Let me note some points of agreement between Minabe and myself. First, I agree that capacity or full employment national income cannot be incorporated into a family consumption function as a ratchet effect. It is the peak income that the family actually earned that determines the extent of their resistance to cuts in living standards and not the peak income that they might have earned if fully employed. Second, I agree that a good statistical fit is not everything. In an age of distributed-lag functions, where investigators seldom put any a priori restrictions on the profile of distributed-lagged weights, any econometrician with access to a computer can come up with decent statistical results. He need only persevere. Where I disagree is on two points he makes early in the note: (1) that the essential spirit of the ratchet effect is lost in my model, and (2) that the Duesenberry model is not suitable for defining conditions of steady growth and therefore not a useful building block in constructing a model of joint interaction. The first point is by far the more important and I will attempt to answer it first. For if the essential spirit of the ratchet effect were missing, a link would be lacking connecting the demand and supply sides of the market in my model. I say a link rather than all links, as Minabe implies, because there is still the influence running from demand to supply that he neglects. To facilitate the discussion, I shall write the DuesenberryModigliani, (D-M), function in a manner more in keeping with Modigliani's formulation. Thus write: ct=0.5yt+0.4yt* where the lower-case letters ct, Yt, and yt* represent family consumption, current income, and peak income attained, which may be the current income. Then the aggregate version of the (D-M) function becomes Ct = 0.5Yt+0.4Yt* where each upper-case letter represents the aggregate version of the family measures. The coefficients chosen are of no consequence as the argument is independent of their values. Now assume that there are only three families whose incomes are represented by Yl, Y2, and Y3. Table I brings out the essential issues. Again the numbers chosen are arbitrary but of no special consequence, chosen primarily for computational convenience. They

I. Introduction, 48. — II. Two alternative interpretations of the stylized facts, 49. — III. The influence of supply on demand, 53. — IV. The influence of demand on supply, 56. — V. Growth and transformation, 60. —VI. Say's law in reverse, 65. — VII. Summary, 68.

T HE postwar growth performance of several European economies has been the cause of coincident feelings of awe, guilt, and envy. It has also been the reason for a number of attempts to explain what has allowed, say, the Germans, French, and Italians to go merrily on their way with only minor interruptions of remarkable growth records, while others, such as the British, have been faced with little other than stagnation. The studies have varied a good deal in the level of sophistication and abstraction, as well as in the relative weight given to empirical in contrast to theoretical considerations. Nevertheless, a common theme is the profound importance of capital formation as a source of growth. Neither of the two recently published studies is an exception, although the heavy weight given to capital formation in one is certainly inadvertent.' Each book is important in its own right, and together they provide an excellent opportunity to examine the main trends in an important and growing body of literature. Therefore, though emphasis will be on the two latest contributions in this area, we will include other studies for comparison and contrast. Together, they provide a sharp contrast to much current analysis which downgrades the importance of capital formation as a source of growth.

Introduction, 608.— I. Forecasting and stabilization policy, 609. — II. Cycle models vs. fiscal models, 611. — III. Stability conditions for fiscal models, 612. — IV. Dynamic vs. static multipliers, 615. — V. How to make investment unimportant, 616. — VI. Supply-determined growth vs. demand-determined growth, 618. —VII. Conclusions, 621.

I. Introduction, 1. — II. Fiscal policy and the multipliers in a static world, 3. — III. The effect of alternative fiscal policies on growth, 6. — IV. The effect of alternative fiscal policies on the budget, 11. — V. Fiscal policy and the multipliers in a dynamic world, 12. — VI. The effect of productivity on growth and the budget, 16. — VII. A Simulation experiment, 18. — VIII. Conclusions, 21. — Appendix, 22.

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.