This post is based on an research paper available here. All comments are welcomed.
In his 1973 “Effective Demand failures” article, Axel Leijonhuvfud, keen on bridging economics and anthropology (not without malice), proposed moving beyond the division between the two “cosmologies” that characterized the 20th century,. The first, allegedly represented by most neoclassical models, presented a view of the world where any deviation of the economy from its stationary equilibrium would immediately trigger “deviation-counteracting feedback control mechanisms.” In contrast, the second cosmology, encapsulated in most Keynesian models, assumed no “automatic” tendency for the economy to converge to this equilibrium. The economy could settle anywhere between zero and full employment, with all “servo-mechanisms” idle. Leijonhuvfud introduced the concept of “corridor stability” as a way of reconciling these two opposing views of the world. It suggests that the economic system is likely to behave differently for large displacements from its stationary equilibrium compared to moderate ones.
Since the 1970s Leijonhufvud’s perspective has struggled to find its way in macroeconomics. While economists such as James Tobin (1975), Peter Howitt (1978), Bradford De Long, Larry Summers (1986), and others have developed models incorporating corridor stability properties, their impact on macroeconomic theory and teaching has been limited (Dimand and Gomez, 2024). However, the concept has been influential in policy decisions. Policy makers like Ben Bernanke (chair of the FED during the 2007 Crisis) and Mervyn King (governor of the Bank of England at the same time) appeared to endorse the notion that certain significant shocks could profoundly disrupt the economy, reflecting Leijonhufvud’s ideas without explicitly citing them.
Ironically, what historical accounts show that the corridor stability notion was already integrated in ealy macroeconomectric model before being consigned to the background.
Corridor stability in early macrodynamic models
As he explored the properties of this macrodynamic model (partially inspired by Fisher debt deflation theory, 1933), Tinbergen was also busy estimating the first large-scale macroeconometric models for both the Dutch and the US economies. In that context, he found it necessary to work with a linearized version of his system (when changing structural coefficients are supposed to remain constant), a decision now mainly driven by a need for simplification. Because he had seriously considered the possibility for an economy to fluctuate in the neighborhood of its stationary state but to cumulatively deviate from it beyond a critical value of some parameters, he knew better than anyone the risks associated with such an estimating method. Despite this awareness, Tinbergen, perhaps driven by his enthusiasm for promoting the development of this approach, did not place significant emphasis on these risks. The same was true for his immediate followers. Soon, this question was hence pushed aside, and the focus shifted as new macroeconometric models were developed
Lawrence Klein was aware that the real world often operates according to nonlinear equations. Like Tinbergen, he did not put much emphasis on the implications of linearizing these relationships. When he constructed the second large-scale macroeconometric model of the US during his time at the Cowles Commission in the maid 1940s, his primary concern was rather to develop new estimation methods and tools that could provide valuable insights and predictions about the behavior of the economy, particularly in the postwar era (Klein 1950: vii). In this context, he prioritized the ability of the model to account for the empirical patterns observed in the US economy, rather than explicitly addressing the possibility for an economy to collapse. It is also the case that at a time when the Great depression became more distant, the idea that the economy may face a risk of global instability moves into the background.
This shift is evident in the second model he developed in collaboration with his PhD student Arthur Goldberger who cautiously argued in 1959 that the linearization they made did not create a misleading picture of how the economy functions. He referred to the study conducted by Irma and Franck Adelman who shown that the nonlinear version of their model was stable. Simulating the US economy for one century, they showed that the economy would adjust cyclically to “large shocks” while all endogenous variables would grow at the same rate as exogenous variables after approximately six years. As the Adelmans put it in the published version of their study, “even a very strong shock will not permanently distort the long-run path of the economy. In other words, the Klein-Goldberger system is stable” (Adelman 1959: 606).
This set the stage for a return to Ragnar Frisch’s explanation of economic cycles driven by random disturbances on the economic system. By applying random disturbances to the Klein-Goldberger model, they were able to extract cycles compatible with historical US economic patterns observed from 1814 to 1938. These included a business cycle of around 40 months and a Kuznets cycle of about 14 years. Consequently, Irving Fisher’s vision largely faded two decades after his influential article.
Interestingly, this shift was reinforced by the development of so-called endogenous business cycle models, which, even if they offered an image of the world cyclicing around its stationary state in absence of shocks, also ruled out the possibility that an economy may face the risk of global breakdown. It is perhaps no accident that Klein (1956) himself, after working with Goldberger, temporarily endorsed that approach and strove to estimate a non linear business cycle model derived from Kaldor’s 1940 famous Economic Journal article (Assous and Raybaut 2024).
Maurice Allais’ works were certainly the only exception. he developed different versions of a nonlinear model of business cycles, with for main innovation an analysis of the relation between the magnitude of perturbation, global instability, and the existence of multiple limit cycles and their empirical verification (Raybaut, 2014). It also came from the outlining of situations displaying a corridor of stability (a point which did not escape to Grandmont 1989) proving that there are disturbances which can end up in the sinking of the boat, here materialized in episodes of hyperinflation due to the existence of multiple limit cycles.
