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REGULARITY AND STABILITY OF EQUILIBRIA IN AN OVERLAPPING GENERATIONS GROWTH MODEL

Published online by Cambridge University Press:  17 July 2017

Jean-François Mertens  and
Anna Rubinchik
Jean-François Mertens
Affiliation:
Université Catholique de Louvain
Anna Rubinchik*
Affiliation:
University of Haifa
*
Address correspondence to: Anna Rubinchik, Department of Economics, University of Haifa, Mount Carmel, Haifa 31905, Israel; e-mail: [email protected]
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Abstract

In an exogenous-growth economy with overlapping generations, the Cobb–Douglas production, any positive life-cycle productivity, and time-separable constant elasticity of substitution (CES) utility, we analyze local stability of a balanced growth equilibrium (BGE) with respect to changes in consumption endowments, which could be interpreted as a transfer policy. We show that generically, in the space of parameters, equilibria around a BGE are locally unique and are locally differentiable functions of endowments, with derivatives given by kernels. Furthermore, those equilibria are stable in the sense that the effects of temporary changes decay exponentially toward ±∞.

Keywords

Regularity of Infinite EconomiesPolicy EvaluationOverlapping GenerationsExogenous Growth
Type
Articles
Information
Macroeconomic Dynamics , Volume 23 , Issue 2 , March 2019 , pp. 699 - 729
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

We would like to thank the Center for Rationality in Jerusalem for its hospitality; A. Gorokhovsky for many useful references; K. Arrow, Cl. d'Aspremont, S. Spear for their comments; and participants of PET'08, SED'08, NBER General Equilibrium Conference in Iowa and Economic Theory Conference in Lawrence, KS, European General Equilibrium Conference at Warwick, Conference in honor of E. Kalai in Jerusalem, as well as the seminar participants at Boulder, Brussels, Cornell, Haifa, Northwestern, Roma, Salerno, Stony-Brook, UPenn, Yale and the “Séminaire de Jeux” in Paris.

This paper presents research results of the Belgian Program on Interuniversity Pôles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The paper has been substantially revised since the first author passed away. The scientific responsibility is assumed by the second author.

