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Reducing Overlapping Generations Economies to Finite Economies

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  • Julio Dávila

Abstract

This paper establishes an identification of stationary equilibria of an infinite-horizon economy and equilibria of a naturally related finite economy. More specifically, the connection is established, firstly, between cycles of an overlapping generations economy and the equilibria of a finite economy with a cyclical structure. Such connection is then extended to hold also when extrinsic uncertainty is introduced in the models. In order to obtain the adequate counterpart of the connection once the extrinsic uncertainty is introduced, we are lead to consider in the overlapping generations framework sunspot equilibria of a broad class, called here sunspot cycles. The previous connections between the equilibria of the two frameworks, with and without sunspots, are used to show that: a) overlapping generations economies allowing for heterogeneity across generations typically fluctuate aperiodically for arbitrarily long periods of time, while nevertheless being able to exhibit an approximate cyclical behavior during those periods and b) the presence of asymmetric information on an extrinsic uncertainty may induce continua of equilibria in finite economies.

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Paper provided by University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences in its series CARESS Working Papres with number 00-08.

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Handle: RePEc:wop:pennca:00-08

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  1. Jan Tuinstra & Claus Weddepohl, 1999. "On the equivalence between the overlapping-generations model and cyclical general-equilibrium models," Journal of Economics, Springer, vol. 70(2), pages 187-207, June.
  2. Forges, Francoise & Peck, James, 1995. "Correlated Equilibrium and Sunspot Equilibrium," Economic Theory, Springer, vol. 5(1), pages 33-50, January.
  3. Guesnerie, Roger, 1986. "Stationary sunspot equilibria in an N commodity world," Journal of Economic Theory, Elsevier, vol. 40(1), pages 103-127, October.
  4. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  5. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  6. Julio Dávila & Piero Gottardi & Atsushi Kajii, 2007. "Local Sunspot Equilibria Reconsidered," Economic Theory, Springer, vol. 31(3), pages 401-425, June.
  7. Yves Balasko & Christian Ghiglino, . "On The Existence Of Endogenous Cycles," Preprints _001, Theory and Mathematics of the Economy and the Society.
  8. Azariadis, Costas & Guesnerie, Roger, 1986. "Sunspots and Cycles," Review of Economic Studies, Wiley Blackwell, vol. 53(5), pages 725-37, October.
  9. Chiappori, P.A. & Geoffard, P.Y. & Guesnerie, R., 1990. "Sunspot Fluctuations around a Steady State: The Case of Multidimensional One-Step forward Looking Economic Models," DELTA Working Papers 90-02, DELTA (Ecole normale supérieure).
  10. Chiappori, P.A. & Guesnerie, R., 1990. "Sunspot Equilibria in Sequential Markets Models," DELTA Working Papers 90-05, DELTA (Ecole normale supérieure).
  11. Davila, J., 1999. "The Connection Between Correlated and Sunspot Equilibria Revisited," Papiers d'Economie Mathématique et Applications 1999.78, Université Panthéon-Sorbonne (Paris 1).
  12. Maskin, Eric & Tirole, Jean, 1987. "Correlated equilibria and sunspots," Journal of Economic Theory, Elsevier, vol. 43(2), pages 364-373, December.
  13. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
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Cited by:
  1. Julio Dávila, . "Time and Uncertainty in Overlapping Generations Economies," CARESS Working Papres 00-09, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.

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