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Global convergence of adaptive learning in models of pure exchange

Author

Listed:
  • Jan Wenzelburger

    (Fakultät für Wirtschaftswissenschaften, Universität Bielefeld, Postfach 100 131, 33501 Bielefeld, GERMANY)

Abstract

This paper develops an adaptive learning scheme for a standard version of the OLG model with pure exchange. Perfect forecasting rules which generate perfect foresight orbits are approximated by cubic spline functions. These approximations are successively constructed using historical data only. Trajectories generated by this scheme converge to perfect foresight orbits globally for all initial conditions. This result holds for all parameterizations guaranteeing the existence of a monetary steady state and hence is independent of consumers' savings behavior. It generalizes to all one-dimensional models of the Cobweb type.

Suggested Citation

  • Jan Wenzelburger, 2002. "Global convergence of adaptive learning in models of pure exchange," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 649-672.
    • Handle: RePEc:spr:joecth:v:19:y:2002:i:4:p:649-672
    Note: Received: October 5, 2000; revised version: February 15, 2001
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    Citations

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    Cited by:

    1. Orlando Gomes, 2010. "Ordinary Least Squares Learning And Nonlinearities In Macroeconomics," Journal of Economic Surveys, Wiley Blackwell, vol. 24(1), pages 52-84, February.
    2. Heemeijer Peter & Hommes Cars & Sonnemans Joep & Tuinstra Jan, 2012. "An Experimental Study on Expectations and Learning in Overlapping Generations Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(4), pages 1-49, October.
    3. Böhm, Volker & Wenzelburger, Jan, 2002. "Perfect Predictions In Economic Dynamical Systems With Random Perturbations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 687-712, November.
    4. Chatterji, Shurojit & Lobato, Ignacio N., 2015. "On divergent dynamics with ordinary least squares learning," Journal of Economic Behavior & Organization, Elsevier, vol. 109(C), pages 1-9.
    5. Jan Tuinstra & Florian Wagener, 2007. "On learning equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 493-513, March.
    6. Cavalli, F. & Chen, H.-J. & Li, M.-C. & Naimzada, A. & Pecora, N., 2023. "Heterogeneous expectations and equilibria selection in an evolutionary overlapping generations model," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    7. Patrick Leoni, 2009. "Market crashes, speculation and learning in financial markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 217-229, May.
    8. Wenzelburger, Jan, 2006. "Learning in linear models with expectational leads," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 854-884, November.

    More about this item

    Keywords

    Learning dynamics; Rational expectations; Bounded rationality.;
    All these keywords.

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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