e s i s so m e w h a t o p e n t o d i s p u t e . ^This implies that fiscal policy be coordinated with other policies such as monetary policy, foreign trade policy, and social policies including urban renewal, edu cation, and many others. 19 separate objectives. One of these conflicts is between the support of economic growth with full employment and the maintenance of price stability; it is difficult for the government to maintain a high level of purchasing power without contributing to demand pull inflation. During times of full employment it is also true that labor has a strong bargaining position, and resulting pay increases can bring about cost push inflation. From the practical stand point, decisions must be made as to whether some price in creases are less harmful to the economy than some unemploy ment. In the United States, the concept of fiscal policy was given legislative acknowledgement by the Employment Act of 1946. This act recognizes the responsibility of the government to maintain conditions under which full employ ment, stability and purchasing power can be maintained. B a s i c E le m e n t s o f t h e T h e o ry First in degree of importance in developing a theory of fiscal policy is the determination of how govern ment taxes and spending affect the growth and stability of the national product. In order to make this determination, the structural components of national product must be de fined. This paper uses a highly aggregate component break down. 20 GNP =C+I+G+F where C = private consumption I = private investment G = government purchases of goods and services F = net exports In order that the GNP may increase, it is necessary that some of its components increase; and if one of the compo nents should at the same time decrease, then it is neces sary that other components increase correspondingly more. In the aggregate sense, then, if the policy calls for an increase of the GNP there are two fiscal tools which may be utilized: the government can adjust either personal or corporate tax rates in an effort to stimulate private consumption and investment expenditure, or the government can increase its expenditures for goods and services and increase transfer payments. If the policy calls for de creasing the aggregate demand, then the opposite action is called for. Certain supporting actions can add to the effec tiveness of a policy. Such actions include adjustments in government lending programs, government guarantee of loans, 5 Restraints in the form of price and wage guide lines have also been tried, and under certain conditions these can have a limited effectiveness. 21 and changes in the form of the government debt. These sup porting programs can change both the total purchasing power and the marginal propensity to consume, but they are sub sidiary to the government tax and spending programs. The tax programs directly affect both motivation and ability to perform the basic economic functions of producing, con suming, saving, and investing; and the government spending program adds directly to aggregate demand. The discussion of the theory of fiscal policy up to this point has been static in method, and therefore it can be seriously misleading if considered only by itslef. For tunately there is a rather well developed theory for com parative static analysis and a less well developed theory for dynamic analysis. The most important tool of comparative statics in relation to fiscal policy is the multiplier. The multi plier theory implies that a change in the level of govern ment spending or taxing will not only have direct effects on the national income and product, but also will have in direct effects through several levels of induced spending. Thus to bring about a movement from one level of national income to another, it is not necessary to assume that the government need increase its expenditures by the total amount because an increase in private spending will be in duced by an autonomous increase in government spending. The simple multiplier relationship may be expressed symbolically as: A y = A g l-c where Y is national income and c is the marginal propensity to consume. The factor • = ——— is the multiplier. This ex- 1—c pression may be explained as follows. A change in na tional income may be viewed as having an autonomous compo nent A ya and an induced component A yj * Thus: A y = A ya + A*i Since induced expenditure depends on the marginal propen sity of the society to spend its earned income, this may be rewritten as follows: A y = A ya + c A y where c = A Y j/ A y Solving for yields: A y = ^ A ya The government tax and transfer payment multipliers are slightly smaller than the above because the transfer ^A similar explanation is found in most principles of economics texts. 23 does not go directly to or from the income stream. In the case of a transfer payment, for example, a portion of the amount would be saved and only a portion would be spent. Thus: A?tp = cAw where A YTp the change in national income induced by the autonomous change in transfer payments TP. If the ex pression for A ytp substituted f°r A ya the equa- tion for A Y' we have: A y = c A tp + c A y Again solving for A Y, Ay = Atp l-c The multiplier in this case is c/l-c. Dynamic Aspects of the Theory In moving from this comparative static analysis to a dynamic analysis we are presented with the greatest prob lems of fiscal policy. These problems are brought about primarily by time lags in the investment process, and time lags in the implementation of the fiscal policy measures. If changes in investment be negatively correlated with changes in capital stock of the preceding period in an ac celerator relationship, then a one period time lag in 24 implementing the fiscal policy measure can be destabilizing. n A number of writers have demonstrated this general point under differing assumptions; they claim that contracycle policy can be destabilizing by increasing the amplitude of cycles over what they would have been if the policy meas ures had not been enacted. O It was shown by Cornwall that the effectiveness of fiscal policy depends on the degree of accuracy of fore casts.^ He bases his argument on an accelerator-multiplier model: Ct = aYt-l Zt = b(Yt-l " Yt-2> W. J. Baumol, "Pitfalls in Contracycle Policies: Some Tools and Results," The Review of Economics and Sta tistics , XLIII (February, 1961); A. W. Phillips, "Stabili zation Policy in a Closed Economy," Economic Journal, XLIV (June, 1954); "Stabilization Policy and the Time Forms of Lagged Response," Economic Journal, LXVII (June, 1957); D. J. Smyth, "Can Automatic Stabilizers be Destabilizing?" Public Finance (1963); Milton Friedman, "The Effects of a Full-Employment Policy on Economic Stability: A Formal An alysis," Essays in Positive Economics (Chicago: University of Chicago, 1953). ^John Cornwall, "The Structure of Fiscal Models," The Quarterly Journal of Economics, LXXIX, No. 4 (November, 1965),608. 9 This is discussed also by H. Theil, Economic Fore casts and Policy (Amsterdam: North Holland Publishing Co., 1958). Theil discusses both predicting the changing en vironment and forecasting the effects of the policy maker's measures. where Ym is the target level of income. If government spending is regulated in accordance with the fourth equation so that Y, = Y1 * 1, and if we assume t that w = 1, then fiscal policy can be stabilizing. The argument is general because once the target-instrument ap proach is used, the behavior of the target becomes exoge nous . But when a time lag in government spending is intro duced, then the situation changes in that the fourth equa tion instructs the fiscal authority to change G based on the previous value of income. This makes the effectiveness of fiscal policy dependent on the accuracy of the forecasts and emphasizes the critical importance of developing good predictive models as fiscal policy tools. A General Theory of Fiscal Policy A general theory of fiscal policy is presented by Hansen, who begins with,a discussion of a model with n equations of the form: -^Bent Hansen, The Economic Theory of Fiscal Policy (Cambridge: Harvard University Press, 1958). Also, Jan Tinbergen, Economic Policy: Principles and Design (Amster dam: North Holland Publishing Company, 1956). 26 F - [ _ , • • • ; a ^ . 9-^) (i 1,. . .n) The Xj_1 s are the n endogenous variables and the a^1 s are the m exogenous variables. Some of the exogenous variables are controllable and some are not. This model provides the technical framework for a "means and ends" discussion. Target values may be assigned to endogenous variables, and under certain conditions the system may then be solved for values of the controllable exogenous variables. Not all of the exogenous variables are controllable, but in the ideal case in which the system is completely interdependent, changes in any of the controllable parameters will influ ence the value of all endogenous variables. In such a sys tem it might be possible to effect any desired end by a sufficiently large change in a controllable variable which is arbitrarily chosen. In reality, there are numerous restraints on the selection of the controllable variable and the amount that it can be changed. Some of these restraints are theoreti cal; for example, dynamic models are normally not com pletely interdependent'*''*' so that only certain means can be used to attain certain ends. Also, different conflicting ends might be postulated for which there is no solution but only some joint optimum combination of the ends. Other 1;LIbid. 27 restraints may be social or institutional in character; for example, there are political and economic constraints to the amount by which taxes can be raised. Goldberger-^ has pointed out that the coefficients of the reduced form of such a model will immediately give a measure of the effect of changes in the exogenous variables on each of the endogenous variables. Goldberger calls these coefficients the "impact multipliers." A similar 13 method is used by Suits m relation to models for policy prediction. The Formation of Fiscal Policy This study is primarily concerned with a model for evaluation of measures which governments may take to imple ment particular fiscal policies. The formulation of an appropriate policy is quite another matter and will be dealt with only briefly. There are many different kinds of economic policies, some of which are concerned with gen eral long-range goals, and some of which represent reac- I O Arthur S. Goldberger, Impact Multipliers and Dy namic Properties of the Klein-Goldberger Model (Amsterdam: North Holland Publishing Company, 1959). 13 Daniel B. Suits, The Theory and Application of Econometric Models (Athens: C. Serbinis Press, 1963). 14 For a treatment of this topic, see Jan Tinbergen, op. cit. See also H. Theil, op. cit. 28 tions to current situations and problems. The kind of fis cal policy which is being discussed here is primarily con cerned with current situations. The general approach in formation of the policy is to first analyze the various aspects of the current situa tion. Ideally, problems of growth, stability, employment, and trade balance are all brought into the study. Goals are then set, and different approaches for the achievement of these goals examined. A specific policy is finally de cided upon in relation to the goals, and an appropriate program is put into operation. Institutional Considerations Some of the important factors in the implementation of fiscal policy are institutional in character because these institutional factors influence the timing and the effectiveness of control measures. The machinery of governmental action is among the most important of the institutional factors for it includes the methods of enacting and carrying out legislation, and these in turn affect the time lags which are required in the recognition of a problem, the taking of action, and the resulting effects. Governmental factors include the nature of the legislative process, the degree of administrative discretion, the availability and acceptance of professional 29 advice, and the administrative organization for carrying out a program. A consensus on goals is required, such as might be provided by economic legislation, and a degree of legislative and popular understanding are essential. To be successful, any program must have the support of the public in general and of the business community in particular. The ability to coordinate fiscal policy with other policy is also extremely important. Most of these institutional conditions fall outside of the usual jurisdiction of the economist, and he must consider them as given conditions in his analysis. II. DEMAND MODELS The previous section provides a review of the back ground and theory of fiscal policy, with the important con clusion that good predictive models are essential to the success of fiscal planning. Before presenting the predic tive model which will be used in this paper, it is appro priate to review the development of demand models so that the study presented here may be placed in proper perspec tive . The first econometric models were those prepared by 30 1 5 Jan Tinbergen for the British and American economies. Recent advances in data collection and in theory which have resulted from the Keynesian influence have made improved models possible due to a better understanding of the struc ture of the economy. The contribution of Tinbergen is nevertheless an important one. The Contributions of Klein Some o f t h e m o s t r e c e n t c o n t r i b u t i o n s w h ic h l i e a l o n g t h e l i n e s o f t h i s p a p e r h a v e b e e n made b y L . R. K l e i n . I n a d d i t i o n t o h i s d e v e lo p m e n t s w h ic h a r e d e s c r i b e d i n t h e c i t e d w o r k , h e h a s b e e n a l e a d i n g f i g u r e i n p u t t i n g t o g e t h e r t h e many c o m p o n e n ts o f t h e B r o o k in g s q u a r t e r l y m o d e l . T h e s e m o d e ls a r e i n t h e K e y n e s i a n fra m ew o rk o f a g g r e g a t e in c o m e , and c o n s t r u c t f u n c t i o n a l r e l a t i o n s h i p s f o r d i f f e r e n t t y p e s o f n a t i o n a l e x p e n d i t u r e . K l e i n h a s Jan Tinbergen, Statistical Testing of Business Cycles Theories, II, Business Cycles in the United States of America 1919-1932 (Geneva: League of Nations, 1939); An Econometric Approach to Business Cycle Problems (Paris: Hermann et Cie, 1937). 16 Lawrence R. Klein and A. S. Goldberger, Econo metric Model of the United States, 1929-1952 (Amsterdam: North Holland Publishing Company, 1957) ; IiT R. Klein, et alr An Econometric Model of the United Kingdom (Oxford: OxForcT University Press, 1961). 17 Duesenberry, Fromm, Klein, Kuh, The Brookings Quarterly Econometric Model of the United States (Chicago: Rand McNally & Co., 1965). 31 also attempted to take into account different types of in come, prices, and wage rates. In so doing, he has effec tively broken the aggregate economy down into several func tional sectors. The Klein-Goldberger model was one of the most sophisticated models of the United States prior to the Brookings model. The Klein-Goldberger model was based on 18 the earlier experience of L. R. Klein, but attempted to explicitly include price and wage changes and to explicitly include the production process. The model is based on the Department of Commerce concepts and definitions, as is the model presented in this paper. Both real and absolute values are used in various aspects of the model, and data for estimation extend back to 1929. The Klein-Goldberger model attempts to describe both aggregate phenomena and the interrelation of sectors. Thus private employee compensation is separated from gov ernment employee compensation, and farm income is separated from non-farm income. The model has fifteen equations. These are labeled as follows: (1) The Consumption Equation; (2) The Invest ment Equation; (3) The Corporate Savings Equation; (4) The ^Lawrence R. Klein, Economic Fluctuations in the United States, Cowles Commission Monograph, No. 11 (New York: John Wiley & Sons, Inc., 1950). 