An analysis of the Keen model for credit expansion, asset price bubbles and financial fragility. (English) Zbl 1264.91133
Summary: We analyze the system of differential equations proposed by Keen to model Minsky’s financial instability hypothesis. We start by describing the properties of the well-known Goodwin model for the dynamics of wages and employment. This is followed by Keen’s extension to include investment financed by debt. We determine the several possible equilibria and study their local stability, discussing the economical interpretation behind each condition. We then propose a modified extension that includes the role of a Ponzi speculator and investigate its effect on the several equilibria and their stability. All models are amply illustrated with numerical examples portraying their various properties.
Keywords:
Minsky’s financial instability hypothesis; Goodwin model; Keen model; credit cycles; dynamical systemsReferences:
| [1] | Aguiar-Conraria L.: A note on the stability properties of Goodwin’s predator–prey model. Rev. Radic. Political Econ. 40(4), 518–523 (2008) · doi:10.1177/0486613408324074 |
| [2] | Arrow, K., Hahn, F.: General Competitive Analysis. Mathematical Economics Texts. Holden-Day, San Francisco (1971) · Zbl 0311.90001 |
| [3] | Desai M.: Growth cycles and inflation in a model of the class struggle. J. Econ. Theory 6(6), 527–545 (1973) · doi:10.1016/0022-0531(73)90074-4 |
| [4] | Desai M., Henry B., Mosley A., Pemberton M.: clarification of the Goodwin model of the growth cycle. J. Econ. Dyn. Control 30(12), 2661–2670 (2006) · Zbl 1162.91476 · doi:10.1016/j.jedc.2005.08.006 |
| [5] | Goodwin R.M.: A growth cycle. In: Feinstein, C.H. (ed.) Socialism, Capitalism and Economic Growth, pp. 54–58. Cambridge University Press, Cambridge (1967) |
| [6] | Goodwin, R.: Economic evolution, chaotic dynamics and the Marx–Keynes–Schumpeter system. In: Rethinking Economics: Markets, Technology and Economic Evolution, pp. 138–152. Edward Elgar, Cheltenham (1991) |
| [7] | Harvie D.: Testing Goodwin: growth cycles in ten OECD countries. Camb. J. Econ. 24(3), 349–376 (2000) · doi:10.1093/cje/24.3.349 |
| [8] | Hirsch M., Smale S., Devaney R.: Differential Equations, Dynamical Systems, and an Introduction to Chaos. Pure and Applied Mathematics. Academic Press, New York (2004) · Zbl 1135.37002 |
| [9] | Keen S.: Finance and economic breakdown: modeling Minsky’s ”Financial Instability Hypothesis”. J. Post Keynes. Econ. 17(4), 607–635 (1995) |
| [10] | Keen, S.: The nonlinear economics of debt deflation. In: Barnett, W.A. (ed.) Commerce, Complexity, and Evolution: Topics in Economics, Finance, Marketing, and Management. Proceedings of the Twelfth International Symposium in Economic Theory and Econometrics, pp. 83–110, Cambridge University Press, New York (2000) |
| [11] | Keen S.: Household debt: the final stage in an artificially extended Ponzi bubble. Aust. Econ. Rev. 42(3), 347–357 (2009) · doi:10.1111/j.1467-8462.2009.00560.x |
| [12] | Kindleberger, C.P., Aliber, R.Z.: Manias, Panics, and Crashes: A History of Financial Crises. Palgrave Macmillan, Houndmills (2011) |
| [13] | Misnky H.P.: Can ’It’ Happen Again? Essays on Instability and Finance. M.E. Sharpe, Armonk (1982) |
| [14] | Solow R.M.: Goodwin’s growth cycle: reminiscence and rumination. In: Velupillai, K. (ed.) Nonlinear and Multisectoral Macrodynamics, Macmillan, London (1990) |
| [15] | Tirole J.: Asset bubbles and overlapping generations. Econometrica 53(6), 1499–1528 (1985) · Zbl 0597.90016 · doi:10.2307/1913232 |
| [16] | van der Ploeg F.: Classical growth cycles. Metroeconomica 37(2), 221–230 (1985) · doi:10.1111/j.1467-999X.1985.tb00412.x |
| [17] | Veneziani R., Mohun S.: Structural stability and Goodwin’s growth cycle. Struct. Change Econ. Dyn. 17(4), 437–451 (2006) · doi:10.1016/j.strueco.2006.08.003 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
