Abstract
“The Essay in Dynamic Theory” (1939) developed further the principle of instability and the idea of endogeneity and inevitability of the trade cycle. However, the conception of dynamics and instability in the Essay differs from that of the Trade Cycle (1936) in two important aspects. Instability is no longer the result of the interaction between the multiplier and the accelerator, but of assuming the independency of the rate of growth, the propensity to save and the incremental capital-output ratio. Also imperfect competition is no longer seen as a microfoundation of the trade cycle. In the Essay, Harrod articulated his dynamics and its central core, the instability principle, around the fundamental equation. He defined it in terms of the warranted rate of growth: that rate of growth that validates the capital accumulation decisions of entrepreneurs. Along with the warranted rate of growth, Harrod introduced the natural and actual rates of growth. The draft Essay (1938) received comments for J. Marschak and J. M. Keynes who pointed out that the model required additional hypotheses that were not made explicit. Marschak also provided the first mathematical formulation of Harrod’s dynamics and raised several important points including the lack of clarity in the definition of the warranted rate of growth. Keynes’s comments led Harrod to compress his discussion of the application of the dynamic determinants to the cycle that give rise to instability of the moving equilibrium and the non-linearities of the trade cycle. This facilitated the interpretation of the fundamental equation as a constant coefficient model.
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Notes
- 1.
Actually as McCord Wright (1949, p. 326) pointed out Harrod provided in the Essay six different definitions of the warranted rate of growth: the rate which “(i) leaves each entrepreneur satisfied with what he has done;…(2) allows for some individual disappointments but keeps entrepreneurs as a group, on balance, satisfied;…(3) keeps them doing the same thing;…(4) equates ex ante S and… (5) concerns only the part of investment directly linked to consumption;…(6) somehow differs from the ‘proper’ warranted rate which would obtain in conditions of full employment.”
- 2.
This derivation is partly based on Shackle (1965, pp. 98–108).
- 3.
This is the definition of \(C_{r}\) provided in the Essay. In Towards Dynamic Economics (1948, p. 82), he defined it as a “…an equilibrium term expressing requirements for new capital.” In his Second Essay (1960, p. 278), it is the “optimum amount of capital required, per unit of time, given current technology, for the output of an extra unit….” In the Essay, he used the term \(C_{p}\) and C for the incremental capital-output ratios corresponding to the actual and warranted rates of growth. In Towards Dynamic Economics (1948) and thereafter he uses the terms C and \(C_{r}\) (Harrod 1948, pp. 77, 81; 1960, p. 279; 1973, pp. 16–17; 1969, pp. 199–200).
- 4.
As Harrod explained (1948, note 1, p. 80): \({GC} = \left({\frac{\Delta Y}{Y}} \right)\left({\frac{I}{\Delta Y}} \right)\) and \({\text{s}} = \frac{S}{Y}\).
- 5.
As Harrod (p. 85) explained: “This capital…covers both equipment and stock-in-trade….C consists in part of consumer goods, including non-durable consumer goods. In an advancing community goods in the pipeline, shops, warehouses, transit and producers’ stores, have to increase in proportion to turnover. All these goods are part of capital.”
- 6.
Also \(G\,\text{and}\,C\) is independent of the unit period chosen. Finally, \(s\) is not a constant but its changes must be small relative to those of G.
- 7.
See also Harrod (1948, p. 89): “\(G_{w}\) itself fluctuates in the trade cycle. Even if savings…is fairly steady in the long run, it is not likely to be so in the short run”.
- 8.
Young (1989) also mentions other possible influences such as G. Cassel, O. Lange, M. Kalecki, and J. Tinbergen. Young also argues that Tinbergen’s influence was decisive in the formulation of Harrod’s dynamic theory. Goodwin (1982, p. vii) refers to the influence of Tinbergen on Harrod’s Essay: “I also told him that Tinbergen reviewing the book in a German periodical, had pointed out that the accelerator plus multiplier gave a first order differential equation and hence could only produce exponential growth. Harrod seems to have been convinced by this, for two years later he produced his famous article on growth.” The evidence regarding Cassel, Lange, and Kalecki is scant and counterfactual. The existing correspondence between Harrod and Tinbergen does not provide evidence for the claim that Tinbergen influenced Harrod. Jolink (1995, p. 435) argues that the influence of Tinbergen on Harrod was “on formal, mathematical grounds” but did not influence Harrod’s methological views. See the discussion on Tinbergen on pages 195–196 and in Chapter 3 (The Trade Cycle). Besomi also contends that Harrod’s instability principle derives from “Hayek’s rendition of A. Lowe” in his Monetary Theory and the Trade Cycle (1933) but is careful to point out that the “evidence is no conclusive” (Besomi 2002, p. 48).