32 Relation Between Corporate Profits and Non-Wage Non-Farm Income; (5) The Depreciation Equation; (6) The Demand for Labor Equation; (7) The Production Function; (8) The Labor Market Adjustment Equation; (9) The Import Demand Equation; (10) The Agricultural Income Determination Equation; (11) The Relation Between Agricultural and Non-Agricultural Prices; (12) The Household Liquidity Preference Equation; (13) The Business Liquidity Preference Equation; (14) The Relation Between Short and Long Term Interest Rates; and (15) The Money Market Adjustment Equation. The system has a number of quite original proper ties. It does not use the classical equation of exchange, and it attempts to include speculation and market bargain ing. The model is highly nonlinear in form, with the de mand for household balances being exponential, and with some variables depending on current money prices and others on absolute prices. The Brookings Quarterly Model The Brookings Quarterly Econometric Model of the United States^ is by far the largest and most ambitious project of its kind which has ever been attempted. With over 150 structural equations and seventy-five identities, ■'•^Duesenberry, Fromm, Klein, Kuh, op. cit. 33 it is not only large but cumbersome. It attempts to put together in the form of a single model the theories and empirical findings of a large number of individual econo mists who are working independently throughout the country. It could be argued that this huge model violates at the outset one of the fundamental tenets of model building; that is, that no model can hope to simulate all aspects of the thing being modeled, and that the preparation of any model must include at the outset a statement of the purpose of the model. After the purpose has been specified and the specific desired outputs are known, then the model can be structured in such a manner that relevant theory and obser vation can be included and the nonrelevant can be excluded. The intentional exclusion of irrelevant information is just as important as the inclusion of the relevant, for it is desirable to abstract from those factors which would only obscure the workings of the system. In line with this observation, it is probable that the greatest contribution that the Brookings model will make will be the information that its development will pro vide into the interrelation between the many different sec tors of the economy. It is doubtful whether any predictive data which are generated by the model itself will ever be of sufficient value to justify the effort required in put ting together this monstrous system. Such specific predic- 34 tive data could surely be generated as well or better by smaller models which are tailored to a specific purpose. But the very structuring of the Brookings econometric model will no doubt prove to be an informative project in itself, and it is therefore not intended here to underemphasize the importance of that model. The Structure of the Brookings Model The Brookings model is block recursive in structure as is the much simpler model presented in this paper. The endogenous values which are generated by each block are de termined by the equation parameters of that block, by exog enous variables, and by the outputs from lower order blocks. The output from the blocks then feeds into the next higher blocks in the recursive causal chain. The lowest order block generates investment antici pations, which depend on lagged values of industry output and capital stocks. In this sector, as in many others, the endogenous variables depend on their own lagged anticipa tions and on lagged investment, output, and profits. Thus it is the lagged values of the fixed capital formation variable that start the system going. The calculation of consumption expenditure is very complex, and depends on the solution of a large simulta neous block of the system because it requires current prices 35 and disposable income in addition to lagged values of con sumption itself. A third important block calculates orders received, labor requirements for fulfilling the orders, inventory changes, and factor income. The fourth big block deter mines market prices, wages, and interest rates. These are all separated into industry blocks to show the interrela tion between sectors, as opposed to the much simpler aggre gative approach taken in the model presented in this paper. Of particular relevance here is the iterative pro cedure used~to solve for labor requirements, gross output, labor compnsation, and prices. After obtaining initial preliminary estimates, the equations within the block are successively solved, and then the solution is repeated un til the values calculated on successive iterations remain approximately constant. Simple vs. Complex Models In relation to the highly complex Brookings model, it is relevant to review articles by Friend, Jones, and ? n Taubman which conclude on both a priori and empirical 20 I. Friend and R. Jones, "Short-Run Forecasting Models Incorporating Anticipatory Data," Models of Income Determination, Studies in Income and Wealth, XXVIII (Princeton, 1964); I. Friend and P. Taubman, "A Short-Term Forecasting Model," The Review of Economics and Statistics, XVIV (August, 1964), 229-36. 36 grounds that simple small-scale models give at least as good results as more complex models for short-run fore casting of the gross national product. They found that the use of a relatively simple model containing four structural equations and one identity gave good fits for the period 1951 to 1960 and good prediction for 1961 and 1962.- They raise serious questions about the theoretical rationale for and the usefulness of results obtained by increasing the disaggregation of the demand equations. They also found that semiannual and annual models gave somewhat better results than the quarterly models. This is attributed to the averaging out of "erratic short term changes in the data (including errors in observation) ." Causal Chain Models The theory of recursive models has been developed 21 by Herman 0. A. Wold, who uses the term "causal chain" to refer to a recursive system "when the system is filled with subject matter content so as to make a full-fledged dynamic model." Wold gives the formal representation of a recursive ^Herman 0. A. Wold, Econometric Model Building (Amsterdam: North Holland Publishing Company, 1964); Herman Wold and Lars Jureen, Demand Analysis (New York: John Wiley & Sons, Inc., 1953). 37 22 system, and proves in theorem form that least-squares re gression will under general conditons provide consistent parameter estimates for eo ipso predictors, where eo ipso 23 predictors are defined as follows: Suppose that a model involves the variables y, Xl'**'Xn' w^ere the variable y allows the representation y = f (X^,...Xn) + U where U is the error term with E (y | Xx,...Xn) = f (Xx,...Xn) . Then y* = pred y = f (X1,...Xn) is called an eo ipso predictor of y. 2 4 Wold also presents the existence theorems about eo ipso predictors. This work of Wold will be used in Chapter IV on the estimation of the model. Some Notes on Other Related Studies It will be useful to review briefly some other re lated articles. While these articles did not contribute to ^ Ibid. , Theorem 2, p. 12. ^ Ibid. , p. 10. 24 Ibid., Theorems 7 and 8, pp. 24-25. 38 the tools of this study as directly as the previously cited works of Klein or Wold, they nevertheless provide an impor tant contribution to the literature and have had an influ ence on this study. One of the following paragraphs is devoted to each of these several articles. A paper which bears directly on the topic discussed 25 in this thesis was prepared by E. M. Gramlich. His study centers on the effect of the federal budget on aggregate demand, and draws the conclusion that an expansionary fis cal policy will be necessary in the years ahead in order to maintain aggregate demand at a full employment level. Demand models for use with national account data of the OEEC countries, the United States, and Canada, were 2 6 p r e p a r e d by B a l d e r v o n H o h e n b a lk e n and G erh a rd T i n t n e r . In general, the models have five equation, including two structural equations and three identities. The five endog enous variables are personal consumption, nominal gross national product, price index of gross national product, real gross national product, and total employment. Exoge nous variables are population, public consumption, gross 2^E. m . Gramlich, "The Behavior and Adequacy of the United States Federal Budget, 1952-1964," Yale Economic Essays (Spring, 1966), 6. 2 6 Balder von Hohenbalken and Gerhard Tintner, "Econometric Models of the OEEC Member Countries, the United States and Canada, and Their Application to Economic Policy," Weltwertschaftliches Archiv, LXXXIX (1962), 29. 39 fixed asset formation, increases in stocks, exports, im ports, and the nominal yearly wage per worker. The object of the models is to study the structural relationship be tween the selected aggregate variables and to examine pol icy alternatives. Given the original assumptions, it is thus possible to calculate the theoretical changes in the instrument variables which would induce desired changes in 2 7 the target variables. The studies of Friend and Taubman^ resulted in the preparation of a short-term forecasting model. This was a semiannual simultaneous equation model with four categories of demand: consumption, housing, plant and equipment, and inventories. The signs of the regression coefficients are all in accordance with theoretical expectations, and magni tudes of the coefficients all appear reasonable. The model uses anticipatory data for the short-run predictions and is therefore of no value for any predictions other than the short-run. The model cannot be criticized on this basis, however, since it makes no claim of being anything other 2^For additional works by the same author regarding theoretical derivation of the elasticities of demand and expenditure in a dynamic framework, see: Gerhard Tintner, "The Theoretical Derivation of Dynamic Demand Curves," Econometrica, VI (1938), 375; Gerhard Tintner, "Elastici ties of Expenditure in the Dynamic Theory of Demand," Econometrica, VII (1939), 266. 2 8 I. Friend and P. Taubman, op. cit. 40 than a short-term model; and it appears to succeed remark ably well in its objectives. 2 9 The Klein-Shinkai model of Japan is tested m an •3 n article by T. Blumenthal. It is found that predictions based on the model are not accurate, so an effort is made to test the assumptions on which it is based. The study finds that the assumption that the prewar and postwar peri ods can be regarded as one sample period is in error due to structural differences. The poor predictive ability of the model is therefore related to changes of the structure of the Japanese economy for the two periods which cannot be explained by a change in levels alone. A study which was in certain respects similar in objective to the study presented in this paper was per formed by Ta-Chung Liu^^ in 1963. Liu constructs a demand model of the U.S. economy using quarterly data from 1947 to 1959. The model is substantially larger than that pre sented in this paper with thirty-six jointly dependent ^L. r. Klein and Y. Shinkai, "An Econometric Model of Japan 1930-59," International Economic Review, IV (January, 1963), 1-28. 30 Tuvia Blumentahl, "A Test of the Klein-Shinkax Econometric Model of Japan," International Economic Review (May, 1965), 211-28. 31 Ta-Chung Liu, "An Exploratory Quarterly Economet ric Model of Effective Demand in the Postwar U.S. Economy," Econometrica, XXXI, No. 3 (July, 1963), 301-48. 41 variables and fifty-two predetermined variables. Liu uses the model to predict the effects of alternative monetary and fiscal policies. He concludes that government spending can be used to speed economic growth, but that a mere re duction in the rate of increase in government spending would be sufficient to bring about a recession. He calculates the time lags between the appearance and the maximum effect of fiscal and monetary policy measures, and concludes that the lag is about five to six quarters. He concludes also that the delayed effects would swing between positive and negative magnitudes and are therefore perverse during cer tain phases of the movement. Liu's conclusions are of par ticular interest here, because they differ somewhat from those suggested by this paper. Among the papers on automatic stabilizers, the most relevant to the present topic is a recent study by P. Eil- 32 bott which measures the quantitative effectiveness of automatic stabilizers by employing a multiplier model to determine the effect of induced tax and transfer payment changes on private spending. The Eilbott model tests the impact of individual and corporate income taxes, and un employment and OASDI benefit payments and contributions. The study attempts to measure the percentage by which these 32 P. Eilbott, "The Effectiveness of Automatic Stabilizers," American Economic Review (June, 1966), 56. 42 stabilizers reduced the potential changes in national in come during the three cycles between 1948 and 1960. Ac cording to his model, the stabilizers prevented from 36 per cent to 52 per cent of the income declines that would have occurred without the effect of the automatic stabilizers. Interest in the use of dynamic models has increased in agricultural economics along with their use in other fields of economics. Some of the forms which these models 33 have taken are described by Crom and Maki. These models are relevant to the present topic in that they may be either simultaneous, or recursive, or both (recursive with simultaneous subsets). Most of these models deal with the production or marketing of specific agricultural products , 3^ III. CONCLUSIONS It can be concluded from the first section of this chapter that the concept of government fiscal policy is a relatively recent development, and that it now provides something less than a panacea for the economic ills of a 33Richard J. Crom and Wilbur R. Maki, "Adjusting Dynamic Models to Improve Their Predictive Ability," Jour nal of Farm Economics, XLVII, No. 4 (November, 1965), 963-72. 34 For example: K. J. Cohen, Computer Models of the Shoe, Leather, Hide Sequence (Englewood Cliffs: Prentice- Hall, 1960); and Factors Affecting the Price and Supply of Hogs, USDA Technical Bulletin 1274, 1962. 43 nation. The objectives may be conflicting, and certain aspects of the theory are incompletely developed. The second section of the chapter provides a review of recent contributions to the development of demand models, and again it is apparent that much work remains before these models can provide consistently accurate forecasts. The present study is therefore carried forward from the point of view that for the present fiscal policy meas ures are at best an imperfect tool. However, it should not be inferred without further evidence that fiscal policy could never have a useful function, or that its theory should not be further developed. It was shown by Cornwall that the effectiveness of fiscal policy depends on the ac curacy of the prediction, and the work of Klein, Wold, and others is contributing to the development of better pre dictive models. CHAPTER III PRESENTATION OF THE MODEL This chapter presents the theoretical model which is used for predicting aggregate demand. The model is dynamic with a block recursive form; the implications of this form relative to the method of estimation and solution are discussed in Chapter IV. The general orientation is Keynesian as with most current models. I. INITIAL CONSIDERATIONS Autonomous Variables Since the model was prepared for the study of fis cal policy measures, it was constructed with the objective of having policy variables as exogenous to the system. Certain lagged or predetermined variables are also exoge nous , and in this way the causal-chain technique can be used to predict the effects of a given policy for a period of several years. Thus initial conditions may be taken from known values for a single year; and if policy vari ables be assigned for a period of several years, then the recursive feature of the model will predict the dynamic 45 movement of the endogenous variables for several time periods. spending for goods and services (G), net exports (F), transfer payments (X), and social security payments (J). Also included are two monetary policy variables: a reserve requirement variable (q), and a measure of member bank un borrowed reserves with the Federal Reserve System (Z^). The exact definitions and implications of the monetary variables are discussed in the section on the money market later in this chapter. Finally, among the exogenous vari ables is a variable labeled 0 which is the sum of "other small factors," the sum of which is usually less than one billion dollars. This 0 is the sum of (1) business trans fer payments, (2) subsidies, (3) surplus of government en terprises, and (4) statistical discrepancy. The exogenous variables will be represented symbolically as follows: The exogenous policy variables include: government (1) G t G (2) (3) t (4) (5) <3t = Sot It is recognized that most of the "policy" vari ables have some endogenous component; for example, endoge nous imports in net foreign investment. The simplifying assumption is made that the total magnitude is under policy control; that is, that foreign aid and the support of mili tary forces abroad may be adjusted to control the total magnitude of net foreign investment. This will be justi fied on the grounds that the government component of the foreign sector is relatively small in relation to the gross national product. Transfer payments and net exports are listed in Table I for the period from 1953 through 1965. It can be seen that both the magnitude and changes in net exports are very small relative to the gross national product. Trans fer payments, while larger in magnitude, change in a very orderly way. The variables which are of greatest interest in a study of fiscal policy are the government purchases of goods and services in equation (1) above, and the tax vari ables which are discussed in a later section. The tax variables are not exogenous because it is the tax rates which are set by policy action rather than the amount of Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 TABLE I NET EXPORTS, TOTAL TRANSFER PAYMENTS, AND GROSS NATIONAL PRODUCT FOR 1953 THROUGH 1965 IN BILLIONS OF CURRENT DOLLARS Total Transfer Net Exports Payments 0.4 14.0 00 • i —! 16.0 2.0 17.3 4.0 18.5 5.7 21.4 2.2 25.7 0.1 26.6 I —1 • 28.5 • in 32.4 5.1 33.3 5.9 35.2 • 00 36.6 1 —1 • t ' ' 39.2 Source: U.S. Department of Commerce. the tax collection. Social security payments are important in the cal culation because they are directly subtracted from wages before consumption expenditure is computed, and their total amount now approaches thirty billion dollars. This seem ingly innocuous term gave trouble when attempts were made to estimate it as a function of wage earnings. Social security is an element of the economy which did not remain "homogeneous" during the period of estimation. New groups of self-employed persons were added to the social security programs at intervals during the period, and the base amount per wage earner was increased from $360 0 a year in 1954 to $4200 for 1955-58, and $4800 a year from 1959-65. In spite of these increases, it was found that a linear function of wage earnings which was fitted to the data from 1954-63 tended to overestimate the social security payments for 1964 and 1965. This was apparently due to an increase in incomes for persons already in the labor force which was proportionately greater than the number of new persons en tering the labor force. It was not desirable to bring the size of the labor force explicitly into the model because it would unnecessarily complicate the model structure; so the social security tax was treated as exogenous. 