References

REFERENCES

Allais, M. (1947) Economie et intérêt. Paris: Imprimerie Nationale.Google Scholar
Burke, J. L. (1990) A benchmark for comparative dynamics and determinacy in overlapping-generations economies. Journal of Economic Theory 52 (2), 268–303.10.1016/0022-0531(90)90034-HGoogle Scholar
Cass, D. and Yaari, M. E. (1967) Individual saving, aggregate capital accumulation, and efficient growth. In Shell, K. (ed.), Essays on the Theory of Optimal Economic Growth, pp. 233–268. Cambridge, MA: MIT Press.Google Scholar
Chichilnisky, G. and Zhou, Y. (1998) Smooth infinite economies. Journal of Mathematical Economics 29, 27–42.10.1016/S0304-4068(97)00009-8Google Scholar
Covarrubias, E. (2010) Regular infinite economies. The B.E. Journal of Theoretical Economics 10 (1), 1–21.10.2202/1935-1704.1651Google Scholar
d'Albis, H. and Augeraud-Véron, E. (2007) Balanced cycles in an OLG model with a continuum of finitely-lived individuals. Economic Theory 30, 181–186.10.1007/s00199-005-0043-9Google Scholar
d'Albis, H. and Augeraud-Véron, E. (2009) Competitive growth in a life-cycle model: existence and dynamics. International Economic Review 50 (2), 459–484.10.1111/j.1468-2354.2009.00537.xGoogle Scholar
Debreu, G. (1970) Economies with a Finite Set of Equilibria. Econometrica 38 (3), 387–392.10.2307/1909545Google Scholar
De La Croix, D. and Michel, P. (2002) A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations. Cambridge, UK: Cambridge University Press.10.1017/CBO9780511606434Google Scholar
Demichelis, S. and Polemarchakis, H. M. (2007) The determinacy of equilibrium in economies of overlapping generations. Economic Theory 32 (3), 3461–475.10.1007/s00199-006-0134-2Google Scholar
Erosa, A. and Gervais, M. (2002) Optimal taxation in life-cycle economies. Journal of Economic Theory 105, 338–369.10.1006/jeth.2001.2877Google Scholar
Geanakoplos, J. D. and Polemarchakis, H. M. (1991) Overlapping generations. In Hildenbrand, W. and Sonnenschein, H. (eds.), Handbook of Mathematical Economics, vol. 4, Chapter 35, pp. 1899–1960. Amsterdam, New York, Oxford, Tokyo: Elsevier.Google Scholar
Hamilton, J. D. (1994) Time Series Analysis, vol. 2. Princeton, NJ: Princeton Univ Press.Google Scholar
Kehoe, T. J. and Levine, D. K. (1985, March) Comparative statics and perfect foresight in infinite horizon economies. Econometrica 53 (2), 433–453.10.2307/1911244Google Scholar
Kolmogorov, A. N. and Fomin, S. V. (1989) Elementu Teorii Funkzii i Funkzionalnogo Analiza (6 ed.) Moscow: Nauka.Google Scholar
Kotlikoff, L. J. (2002) Generational policy. In Auerbach, A. J. and Feldstein, M. (eds.), Handbook of Public Economics, vol. 4, Chapter 27, pp. 1873–1932. Amsterdam, London, New York, Oxford, Paris, Shannon, Tokyo: Elsevier.10.1016/S1573-4420(02)80006-4Google Scholar
Lang, S. (1969) Real Analysis. Reading, MA: Addison-Wesley.Google Scholar
Lee, K., Kang, W. and Ratti, R. A. (2011, 11) Oil price shocks, firm uncertainty, and investment. Macroeconomic Dynamics 15, 416–436.10.1017/S1365100511000496Google Scholar
Mertens, J.-F. and Rubinchik, A. (2009) Regularity and Stability of Equilibria in an Overlapping Generations Model with Exogenous Growth. Discussion paper 2009/5, CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.Google Scholar
Mertens, J.-F. and Rubinchik, A. (2012) Intergenerational equity and the discount rate for policy analysis. Macroeconomic Dynamics 16, 61–93.10.1017/S1365100510000386Google Scholar
Mertens, J.-F. and Rubinchik, A. (2013) Equilibria in an overlapping generations model with transfer policies and exogenous growth. Economic Theory 54 (3), 537–595.10.1007/s00199-012-0725-zGoogle Scholar
Mertens, J.-F. and Rubinchik, A. (2014) Essential properties of Lp, q spaces (the amalgams) and the IFT for equilibrium analysis in continuous time. Journal of Mathematical Economics 50, 187–196.10.1016/j.jmateco.2013.06.002Google Scholar
Muller, W. J. I. and Woodford, M. (1988) Determinacy of equilbrium in stationary economies with both finite and infinite lived consumers. Journal of Economic Theory 46, 255–290.10.1016/0022-0531(88)90131-7Google Scholar
Samuelson, P. A. (1958) An exact consumption-loan model of interest with or without the social contrivance of money. The Journal of Political Economy 66 (6), 467–482.10.1086/258100Google Scholar
Sard, A. (1942) The measure of the critical values of differentiable maps. Bulletin of the American Mathematical Society 48 (12), 883–890.10.1090/S0002-9904-1942-07811-6Google Scholar
Shannon, C. (2006) A prevalent transversality theorem for lipschitz functions. Proceedings of the American Mathematical Society 134 (9), 2755–2766.10.1090/S0002-9939-06-08607-2Google Scholar
Shannon, C. and Zame, W. R. (2002) Quadratic concavity and determinacy of equilibrium. Econometrica 70 (2), 631–662.10.1111/1468-0262.00298Google Scholar
Smale, S. (1965) An infinite dimensional version of sard's theorem. American Journal of Mathematics 87 (4), 861–866.10.2307/2373250Google Scholar
Wiener, N. (1932) Tauberian theorems. Annals of Mathematics 33 (1), 1–100.10.2307/1968102Google Scholar
Yaari, M. E. (1964, Sep) On the consumer's lifetime allocation process. International Economic Review 5 (3), 304–317.10.2307/2525515Google Scholar