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On Learning Equilibria

Author

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  • Florian Wagener
  • Jan Tuinstra

Abstract

We investigate an inflationary overlapping generations model where households predict future inflation rates by running a least squares regression of inflation rates or prices on their past levels. We critically examine the results on learning equilibria obtained by Bullard (1994) and Schönhofer (1999) in this framework. They show that an increase in the money growth rate may lead to limit cycles and endogenous business cycles. We suggest an alternative estimation procedure, that starts from the same perceived law of motion, but is more sensible from an econometrician's point of view. We prove that for this estimation procedure there is global convergence on the monetary steady for a large set of savings functions. We also study, in a heterogeneous agents framework, evolutionary competition between the two estimation procedures, where the fraction of the population using a certain estimation procedure is determined by its past average quadratic forecast error. Interestingly, the more sensible estimation procedure is not always able to drive out the other estimation procedure, and endogenous business cycles may still be observed in this heterogeneous world

Suggested Citation

  • Florian Wagener & Jan Tuinstra, 2004. "On Learning Equilibria," Computing in Economics and Finance 2004 217, Society for Computational Economics.
  • Handle: RePEc:sce:scecf4:217
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    References listed on IDEAS

    as
    1. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    2. Schonhofer, Martin, 1999. "Chaotic Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 89(1), pages 1-20, November.
    3. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    4. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    5. Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, vol. 59(4), pages 401-426, October.
    6. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    7. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, pages 468-485.
    8. Tuinstra, Jan, 2003. "Beliefs equilibria in an overlapping generations model," Journal of Economic Behavior & Organization, Elsevier, vol. 50(2), pages 145-164, February.
    9. Jan Tuinstra & Florian Wagener, 2007. "On learning equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 493-513.
    10. repec:cup:macdyn:v:2:y:1998:i:3:p:287-321 is not listed on IDEAS
    11. Jan Wenzelburger, 2000. "Convergence of Adaptive Learning Models of Pure Exchange," Econometric Society World Congress 2000 Contributed Papers 1070, Econometric Society.
    12. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 2(03), pages 287-321, September.
    13. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    14. Duffy John, 1994. "On Learning and the Nonuniqueness of Equilibrium in an Overlapping Generations Model with Fiat Money," Journal of Economic Theory, Elsevier, vol. 64(2), pages 541-553, December.
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    More about this item

    Keywords

    overlapping generations; learning; endogenous business cycles; heterogeneous beliefs; evolutionary dynamics;

    JEL classification:

    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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