49 Initial Conditions Lagged values of certain variables appear in the equations of the model. These lagged variables are pre determined, and are therefore handled in a different way than are the exogenous policy variables listed above. Values of policy variables (i.e., government spending, net foreign investment, tranfer payments, etc.) must be pro vided for each time period, while values of lagged vari ables need be provided only for the initial period and cal culated values may be used for subsequent time periods. The lagged variables required as initial conditions are the following: K^_ = capital stock It_2 = gross investment Lt_j_ = capital consumption Dt_i = monetary constraint variable (discussed later in this chapter) Et_j = non-wage components of personal income Capital Formation and Capital Consumption The capital stock is calculated at the beginning of each time period by adding the net capital formation of the 50 previous period to the capital stock existing at the begin ning of that period. (8) Kt = Kt_x + It_x - Lt_1 where K = capital stock I = gross investment L = capital consumption During each time period a certain amount of the ex isting capital will be consumed in the production process. Not only is capital consumed through ordinary depreciation and depletion, but also through the process of obsolescence. The model calculates capital consumption as a function of the capital stock in existence at the beginning of the time period. (9) Lt = L (Kt) II. THE SIMULTANEOUS BLOCK The six equation presented in this section repre sent a simultaneous block within the recursive system. This block is extremely important for it calculates invest ment, consumption, and gross national product. The block fits into the overall recursive scheme because variables which are exogenous to the block are all previously deter mined, while variables endogenous to the block are required 51 for subsequent computations for the same time period. The equations within this block must be solved simultaneously because the endogenous variables are simultaneously deter mined with feedback between them. By this it is meant, that private consumption is a component of the gross national product and consumption is dependent on current wage income; but wage income depends in turn on gross national product. The six equations must be solved as a simultaneous block because such feedback effects are not allowable in a recur sive system; each relation of the recursive system must represent a one-way link in the causal chain. Investment The investment term is developed from the accelera tor concept, but with a monetary constraint. Later in this section the work of Dale Jorgenson^ will be used to show that this becomes a special case of the neoclassical theory. In using the accelerator to predict investment, the basic hypothesis must be accepted that at any given time the desired volume of capital stock is determined by pre vailing technology and the level of the gross national product. Producers wish to maintain a given level of ag- 1-Dale W. Jorgenson, "Anticipation and Investment Behavior," The Brookings Quarterly Econometric Model of the United States (Chicago: Rand McNally & Co., 1965). 52 2 g r e g a t e c a p i t a l i n r e l a t i o n t o g r o s s o u t p u t . A l g e b r a i c a l l y t h i s i s e x p r e s s e d a s : The is gross national product. The coefficient a is the capital coefficient; it changes over time as technology changes, but it is regarded as stable over a short period. There are several kinds of errors inherent in the use of theories of this kind, and these will be discussed in the first section of the next chapter.^ The expression was rewritten to represent the de sired capital stock at a given level of output. ^This assumes (1) U shaped average cost curves in most industries, (2) that producers wish to maximize prof its, (3) a generally competitive market structure, (4) that technology changes little during the period of study, and (5) linear homogeneous production functions in most indus tries. Under the first three assumptions, producers will in general be producing near the low points of their aver age cost curves; and under the last two assumptions, in creases in inputs will result in proportional increases in production. From 1954 to 1963, a increased by about 10 per cent, with the rate of increase being steady over the period. ^An excellent discussion of these kinds of errors is presented by Oskar Morgenstern, On the Accuracy of Economic Observations (Princeton: Princeton University Press, 1950) . 53 For the time increments of the study, this may be expressed as: K + (I - L ) = a Y,, t t t wt where I is gross investment. This expression states that a volume of investment will be undertaken during the period which will bring the capital stock up to a desired level, and it states also that the capital which is lost through capital consumption will be replenished. Investment in the Brookings Model It will be useful to relate the preceding invest ment argument to the presentation of Dale Jorgenson^ for the Brookings model. Jorgenson's thesis is based on the neoclassical theory of demand for capital services as de termined by the optimal accumulation of capital. He refers to previous findings by researchers who claimed that the neoclassical theory is inconsistent with the facts, and points out that these findings resulted from nonrigorous formulations of the theory. Let us therefore examine c Dale W. Jorgenson, "Anticipation and Investment Behavior," The Brookings Quarterly Econometric Model of the United States (Chicago: Rand McNally & Co., 1965). Jorgenson's formulation, and relate it to our own. Jorgenson separates investment into two types— new additions to capital stock and replacement investment. The replacement investment (IR) is taken to be a fraction of the capital stock existing at the end of the previous time period:^ IRt = dKt-1 Additions to capital stock are calculated from new invest ment starts (IN), which for each period are equal to the E period-to-period change in desired capital stock (K ). INt = Kf.i Since there is a time lag from the start of new investment projects to the fruition of the projects, a distributed lag function u(9) is introduced. These completed new invest ment projects (IE) are given by: IEt = u (0) (K® - K^_x) Gross investment is the sum of the two types of investment. It = IEt + ^ J o r g e n s o n ' s n o t a t i o n i s u s e d h e r e . N o t e t h a t h e u s e s K. t o r e p r e s e n t c a p i t a l s t o c k a t t h e en d o f t h e p r e v i o u s t im e p e r i o d , w h i l e i n t h e p r e c e d i n g d i s c u s s i o n K w o u ld r e f e r t o c a p i t a l s t o c k a t t h e b e g i n n i n g o f t h e p r e c e d i n g p e r i o d . Substituting for IE and IR gives: It = u (©) (K^ - K®_1) + dKt_x This represents the theory of investment behavior as pre sented by Jorgenson. The argument is then extended to re late the capital stock to the national output, with output determined by the production function and by the marginal productivity condition for current input. If the actual level of capital stock be given, the desired capital stock may be found from the relation: KE + a|x where X is the national output, p is the price level of the output, and c is the cost of the inputs. It is apparent at this point that our investment function which is based on the accelerator concept is merely a special case of the neoclassical theory presented by Jorgenson. The lag function is unity in the accelerator model, meaning it is assumed that investment starts are completed in the same time period in which they are started, or that the volume of unfinished investment which is car ried over into successive years remains reasonably stable. This can be an acceptable assumption in an annual model which is estimated over a fairly homogeneous time period, due to the length of the time increment and the slowing of 56 investment activity around the first of the calendar year which results from environmental and institutional con straints. The assumption would not be valid in a quarterly model. Investment and the Money Market It can be argued from economic theory that the level of investment is influenced by monetary variables. This thesis was supported by two overt events of recent years. First, following the tax cut of 1964, the deposits of the savings and loan type of financial institutions rose as a result of the larger amounts of money savings which were made available to them by the household sector. This brought about an aggressive policy to sell additional loans, and in turn, the business sector responded with increased investment plans in 1964. The actual increases in invest ment expenditure began early in 1965. The time lag was due, to the time required for the pressure of additional money savings to build up in certain of the financial institu tions, for these institutions to become more aggressive in their selling of loans, and for the resulting new invest ment plans of businesses to be carried out. The events which resulted from the tax cut of 1964 support the thesis that part of the effect of fiscal policy 57 measures work through the resulting monetary phenomena. It is therefore desirable that a monetary constraint for the investment function be investigated. A second recent event which would support inclusion of such a monetary constraint is the "tight money" policy of 1965 and 1966. This had the apparent effect of de pressing investment in some sectors of the economy in 1966. Some monetary policy measures were also attempted during the decade of this study, and it is important that any re sulting effects should not be falsely attributed to fiscal policy. Preliminary investigations were undertaken to de termine the form which the monetary constraint should take, and a regression of investment was attempted on such vari- 7 ables as interest rate, money supply, and free reserves. No meaningful relationship was found in these early investi gations . A loanable funds constraint variable (B) was there fore tried with somewhat greater success. This variable is discussed in the next section of this chapter, and is de fined in equation (31). It is a lagged variable, so it is exogenous to the simultaneous block. The functional form of investment then appears as: ^Free reserves are defined as excess reserves less borrowings by member banks. 58 (10) The capital consumption variable (L) has been ex cluded because equation (9) expresses Lt as a function of Kt. Disposable Wage Income Disposable wage income is important in the deter mination of private consumption expenditure. The total wage earners1 share of the national product has remained remarkably stable over the years, at slightly over 60 per cent of GNP. Wage earners' compensation is found as a function of GNP. Taxes and social security payments must be sub tracted before net wage earnings may be obtained. There fore : (11) AWt ” Aw (Yw} where A^ = total wage earnings. (12) TAt ~ TA (AWt> (13) A, l N A l W t t t where T^ = taxes on wage earnings A^j = net or disposable wage income 59 It would be possible to combine equations (11), (12), and (13) into two equations because T is a function ri of A^, ^ is a function of Y^, and is subtracted from A^ to determine A^. This is not done, however, and equation (12) is kept as a separate function in order to study more directly the effects of changes in the tax rates. P r i v a t e C o n su m p tio n E x p e n d i t u r e A Keynesian consumption function is used; however, an effort was made to include the distribution of income explicitly in the function. The small number of degrees of freedom in the estimation prohibits a complete breakdown of income recipients, but distribution between wage and non wage earners was considered. Current values of wages are used, while lagged values of the non-wage component of earnings are used in the calculation. This expresses an assumption that the spending habits differ between the dif ferent kinds of income recipients. The consumption of the recipients of wage earnings and transfer payments is depen dent on their current earnings. Recipients of other types of income are less dependent on the ups-and-downs of their current income, so that the calculation of their consump tion expenditure may be based on lagged values of earnings. This assumption is somewhat similar to the permanent income hypothesis of Friedman, but it assumes also a high degree 60 of autocorrelation of both annual income and consumption in the non-wage earner class. The assumption will be tested by trying also Et in place of The consumption function was therefore written as: (14) Ct = C(AN , Et_1) where E is the sum of non-wage components of personal in come; that is, the sum of rental income, interest income of individuals, dividends, and proprietorship income. Gross National Product The gross national product is calculated as the sum of its component parts. i (15) Y = Ct + It + Gt + Ft III. DISTRIBUTION OF THE NATIONAL PRODUCT One of the important assumptions of the model is that the distributive shares of the GNP remain stable. This has held true for a considerably longer period than the period of this study, and the empirical results pre sented in the next chapter show that the assumption holds well during the period of the study. 61 Indirect Business Taxes While indirect business taxes are not part of the national income, they are nevertheless a component in the allocation of the GNP. The tax laws had no significant changes during the period of the study, so it is appropri ate to use a single function for the entire period. National Income Shares The distributive shares of the national income are calculated as functions of the GNP. These shares have re mained stable as previously mentioned, but this should not be taken to mean that they have remained constant. The share of interest income has increased as the GNP has in creased, while the share of rental income and proprietors' income have declined slowly. These changes have occurred in a consistent and predictable way; the data are shown in Table XIV, Chapter IV. The relations are expressed as follows: (16) where T I indirect business taxes. (17) (18) Rt ■ R(v 62 (19) (20) where NN = net interest (total interest payments less government interest payments) R = rental income of persons Pp = personal proprietor's income = corporate profits The gross national product is by definition the sum of its distributive shares in allocation. At this point the model must be over-determined because equation (21) holds by definition, but each of its terms has been previously determined. The relation which deter mines one of its terms may therefore be dropped; the selec tion of which one to drop will be left until the estimation process. Personal Income Aggregate personal income is the sum of factor pay ments to persons. It includes transfer payments and inter est payments made by the government, both of which were excluded from the national income. It includes dividends (21) Ytt = a , + N + R, + P_ + Tt + L. + P_ + 0. Wt % Nt t pt It t Ct t 63 paid to corporate owners, but it does not include the por tion of profits which are retained by the corporation. , Before calculation of personal income, it is there fore necessary to predict total interest payments and divi dends. The yearly changes in both are small; both can be O predicted with reasonable accuracy as functions of GNP. (22) Dt = D (Yw ) (23) N = N (Y ) K ’ wt w vxwt' where D = dividend income N^ = total interest income of individuals It is convenient at this point to sum up the non wage components of personal income, as the lagged value of this sum will be needed for calculating consumption expen diture in the next time period. (24) Et = Rf c + + Dt + Ppt Personal income may be calculated as the sum of its component parts. Payments for social insurance are not The effect of fiscal policy measures act on D and Nw through Yw in the model. It should be recognized that both D and Nw are also dependent on other variables. 