Abstract
Richard Goodwin was the pioneering endogenous, non-linear theorist of macrodynamic fluctuations, once referred to as trade cycle theory but now known as business cycle theory. His theoretical and policy frameworks spanned optimal growth planning, stabilization policy, iterative dynamics, coupled dynamics, capital theory, and, above all, innovative teaching. He worked on synthesizing the imaginative insights of Schumpeter on innovations, Keynes on the multiplier, Harrod on the accelerator, Leontief on an applicable model of Walrasian interdependence, and Sraffa on capital theory. His non-linear mathematics owed a great deal to Philip Le Corbeiller’s personal teaching and the development of classical theory of non-linear differential equations. His important discovery of a one-sided oscillator which does not depend on the cubic characteristic was made in the context of reviewing Hicks’s theory of the trade cycle. In this chapter, these elements are made to tell the story of Goodwin’s wonderful contributions to economics.
Much of the pure facts of Richard Goodwin’s life are taken from one or another of my own earlier writings on Goodwin (particularly, Velupillai 1996, 1998). Goodwin never failed to remind me that his middle name was ‘Murphey with an “e”’! My indebtedness to the written contributions, and personal friendship, of Ralph Abraham, Richard Day, Geoff Harcourt, Ragu Ragupathy, Otto Rössler, and Stefano Zambelli are too obvious to require explicit acknowledgement. They are, alas, not responsible for the remaining infelicities.
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Notes
- 1.
Le Corbeiller’s letter to Goodwin, dated 29 March 1958 (the original, handwritten version of which was given to me by Goodwin, at the time of his formal retirement at Cambridge, in 1980), illustrates the way he came to the conclusion that a characteristic with only one bend—‘one nonlinearity’, as he called it—was sufficient to generate a limit cycle on the plane. See also Goodwin (1950, 1990) and Velupillai (1998).
- 2.
However, it is not the kind of ‘mindless simulation’ that is currently fashionable in many frontiers of so-called computational economics, agent-based economics, and even stock-flow consistent modelling of disaggregated economies. Goodwin’s simulations were in the mode of what I have come to call the Fermi–Pasta–Ulam method of analysis (Fermi et al. 1955), and its perfect execution was in Goodwin (1947). I have always maintained that this is the authentic, and proper, way to do ‘agent-based economics’.
- 3.
It is useful to contrast this with what I call Turing’s Precept: ‘Description must be non-linear; prediction must be linear’ (quoted in Gandy 1954 [2001]: 266; italics added).
- 4.
As Goodwin told me during a personal conversation in September 1977 at my home in Svanshall, Sweden: ‘I was walking down the corridor of the Physics Department when I saw the name “Ph. Le Corbeiller” on one of the doors. I knocked, the door was opened by a distinguished looking, elegantly dressed, gentleman. I asked him whether he was the Le Corbeiller who had written on the desirability of using van der Pol’s theory of relaxation oscillations in the first volume of Econometrica (Le Corbeiller 1933). He answered yes. I asked him whether he would teach me the theory of nonlinear dynamics. He, then, literally took me “by the hand” and taught me nonlinear dynamics’. Goodwin had not only read Le Corbeiller’s 1933 piece, but also Le Corbeiller (1931) and, later, mastered the geometry of relaxation oscillations that was a pedagogical masterpiece in Le Corbeiller (1936). This latter method remained his lifelong way of devising, drawing, and explaining the geometry of non-linear macrodynamics. It was this method that enabled him to discover the one-sided oscillator, mentioned above. It is a method that seems to have been ‘hollowed out’ in this modern age of blind computer simulations. I am, now, the proud owner of Goodwin’s copies of Le Corbeiller (1931, 1936).
- 5.
He told me, in a personal conversation in the mid-1970s, that Dennis Robertson was sent Goodwin’s papers for evaluation by the Governing Body of Peterhouse and that the great successor to Pigou and Marshall responded by writing in his official report: ‘I do not agree with anything Goodwin writes, but I would not miss them for the world!’ Later, it was Harry Johnson who was sent by Richard Kahn and Joan Robinson to ‘interview’ Goodwin, to ‘investigate his suitability to become a member of the Cambridge Faculty of Economics and Politics’.
- 6.
Following, therefore, in the footsteps of H.O. Meredith, later a distinguished Professor of Economics at Queen’s University in Belfast (where, several generations later, this minor author ‘succeeded’ that legendary scholar), who was himself succeeded by Maynard Keynes. When Goodwin retired as Director of Studies in Economics at Peterhouse, I had the pleasure and privilege of taking over that coveted post, not least due to Goodwin’s efforts and influence.
- 7.
The last time I visited the fourth floor of the Sidgwick site, a decade or so ago, where the Faculty of Economics and Politics of the University of Cambridge is housed, the corridors were adorned by some of Goodwin’s paintings which, he told me, had been bought during Professor Aubrey Silbertson’s tenure as the Chairman.
- 8.
During my own years at the European University Institute in Fiesole, 1981–1985, picturesquely located in the hills outside Florence, he was a frequent visitor to the graduate and staff seminars there.
- 9.
