# Minskyan classical growth cycles: stability analysis of a stock-flow consistent macrodynamic model

- 33 Downloads

## Abstract

This paper follows van der Ploeg (Metroeconomica 37(2):221–230, 1985)’s research program in testing both its extension of Goodwin (in: Feinstein (ed) Socialism, capitalism and economic growth, Cambridge University Press, Cambridge, 4, 54–58, 1967) predator–prey model and the Minsky Financial Instability Hypothesis (FIH) proposed by Keen (J Post Keynes Econ 17(4):607–635, 1995). By endowing the production sector with CES technology rather than Leontief, van der Ploeg showed that the possible substitution between capital and labor transforms the close orbit into a stable focus. Furthermore, Keen (1995)’s model relaxed the assumption that profit is equal to investment by introducing a nonlinear investment function. His aim was to incorporate Minsky’s insights concerning the role of debt finance. The primary goal of this paper is to incorporate additional properties, inspired by van der Ploeg’s framework, into Keen’s model. Additionally, we outline possibilities for production technology that could be considered within this research program. Using numerical techniques, we show that our new model keeps the desirable properties of Keen’s model. However, we also demonstrate that when the economy is endowed with a class of CES production function that includes the Cobb–Douglas and the linear technology as limit cases, the unique stable equilibrium is an economically desirable one. Finally, we propose a modified extension that includes speculative component in the economy as in Grasselli and Costa-Lima (Math Financ Econ 6(3):191–210, 2012) and investigate its effect on the dynamics. We conclude that CES production function is a more suitable assumption for empirical purposes than the Leontief counterpart. Finally, we show, using numerical simulations, that under plausible calibration, the model endowed with CES production function eventually lose the cyclical property of Goodwin’s model with and without the speculative component.

## Keywords

Prey–predator Goodwin model Keen model Minsky’s financial instability hypothesis Dynamical systems Speculation## JEL Classification

C02 E10 E22 G01## Supplementary material

## References

- 1.Acurio Vasconez, V.M.: What if oil is less substitutable? A new-Keynesian model with oil, price and wage stickiness including capital accumulation. Documents de travail du Centre d’Economie de la Sorbonne 15041 (2015)Google Scholar
- 2.Freĭdlin, M.I., Wentzell, A.D.: Random perturbations of dynamical systems. Number 260 in Grundlehren der mathematischen. Wissenschaften. Springer (1998)Google Scholar
- 3.Goodwin, R.: A growth cycle In: Feinstein, C.H. (ed.) Socialism, Capitalism and Economic Growth. Cambridge University Press, Cambridge, (4):54–58 (1967)Google Scholar
- 4.Grasselli, M., Nguyen-Huu, A.: Inflation and speculation in a dynamic macroeconomic model. J. Risk Financ. Manag.
**8**, 285–310 (2015)CrossRefGoogle Scholar - 5.Grasselli, M., Nguyen-Huum, A.: Inventory growth cycles with debt-financed investment. Working papers chair energy and prosperity (2016)Google Scholar
- 6.Grasselli, M.R., Costa Lima, B.: An analysis of the keen model for credit expansion, asset price bubbles and financial fragility. Math. Financ. Econ.
**6**(3), 191–210 (2012)MathSciNetCrossRefGoogle Scholar - 7.Harvie, D.: Testing Goodwin: growth cycles in ten OECD countries. Camb. J. Econ.
**24**, 349–376 (2000)CrossRefGoogle Scholar - 8.Keen, S.: Finance and economic breakdown: modeling Minsky’s ’financial instability hypothesis’. J. Post Keynes. Econ.
**17**(4), 607–635 (1995)CrossRefGoogle Scholar - 9.Keen, S.: A monetary Minsky model of the great moderation and the great recession. J. Econ. Behav. Org.
**86**(C), 221–235 (2013)CrossRefGoogle Scholar - 10.Klump, R., McAdam, P., Willman, A.: The normalized CES production function: theory and empirics. J. Econ. Surv.
**26**(5), 769–799 (2012)CrossRefGoogle Scholar - 11.Mc Isaac, F.: Testing Goodwin with a stochastic differential approach—the united states (1948–2017). AFD Research Papers Series, (61) (2017)Google Scholar
- 12.Mohun, S., Veneziani, R.: Goodwin cycles and the U.S. economy, 1948–2004. MPRA Papers 30444. University Library of, Munich, Germany (2006)Google Scholar
- 13.Nguyen-Huu, A., Costa-Lima, B.: Orbits in a stochastic Goodwin–Lotka–Volterra model. J. Math. Anal. Appl.
**419**(1), 48–67 (2014)MathSciNetCrossRefGoogle Scholar - 14.Nguyen-Huu, A., Pottier, A.: Debt and investment in the keen model: a reappraisal. Chair energy and Prosperity working paper (2016)Google Scholar
- 15.Pomeau, Y., Manneville, P.: Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys.
**74**(2), 189–197 (1980)MathSciNetCrossRefGoogle Scholar - 16.Solow, R.: A contribution to the theory of economic growth. Q. J. Econ.
**70**(1), 65–94 (1956)CrossRefGoogle Scholar - 17.Solow, R.: Nonlinear and multisectoral macrodynamics: essays in honour of Richard Goodwin, chapter Goodwin’s growth cycle: reminiscence and rumination, pp. 31–41. Palgrave Macmillan, UK, London (1990)CrossRefGoogle Scholar
- 18.van der Ploeg, F.: Classical growth cycles. Metroeconomica
**37**(2), 221–230 (1985)CrossRefGoogle Scholar