64 regarded as part of personal income, so they are subtracted out. (25) YP ~ AW Jt + Rt + NW + Dt + Xt + PP t t t t where Y^ = personal income Tax Payments and Disposable Income Personal taxes are found as a function of personal income, and corporate taxes as a function of corporate profits. The tax payments referred to are the sum of fed eral, state and local taxes. Since a new federal tax rate was put into effect in 1964, the tax function will have to be re-estimated for data after that date. Total taxes are the sum of indirect business taxes, per sonal taxes, and corporate taxes. Total taxes are of in terest because we may wish to determine the effect of a change in the tax laws on the total receipts of governments. (26) T = T (Y ) xp p ' p > t (27) where Tp = personal taxes Tc = corporate taxes where = total tax payments Disposable income is defined as personal income less personal taxes. where = disposable income The Money Market A lagged variable called B was used in the section on investment, and it was briefly defined as a monetary constraint variable. It is at this point in the recursive system that the information is available for the calcula tion of B, so it may now be discussed at greater length. It is intended that B should be a measure of loan able funds, and a contribution to these funds can be made by each sector: business, household, government, and foreign, and by the banking system. From the information which has been thus far determined by the model, we have the following measures of the contributions of these sec tors : Household (Yp - C) Business (Pc - D + L) Government (Tw - G - X) Foreign (-F) The above contributions to loanable funds represent in effect the voluntary savings of the respective sectors, but there is in addition a contribution to loanable funds which originates with the central banking authority. As pointed out previously, the increase in the money supply is not in itself an adequate measure of the resultant policy actions of the monetary authority. What is more pertinent as a policy variable is the potential loan expansion which could come about as a result of the Q policy action. For this we will use the method of Teigen which can be summarized as follows. Let: M = total money stock M* = amount of money which could be supported by unborrowed reserves, based on given reserve requirements and other institu tional characteristics of the system Zu = unborrowed reserves ZR = member bank required reserves on demand deposits P = currency in circulation Q Ronald L. Teigen, "Demand and Supply Functions for Money in the United States: Some Structural Estimates," Econometrica, XXXII (October, 1964), 476-509. 67 D„„ = demand deposits in member banks M Dn = demand deposits in non-member banks Now by definition: M = P + + Dn Assume: P = p M DN = h M Then: M = p M + hM + D.. * M 1 where Zp is free reserves (defined as excess reserves less borrowed reserves). The largest money stock could occur when excess reserves are zero, and borrowed reserves may be omitted from policy variables because they are under the control of the commercial banks. Therefore we have finally: A measure of the loanable funds which are generated during the time period by the four sectors of the economy and by the monetary authority may then be expressed as: 1 (30) Mi = rr t q(l-p-h) ut (31) B t * 68 Further examination of equation (31) indicates that the expression on the right less the money supply term must also be identically equal to investment in time period t. This comes from the identity that national income must equal national output, which expressed in our notation for the several sectors gives: YDt+ <pCt-Dt+Lt> + <TWt‘Xt)5YWt= Ct + It + Gt + Ft and in turn yields the following expression for I. Jt = <YDt-ct> + <TWt'Xt"Gt) + (PCt-Dt+Lt> - Pt The terms on the right represent the sources of real saving during the current period. The question then arises as to why we should go to the trouble of calculating B, since is predetermined. The answer lies in the fact that this makes it possible to disaggregate saving among the sectors, and to consider the effect on investment decisions of the different saving levels of the individual sectors. The saving of the indi vidual sectors and the actions of the different financial intermediaries by which they are served may influence the lines of credit which are established in one time period, but for which the corresponding investment projects do not come to fruition and appear in the national income accounts until the following period. 69 Thus in the estimation study of the next chapter, the imperfection of the money market will be considered by investigating the effect of including only certain sectors in the lagged loanable funds variable. It is important to consider that the capital funds market is an imperfect market,'*'® and that funds which originate as savings from the various sectors are not all placed initially in a single source from which all borrowers have equal access. For ex ample, saving by the business sector which is used for in ternal financing cannot be regarded as homogeneous with funds which originate from the household sector in their effect on business decisions. IV. SUMMARY OF THE MODEL TO BE TESTED (U Gt = Gq^ (2) Ft = F0t < 3> xt = xGt (4) Jt = JQ (5) t *t = *ot •*-®A related discussion of the capital funds market is presented by Kalman J. Cohen and Richard M. Cyert, Theory of the Firm: Resource Allocation in a Market Economy (Engle wood Cliffs, N.J.: Prentice-Hall, Inc., 1965). 70 (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) Zut Kt = Kt-1 + V l " Lt-1 Lt = L (Kt) It = I (YW , Kt, Bt_!) Awt ” Aw (YwtJ — A (AT a 7 ) W4 flNt *W " TA - Jt Ct = C (ANt, Et_1) YWt = Ct + Lt + Gt + Ft T w t T i ( Y w t > NNt _ NN !YWt* Rt = R (Y„t) PPt = PP (Ywt> PCt = PC < Ywt> YWt “ AWt+ NNt+ Rt+ PPt+ TX + Lt+ PCt+ °t Dt = ° <YW > 71 (23) N w t - N w < V (24) Et = Rt + % t + Dt + Ppfc (25) Ypt = AWfc - Jt + Rt + NW(. + Dt + Xt + Ppf c (26) Tpt = Tp (Ypt) (27) TCt = Tc (PCt> (28) TWt = Tpt + TCt + TIt (29) *Dt - *Pt - Tpt * 1 (30) M, = ——--r-r- Zn where p and h are re- t g(l-p-h) ut spectively the ratios of currency and non member bank demand de posits to total money supply (currency in circulation plus demand deposits) (31) Bt = (YDt-C) + (%t-Gt-Xt) + (Pct+Lt-Dt) " Ft + A m? Definitions of Symbols G = government spending for goods and services F = net exports of goods and services 72 X = total transfer payments K = total capital at beginning of the period L = capital consumption Aw = compensation of employees J = social security Ta = income tax on wage earnings C = personal consumption expenditure An = disposable income of employees Yw = gross national product Tj = indirect business taxes Nn = net interest payments (net of government interest payments) R = rental income Pp = proprietors1 income Pq = corporate profits D = dividends = total personal interest income Yp = personal income Tp = personal taxes Tc = corporate profits taxes Yd = disposable income Tw = total taxes M = money supply (demand deposits plus currency in circulation) 73 M = potential money supply based on policy variables B = increase in loanable funds Zu = total unborrowed reserves 0 = other factors, the sum of which seldom exceeds one billion dollars. These include: (1) business transfer payments, (2) subsidies, (3) surplus of government enterprises, and (4) statistical discrepancy. 1 = gross investment q = average reserve requirement on demand deposits E = sum of the non-wage components of income Summary of the Form The model as a whole is recursive'*'"*' with a simul taneous block. The simultaneous block includes equations (10) through (15). The variables which are exogenous to the model are the lagged variables, and the "policy" vari ables of equations (1) through (7). Variables exogenous to the simultaneous block are: K^., Jt, Et_^, and Ht (H = F+G). Variables endogenous to the simultaneous block are It, H-The recursive form is demonstrated in the next chapter, and resulting implications regarding solution are considered there. 74 Ta^, An^, and T^e simultaneous block is over- identified,-*-^ and will be estimated in the next chapter by the two-stage least squares method. l^See Gerhard Tintner, Econometrics (New York: John Wiley & Sons, Inc., 1952), pp. 155-66. CHAPTER IV ESTIMATION OF THE PARAMETERS This chapter is devoted to the estimation of para meters of the equations. The simultaneous block is dis cussed separately from the recursive system because a two stage least squares method is used for simultaneous estima tion of the block, while single equation methods are shown to be appropriate for the equations of the recursive sys tem. The data used for the estimation were reduced to constant dollar 1958 terms. Some parts of the model are reformulated, as dic tated by the significance of the coefficients. I. METHOD OF ESTIMATION Estimating a Causal Chain System It is shown by Wold"^ that single equation least squares regression will under very general conditions be appropriate for parameter estimation of recursive systems, -^Herman 0. A. Wold, "Forecasting by the Chain Prin ciple," Econometric Model Building: Essays on the Causal Chain Approach (Amsterdam: North Holland Publishing Co., 1964), pp. 5-36. 75 76 and that the regression technique applies to the model both p m primary and in reduced form. In order to be recursive in the sense of Wold, the model must have the primary form: Yit = Li (ylt' y2t' * * * ,Yi-l,t; Yt-1' Yt-2 ' • • •' Xt' Xt-1'* * + uit where i = 1,...,n. The X is the vector of exogenous variables for the time period, while the y is the vector of endogenous variables for the time period. This expression implies that each equation of the recursive system is the formal representa tion of a-causal dependence. While the concept of causal ity is highly controversial from a philosophical sense, for the purpose at hand it is less complex. Causality in the sense of Wold requires^ "a definition of causality that re fers to the clear-cut relationship between the explanatory variable and the effect variables. . . . It enables us to estimate the effect variables when the explanatory vari ables are given." The "explanatory" variables may be exog enous, or they may be endogenous variables which have been ^The following discussion draws from Wold's presen tation, Ibid., pp. 12-23. Herman Wold and Lars Jureen, Demand Analysis (New York: John Wiley & Sons, Inc., 1953), p. 32. 77 previously determined in the recursive process. This is implied by the primary form given above in that all values of the first subscript of the endogenous variables are less than i for time t. A recursive system expresses a cumula tive process and therefore implies a dynamic system. By substituting y^into the relation for an^ then substituting the result into the relation for Y^t' anc^ then continuing the process consecutively, the primary form of the model is transformed into the reduced form. Wold shows that the reduced form is a linear system of the type: Yit = Ri (yt-l' Yt-2',,,; Xt' Xt-1'**‘^ + wit where i = 1,...m and w is linear in u^t, U2^,...u^_^ 4 From Wold's Substitution Theorem, the relations of the re duced form will be eo ipso predictors, where an eo ipso predictor is defined in Chapter II, Section II. It is pre sented by Wold as a theorem^ that least squares regression will under general conditions provide consistent parameter estimates for eo ipso predictors, and this theorem holds whether the predictors are unirelation models or form part ^Ibid., Theorem 4, p. 13. ^Ibid., Theorem 2, p. 12. 78 of multirelation models. The regression technique applies to the model both in primary and in reduced form. Wold states that it is of great advantage to perform the para meter estimation on the basis of the primary form because as a rule this involves only a few explanatory variables and coefficients to be estimated. It remains therefore to observe that all of the equations of the model are of Wold's primary form except those of the simultaneous block (equations 10 through 15). This may be seen from the fact that all of the dependent variables in the recursive system are either exogenous variables, lagged endogenous variables, or endogenous vari ables which have been previously determined in the consecu tive calculation sequence. Single equation methods are therefore applicable to all but the simultaneous block of equations. The Simultaneous Block The simultaneous block is solved by the two stage least-squares method. The block includes the following equations: (10) It = I (Y„t, Kt, Bt_1) ^This was first established by Bentzel and Wold in 1946, but was proved in theorem form by Wold, "On the Con sistency of Least Squares Regression," Sankhya, XXV, A, 211-15. ------- 79 (11) Aw^ = Aw (Ywt) (12) TAt = TA (AWfc) (13) ANt = AWt - TAt (14) Ct = C (ANt, Et_]_) (15) YWfc = Ct + It + Htf Ht = Ft + Gt The variables which are exogenous to the block are Kt' Bt-1' Et-1' and- Ht* The reduced form of the block therefore appears as: J t = I (Kt, Bt . 1( Et _ l f Ht) Awt = AW ^Kt' Bt-1' Et-1' Ht^ ^At = Ta (Kt, Bt_X, Et_lr Ht) ANt ” AN ^Kt' Bt-1' Et-1' Ht^ Ct - C (Kt, Et-1' Ht^ YW^ = YW (Et' Bt-1' Et-1' Bt) The second stage then becomes: It = Kt' Bt-1> = Aw V - <Swt> 80 ANt " AWt TAt Ct = C YWt = ct + It + Ht The Kinds of Errors It is appropriate to emphasize that there are sev eral kinds of errors inherent in the use of theories of the kind used here. Morgenstern^ lists four sources of error: (1) the basic economic problem may be expressed only with idealization, simplifications and omissions. The mathe matical formulation therefore represents only some phase of reality and not the total situation. (2) The estimated parameters will contain errors due to observation error. This class of errors results from the fact that the para meters of the equations must be estimated from observations of the independent variables, and errors in the observa tions will also cause errors in the calculations. (3) There are errors in approximating transcendental operations 7 The following paragraph, while very brief, follows the presentation of Oskar Morgenstern, On the Accuracy of Economic Observations (Princeton: Princeton University Press, 1950), pp. 40-41. See also J. Von Neumann and H. H. Goldstein, "Numerical Inverting of Matrices of High Order," Bulletin of the American Mathematical Society, LIII (1947), 1021-99. 81 such as sin and log. (4) There are errors in the computa tional procedure. Errors of the first two types are the most serious for this study. In the first place, equations such as the accelerator equation given above are highly simplified. In the second place, the collection of aggregate data involves many problems^ because there is little precise information on some parts of the economy. In the national income sta tistics there are not only errors arising from the collec tion of data, but also in attempting to fit the available data to the concepts required by the aggregation. A more complete discussion of these errors is given in the cited work of Morgenstern. First Differences First differences are used in the estimation due to the problems of linear trend caused by the influence of 9 neglected factors, and of non-independence of residuals. Stone points out that there is usually an autoregressive association between neighboring values of the residual, and by taking first differences instead of the original series, ^See 0. Morgenstern, op. cit., pp. 73-85. ^This topic is discussed by Richard Stone, The Role of Measurement in Economics (Cambridge: Cambridge Univer sity Press, 1951), pp. 67-71. 82 this autoregressiveness can be reduced. II. THE SIMULTANEOUS BLOCK This section contains the results of the estimation of the simultaneous block of equations and the study of possible revisions for improving the significance of the estimates. Estimation of the Reduced Forms The coefficients of the reduced form equations listed in the previous section are given in Tables II and III. The t-test was used as a test of significance of the coefficient,and the results of the test are also shown in the tables. The coefficient of determination (R ) and the normalized coefficient of determination (R2) are listed l^With only ten observation, and with four indepen dent and one dependent variables in each equation, there are only five degrees of freedom. The null hypothesis that the coefficients are zero was tested. The t-distribution table gives 2.571 at the 5 per cent level for a two tail test, and it is this value against which the t values in Tables II and III are compared. 1 1 Should the serial correlation coefficient of the residuals be unity, then taking first differences will cause the residual to become a random deviate. See Lawrence R. Klein, An Introduction to Econometrics (Engle wood Cliffs, N.J.: Prentice-Hall, 1962), pp. 51-52. TABLE II REGRESSION COEFFICIENTS FOR A % ' A c , AND A % AGAINST AK' AEt-lr A Bt-l' AN0 AH r f f <1 Ac A% Coefficient t Coefficient t Coefficient t W <3 - .8928 2.006 - .5079 .752 - 2.5577 2.747 A = t - i 4.8592 3.280 6.5629 2.918 8.5509 3.080 A ^ t-i. .1686 .880 .1211 .415 .3424 .852 A h - .7979 1.205 - 1.2324 1.225 - 1.3444 .970 Constant 26.4643 21.0170 79.1941 R2 .726 .660 .762 R2 .589 .500 .643 co CO TABLE III REGRESSION COEFFICIENTS FOR A l , A aw , AND A^ a AGAINST AK' AEt-l' ABt-l' AH Ai A aW A^a Coefficient t Coefficient t Coefficient t A k - 1.5795 3.248 - 1.2349 2.100 - .2232 2.103 AEt-i 4.2097 2.600 6.5884 4.125 1.1911 3.373 Ab^-i .2202 1.047 .2684 1.059 .0487 1.065 A h - 1.0923 1.510 - 1.0948 1.252 - .1990 1.259 Constant 46.1304 37.7004 6.8193 R2 .808 .733 .733 R2 .712 .599 .599 oo i t * 85 12 in the tables for each function. It may be seen that the capital stock is significant at 5 per cent for deter mining investment I and gross national product It is not significant as a determinant of C, but this might be explained by the fact that effects of changes in capital stock on changes in consumption are indirect. On the wage and tax variables AT^, and A^, the K is significant at about the 10 per cent level (t = 2.015). The lagged values for the non-wage component of in come proved to be highly significant as a determinant of the wage and consumption variables; they are significant not only at a 5 per cent level, but also at a 1 per cent level (t = 4.032). The is somewhat less significant as a determinant of I, but passes the 5 per cent test. The lagged loanable funds variable did not pass the 5 per cent test, nor did it pass a 10 per cent test. As suggested in Chapter III, different measures of funds were tried. It was found that the significance of •*-^The coefficient of determination is normalized for the small number of. degrees of freedom by the following: —2 ? n-1 R = 1 - (1-R ) (^r^-) The n is the number of observations and the k is the number of variables. 1 O Recall that K^. is defined as the capital stock m existence at the beginning of the period. 