Summary
Local convergence results for adaptive learning of stochastic steady states in nonlinear models are extended to the case where the exogenous observable variables follow a finite Markov chain. The stability conditions for the corresponding nonstochastic model and its steady states yield convergence for the stochastic model when shocks are sufficiently small. The results are applied to asset pricing and to an overlapping generations model. Large shocks can destabilize learning even if the steady state is stable with small shocks. Relationship to stationary sunspot equilibria are also discussed.
This paper is in honour and remembrance of Birgit Grodal, a great collegue and friend. Support from the Academy of Finland, Bank of Finland, Yrjö Jahnsson Foundation and Nokia Group is gratefully acknowledged.
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References
Chen, X. and H. White (1998): “Nonparametric Adaptive Learning with Feedback,” Journal of Economic Theory, 82, 190–222.
Chiappori, P. and R Guesnerie (1991): “Sunspot Equilibria in Sequential Market Models,” in [9], pp. 1683–1762.
Evans, G. W. and S. Honkapohja (1994): “On the Local Stability of Sunspot Equilibria under Adaptive Learning Rules,” Journal of Economic Theory, 64, 142–161.
Evans, G. W. and S. Honkapohja (1995): “Local Convergence of Recursive Learning to Steady States and Cycles in Stochastic Nonlinear Models,” Econometrica, 63, 195–206.
Evans, G. W. and S. Honkapohja (1998): “Convergence of Learning Algorithms without a Projection Facility,” Journal of Mathematical Economics, 30, 59–86.
Evans, G. W. and S. Honkapohja (2001): Learning and Expectations in Macroeconomics. Princeton University Press, Princeton, New Jersey.
Hamilton, J. D. (1989): “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle,” Econometrica, 57, 357–384.
Hamilton, J. D. (1994): Time Series Analysis. Princeton University Press, Princeton, NJ.
Hildenbrand, W., and H. Sonnenschein (eds.) (1991): Handbook of Mathematical Economics, Vol. IV. North-Holland, Amsterdam.
Ljungqvist, L., and T. J. Sargent (2000): Recursive Macroeconomic Theory. MIT Press, Cambridge Mass.
Mehra, R., and E. Prescott (1985): “The Equity Premium: A Puzzle,” Journal of Monetary Economics, 15, 145–162.
Sargent, T. J. (1976): “Observational Equivalence of Natural and Unnatural Rate Theories of Unemployment,” Journal of Political Economy, 84, 631–640.
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Honkapohja, S., Mitra, K. (2006). Learning of Steady States in Nonlinear Models when Shocks Follow a Markov Chain. In: Schultz, C., Vind, K. (eds) Institutions, Equilibria and Efficiency. Studies in Economic Theory, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28161-4_14
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DOI: https://doi.org/10.1007/3-540-28161-4_14
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