Many interpret Goodwin as assuming just a ‘ceiling’ on employment in the labour market; this was never so. He interpreted Harrod as assuming a ceiling of resources in any advanced industrial economy, but particularly in a largely free enterprise (but not perfectly competitive) capitalist system. These resources could be labour, but not necessarily always the constraining ‘ceiling’. Incidentally, it was Harrod, not Hicks, who first introduced the concept of a ceiling in an endogenously fluctuating aggregate macroeconomy.
- 10.
See also Ichimura (1955: 217, fn. 28), the book in which this splendid article appeared was the first, to the best of my knowledge, to use the phrase Post-Keynesisan Economics in its title); in many ways Harrod (ibid.) is a forerunner of so-called New Keynesian macroeconomics. However, the uncompromising drive to found macroeconomics on futile orthodox rationality—dressed up as mathematical microeconomics—by the New Keynesians makes them uncomfortable bedfellows with Harrod (1951).
- 11.
I prefer the phrase dynamic contours to Kaldor’s—now much maligned—notion of stylized facts, simply because the former retains fidelity to Goodwin’s Schumpeterian vision of capitalism’s intrinsically unstable dynamic evolution.
- 12.
That it was not published earlier was entirely due to the fact that Schumpeter’s untimely death, in January 1950, intervened. Samuelson’s handsome acknowledgement of Goodwin’s priority in this field was expressed in his letter to me, dated 12 September 1996 (italics added): ‘I grieve that Hicks got a lot of credit for non-linear cycles, even though he had learned much from earlier work by Dick [Goodwin]’.
- 13.
This criticism was incorrect, as pointed out by Ichimura (1955: 217, fn. 28): ‘Mr. Harrod combines the multiplier and the accelerator, which latter is made nonlinear by reason of the following effects of the changes in the level of output on the acceleration coefficient: (1) the influence of the rising rate of interest in the upswing and that of the falling rate in the downswing; (2) the changes in the relative prices of capital goods; and (3) the variations in profitability due to the law of diminishing returns and the elasticity of demand’.
- 14.
In a footnote in his famous paper, Goodwin says: ‘My debt to Professor Le Corbeiller is very great, not only for the original stimulation to search for the essential nonlinearities, but also for his patient insistence, in the face of the many difficulties which turned up, that this type of analysis must somehow be worked out’ (Goodwin 1951a: 2; italics in original).
- 15.
The role of an autonomous, exogenously specified level of investment in Hicks (1950), which explains the lower turning when the system hits the floor. But, as Goodwin observed (1994: 77; italics added): ‘When output has fallen, leaving general excess capacity, there is no reason to invest and the accelerator is dead’. Moreover, the piecewise linear Hicks model is capable of generating unstable, globally attracting, equilibria (cf. Sedaghat 1997: 357).
- 16.
Goodwin rarely—but not never—resorted to non-linear, difference equation, NENAF modellng, reflecting, perhaps, the apprehension he perceptively noted (Goodwin 1950: 319, fn. 6): ‘Combining the difficulties of difference equations with those of non-linear theory, we get an animal of a ferocious character and it is wise not to place too much confidence in our conclusion as to behavior’.
- 17.
Curiously, Goodwin never tried to generate, by actual simulation, the limit cycle embedded in the Goodwin–Le Corbeiller equations. Had he done so, he would have realized that the system would have to be integrated backwards in time to generate the limit cycle! This is because it is an unstable limit cycle. Of course, a ‘trivial’ change of sign for the parameter in the system leads to the generation of a stable limit cycle. However, whether the ‘trivial’ change of sign preserves fidelity with the economics underpinning the models he constructed is a much more difficult question to answer, especially in a footnote.
- 18.
Simon’s felicitous use of this concept (e.g. in Simon 1952), to develop a rich repertoire of concepts on causality, identifiability, semi-decomposability, evolutionary dynamics—and much else—is a testimony to the fertility and originality of Goodwin’s innovative theoretical contributions, even within the framework of linearity.
- 19.
A ‘free’ translation, by me, from the original Swedish version of the letter, which was made available to me by the late Professor Thalberg, in 1976.
- 20.
Goodwin was also always careful to choose the phrase ‘existence of a solution’ rather than the more orthodox ‘existence of an equilibrium’. Had this distinction been as carefully observed by computable general equilibrium theorists, the nonsensical constructive and computable claims they—and their dynamic stochastic general equilibrium (DSGE) followers—have been making would have shown to be the true non sequiturs they actually are.
- 21.
In a footnote to this Schumpeterian point, Goodwin adds (ibid.: 60; italics in original): ‘From the unpublished manuscript of his History of Economic Analysis’. My reading of this monumental text by Schumpeter (1954) does not show any evidence of this important paragraph on his meeting with Walras at least in the published version of the History of Economic Analysis. Modern readers of this classic should, perhaps, be reminded that Goodwin was the one who ‘put together…the material in Part IV, Chapter 7’, that is, the chapter on Equilibrium Analysis (see the concluding paragraph in the ‘Editor’s Introduction’ by Elizabeth Boody Schumpeter).
- 22.
To the best of my knowledge this appendix has never been published in its entirety.
- 23.