86 the variable could be improved by excluding both the foreign sector and the business sector. A current surplus or deficit in the foreign sector was apparently not an im portant determinant of planned investment for the following period. The business sector must be regarded as extremely important due to the amount of investment in plant and equipment which is financed by internal financing, but cur rent saving in the business sector was found to be corre lated only with investment during the current year. The prime (') on the ®t-l s^own - * - n tables indicates that the values given are those which have been derived by eliminating these two components. The variable will still not pass the t-test of significance at the usual levels of 1, 5, or 10 per cent, though the test suggests that it is not without significance. The coefficients for were by far the worst, with the signs of the coefficients even being opposite to what one would expect. It should be observed that the signs of all the coefficients except those for H are what would be expected, including the strongly negative coeffi cients of K. An attempt was made to improve H by separating F and G and testing the significance of the two separately. ■^Recall that H comprises the sum of G (government spending for goods and services, and F (net exports). Federal, state, and local spending are all aggregated in G. 87 This offered some slight improvement, for F proved to be i s . insignificant by itself, and it was discarded without loss, since it is not of direct interest in this study. This left the G coefficient with a positive sign which is more reasonable, but still without significance which would pass the standard t-test. These coefficients which were obtained by replacing H with G are shown in Tables IV and V. Interpretation of the Results The lack of significance of G presents a problem because the primary objective of the project is to study the effects of fiscal policy measures. One solution might be' to conclude at this point that this kind of model is ap plicable only to the study of taxation policy for the time period of interest here. It is informative, however, to seek reaons for the lack of significance of G, for economic theory would support an argument that G is one of the de terminants of the national income and that changes in G might be expected to lead to changes in Y^. Thus an expla nation of the lack of significance may lead to conclusions which are themselves important to the interpretation of 15 Replacing net exports by exports alone did not improve the significance, and the coefficient was still negative. 5 TABLE IV REGRESSION COEFFICIENTS FOR A * » - A %/ AND A?a AGAINST AK, AEt-l' ABt-l' AND Ag A i A aW A ta Coefficient t Coefficient t Coefficient t A k - 1.4422 4.697 - 1.0095 2.481 - .1825 2.459 A e t - i 4.1927 2.642 6.0126 2.861 1.0870 2.860 A » t - i .4246 1.656 .4699 1.390 .0847 1.393 A s - .1537 .366 .1279 .230 .0229 .227 Constant 30.3330 18.8829 3.4177 R2 .714 .740 .860 -2 R .571 .610 .610 co CO TABLE V REGRESSION COEFFICIENTS FOR A ANr Ac, AND A YW AGAINST A*, AEt-l' ABt-l' AND AG A an Ac Coefficient t Coefficient t Coefficient t A k - .7777 2.655 - .6521 1.417 - 2.2531 3.864 A ^ t - i 4.3539 2.875 6.8234 2.876 8.1671 2.713 A h - i .3810 1.561 .4016 1.052 0.8084 1.665 A g .1725 .428 - .2392 .385 0.5756 .722 Constant 13.4691 11.1212 51.4021 R2 .759 .682 .812 _2 R .639 .523 .718 oo KD 90 fiscal policy during the time period of the study. An explanation is suggested by the proposition that the policy variable which was considered by budget planners was not G but rather som§_variable d which is the differ ence between government taxes and expenditures. Thus: G = d + Tw where d is the exogenous variable, or: d = dQ. This implies that it was the government deficit which was the exogenous policy variable during the two Presidential administrations of the period under study. This corre sponds to statements which were made by government offi cials at that time. For example, Sumner H. Slichter made the following statement: The greatest accomplishment of the Eisenhower ad ministration has been its management of the budget. The cash budget for the fiscal year 1953-54 was almost brought into balance, and the deficit in the conventional budget was cut from $9.4 billion the previous year to $3.1 billion.- * - 6 Early in the same year, the following public statement was •^Seymour Harris, Sumner H. Slichter, et al.,"The Economics of Eisenhower: A Symposium," Review of Economics and Statistics, XXXVIII (November, 1956), 357-6T5. 91 made by President Eisenhower, "Over the long term, a bal anced budget is a sure index of thrifty management— in a 17 home, in a business, or in the Federal Government." The variable G therefore had a large endogenous component T^, and this is consistent with the announced policy of "fiscal responsibility" of these administrations. Testing the Hypothesis The above hypothesis was tested by inserting d in the reduced form equations in place of G. The results (shown only for Yw in Table VI) indicate a somewhat greater significance for d than for G. However, these results show a decreased significance for which could indicate collinearity between d and B^_^. A regression analysis was performed which eliminated first and then d from the regression, and the results of this analysis are shown in Tables VII and VIII. These show d to be significant, and this would support the hypothesis that it was d which was the exogenous policy variable during the period. Table VIII shows that Bt-1 stiii not significant at the 5 per cent level, however it is interesting to note that in the expression for I it is significant at the 10 per cent level. ^president Eisenhower, State of the Union Address, January 5, 1956. 92 TABLE VI REGRESSION COEFFICIENTS A k> A^t-i' A^t-i' OF A % ON AND Coefficient t w <1 - 1.5946 2.349 AEt-l 6.7693 2.372 A b;_! .21273 .439 Ad .83167 1.481 Constant 46.9829 R2 .856 R2 .783 TABLE VII REGRESSION COEFFICIENTS FOR Al « ■ Ac, AND A^w AGAINST A K' A Et-lf AND A d H < Ac Coefficient t Coefficient t Coefficient t A k - .8825 3.907 - .0668 1.155 - 1.4774 2.546 A E t.i 1.8854 1.973 4.2895 2.361 6.2850 2.537 A* 0.7077 4.397 .7391 2.415 . 9837 2.388 Constant 25.6880 5.5448 48.3111 R2 .966 .880 .922 _2 R .914 .710 .807 VO u> TABLE VIII REGRESSION COEFFICIENTS FOR A 1c Ac, ANdA y AGAINST /\k, /^E-t--!, AND 1 H < i o <1 A yw Coefficient t Coefficient t Coefficient t A k - 1.4418 5.077 - 0.6514 1.531 - 2.2547 4.033 Ast-i 3.9340 2.993 6.4209 3.266 9.1357 3.534 A^t-i 0.4656 2.198 0.4655 1.462 0.6547 1.567 Constant 29.7061 10.1455 53.7502 R2 .841 .672 .792 CM .796 .579 .733 CD An Alternative Formulation 95 Tables IX and X show an additional regression of each of the dependent variables of the simultaneous block as functions of K, E^-l' and G. The normalized coefficient 2 of determination R is given for each function, and it may be seen that the coefficients are all greater than .5. The coefficients of Tables IX and X were used in the studies in the sections which follow rather than the form containing d, because while some significance could be gained by using the other form, a sacrifice would be required in that a large expansion of the simultaneous block would be necessi tated. Such an expansion would include virtually all of the model within the simultaneous block, and this would in- - volve modifying the objective of experimenting with the use of a recursive model for such studies. Second Stage Estimates Estimation of the parameters of the second stage yielded the system shown below. /\l = .4216 /\yw - .4919 /\K + 10.6274 t (2.306) (1.963) R2 = .712 R2 = .630 TABLE IX REGRESSION COEFFICIENTS FOR A l , A aw, AND AT a AGAINST AEt-l' AND AG' A* Aaw Ata Coefficient t Coefficient t Coefficient t A k - 1.4521 4.160 - 1.0205 2.334 - .1844 2.329 i —1 1 -P <] 4.5737 2.561 6.4344 2.880 1.1630 2.878 A g .4601 1.072 .2112 1.392 .0382 1.391 ; Constant 38.2487 27.6438 4.9975 ■ R2 .760 .640 .640 -2 R .705 .537 .537 vo C T l TABLE X REGRESSION COEFFICIENTS FOR A^' A C / AYw AGAINST AK' AEt-l' AG s < Ac Ayw Coefficient t Coefficient t Coefficient t A k - .7866 2.406 - 1.0381 4.007 - 2.2720 3.421 A^t-i 4.6959 2.828 3.829 3.126 8.8927 2.622 As .10244 1.254 .3010 1.970 .0077 1.009 Constant 20.5731 18.6093 66.4737 R2 .642 .611 .707 R2 .540 .501 .624 < £ > A a„ = .5339 = -9443 98 t (3.276 R2 = .571 R2 = .518 /\TA = .1747 /\AW + ‘07231 t (3.888) R2 = .651 R2 = .608 Aan = Aaw " Ata 18 (From the definition) Ac = 1.3477 A^j “ 2.7423 A Et - l + 7-7226 t (4.334) (1.955) R2 = .745 10Regression coefficients were calculated for A an as a function of A aW and A tA' an^ f°r A YW as a function of A 1' Ac, an<3 - AG. The null hypothesis that these were different from unity was tested and rejected at the 1 per cent level. The derived coefficients were therfore re placed by the definitions. 99 R2 = .672 A yw = A 1 + Ac + A g + A f (From the definition)^ The regression coefficients are all significant at the 5 per cent level2^ except the coefficient for Ak in the expression for A 1 anc^ t*16 A Et-l ^ - n t* ie expression for Ac (both of which are significant at 10 per cent). The normalized coefficient of determination R2 shows that the amount of the change in the dependent variable which is explained by changes in the respective independent vari ables varies from slightly more than one-half for Aaw to more than two-thirds for Ac. III. THE RECURSIVE EQUATIONS A Preliminary Study of the Distribution of Income The distributive components of personal income are expressed in the model as functions of the gross national product. The results of a preliminary study of some of •l^Ibid. o n The value of the t-distribution at 5 per cent is 2.365 for seven degrees of freedom, and 2.306 for eight degrees of freedom. these relationships are shown in Table XI. The data used for deriving the coefficients in Table XI were the actual 21 data, reduced to 1958 dollar terms. The normalized co efficients of determination are very high, and this is what one would expect when regressing a stable component against the total, for the coefficient of determination is a meas ure of the proportion of the variance of the dependent variable which can be explained by changes in the indepen dent variables. This preliminary study is of interest be cause it shows the stability of the composition of the whole, and shows the distribution of a marginal dollar of national income among non-wage recipients during the period under review. Not only the coefficients but also the constant terms are what would be expected in both magnitude and sign. For example, Pp (the profit of individual enter prises) has a strongly positive constant term with a rela tively small coefficient of Yw, indicating that the profits of this kind of business do not fluctuate (with changes in Y ) as much relative to its size as do some of the other W components. Dividends, on the other hand, can be seen to fluctuate a great deal with changes in Y^. ^The results from using first differences of the predicted values Y^ are shown in a later table; however, it was informative to start with the simple study shown in Table XI. 101 TABLE XI REGRESSION COEFFICIENTS FOR NON-WAGE DISTRIBUTIVE COMPONENTS OF NATIONAL INCOME AS FUNCTIONS OF GROSS NATIONAL PRODUCT Dependent Variable Coefficients YW Constant R2 Ti .1204 -15.1209 .991 nn .05807 -19.8911 .932 pp .02667 33.1154 .748 R .01015 10.5594 .875 D .02966 - 1.4975 .964 102 The Capital Consumption Function Several problems arise in the estimation of the depreciation function. One of the foremost is that the depreciation data which are reported in the national income accounts are based on capital consumption allowances which are reported for tax purposes, and the accuracy of this data can therefore be expected to be quite bad. A second problem is that the depreciation data can not be regarded as homogeneous due to a change in policy in 1962, for in that year the capital consumption allowance was changed by executive order to allow accelerated depre ciation. The model assumes that each year a portion of the capital stock depreciates, either through actual deteriora tion or through obsolescence. One function is estimated for data through 1961, and another is estimated for the years 1962 and 1963. A regression analysis is used for the first estimation, and a two point linear curve is fit to the data for the latter period. The results are shown in Table XII. Department of Commerce data were used for the ag gregate capital consumption allowance. Capital stock data 2 2 were calculated by using Kuznet's figure for 1955, and 2 2 . Simon Kuznets, Capital in the American Economy (Princeton, N.J.: Princeton University Press, 1961>. 103 deriving values for subsequent years by adding net invest ment. TABLE XII COEFFICIENTS OF THE DEPRECIATION FUNCTION Dependent Variable Constant Coefficient t R2 l54-61 l62-63 10.1868 3.8873 .05176 .06515 7.021 .897 Estimating with First Differences The relative stability, of the components of the national income is of interest for forecasting purposes; but as discussed in the first section, for the present study of the effects of fiscal policy measures it is more instructive to reduce the linear trend which appeared to dominate the results presented in Table XI by performing the regression on first differences, as was done for the simultaneous block. The significance of the regression co efficients on equations using first differences was tested as before by using the t-test to test the null hypothesis that the coefficients are not significantly different from zero. 104 The coefficients are shown in Table XIII along with _2 the normalized coefficients of determination R , and the values of t. It may be seen from the t-test that all co- 23 efficients are significant at the 5 per cent level, ex cept for the coefficient for Pp which appears to have no _2 significance at all. From the R values it is evident that only the expressions for All- A pC' and A nw are above or near .5, and this means that for the other expressions changes in the independent variable account for less than half of the changes in the dependent variable. The small _2 values for R here can be explained by the many other vari ables which influence interests and rents. The profits of individual enterprises are also influenced by many factors, and the complete lack of significance of the coefficient of Yw for Pp would indicate that the level of national income had no measurable influence on that variable during the period under review. A modification of the model is sug gested by the complete lack of significance of the coeffi cient for Pp. This may be accomplished by eliminating the equation for Pp from the system and calculating Pp from equation (21) which defines Yw as the sum of its distribu tive components. ^For eight degrees of freedom the value of the t-distribution at 5 per cent is 2.306. 105 TABLE XIII REGRESSION COEFFICIENTS OF FIRST DIFFERENCES OF NON-WAGE COMPONENTS OF NATIONAL INCOME Dependent Variable Coefficients Constant A % t — 2 R > ►3 h .6507 .0684 3.130 .501 A nn .8646 .00593 2.460 .262 A r - .2388 . 0184 1.978 .242 A pp .3841 .00171 .058 .0043 A pc -3.2396 .2685 2.301 .571 1.0597 .03176 3.338 .329 A nw .000182 .02826 2.774 .496 106 Corporate and Personal Taxes The federal tax code of 1954 remained in effect during the entire period over which the model was estimated. The state and local tax laws of course changed in many ways, but investigation of the data shows that changes in state and local tax collections did not vary significantly, and changes in this term therefore apply within the trend. The estimated tax functions for 1954-63 are as follows: ATp = .19236 A*p " -73187 t 3.254 R2 = .513 Atc t R2 The data are listed in Table XV. IV. CONCLUSIONS Certain conclusions about the model can be drawn at this point. The normalized coefficients of determination indicate that the relationships considered will in general = .39607 A?c " -16152 9.428 = .906 107 TABLE XIV COMPONENTS OF NON-WAGE PERSONAL INCOME IN BILLIONS OF CURRENT DOLLARS Year Rental Income Corporate Dividends Individual Enterprises Total Interest Payments 1953 12.7 8.9 40.5 11. 8 1954 13.6 9.3 40.0 13.1 1955 13.9 10.5 41.7 14.2 1956 14.3 11.3 42.7 15.7 1957 14.8 11.7 44.1 17.6 1958 15.4 11.6 46.6 18.9 1959 15.6 12.6 46.6 20.7 1960 15.8 13.4 46.2 23.5 1961 16.0 13.8 48.4 25.0 1962 16.7 15.2 50.1 27.7 1963 17.6 15.8 50.8 31.1 1964 18.2 17.2 51.1 34.3 1965 18.6 18.9 54.5 37.1 Source: U.S. Department of Commerce. 108 TABLE XV PERSONAL INCOME TAXES AND CORPORATE PROFITS TAXES IN BILLIONS OF CURRENT DOLLARS Year Corporate Profits Corporate Profits Taxes Personal Income Personal Income Taxes 1953 40.6 20.3 288.2 35.6 1954 38.3 1717 290.1 32.7 1955 48.6 21.6 310. 9 35.5 1956 48.8 21.7 333.0 39.8 1957 47.2 21.2 351.1 42.6 1958 41.4 19.0 361.2 42.3 1959 52.1 23.7 383.5 46.2 1960 49.7 23.0 401.0 50.9 1961 50.3 23.1 416.8 52.4 1962 55.4 24.2 442.6 57.4 1963 58.6 26.0 464.8 60.9 1964 64.8 27.6 495.0 59.2 1965 73.1 30.1 530.7 65.4 Source: U.S. Department of Commerce. 