Abstract
“If the theory which is here offered stands up to theoretical criticism, the next stage will be the concern of statisticians, econometrists, and (most of all) economic historians, who will have to see whether it does prove possible to make sense of the facts in the light of these hypotheses”.
A review of A Contribution to the Theory of the Trade Cycle. By J. R. Hicks (Oxford University Press, 1950). Pp. vii + 201. Trevor W. Swan, “Progress Report on the Trade Cycle”, The Economic Record, 26, No. 51 (December 1950): 184–197.
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Notes
- 1.
P. A. Samuelson: “The laborious literary working over of essentially simple mathematical concepts such as is characteristic of much of modern economic theory is not only unrewarding from the standpoint of advancing the science, but involves as well mental gymnastics of a peculiarly depraved type”. (Foundations of Economic Analysis, p. 6. But there is much to be said on the other side. See the review articles by W. J. Baumol (Economica, May, 1949) and R. G. D. Allen (Quarterly Journal of Economics, February, 1949).
- 2.
In his contribution to A Survey of Contemporary Economics (ed. Howard S. Ellis, 1948), Samuelson (under the heading “Dynamic Process Analysis”) has given an elementary short introduction to the solution of difference equations. See also D. H. Robertson’s comments in his review article, “A Revolutionist’s Handbook” (Quarterly Journal of Economics, February, 1950). Other useful sources are A. Smithies in “Equilibrium Analysis and Process Analysis”, Econometrica, 1942; Appendix B to Foundations of Economic Analysis—for a much more advanced approach; and M. G. Kendall, The Advanced Theory of Statistics, Vol. II, Chapters 29 and 30, especially pp. 399–423.
- 3.
Hicks points out that, if the true relationship is lagged, least-squares regression ignoring time-lags is likely to over-estimate the marginal propensity to save, and underestimate the marginal propensity to consume. This, Hicks suggests, is what went wrong with the American post-war employment forecasts (pp. 29–35), and he therefore assumes that the true figures correspond more closely with the long-term Kuznets estimates (giving a marginal and average propensity to consume in the vicinity of 0.9) than with the interwar “cyclically-biased” estimates which give a marginal propensity of about 0.5 in relation to net national income. He quotes Modigliani in general support of this view (Hicks, p. vi; F. Modigliani, Vol. XI, Studies in Income and Wealth, National Bureau of Economic p. vi; F. Modigliani, Vol. XI, Studies in Income and Wealth, National Bureau of Economic the inter-war regression points do not show the overall movement of Hicks’s diagrams, nor the inter-war regression points do not show the oval movement of Hicks’s diagrams, nor the true regression line was shifting during the period, without abandoning the attempt the true regression line was shifting during the period, without abandoning the attempt to derive a statistical consumption function (in relation to income) altogether. Both to derive a statistical consumption function (in relation to income) altogether. Both Modigliani and J. J. Duesenbury (Income, Consumption, and the Theory of Consumer Behaviour, Harvard University Press, 1948, and in Income, Employment, and Public Policy, Norton and Co., 1948) explain the observed facts by giving a privileged position to the income of one year—the last peak. Thus their time-lag is not constant, as Hicks’s theory requires; and within a cycle—but not as between cycles—their estimates do not differ greatly from the older “biased” estimates, when allowance is made for corporate savings. It is of course the intra-cycle marginal propensities which are relevant for Hicks’s purposes in calculating the duration, dam** factor, etc., of his cycle.
- 4.
All variables are measured in “real” terms, and income is synonymous with output. The definition of Hicks’s “period” (p. 53) is a matter of some complexity, which cannot be considered in this review, but which I hope to discuss elsewhere.
- 5.
Review of Economic Statistics, May, 1939; also in Hansen, Fiscal Policy and Business Cycles; and reprinted in Readings in Business Cycle Theory. Samuelson’s assumption of a one-period lag for consumption, and no lag for investment, is equivalent to a one-period lag for both, when allowance is made for the fact that Samuelson relates investment to consumption, whereas Hicks relates it to income. Samuelson’s \(\alpha \beta\alpha \beta\) is the equivalent of Hicks’s v, and his a the equivalent of Hicks’s \(c\).