- 9.
Keynes’s dependent variable is the rate of growth of capital not of output as in Harrod. Keynes pointed out that steady growth in capital and output are the same when the relation is constant (Keynes, ibid.).
- 10.
As Keynes (1964 [1936], p. 120) explained: “The marginal propensity to consume is not constant for all levels of employment, and it is probable that there will be, as a rule, a tendency for it to diminish as employment increases; when real income increases…the community will wish to consume a gradually diminishing proportion of it.”
- 11.
Note that Joseph Alois Schumpeter (1883–1950). Schumpeter also argued that the wave motion is a key characteristic of capitalist development, and that the cycle is the normal way through which capitalism develops and grows (Elliott 1997). As Schumpeter (1997 [1934], pp. 214–215) put it: “The point of view according to which the wave-like fluctuation in business…appears to be the fundamental thing to be explained….We agree in this conception…that the alternating situation are the form economic development takes in an era of capitalism.” Schumpeter published in 1946 an article also arguing that Keynes’s GT was anchored in static analysis. As he put it (1946, p. 511), “The exact skeleton of Keynes’s system belongs, to use the terms proposed by Ragnar Frisch, to macro statics, not to macro dynamics…” and (ibid., p. 512): “All the phenomena incident to the creation and change in this apparatus, that is to say, the phenomena that dominate the capitalist processes, are thus excluded from consideration.” Years later Hyman Minsky (1919–1996), a former student of Schumpeter, made a similar criticism of Keynes (Minsky 1975).
- 12.
Young (op. cit.) also argues that Harrod developed the idea of instability in his critique of Lundberg.
- 13.
He made the distinction in Economic Dynamics (1973, pp. 16–17).
- 14.
It is curious to note that in his correspondence with Marschak on the draft Essay, Harrod explicitly stated that the natural rate of growth did not represent the ceiling of full employment (CIPC, Vol. II, p. 859).
- 15.
Harrod (ibid.) provided a different definition for \(C_{r}\) in the boom (“…the amount of extra capital required per unit increment of output”) and in the slump (“…the amount of capital that can most conveniently be dispensed with”). This adds to the confusion regarding the different definitions of \(C_{r}.\) See footnote 1. Harrod also pointed out that a quicker turnover of equipment during the slump would increase the value of \(C_{r}\) (CIPC, Vol. III, p. 1201).
- 16.
- 17.
Marschak’s comment was made in relation to Harrod’s statement that “those who define dynamics as having a cross reference to two points in time will not regard this equation (the fundamental equation) as dynamic” (CIPC, Vol. II, p. 1191).
- 18.
In this regard, Besomi (2003, CIPC, Vol. III, p. 1206, n. 5) argues that Harrod “pigeon-holed numerous trade cycle theories under the heading of ‘time.lag’ theories of the trade cycle.” He includes here Robertson’s period analysis, Lundberg’s analysis in his Theory of Economic Expansion (1937), Tinbergen’s work (1935, 1938) and Hicks’s Value and Capital (1939). See also Besomi (1998b).
- 19.
While it is true that the Special Theory of Relativity (1905) requires only elemental mathematics, the General Theory of Relativity (1915) requires more sophisticated mathematics, including non-Euclidean geometry and non-linear differential equations.
- 20.
As Besomi (1996, p. 292) points out Marschak’s remarks on the non-constancy of C suggests that at the time “the econometricians were aware of the limitations of linear analysis” and speculates that Le Corbeiller’s article (1933) of the application of the van der Pol oscillator to problems of political economy including crises and price movements did not go unnoticed. But once again the van de Pol oscillator provides periodic solution and thus suffers from the same type of weakness as Tinbergen’s linear difference equation. Some of the current literature on Harrod’s dynamics (i.e. Sportelli 2000) also provides a periodic solution and thus assumes regularity and predictability on the part of entrepreneurs and thus, in spite of the use of modern mathematical techniques, suffers from the same weakness in the conceptual interpretation of Harrod’s dynamics and the instability principle.
- 21.
He made a similar comment earlier on in the Trade Cycle (1936, p. 31): “In the actual course of the trade cycle the movement is not found to be uniform. This is largely connected with the relation between capital and consumable goods, a matter reserved for discussion at a later stage. The lack of uniformity may be connected with the fact that the stabilizing principles or their inverse operate with different force in different occupations.”