109 explain from half to two-thirds of the deviation of the aggregate variables from the trend. The t-test revealed that many of the relationships between variables were sig nificant to the 5 per cent level, although some were signi ficant to no more than 10 per cent and some of the distrib utive components did not satisfy even a 10 per cent test. An important difficulty was reported in Section II, in that the level of government spending did not pass the significance test in the reduced form equations. Further study supported the hypothesis that the significant fiscal policy variable for the period under review was in reality the government deficit. CHAPTER V ADDITIONAL TESTS OF THE MODEL The testing of the model had several aspects. The previous chapter has presented the coefficient of determi nation for each equation, and the t-test of each of the co efficients. The t-test gives a measure of the level of significance of each individual coefficient, while the co efficient of determination gives a measure of the percent age change of the dependent variable which is explained by the changes in the specified independent variables. Both parameters give a measure of how well the individual equa tions fit the data that are used for the estimation. The tests which are reported in this chapter in volve use of the completed model to predict under known conditions. It is always possible that the individual equations might perform well individually over the region of estimation, but that the equation system might perform badly as a whole. I. TESTING THE SYSTEM Recession and Recovery from 1954 through 1956 The first test of the equation system was to use 110 Ill 1953 data as initial conditions to predict the recession of 1954 and the subsequent recovery of 1955 and 1956. While the equation estimates were performed with data beginning in 1954, they did not use the 1953 data which were used as initial conditions in this test. The prediction with 1953 data of the 1954 recession and the subsequent recovery is therefore a test of the structural correctness of the model as a whole. This is an interesting test from the point of view of fiscal policy, because the national budget was re duced by seven billion dollars in 1954. The recursive feature of the model was used in the prediction of 1955 and 1956, so that no new information was introduced other than the policy variables. Thus the ini tial conditions of 1953 were used as the basis of predic tions for the subsequent three years. The actual values of government purchases, transfer, payments, and net exports are listed in Table XVI; the values of the actual and the predicted values of the income variables are listed in Table XVII and Table XVIII. The model can be seen to pre dict both the sign and magnitude of the aggregate changes. The model slightly over-predicts the recession of 1954, and then predicts the subsequent rapid recovery of 1955 and 450 440 430 Actual GNP . 420 Predicted GNP 410 400 390 380 1953 1954 1955 1956 FIGURE 1 ACTUAL AND PREDICTED GNP IN CONSTANT 1958 DOLLARS FOR 1954 THROUGH 1956 112 Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 TABLE XVI EXOGENOUS POLICY VARIABLES IN BILLIONS OF CURRENT DOLLARS Government Purchases of Net Goods and Services Exports 81.6 .4 74. 8 1.8 74.2 2.0 78.6 4.0 86.1 5.7 94.2 2.2 97.0 .1 99.6 4.1 107.6 5.6 117.1 5.1 122.6 5.9 128.4 9.6 134.8 7.1 Source: U.S. Department of Commerce. 114 TABLE XVII PREDICTED VS. ACTUAL CHANGES IN INCOME VARIABLES FOR 1954 Item Predicted Actual Investment -2.2 -1.2 Consumption 4.3 2.9 GNP o • l -1.5 Wage Earnings -2.0 -2.1 Net Interest Payments .8 .8 Rental Income - .3 - .9 Proprietors1 Income -1.5 - .7 Corporate Profits -4.3 -2.6 Dividends 1.0 .4 Personal Income 1.3 .7 115 TABLE XVIII PREDICTED VS. ACTUAL CHANGES IN INCOME VARIABLES FOR 1955 AND 1956 Item Predicted Actual 1955 1956 1955 1956 Investment 11.9 11.6 17.0 1.7 Consumption 12.7 15.7 20.0 8.9 GNP 24.4 32.7 36.8 16.1 Indirect Taxes 2.9 2.8 3.0 2.4 Wage Earnings 13.0 19.6 18.4 16.1 Net Interest Payments 1.1 1.0 .5 .5 Rental Income .4 .4 .4 .2 Proprietors' Income 10.0 2.0 1.9 .4 Corporate Profits 6.0 5.5 11.2 .6 Dividends 2.2 1.1 1.3 .7 Total Interest Payments 1.0 .9 1.2 1.4 Personal Income 26.6 23.5 33.3 18.4 Personal Income Taxes 4.4 3.8 3.1 4.0 Corporate Profits Taxes 2.2 2.0 4.2 .2 Total Tax Payments 9.5 8.6 10.3 6.6 116 1956. The model under-predicts"*" the full extent of the in crease in GNP during 1955, but makes up for this by over predicting in 1956. This illustrates one of the properties of an accelerator model: an under-prediction of investment in one year will be followed by an increase in the predic tion for the next year due to the negative capital coeffi cient. In recursive prediction of subsequent years, the errors are therefore not necessarily cumulative, but will sometimes tend to be corrected. It is considered that the model has passed this test of predicting the recession of 1954 and the subsequent recovery. Table XIX shows Investment, Consumption, and GNP as they are predicted by the model while assuming that gov ernment spending had not been reduced in 1954, but had re mained at the same level through 1956. The table then com pares these values with predictions based on the actual G. It can be seen that the pattern of predicted events with assumed unchanged G is quite different from the actual events which are shown in Table XVII and Table XVIII, and that the model apparently interprets correctly the signifi cance of the reduction in government spending which oc curred. lit is characteristic of models of this type to under-predict large changes. A discussion of this topic is presented by H. Theil, Economic Forecasts and Policy (Am sterdam: North Holland Publishing Co., 1958) , pp. 154-92. I TABLE XIX PREDICTED CHANGES OF INCOME VARIABLES FOR 1954 THROUGH 1956 SHOWING THE EFFECT OF THE REDUCED GOVERNMENT SPENDING Predicted with G Unchanged from 1953 Predicted with Actual G 1954 1955 1956 1954 1955 1956 G 0.0 0.0 0.0 -7.6 - .4 3.5 I -1.6 14.2 .6 -2.2 11.9 11.6 C 9.2 18.2 7.0 4.3 12.7 15.7 GNP 9.1 32.6 9.5 -4.0 24.4 32.7 118 The Tax Cut of 1964 The next test of the system was based on the tax cut of 1964. This test is particularly relevant to the discussion of a model whose purpose is to predict the re sults of fiscal policy measures. The model first uses 1963 data as initial conditions to predict 1964 with actual tax data. Then for comparison purposes, the same prediction is made with the tax function representing the old 1954 tax code. The purpose of the test is to determine not only whether the model will predict these years with a reason able degree of accuracy, but also to show the difference which resulted from enactment of the new code. The data are listed in Table XX. The model predicted a change in GNP of $27.6 bil lion for 1964, and this compares well with the actual change of $2 9.4 billion. It may be seen from Table XX that the predicted change in investment was $3.7 billion as com pared with actual change of $4.5 billion, while the pre dicted change in consumption was $15.5 billion compared with $18.7 billion actual. A prediction of GNP with the 1954 tax code used in the computations gives a change of only $22.6 billion. This would tend to support a thesis that the tax cut was instrumental in increasing the na tional income, but by an amount that is little more than 119 TABLE XX ACTUAL AND PREDICTED INCOME DATA FOR 1964 Variable Change Actual 1964 Predicted 1964 Using Current Data Predicted 1964 Using 1954 Tax Code Investment 4.5 3.7 3.7 Consumption 18.7 15.5 10.5 GNP 29.4 27.6 22.6 Indirect Taxes 2.6 2.4 2.1 Net Interest Payment 1.3 1.0 1.0 Rental Income .3 .3 .2 Proprietors 1 Income - .3 5.6 2.4 Corporate Profits 5.0 4.2 6.6 Dividends 2.0 1.9 1.8 Total Interest Payment 2.6 .6 .8 Personal Income 22.3 20.9 17.3 Personal Income Taxes - 2.3 - 2.3 2.6 Corporate Profits Tax 1.1 1.5 .9 Total Tax Payments 1.4 1.6 5.6 120 2 the tax cut itself. This will be discussed m greater detail in the next two chapters. II. CONCLUSIONS The model as a whole performs sufficiently well in these tests so that support is given to justify its use as a tool for studying and predicting the effects of fiscal policy measures. It must be kept in mind, however, that the model has been estimated and tested over a time period which was intentionally selected for its overall homoge neity. It is observed that in years during which large changes take place, this model performs less well. Such years are nevertheless of particular interest because the periods in which fiscal policy measures are most needed may include years which lack the property of homogeneity in their relation to the immediately preceding years. ^This corresponds to the tax multiplier of approxi mately unity which was found in Chapter IV. CHAPTER VI A FISCAL POLICY CRITIQUE This chapter will use the model as a tool for per forming a critique of fiscal policy during the time period under review. Some comments will be made regarding the limitations of the model for the purpose at hand, but an overall evaluation of the model will be left for the con cluding chapter. The critique is limited to aspects of fiscal policy to which the model is relevant; no attempt is made at a general critique. In the final chapter there will be com ments regarding the applicability of this study in relation to a broader consideration of fiscal policy which would in clude such matters as price stability, the distribution of income, and the allocation of resources. I. ESTIMATED IMPACTS Tax Policy As already noted, there was little or no change in federal tax policy during the period. The tax law of 1954 remained unchanged and new interpretations of the law by 121 122 the courts and by administrative agencies were relatively insignificant in their relation to fiscal policy. It is nevertheless possible to draw certain conclusions from the model regarding the effects of incremental changes in the level of aggregate taxes. The effect of taxes enters the original form of the model (presented in Chapter III) in three ways. First, since net wages of the current period are a term in the consumption function, a change in the level of taxes on wage income will change the consumption component of the GNP. A measure of the quantitative amount by which con sumption will be raised in this way is given by the coeffi cient of 1.348. Thus each dollar of increased personal taxes during the period could be expected to lower consump tion by about $1.35. This figure must be regarded as a very rough approximation because the tax on wage income is in itself endogenous to the system, and a change in the GNP which results from a change in the level of taxation will in turn change the dollar volume of tax collections. A second effect of a change in the level of taxa tion can be seen in the lagged impact of the non-wage com ponent of the national income • Since this variable is predetermined before the current time period, it is treated as exogenous and appears in the reduced form of the 123 simultaneous block. The reduced form coefficients'*- give an immediate measure of the effect of changes in this variable. The relatively large size of the coefficients (8.893 for the GNP) suggests that the model overemphasizes the lagged effect which can be expected from changes in taxes which affect the non-wage components of income. The model in Chapter III shows a third mechanism through which changes in the level of taxation can affect the level of the GNP. This is through the effect on the money market; however, in the estimation of the model in Chapter IV this effect was excluded due to apparent collin- earity with the government expenditures variable. Government Spending Policy As discussed at some length in Chapter IV, the co efficients of G in the reduced form equations are both small and insignificant. It was demonstrated that the ap parent reason for this was that the policy variable during the period was in reality the government deficit, and that this in effect makes government spending endogenous to the system. For an evaluation of the quantitative effect of ■*-These are the "impact multipliers" in Goldberger's terminology. See Arthur S. Goldberger, Impact Multipliers and Dynamic Properties of the Klein-Goldberger Model (Am sterdam: North Holland Publishing Company, 1959) . 124 changes in the deficit it is therefore necessary to go back to the suggested modification of the model which would in clude the deficit d in the reduced forms (Table VII). The /\d coefficient for 0.9837, which suggests that for each dollar of increase in the government deficit, the real GNP will increase by only $.98. II. POLICY CRITIQUE General Economic Character istic of the Period Most relevant institutional factors remained rela tively constant during this period. The accord between the Federal Reserve and the Treasury had taken place and the Federal Reserve was no longer committed to support Treasury issues. The time period was one of growth, but not one of rapid growth. The growth was temporarily slowed by peri odic recessions, but these were relatively minor in their impact and experience would even indicate that these reces sions could be regarded as "normal." The policies and attitudes of business had no radi cal changes during this period. The prevailing viewpoint was one of optimism but caution. The permanent importance of the government sector was increasingly realized, but most businesses did little in the way of shifting from 125 products for private consumption to products for public consumption. The opposite may even have been the case, as the government market was recognized as being an unstable one, and firms sought stability by diversifying in the con sumer goods industries. Technological progress during the period may be regarded as slow in comparison with the preceding war years. Nor were there other outstanding innovations of the Schumpeterian type. While some new sources of supply for raw materials were found, and many firms were able to ex pand their markets, the impact was in the form of steady progress rather than sudden change. This makes the period well adapted to a study of the type described here. Government policy and action also remained rela tively constant. The tax reductions of 1953-54 went into effect at the beginning of the period, and no other changes in tax were effected until 1964. While strong fiscal pol icy was not attempted in the recessions, some programs were attempted, and these will be considered in more detail. The Background of 1953 It will be useful to briefly outline the events of 1953 which immediately preceded the period under review. The Eisenhower administration came into office in January 1953 with enthusiasm for fulfilling election prom- 126 ises to cut taxes, reduce government spending, and maintain a strong currency. A tight money policy was adopted imme diately, and was generally supported both by the Treasury in its debt management operations and by the Federal Re serve. Plans for reducing the budget were laid out, but due to time lags and the continuation of the Korean War they were not put into effect until the latter half of 1953 and most, did not show up in the budget until 1954. The Recession of 1953-54 The recession which had begun late in 1953 reached its bottom in 1954. It has already been suggested that this recession might have been avoided or at least greatly reduced in magnitude if the administration had pursued somewhat different monetary and fiscal policies. The tight monetary policy of early 1953 was indeed reversed during the second half of the year, but the lagged effect of tight money for early 1953 in restraining investment was rein forced by the cut in government expenditures. The model indicates (see Table XVI, Chapter V) that if the level of government expenditures had been maintained at the 1953 level for the subsequent three years, the econ omy would have experienced steady growth during the period. ^Chapter V. 127 Such a policy would not, however, have immediately accom plished the then current objective of transferring re sources from the public sector back to the private sector following the end of the Korean conflict. This readjust ment might have been accomplished without bringing on a temporary recession if taxes had been lowered accordingly. Some attempt was made to lower taxes with the enactment of the 1954 tax code, but most of the revisions of the code merely placed the business sector in a more favorable tax position. The revenue reduction brought about by the code 3 was estimated at $1.4 billion, with an additional reduc tion of five billion dollars which came from repeal of the excess profits tax. While tax reductions and automatic stabilizers may have helped to cushion the decline of 1953-54, there was actually little in the way of discretionary controls in the fiscal policy area. The tax cuts which occurred were for tunate in their timing, but they were not planned in rela tion to the recession. Automatic stabilizers such as unem ployment insurance served to cushion the recession, but these also fall outside of the category of discretionary controls. ^The most important new features of the bill in cluded accelerated depreciation, the dividend credit, and extended depletion allowances. 128 Expansion and Recession in 1955 to 1958 The economy expanded rapidly following the reces sion of 1954. The expansion which began in late 1954 con tinued through 1955 and 1956, and then into 1957. The ex tremely rapid expansion of 1955 slowed in 1956 and early 1957, but aggregate output remained at a high level. Pri vate investment can be seen to increase very rapidly in 1955 and remain at a high level during 1956. Private in vestment began to decrease late in 1957, and in constant dollar terms investment was slightly lower for 1957 than for 1956. The model predicts the recession of 1957 and 1958 primarily on the basis of the accelerator relationship. The increase in investment was very high in 1955-56 in re lation to the increase in the national income, and this caused the negative capital coefficient to bring about a reduction in investment in the model. An evaluation of fiscal policy during this period would tend to support the conservative spending policy of 4 the Eisenhower administration during 1955 and 19.56. Since, the economy was expanding rapidly during this period and ^There was a surplus of $2.8 billion in 1955 and $5.7 billion in 1956. 