- 6.
Frisch, Ragnar, “Propagation Problems and Impulse Problems,” in Economic Essays in Honour of Gustav Cassel, 1953. M. G. Kendall, op. cit.
- 7.
Samuelson, Foundations, p. 340.
- 8.
Duesenbury, in his review of Hicks (Quarterly Journal of Economics, August, 1950) argues this point, evidently without noticing that Hicks has anticipated him.
- 9.
p. 107. The latter part of this proposition will be contested in Part V below.
- 10.
This concept will be further considered in Part IV below.
- 11.
Hicks suggests that his moving equilibrium is determined by the equality of saving and investment, presumably as an ex ante equilibrium condition rather than the ex post definitional identity (pp. 57–59). But in the presence of time-lags this does not seem to be possible. In Hicks’s system, investment ex ante always equals investment ex post, whereas if income is rising, and ex ante saving is determined by previous income levels, saving ex post must always exceed saving ex ante; and since by definition saving equals investment ex post, the ex ante magnitudes can never be equal. In fact, the ex ante equality of saving ex post, the ex ante magnitudes can never be equal. In fact, the ex ante equality of saving ex ante saving depends only on current income; and it can define a unique moving ex ante saving depends only on current income; and it can define a unique moving equilibrium only if neither investment nor saving (consumption) are subject to time-lags.—If we make this last assumption, and employ Hicks’s symbols, then the formula for the If we make this last assumption, and employ Hicks’s symbols, then the formula for the Lower Equilibrium Line becomes the ordinary “simultaneous multiplier” relationship—
$${\mathbf{Y}}_{n} = [{1}/{(1 - c)}]A_{0} (1 + {\mathbf{g}})^{n}$$(1)To calculate the Upper Equilibrium Line, the value of investment In induced in the steady advance must be included alongside autonomous investment A0(1+g)n. According to the acceleration principle, \(I_{n} = v\left( {Y_{n} - Y_{n - 1} } \right)\), which for a geometric progression of income reduces to \(I = \frac{vg}{{1 + g}}Y_{n}\). Adding this to the autonomous investment in (I), we obtain the formula for the Super-Multiplier which determines the Upper Equilibrium Line-
\(\begin{aligned} {\mathbf{X}} & = \left[{1}/{(1 + c)}\right] {\{A_{0} (1 + g)^{n} + \left[{{{\text{vg}}}}/{(1 + g)}\right]{\mathbf{Y}}_{n} \}} \\ & = [{1}/({{1 - c - {{{\text{vg}}}}/{(1 + g))}}}]A_{0} (1 + g)^{n} .\\ \end{aligned}\)
This formula is of the same form as that given by Hicks in equation \(18.4\) on page 184, but the latter is of course adjusted for time-lags (the effect of which is constant in a geometric progression), thus shifting the Equilibrium Line bodily to the right (or downwards). Once the time-lags are introduced, saving the investment ex ante can no longer be equal, but the proportional difference between them in a geometric progression is constant, and ex post they are not only equal but a constant proportion of income. Essentially, however, Hicks’s moving equilibria appear to be merely mathematical expedients for the solution of the difference equations, and hence presumably fall into the class of moving equilibria mentioned by Samuelson in footnote 23, p. 325, Foundations. Perhaps they can also be interpreted in terms of Samuelson’s boy with the stone at the end of a piece of string: if he has always been walking at a constantly accelerating pace, the stone will hang steady, but lagging somewhat from the perpendicular; if he stumbles, it will swing like a pendulum even after his regular progression has been resumed. Similar concepts of moving equilibrium were first employed (as far as I know) by R. Goodwin, in Review of Economic Statistics, May, 1946.
- 12.
Economica, May, 1949.
- 13.
