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On Learning Equilibria (Revised June 2003)

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  • Tuinstra, J.
  • Wagener, F.O.O.

    ()
    (Universiteit van Amsterdam)

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 heterogeneou 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.

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Bibliographic Info

Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 03-07.

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Date of creation: 2003
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Handle: RePEc:ams:ndfwpp:03-07

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Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
Phone: + 31 20 525 52 58
Fax: + 31 20 525 52 83
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Web page: http://www.fee.uva.nl/cendef/
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  1. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, Econometric Society, vol. 53(5), pages 995-1045, September.
  2. 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, University of Chicago Press, vol. 98(4), pages 703-38, August.
  3. James Bullard, 1991. "Learning equilibria," Working Papers, Federal Reserve Bank of St. Louis 1991-004, Federal Reserve Bank of St. Louis.
  4. Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 59(4), pages S401-26, October.
  5. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, Elsevier, vol. 6(4), pages 345-354, August.
  6. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 2(03), pages 287-321, September.
  7. Florian Wagener & Jan Tuinstra, 2004. "On Learning Equilibria," Computing in Economics and Finance 2004, Society for Computational Economics 217, Society for Computational Economics.
  8. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers, Wisconsin Madison - Social Systems 9530r, Wisconsin Madison - Social Systems.
  9. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, Elsevier, vol. 48(2), pages 337-368, August.
  10. Tuinstra, Jan, 2003. "Beliefs equilibria in an overlapping generations model," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 50(2), pages 145-164, February.
  11. Schonhofer, Martin, 1999. "Chaotic Learning Equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 89(1), pages 1-20, November.
  12. Duffy John, 1994. "On Learning and the Nonuniqueness of Equilibrium in an Overlapping Generations Model with Fiat Money," Journal of Economic Theory, Elsevier, Elsevier, vol. 64(2), pages 541-553, December.
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