129 employment was high, there was little reason for government spending for fiscal policy purposes, and a higher level of government spending would have added inflationary pressure. The stabilized federal budget during this period of growth also served to increase the resources of the private sector relative to the public sector. The model correctly predicts that the recession which began in 1957 would last into 1958. The lagged ef fect of lower non-wage income is the dominant term in caus ing the model to predict a continuation of the recession into 195 8. The fiscal policy actions which were taken by the administration during this 1957-58 recession were very mild. One action was to speed up the expenditure of funds which had already been allocated; another action was to extend unemployment compensation.^ Aggregate government spending which had declined in 1954 and 1955, and risen by only $3.5 billion in 1956 (in constant 1958 dollars), was allowed to rise by approximately five billion and six billion dollars in 1957 and 1958 respectively.^ With tax revenues changing little during the recession, this small increase in aggre- ^There were other, still more minor, actions such as easing VA and PHA credit terms. ^The federal government actually had a surplus of two billion dollars in 1957. 130 gate government spending was not able to compensate for the reduction in private investment of $13.5 billion. The rapid expansion which the economy had experienced during 1955 and 1956 therefore came to an abrupt halt in late 1957 and 1958, and since prices continued to rise during this period, the GNP actually declined in 1958 in constant dol lar terms. The model indicates that effective fiscal policy action for averting the recession of 1957-58 would have been extremely difficult if one assumes as given the events of the preceding three or four years. With the benefit of our model and a degree of hindsight it is of course pos sible to suggest that if government spending had not been cut so drastically in 1954, and if the excess-profits tax had not been completely abolished, then the rate of invest ment in 1955 and 1956 might not have been so great and the downward accelerator effect might not have been felt so strongly in late 1957. The model was used to predict the level of the national income variables under the assumption that govern ment spending was not reduced in 1954, but remained con stant at the 1953 level until 1956. It is then assumed that G was increased by five billion dollars and six bil lion dollars in 1956 and 1957 respectively. The values of Ag and are listed in Table XXI, and plotted in 1 I TABLE XXI CALCULATED GNP (IN CONSTANT 1958 DOLLARS) WITH G ASSUMED UNCHANGED THROUGH 1956 BUT WITH ACTUAL CHANGES FOR 1957 AND 1958 1954 1955 1956 1957 1958 Ag 0.0 0.0 0.0 5.0 6.0 A % 9.1 32.6 9.5 11.0 13.2 Ag -7.6 - .4 3.5 4.9 5.7 Ay -4.0 34.4 32.7 8.3 -6.4 CO I —1 132 Figure 2, along with the GNP which is calculated from ac tual conditions of government taxation and spending. The model predicts that under these conditions we would have avoided both of the first two recessions of the period. On the other hand, if one is placed in the position of those who are doing contemporary planning, then one's past decisions must be taken as "given." In late 1957, the planning and timing of government expenditures which could have compensated for the actual $13.5 billion drop in real investment would have been extremely difficult in any case. In this situation in which the sharp recession followed a period of rapid expansion, the accurate prediction of the recession, planning of the programs, and timing of the ex penditures would have been realistically impossible. It is possible to state in all fairness, however, that the administration during this recession did less than could have been done to cushion the impact of the recession. There was sufficient time to have pushed emergency pro grams of spending and tax reduction through the Congress if these had been put into effect with expediency. The fed eral government surplus of two billion dollars in 1957 leaves room to expand the budget by even a conservative administration. Yet no effort was made in this direction. There was some public discussion of a "tax cut to increase consumption," but this proposal died in Congress, and no Assumes G Unchanged Through 1956 460 450 "" Calculated With Actual G 420 -- 410 -- 390 1953 1954 1955 1956 1957 1958 FIGURE 2 CALCULATED GNP (IN CONSTANT 1958 DOLLARS) WITH G ASSUMED UNCHANGED THROUGH 1956 BUT WITH ACTUAL CHANGES FOR 1957 AND 1958 133 134 action was taken. From 1958 to 1961 By late 1958 the economy was making a strong re covery from the recession, and during the last quarter of 1958 the GNP was increasing at an annual rate of $7.7 bil lion. It continued to increase in 1959, but most of the increase took place during the first half of the year. (There was a large steel strike during the second half.) The slowing of growth due to the steel strike came to an end with the conclusion of the strike, and the GNP con tinued to increase until the middle of 1960. The recession which began in 1960 was short and comparatively mild. The GNP was increasing once more be fore the middle of 1961. The model predicts the recession reasonably well, as can be seen in Table XXII. The model explains that there were apparently two causes of the recession. The first was a decrease in investment which the model explains in terms of the high level of capital formation during the preceding year. The second is a slowing in the expansion of the government sector. The new administration was dem onstrating its "fiscal responsibility" in an effort to re main popular with the voters, but this demonstration was poorly timed. Monetary policy was also tight during the 135 period as the Federal Reserve guarded against inflation, but the estimated form of the model is not equipped to dis tinguish the effect which this had. TABLE XXII PREDICTED AND ACTUAL CHANGES IN INVESTMENT, CONSUMPTION, AND GNP FOR 1960 AND 1961 1960 1961 Predicted Actual Predicted Actual A i -4.3 - 1.6 4.8 - 3.7 Ac 7.7 8.8 6.0 6.3 Ay w 8.4 12.2 15.4 10.5 The model suggests that the small increase in gov ernment spending in 1959 was well advised and that a sur plus might have been good at that time in order to slow and to offset the rapid expansion of investment. In 1960 an expansion of government spending would have been well timed in order to offset the reduced investment spending in the private sector. Had the increase in government spending which came in 1961 occurred in 1960 instead, the recession could probably have been averted. 1961 Through 1963 During the early 1960's, there was general public concern over the rate of growth of the American economy. This concern was brought about by two considerations. First there was a slowly rising unemployment rate. The government news releases at first attempted to define this away by increasing the percentage of unemployment which was regarded as "normal," but the problem was finally admitted. The second consideration in measuring growth was a compari son of the growth rate of the United States with the growth rate of other countries such as the European countries and Japan. Sufficient time had elapsed since World War II so that war reconstruction could no longer be credited with a major role in the European expansion. Aggregate government spending and taxing are doubt less relevant considerations in the determination of a general climate which is stimulating to economic growth. However, an analysis of growth must of necessity include many factors. Paramount among these is the long term ex pansion of both production and demand. The degree of ag gregation used in this model could be quite misleading in such a study, because changing product mix and changing technology are not included. 137 III. CONCLUSIONS The results of this chapter would indicate that aggregate government spending and taxing policy can change the level of the national product in the current year, but only by approximately the amount of the change in the gov ernment deficit. Both the taxation and spending multi pliers were approximately equal to unity during the period of the study, and no evidence was observed to support a balanced budget thesis. A lagged effect of fiscal policy measures is demonstrated through its relationship to capi tal formation, and through changes induced in the non-wage component of personal income. The calculations of this chapter suggest that the cut in government spending by the newly elected Eisenhower administration was one of the factors which brought about the recession of late 1953 and 1954. The model indicates that only very drastic action during 1957 and 1958 could have averted the recession of those years, but that more could have been done to cushion the effects. Also, an ap propriate spending and taxing policy during 1955 and 1956 could have modified the events prior to the recession so that it could have been lessened or even possibly prevented. The recession of 1960-61 was very mild, and it could have been easily mitigated by appropriate fiscal policy actions. 138 It is concluded also that this model is not appro priate for the consideration of the problem of growth which was a topic of public concern during the later part of the period under review. CHAPTER VII CONCLUSIONS This final chapter will draw conclusions in rela tion to the economic meaning of the results of the study. These conclusions will consider the form of the model, the estimation process, and the calculated predictions. Fi nally, concluding remarks will be made about the relevance of the study to the practical problems of fiscal planning. I. EVALUATION OF RESULTS The Form of the Model The experiment with using a recursive model was only moderately successful. It was necessary to insert a simultaneous block in the model, and this block contained the more important variables of the system. The block re cursive form did make it possible to keep the size of the simultaneous block small and thereby make it more manage able. The individual equation elements of the recursive system were easy to estimate because single equation meth ods were applicable. The discovery that the government deficit d was the 139 140 true fiscal policy variable for the period, rather than the government expenditure variable G, was damaging to the re cursive philosophy because to include d in the simultaneous block would have placed virtually the entire model within the simultaneous block. It may therefore be concluded from this experience that purely recursive models are not entirely satisfactory for studies such as the present one because the actual eco nomic system which is being simulated is at least partly simultaneous in its operational determination of the vari ables within a time period. A block recursive structure, may, however, be useful for simplifying the handling of a large model. Another difficulty with the form is related to the objective of making only the policy variables exogenous to the system. An example is the difficulty discussed in Chapter III of deriving a social security function for the period. The Estimation Process The estimation of the reduced forms supported the original hypothesis that spending behavior is different in the consumer sector for wage income than it is for non-wage income. Consumption was correlated with wage income for the current period, while it was correlated with non-wage 141 income of the previous period. This would support a con clusion that wage earners need to spend most of their cur rent income for current living expenses, but that the re cipients of non-wage income are not as highly dependent on this income for current living expenses. It suggests that the recipients of increased non-wage income will indeed increase their spending, but only after a time lag. This lagged relationship therefore made it possible to include non-wage income as an exogenous variable in the simulta neous block. The removal of the loanable funds variable B1 due to apparent collinearity with the government expenditures variable was rather disappointing. This variable repre sented a link between the real and monetary spheres of the economy, and showed the effect which changes in taxes could have through their impact on the monetary sphere. The second stage estimates generally supported the validity of the simultaneous block of the model. The t~ test of the coefficients showed them all to be significant at the 5 per cent level except the coefficient for A k in the expression for Al and the in the expression for Ac. The coefficients for these two were significant at only 10 per cent. The coefficients of determination after being normalized for the small number of degrees of freedom still indicated that changes in the independent variables 142 accounted for from half to two-thirds of the changes in the dependent variables. Better results could not be expected in view of the high degree of aggregation. The Distribution of Income The recursive relations which come after the simul taneous block perform several functions in the model. They calculate the non-wage portion of personal income, which in turn becomes a predetermined variable for the next time period; they calculate the loanable funds variable which appears in the original model presented in Chapter III but is eliminated in Chapter IV; and they determine the effect of aggregate government spending and taxing on the several distributional components of national income. The estimation of the distribution of income func tions presented in Table XIII shows that the constant term is large in all cases in relation to the coefficient of A y . This indicates that the magnitudes of the variables change in a very predictable way over time. The fact that the normalized coefficient of determination is less than .5 in most cases indicates that the most important variables which produce changes in the distribution of income are not included in the model. The t-test of the coefficients in dicates, however, that YW was indeed one of the important determinants of changes in the distribution of income 143 during the period of the study. Changes in government spending and taxing will in fluence the distributive components of income in the model through changes in Y^. The coefficients indicate that cor porate profits and dividends are affected the most by fluc tuation in Y^, while interest payments and the profits of individual enterprises are affected the least. This effect might be most pronounced in cycles such as those of this particular period, in which inventories played a signifi cant role in the cyclical behavior. The Accuracy of the Predictions The tests described in Chapter V show that the com pleted model predicts the direction of movement of the economy rather well, and that it predicts the magnitude of the change with relative accuracy except in those years in which the change is unusually large. When the change is large, the model tends to underestimate and give predic tions which are too conservative. Recall that the model estimated the recession of 1954 and predicted the rapid re covery of 1955 and 1956, but it tended to underestimate the complete extent of the recovery in 1955. This feature can be attributed to the linear regression analysis on which the model is based, and it is a limiting characteristic of most similar models. 144 The user of models such as this for forecasting must therefore be especially cautious in those cases in which the model predicts changes which diverge considerably from the trend, for these predictions can be expected to have the greatest inaccuracy. Furthermore, these predic tions are likely to be underestimated in their magnitude. In using the recursive features of the model to predict several years in advance, the accuracy is difficult to predict. In using 1953 data to predict 1954, 1955, and 1956, the results were good even though this was a period of relatively rapid change. The errors in one year's pre diction do not necessarily accumulate additively into the following year's prediction because of the use of the ac celerator concept in predicting investment. If the predic tion for one year is too small, then the accelerator will cause investment and the GNP to be appropriately larger for the next period, while if the estimate is too large the opposite will be the case. II. RELEVANCE OF THE STUDY Value Judgments In writing a paper which deals with fiscal policy matters, it is difficult to avoid implicit value judgments. The conventional definition of economics deals with the 145 problem of unlimited wants and limited resources, and the users of the definition usually assume implicitly that it is good to satisfy as many human wants as reasonably pos sible. This assumption is accepted here, and since it motivated the inception of this paper, it has no doubt mo tivated its content. Therefore the assumption will be stated explicitly as follows: The fundamental purpose of the complex economic sys tem of the modern society is to increase the economic welfare of the country's inhabitants— that is, to provide more goods to satisfy their material wants, present and future.^ We are then led to a consideration of economic effi ciency, which in turn deals both with the utilization and the allocation of resources. Depressions cost heavily in terms of wasted labor and other resources; for example, the depression of the 1930's cost about the same amount as it cost to fight World War II. Yet it was pointed out in Chapter I that it is a matter of dispute as to whether small economic fluctuations or cycles lead to real economic inefficiency. Those who would argue the affirmative can point to lost output due to increased unemployment. The opposing argument is Schumpeterian in content and contends that minor cycles are a necessary part of economic growth ■'•This statement was formulated by Simon Kuznets, Capital in the American Economy (Princeton, N.J.: Prince ton University Press, 1961). 