- 22.
- 23.
See Kregel (1980), pp. 102–113.
- 24.
Keynes explained Harrod’s model in the following terms. \(\Delta S = sY\), where \(s\) is the proportion of income saved in any period, \(\Delta S =\) increment of savings per unit of time; \(\Delta I = C_{r} \Delta Y =\) ‘increment of capital, corresponding to increment of income at a rate \(\Delta Y\) per unit of time required by “normal” technological considerations’; and \(\frac{{\Delta Y_{W} }}{Y} = \frac{s}{{C_{r} }} =\) warranted rate of growth during the time period (ibid., p. 333). From here the equation \(C_{r} \Delta Y_{w} = sY\) can be obtained (ibid., p. 333). As Besomi (1995, p. 328) indicates Keynes forgot that \(\Delta S = sY + s\Delta Y\), so that \(C_{r} \Delta Y = sY + s\Delta Y\) as Harrod correctly stated. Thus \(C_{r} \Delta Y = sY + s\Delta Y \Leftrightarrow \Delta Y\left({C_{r} - s} \right) = sY\) and \(\Delta Y > 0\) implies that \(C_{r} > s.\)
- 25.
It is curious to note that in his discussion on policy proposals and more specifically public works he does refer in one instance to the normal warranted rate (ibid., p. 32).
- 26.
Following the introduction of capital that is independent of income and the external sector, Harrod does not describe the effects of the downward and upward phase of the cycle on the warranted rate due to lack of space (Harrod, ibid., p. 28).
- 27.
From late 1924 on, Keynes consistently recommended the undertaking of public works as a way to overcome recessions. In his earlier articles, “Does Unemployment Need a Drastic Remedy?” and a “Drastic Remedy for Unemployment” (1924) Keynes analyzed unemployment in terms of structural causes, wage rigidity, and demand considerations. While he thought structural programs, reconversion, and reorganization of depressed sectors, and wage flexibility could improve competitiveness, it was de facto an impractical solution. He thus favored increasing aggregate demand through a program of public work expansion. Kahn’s multiplier provided, eventually, the basis for its rationale. Increasing demand could transfer workers from less to more productive sectors. Keynes’s case for demand and output expansion through fiscal policy, in the guise of public works, was the basis for his recommendations to the Macmillan Committee, for the views presented in “Can Lloyd George Do It?,” and for his earlier views on the “Great Slump.” In the Treatise on Money (1930), Keynes made the case for public works for an open economy under conditions of wage rigidity and a fixed exchange rate regime. As a group, Chicago economists advocated on more than one occasion an increase in aggregate demand to revamp a stagnant economy. In January 1932, twenty-four economists participating at a conference at the University of Chicago urged President Hoover to pursue more aggressively open market operations and to continue the government’s public works program. Kahn (1984, pp. 128–129) identifies only one passage in the GT (Chapter 10) where Keynes refers to “loan expenditure ‘by public authorities’”: “‘wasteful’ loan expenditure may […] enrich the community on balance. Pyramid building, earthquakes…may serve to increase wealth.” Public works were also advocated by Robertson as exemplified in his article in the Listener (“Is Another Slump Coming?” 28 July 1937) which led Keynes to remark. “I doubt if there is a sentence from which I disagreed” (Keynes, CW, Vol. XIV, p. 250). Pigou also supported public works as attested by the evidence he gave to the Macmillan Committee (Howson and Winch 1977, p. 66). The Twenty Second Report of Committee on Economic Information (February 1937) also advocated public works (ibid., pp. 346–350). In 1938, Keynes focused on policy measures (monetary, fiscal, and also related to trade) to restrain the boom phase of the cycle (Moggridge and Howson 1974, pp. 240–242).
- 28.
One of the drawbacks mentioned by Harrod was the difficulty in implementing public works. This is an aspect also mentioned by Galbraith (1940, pp. 107–111).
- 29.
In the draft Essay, Harrod explicitly associated the use of the short-term rate of interest in connection to the control of inflation (CIPC, Vol. III, p. 1025), whereas in the Essay it is associated simply with mitigating cycle fluctuations.
- 30.
- 31.
Besomi (2002, p. 42).
- 32.
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Pérez Caldentey, E. (2019). The Essay in Dynamic Theory. In: Roy Harrod. Great Thinkers in Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-74085-7_4
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