Corridor stability in modern macroeconomics
Since the publication of Leijonhuvfud’s 1973 paper, the corridor stability assumption aroused only lukewarm interest. Some notable contributions are however worth mentioning . Like Leijonhuvfud, Tobin (1975) saw in that hypothesis a possibility to transform the debate between classical and Keyensian economists. The particular nature of corridor-effects that Tobin has argued exist in the economic system was pictured in terms of what he called price level and price change effects, the two broad forces acting on the stability of the economy. The price-level effect (Pigou or Keynes effect) would tend to make real output rise back to its full-employment value. On the other hand, the price-change effect (Fisher’s effects, etc) would tend to amplify the departure of the economy from its stationary state.
Later on, Groth (1993) notably showed that Tobin’s stability condition was formally identical to the stability condition found by Cagan (1956) in his classical analysis of the purely monetary dynamics in situations of hyperinflation. On the basis of “Familiar Macro Model” (IS-LM model with adaptive expectations), Groth could hence show that such a condition only entails local stability and was in fact, given the non-negativity of the nominal rate of interest, both a necessary and a sufficient condition for the “existence of a corridor” (Groth 1993: 302).
Howitt (1979) and more recently economists from the Biefeld school (Rosser, 2023) as well as more policy oriented macroeconomists (Eusepi 2010, Borio 2021) also attempted to find other “concrete embodiments” of Leijonhuvfud’s corridor hypothesis. However, these models (very much to the regret of Leijonhufvud, 2009) did not carry much weight in the face of the growing prominence of Dynamic Stochastic General Equilibrium (DSGE) models. In the end, and despite significant evolutions of mainstream macroeconomics which have occurred since the 2008 Global crisis, no “cosmology” change has occurred. More than a century after the publication of Fisher’s 1933 article, the challenge still remains.
References
Adelman, I, and F. L. Adelman. (1959). The Dynamic Properties of the Klein-Goldberger Model. Econometrica, 27 (4), 596–625. https://doi.org/10.2307/1909353.
Assous, M and V. Carret. 2022. Modeling Economic Instability: A History of Early Macroeconomics. Cham: Springer.
Assous, M and A. Raybaut, 2024. Le colloque international d’économétrie de Paris de 1955 et les transformations de l’analyse macrodynamique non linéaire. Revue d’histoire de la pensée économique. (forthcoming)
Assous, M and A. Raybaut, 2025. Grappling with instability: A History of Early Post World War II Macroeconomics. Cham: Springer. (forthcoming)
Borio, C (2021). Monetary and fiscal policies: in search of a corridor of stability, BIS /CEPR- VoxEU
De Long, J. Bradord, and L. H. Summers. (1986). Is Increased Price Flexibility Stabilizing? The American Economic Review. 76 (5), 1031–44.
Dimand, R. W., and R, Gomez Betancourt (2024). James Tobin on macroeconomic instability: an old Keynesian changes ground. The European Journal of the History of Economic Thought, 1–13. https://doi.org/10.1080/09672567.2024.2305945
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Klein, L. R. (1950). Economic fluctuations in the United States, 1921–1941. Number 11 in Cowles Commission Monographs. New York: Wiley.
Klein, L. R. (1956). Quelques aspects empiriques du modèle de cycle économique de Kaldor. 2ème Colloque International d’Économétrie 23-28 Mai, in Les modèles dynamiques en économétrie, 1956 p. 127-44.
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Howitt, P (1978). The Limits to Stability of a Full-Employment Equilibrium.” The Scandinavian Journal of Economics. 80 (3), 265–82. https://doi.org/10.2307/3439581.
Leijonhufvud, A. (1973). Effective Demand Failures. The Swedish Journal of Economics, 75(1), 27–48. https://doi.org/10.2307/3439273
Leijonhufvud, A, (2009). Out of the corridor: Keynes and the crisis, Cambridge Journal of Economics , 33 (4), 741-757.
Raybaut, A. (2014). Toward a non-linear theory of economic fluctuations: Allais’s contribution to endogenous business cycle theory in the 1950s. The European Journal of the History of Economic Thought, 21(5), 899–919. https://doi.org/10.1080/09672567.2014.934871
Raybaut, A. (2014). Toward a non-linear theory of economic fluctuations: Allais’s contribution to endogenous business cycle theory in the 1950s. European Journal of the History of Economic Thought. 21(5), 899
Rosser, J. Barkley and Rosser, M. V., 2023. “The Bielefeld School of economics, Post Keynesian economics, and dynamic complexity,” Journal of Economic Behavior & Organization, Elsevier, 212(C), 454-465.
Tobin, J. (1975). “Keynesian Models of Recession and Depression.” The American Economic Review. 65 (2), 195–202. http://www.jstor.org/stable/1818852.