146 and that they play a useful role in helping various indus tries and sectors adjust to change. The point of view that is taken in this paper is that it is useful to learn more about the mechanics of our economic system and how they might be controlled, whether we choose to exercise such control or not. Relevance Beyond the Period of the Study A time period was selected for the study which was relatively homogeneous, as discussed in Chapter I. The homogeneity ends at the two boundaries of the study; not only was the period sandwiched between two war periods, but the tax structure was changed significantly just prior to and just after the period. While the primary objective was to analyze the specified period, the question nevertheless arises as to whether the study has further relevance beyond the time period considered. The answer to this question has many qualifications. The estimated coefficients depend on the underlying condi tions during the period of estimation. These coefficients depend not only on the stability of the conditions under lying demand, but also on the conditions underlying produc tion. The demand-side conditions include the distribution of income among the recipient groups, and the consumption 147 function of each of the groups; they also include invest ment behavior, which depends in turn on such factors as the capital depreciation function and the desired ratio of capital to output. The production conditions involve such factors as the level of technology, the degree of resource employment, and the mobility of resources. If these fac tors do not remain stable or change in counterbalancing ways, then the coefficients of the system change. On the other hand, the structure of the economy would have to change drastically for the form of the equa tion system to be no longer applicable to the study of the specific kind of problem which we have chosen to discuss. Thus the model might be reestimated for use in studying a different time period which had the basic property of homo geneity in the sense described. Further Limitations Another limitation of the model lies in its degree of aggregation and simplification. For example, in its estimated form it does not include the effects of monetary controls such as adjustments of the discount rate, money supply, and credit conditions. Yet the accord of the Fed eral Reserve and the Treasury had taken place, and monetary controls were attempted on a continuing basis during the period under review. This was mentioned in Chapter VI in 148 relation to years such as 1953, 1957, and 1958. The actual effectiveness of monetary controls during the period is somewhat open to question because the monetary policy tar- 2 get was apparently the "reserve position." There are many conditions which determine the ef fectiveness of fiscal policy itself which are not explic itly included as factors in the model. These conditions include, for example, the sources of borrowed funds and the sources to whom previously borrowed funds are repaid. They include the structure of employment and unemployment, and the nature of government expenditures. An attempt was made to perform a study over a peri od in which as many as possible of these factors remain constant, and this was the reason for estimating the model over a relatively short time period which was homogeneous in many of these factors. Yet this in turn causes the small number of degrees of freedom to be a limitation. Usefulness of the Results The seriousness of the limitations of the model 2 The term "reserve position" as used by the Federal Reserve Board is synonymous with free reserves, which are the commercial banks1 reserves with the Federal Reserve System less borrowed reserves. It has been suggested that using free reserves as the target is tantamount to follow ing the demand for changes in the money supply. See W. G. Dewald, "Free Reserves, Total Reserves, and Monetary Con trol," Journal of Political Economy (1963). 149 must be considered in relation to their effect on its use fulness. The question to be answered in a study such as this is not whether the kind of model presented will ex plain everything or nothing, but rather the question is one of how much of the movement of the dependent variables is explained. For this purpose the impact multipliers of the independent variables were presented, and a t-test of sig nificance was calculated for each. For each equation the coefficient of determination was calculated, and this was normalized to the number of degrees of freedom for each particular case. It should be emphasized that while it is useful to study situations under given underlying conditions, one must use great caution in extrapolating the results to an other period with conditions which are different. One of the ultimate objectives of studies such as this one is to be able to make predictions and to arrive at policy con clusions in relation to those predictions. However it is not correct to use the estimated relationships to extrapo late forward unless there is reason to believe that the underlying conditions have remained stable. In practice this implies that such models may be most useful when used in relation to fiscal policy which is intended to stabilize small recessions such as those which occurred in 1954, 1957, and 1960. Such small and temporary 150 pauses in the upward movement of the economy are not asso ciated with large disruptions in the structure of the econ omy, and the effects of fiscal policy measures_may be pre dicted effectively with this type of model. On the other hand, serious depressions such as that of the 1930's bring about severe structural changes. The coefficients of the equations which were estimated for a previous period would therefore not necessarily represent the changing relationships of the economy. In addition, the problem of fiscal policy may in a depression be to effect a change in the actual structural relations— for ex ample, it may be desirable to attempt to increase the mar ginal propensity to consume. It is concluded that such a model as this would have severely limited usefulness in times of serious depression. A possible exception might be the use of the model to predict a recession and to predict the effects of alternative fiscal policy actions which could prevent the recession from degenerating into a full- scale depression. Still a further limitation lies in the aggregation of federal, state, and local spending and taxing levels. This assumes that federal policy makers must take cogni zance of the level of state and local spending and taxing in arriving at fiscal policy decisions. 151 Capital Formation as a Key Factor The importance of investment and depreciation in the model emphasizes the key role of capital formation as a determinant of the level of aggregate economic activity. Capital formation is therefore an important consideration relative to the formation and evaluation of fiscal policy, 3 and we turn to the long term studies of Kuznets for some general conclusions which will be relevant to the present study. First, over the entire period since 1870, gross capital formation accounted for a fairly constant propor tion of gross national product in current prices. This percentage was slightly more than one-fifth, with the long term trend for this ratio being slightly downward. The proportion during the 1954-63 decade was slightly under one-sixth. Second, the ratio of net capital stock to net na tional product in constant prices has been relatively stable with no consistent trend for many years. From early values of about 3.2 in the 1870's, it rose slowly to 3.6 in the 1920's, and then declined to 2.9 in the period from 1939 to 1955. The ratio has remained stable during the 3 Simon Kuznets, Capxtal in the American Economy (Princeton N.J.: Princeton University Press, 1961). 152 past ten years, increasing slowly over the period. From Department of Commerce data, business inven tories were closely associated with the aggregate business cycles during this period and are classified as a "leading indicator." Business inventories are therefore an impor tant part of the net capital stock. A sharp decline in inventories was associated with each of the recessions of the period, and this decline began shortly before the con traction in all cases. The model takes these factors into consideration by using a special case of the neoclassical investment theory for determination of real investment demand. The signifi cance of the estimated coefficients suggests the correct ness of the assumptions for the period of the study. Kuznets also points out that one of the important institutional changes which has occurred during the past several decades is the rise in the share of the government sector in total capital formation. The important aspects of this factor are dealt with at some length by Kuznets, who points out that there are two trends involved: first, there is the overall increase of the government in the eco nomic activity of the nation; and second, there is the rise in the amount of economic activity which is conducted under the auspices of the government with the accompanying accu mulation of capital which is necessary to bring about this 153 activity. The rise in the share of the government in eco nomic activity may be measured in several ways, including the measurement of factor payments originating in the gov ernment sector, measurement of the share of employment under government auspices, or measuring the share of the total finished product purchased by the government. The increased share of government in economic ac tivity, says Kuznets, is associated with other institu tional changes such as the increasing density of population in urban areas, and the growing scale and complexity of the forms of economic organization. The effect of the changing share of government is included implicitly in the model by the inclusion of G as an exogenous variable in the simulta neous block. Kuznets discusses additional institutional changes which have taken place in the economy such as the increase in gross capital formation and the increase in the consump tion of capital. Much of the capital consumption, he points out is due to economic obsolescence rather than to physical wear and tear; and this economic obsolescence is indicative of more fundamental institutional changes which include not only the results of scientific and engineering research and development, but also other forms of Schumpe terian innovation such as the discovery of new sources of materials and different business organizatiion. Both the 154 increase of gross capital formation and the increase in capital consumption are illustrated for the period by the significance of the positive coefficients in the estimated form of the model. Fiscal Policy in the Period Under Review Use of the model for evaluating fiscal policy during the period under review suggests that the largest error in fiscal policy was the very sharp cutback in gov ernment expenditures in 1953 and 1954 following the Korean conflict. Taxes were lowered somewhat at the same time, but not enough to avoid the recession which came in late 1953 and 1954. It is suggested also that this sharp cut back not only added to the factors which brought on that recession, but that the recession itself was a factor in inducing the oscillations of the following four years, with investment increasing at an unsustainable rate in 1955 and 1956 and then falling off sharply in 1957 and 1958. The tests of Chapter VI suggest that prevention or abatement of the recession of 1954 would have led to a more steady growth during the ensuing four years. Even if we assumed the recession of 1954 as given, it might have been possible for the government to have slowed the rapid expansion of 1955 and 1956, and thereby lessened the recession of 1957 and 1958. This might have 155 been done by a further reduction in government spending in 1955, or by reenactment of an excess profits type of tax in that year. If finally we assume the events through early 1957 as given, then the model suggests that there is little that could have been done at that late date to avoid the reces sion. However, it is pointed out in Chapter VI that more might have been done to cushion its impact. The recession of 1960 and 1961 was mild and short lived, and if it had been correctly forecast it undoubtedly could have been prevented by fiscal policy action. It is not intended that this critique be overly critical of policy during the period. None of the reces sions of the period were of major seriousness, and certain readjustments of long-run value may take place during a mild recession. These adjustments affect such things as the allocation of resources and the efficient use of re sources in the production process. 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"Adjusting Dynamic Models to Improve Their Predictive Ability," Journal of Farm Economics, XLVII, No. 4 (November, 1965), 963-72. Dewald, W. G. "Free Reserves, Total Reserves, and Monetary Control," Journal of Political Economy (1963). Friend, Irwin, and Paul Taubman. "A Short Term Forecasting Model," Review of Economics and Statistics, XLVI (August, 1964), 229-36. Gramlich, E. M. "The Behavior and Adequacy of the United States Federal Budget, 1952-1964," Yale Economic Essays (Spring, 1966), 6. Hahn, F. H. "The Rate of Interest and General Equilibrium Analysis," Economic Journal, LXV (March, 1955), 52-66. Harris, Seymour, et al. "The Economics of Eisenhower: A Symposium," Review of Economics and Statistics, XXXVIII (November, 1956), 357-85. Hart, Albert Gailord. "Model Building and Fiscal Policy," American Economic Review, XXXV (1945), 325-33. Hicks, J. R. "Mr. Keynes and the Classics: A Suggested Interpretation," Econometrica, V (1937), 1947-55. Hildreth, C. "Simultaneous Equation Estimation: Any Ver dict Yet?" Econometrica, XXVIII (1960), 846-54. Klein, Lawrence R. "Adjusting Dynamic Models to Improve Their Predictive Ability," Journal of Farm Economics (November, L965), 963-72. ________ . "Single Equation Versus Equation System Methods of Estimation in Econometrics," Econometrica, XXVIII (1960), 866-71. ________ , and Y. Shinkai. "An Econometric Model of Japan, 1930-1959," International Economic Review, IV (1963), 1-28. Kshirsagar, A. M. "Prediction from Simultaneous Equation Systems and Wold's Implicit Causal Chain Model," 163 Econometrica, XXX(October, 1962), 801-11. Kuh, Edwin. "Econometric Models: Is a New Age Dawning?" American Economic Review, LV, No. 2 (May, 1965). Liu, Ta-Chung. "An Exploratory Quarterly Econometric Model of Effective Demand in the Postwar Economy," Econo metrica, XXXI (July, 1963). ________ . "Underidentification, Structural Estimation, and Forecasting," Econometrica, XXVIII (1960), 855-65. Modigliani, F. "The Monetary Mechanism and Its Interaction with Real Phenomena," Review of Economics and Statis tics , XLV, Supplement (February, 1963), 79-107. Musgrave, R. A. "Alternative Budget Policies for Full Employment, American Economic Review, XXXV (1945), 387-99. Niehans, Jurg, and Heidi Schelbert-Syfrig. "Simultaneous Determination of Interest and Prices in Switzerland by a Two-Market Model for Money and Bonds," Econometrica, XXXII (1966), 408-23. Phillips, A. W. "Stabilization Policy in a Closed Econ omy," Economic Journal, XLIV (June, 1954). Polka, J. J., and W. H. White. "The Effect of Income Ex pansion on the Quantity of Money," International Monetary Fund Staff Papers, XIV, No. 3 (August, 1955). Smyth, D. J. "Can Automatic Stabilizers Be Destabilizing?" Public Finance (1963). Smithies, Arthur, et al. "Forecasting Postwar Demand," Econometrica, XIII (1945), 1-50. Suits, Daniel B. "Forecasting and Analysis with an Econo metric Model," American Economic Review, LI (March, 1962), 104-32. Teigen, Ronald L. "Demand and Supply Functions for Money in the United States: Some Structural Estimates," Econometrica, XXXII (1964), 476-509. Theil, H., and A. L. Nager. "Testing the Independence of Regression Disturbances," Journal of the American Statistical Association, LVI (1961), 793-806. 164 Tintner, Gerhard. "Elasticities of Expenditure in the Dynamic Theory of Demand," Econometrica, VII (1939), 266. ________ . "The Theoretical Derivation of Dynamic Demand Curves," Econometrica, VI (1938), 375. ________ , and Balder von Hohenbalken. "Econometric Models of the OEEC Member Countries, the United States and Canada, and Their Application to Economic Policy," Weltwertschaftliches Archiv, LXXXIX (1962), 29. Von Neumann, J., and H. H. Goldstein. "Numerical Inverting of Matrices of High Order," Bulletin of the American Mathematical Society, LIII (1947), 1021-99. Wold, H. "Causal Inference from Observational Data: A Review of Ends and Means," Journal of the Royal Statis tical Society, A-CXIX (1956), 28-61. _. "A Generalization of Causal Chain Models," Econometrica, XXVIII (1960), 443-63. _. "On the Consistency of Least Squares Regression," Econometrica, XVII, Supplement (1949), 1-22. C. UNPUBLISHED MATERIALS Hanrahan, George D. "Three Econometric Monetary Models of the United States." Unpublished PH.D. dissertation, University of Minnesota, Minneapolis, 1964.

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Creator White, Hubert Dale (author)

Core Title A Dynamic Model For Predicting The Effects Of Fiscal Policy Measures

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Economics

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

Tag economics, history,OAI-PMH Harvest

Language English

Advisor Tintner, Gerhard (committee chair), DePrano, Michael E. (committee member), Ward, Richard A. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-137093

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Rights White, Hubert Dale

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