Economic Implications of the Klein-Goldberger Model

Abstract

EVER since Samuelson's I939 article in this REVIEW on the interaction of the accelerator and multiplier, business cycle theory has been concerned with drawing out the implications of a set of differential or difference equations. It was never assumed that these models adequately described the basic structure of the economy but it was felt that a better understanding of the forces producing cyclical movements could be obtained in this manner. The basic mechanism generating the movements of the system in the models of Hicks, Harrod, Goodwin, and Kaldor was an interaction of the accelerator and multiplier.' In whatever form, such an endogenous income-generating mechanism was the core of these cycle theories. In many cases, the implications of such a set of dynamic equations were then found by deriving an analytical solution for the system. By determining the nature and size of the roots of the characteristic equation, it was possible to determine the type of movements implied by the basic mechanism. The effects of changes in the structural constants were also studied and boundaries derived separating the various kinds of movements. Two additional elements were usually incorporated in these models. Some exogenous expenditure was included to take account of the fact that not all expenditures could be explained by economic factors. Various assumptions were then made about its behavior over time. Thus, Hicks assumed an exponential trend for exogenous investment, whereas Goodwin's more Schumpeterian approach assumed that exogenous investment would occur in wavelike patterns.2 In addition, two different types of constraints were added, limiting the values the variables could take. full employment ceiling was introduced in the form of a production function setting a maximum value for output. And since gross investment could never be negative, it was sometimes necessary to substitute the rate of depreciation for the accelerator during the downswing. As a result of these additions, drawing out the implications of such systems was no longer simply a matter of examining the roots of the characteristic equation. One can approach the econometric models of Klein, Tinbergen, Valavanis,3 and others in the same spirit and consider their studies to be more complex models of the trade cycle. By specifying in more detail the various factors influencing the different types of expenditure and income, these models can be thought of as more adequately describing the forces at work producing cycles or any other type of movement. In particular, the econometric model developed by Klein and Goldberger lends itself to such treatment.4 As with the cycle models just mentioned, it contains exogenous variables, technological constraints, and an endogenous incomegenerating mechanism. Of the many exogenous variables in the model, those representing the influence of population and government activity *The material contained in this article has been taken from the author's doctoral dissertation Implications of Some Dynamic Models (Harvard University, I958). While taking full responsibility for the work, the author would particularly like to thank Professor James S. Duesenberry, who suggested the topic and followed the study through all its stages. In addition, W. H. Locke Anderson advanced the work through criticism and assistance in programming. earlier draft of this paper was presented at the Philadelphia meetings of the Econometric Society on 30 December I957. 1J. R. Hicks, Contribution to the Theory of the Trade Cycle (Oxford, I950), Roy Harrod, Towards a Dynamic Economics (London, I948); Richard Goodwin, Econometrics in Business-Cycle Analysis, reprinted in Alvin Hansen, Business Cycles and National Income (New York, 1957); Nicholas Kaldor, A Model of the Trade Cycle, Economic Journal, L (March I940). 2Richard Goodwin, A Model of Cyclical Growth, The Business Cycle in the Post-War World (London, I955). 'L. R. Klein, Economic Fluctuations in the United States, I92I-I94z (New York, 1950); J. Tinbergen, Business Cycles in the United States, z9z9-z932, Vol. II (Geneva, I939); S. Valavanis-Vail, An Econometric Model of Growth: U.S.A. i869-i953, Papers and Proceedings, American Economic Review, XLV (May I955). 'L. R. Klein and A. S. Goldberger, Econometric Model of the United States z929-I952 (Amsterdam, I955). The estimates considered in this paper are for the original model. Their equations have been reproduced in the appendix with slight modifications. The num;bering is my own, and Klein and Goldberger's expression Y + T + D has been replaced by GNP.