Towards a Dynamic Economics, pp. 89–91, pp. 115–117.
- 14.
p. 86.
- 15.
See especially pp. 63–58, 88–106, 160–167.
- 16.
For instance, it was never clear in Harrod’s essay that a constant (linear) set of consumption and investment coefficients could produce a cyclical downturn: it always depended on non-linear relationships. Similarly, Harrod believed that his system explained the (alleged) sharpness of the downswing as compared with the upswing-belief which Hicks can now show to have been an optical illusion (Harrod, pp. 97–99; Hicks, pp. 115–118). Such differences as there are appear to be typically those which one would expect as between a literary and a mathematical formulation.
- 17.
p. 183.
- 18.
The equivalent of Hick’s autonomous investment is the sum of the fractions k and d. (Towards a Dynumic Economics, pp. 79–80, and p. 96.) The fraction k refers to “long range investment” on the assumption that inventions are neutral: “in the long run k must disappear, for in the long run all capital outlay is justified by the use to which it is put” (p. 79). The fraction d refers to investment of a “deepening” character which may result from “labour-saving” technical innovations or a falling rate of interest. Since both k and d are expressed as fractions of income, and operate so as to reduce the warranted rate of growth \(\left( {G_{W} C_{r} = g - k - d} \right)\), the warranted rate can be made as high or as low as you please by altering the fractions, but the total of autonomous investment will always necessarily rise in geometric progression (at the warranted rate) in Harrod’s moving equilibrium. Further, if both the absolute level of autonomous investment and its fraction of income were specified, as they could be, the warranted rate of growth of income and its absolute level would both clearly be determinate from Harrod’s equation. This manner of arbitrary specification would not differ in the upshot from Hicks’s procedure, which is to specify the rate of growth of autonomous investment and its absolute level, which is to specify the rate of growth of autonomous investment and its absolute level, to understand Hicks’s statement in the footnote on p. 59 that “Mr. Harrod’s failure to perceive these consequences [of autonomous investment] is… responsible for most of the weaker points in his otherwise very suggestive analysis”.
- 19.
Footnote, p. 123. See also footnote 2, p. 39.
- 20.
Hicks’s definition of autonomous investment is given on p. 59: “It is not necessary to assume that all investment is induced investment. While there can be little doubt that quite a large proportion of the net investment which goes on in normal conditions has been called forth, directly or indirectly, by past changes in the level of output, there is certainly some investment for which this effect is so small as to be insignificant. Public investment, investment which occurs in direct response to inventions, and much of the “long-range” investment (as Mr. Harrod calls it) which is only expected to pay for itself over a long period, all of these can be regarded as Autonomous Investment for our purposes. Naturally period, all of these can be regarded as Autonomous Investment for our purposes. Naturally serve for the articulation of a theory”.
- 21.
E. D. Domar, in Econometrica, 1946; American Economic Review, March, 1947; Income, Employment, and Public Policy, 1948; (esp. p. 47). J. J. Duesenbury, in Quarterly Journal of Economics, August, 1950.
- 22.
See especially p. 287 and pp. 295–296.
- 23.
p. \(107.\)
- 24.
p. 91
- 25.
D. 193
- 26.
M. G. Kendall, The Advanced Theory of Statistics, Vol. II, p. 412.
- 27.
E. Slutsky, in Econometrica, \(1937.\)
- 28.
N. Kaldor, “A Model of the Trade Cycle,” Economic Journal, March, 1940.
- 29.
J. A. Schumpeter, Business Cycles, 1939, Vol. I, p. 34.
- 30.
“This does appear to be a case in which, in the deathless words of the Dodo, everybody has won and all must have prizes.” D. H. Robertson, \(A\) Study of Industrial Fluctuation, 1915, p. 1.
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Swan, P.L. (2022). T. W. Swan: “Progress Report on the Trade Cycle”. In: Trevor Winchester Swan, Volume I. Palgrave Studies in the History of Economic Thought. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-13737-2_10
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