In addition, see some of the essays republished in Goodwin (1982).
- 24.
As Solow (1990: 32; italics added) recalled, with charm and fondness: ‘I may be inventing this, but I seem to recall that [Goodwin] sometimes suggested that, well, one could not actually believe this or that, but it was an ingenious line of thought, perhaps worth following just to see where it came out. One could always reject it later, and then one would have a better idea of what one was rejecting. If that actually happened, then I was getting my introduction to the theorist’s frame of mind’.
- 25.
In my personal copy of this wonderfully original book, he wrote: ‘Vela, his very own copy, not presented by, but blessed by me the poor scribbler of it. Dick Goodwin, Sept 29 1977’. This inscription was written when he was staying with me, at my home in Svanshall, at the time of the Wicksell Symposium, held in Frostavallen.
- 26.
I know this because it was I who provided him with, first, the Italian original of Kolmogorov (1936), and, then, an English translation of this classic prepared for me by my good friend, and a fellow Goodwin pupil, Professor Guglielmo Chiodi.
- 27.
When I had successfully completed my doctoral dissertation, under his supervision, at Cambridge in 1979, he presented me with a Château Léoville-Barton, 1949.
References
Cited Works by Richard Goodwin
Goodwin, R.M. (1943). ‘Keynesian and Other Interest Theories’. Review of Economics and Statistics, 25(1): 6–12.
Goodwin, R.M. (1946). ‘Innovations and the Irregularity of Economic Cycles’. Review of Economics and Statistics, 28(2): 95–104.
Goodwin, R.M. (1947). ‘Dynamical Coupling with Especial Reference to Markets Having Production Lags’. Econometrica, 15(3): 181–204.
Goodwin, R.M. (1949a). ‘The Multiplier as Matrix’. Economic Journal, 59(236): 537–555.
Goodwin, R.M. (1949b). ‘The Business Cycle as a Self-Sustaining Oscillation’. Econometrica, 17(2): 184–185.
Goodwin, R.M. (1950). ‘A Non-Linear Theory of the Cycle’. Review of Economics and Statistics, 32(4): 316–320.
Goodwin, R.M. (1951a). ‘The Nonlinear Accelerator and the Persistence of Business Cycles’. Econometrica, 19(1): 1–17.
Goodwin, R.M. (1951b). ‘Iteration, Automatic Computers, and Economic Dynamics’. Metroeconomica, 3(1): 1–7.
Goodwin, R.M. (1953). ‘Static and Dynamic Linear General Equilibrium Models’. In The Netherlands Economic Institute (ed.) Input-Output Relations. Proceedings of a Conference on Inter-Industrial Relations Held at Driebergen, Holland. Leiden: H.E. Stenfert Kroese NV: 54–87.
Goodwin, R.M. (1961). ‘The Optimal Growth Path for an Underdeveloped Economy’. Economic Journal, 71(284): 756–774.
Goodwin, R.M. (1967). ‘A Growth Cycle’. In part I of C. Feinstein (ed.) Socialism, Capitalism and Economic Growth: Essays Presented to Maurice Dobb. Cambridge: Cambridge University Press: 54–58.
Goodwin, R.M. (1970). Elementary Economics from the Higher Standpoint. Cambridge: Cambridge University Press.
Goodwin, R.M. (1974). ‘The Use of Normalized General Coordinates in Economic Planning’. Chapter 3 in A. Mitra (ed.) Economic Theory and Planning: Essays in Honour of A.K. Das Gupta. Calcutta: Oxford University Press: 26–38.
Goodwin, R.M. (1977). Capital Theory in Orthogonalised General Co-ordinates. Presented at the Wicksell Symposium, held in Frostavallen, Sweden. Republished as Chapter 8 in Essays in Economic Dynamics (1982) by R.M. Goodwin. London: Macmillan: 153–172.
Goodwin, R.M. (1982). Essays in Economic Dynamics. London: Macmillan.
Goodwin, R.M. (1988). ‘The Multiplier-Accelerator Discretely Revisited’. In part I of R. Gianni and K. Velupillai (ed.) Growth Cycles and Multisectoral Economics: The Goodwin Tradition. Lecture Notes in Economics and Mathematical Systems. Number 309. Heidelberg: Springer-Verlag: 19–29.
Goodwin, R.M. (1990). Chaotic Economic Dynamics. Oxford: Clarendon Press.
Goodwin, R.M. (1991). ‘Letter to Nick Stern’. 16 August. Copy in the possession of the author.
Goodwin, R.M. (1994). ‘A Reformulation and Extension of Hicksian Dynamics’. Chapter 6 in H. Hagemann and O.F. Hamouda (eds) The Legacy of Hicks: His Contributions to Economic Analysis. London: Routledge: 75–86.
Goodwin, R.M. (2000). ‘A Superb Explanatory Device’. Chapter 13 in R. Leeson (ed.) A.W.H. Phillips: Collected Works in Contemporary Perspective. Cambridge: Cambridge University Press: 118–119.
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Velupillai, K.V. (2017). Richard Murphey Goodwin (1913–1996). In: Cord, R. (eds) The Palgrave Companion to Cambridge Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-41233-1_36
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