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Transformations of the state variable and learning dynamics

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  • Shurojit Chatterji
  • Ignacio N. Lobato

Abstract

This article studies dynamics in a model where agents forecast a one dimensional variable via ordinary least squares regressions on the lagged values of the state variable. We study the stability properties of alternative transformations of the state variable that the agent can endogenously set forth. We study the consequences on the economy's stability of the typical transformations that an econometrician would attemp, such as differencing, detrending, or taking instantaneous concave transformations, such as logarithms. Surprinsingly, for the considered class of economies, we found that these transformations are destabilizing, whereas alternative transformations, which an econometrician would never consider, such as convex transformations, are stabilizing. Therefore, we ironically find that in our set-up. an active agent, who is concerned about learning the economy's dynamics and transforms the state variable, in an attempt to improve forecasting, is more likely to deviate from the steady state than a passive agent.
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  • Shurojit Chatterji & Ignacio N. Lobato, 2010. "Transformations of the state variable and learning dynamics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(4), pages 385-403.
  • Handle: RePEc:bla:ijethy:v:6:y:2010:i:4:p:385-403
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    References listed on IDEAS

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    1. Chatterji Shurojit, 1995. "Temporary Equilibrium Dynamics with Bayesian Learning," Journal of Economic Theory, Elsevier, vol. 67(2), pages 590-598, December.
    2. George W. Evans & Seppo Honkapohja, 1998. "Economic Dynamics with Learning: New Stability Results," Review of Economic Studies, Oxford University Press, vol. 65(1), pages 23-44.
    3. Shurojit Chatterji & Ignacio N. Lobato, 2010. "Transformations of the state variable and learning dynamics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(4), pages 385-403.
    4. 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.
    5. Chatterji, Shurojit & Chattopadhyay, Subir, 2000. "Global stability in spite of "local instability" with learning," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 155-165, March.
    6. Tillmann, Georg, 1983. "Stability in a simple pure consumption loan model," Journal of Economic Theory, Elsevier, vol. 30(2), pages 315-329, August.
    7. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    8. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    9. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
    10. Chatterji, Shurojit & Ghosal, Sayantan, 2004. "Local coordination and market equilibria," Journal of Economic Theory, Elsevier, vol. 114(2), pages 255-279, February.
    11. Grandmont, Jean-Michel & Laroque, Guy, 1986. "Stability of cycles and expectations," Journal of Economic Theory, Elsevier, vol. 40(1), pages 138-151, October.
    12. Van Zandt, Timothy & Lettau, Martin, 2003. "Robustness Of Adaptive Expectations As An Equilibrium Selection Device," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 89-118, February.
    13. Spear, Stephen E., 1985. "Rational expectations in the overlapping generations model," Journal of Economic Theory, Elsevier, vol. 35(2), pages 251-275, August.
    14. Hellwig, Martin F., 1982. "Rational expectations and the Markov property of temporary equilibrium processes," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 135-144, January.
    15. Frydman, Roman, 1982. "Towards an Understanding of Market Processes: Individual Expectations, Learning, and Convergence to Rational Expectations Equilibrium," American Economic Review, American Economic Association, vol. 72(4), pages 652-668, September.
    16. Lobato, Ignacio N, 2003. "Testing for Nonlinear Autoregression," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 164-173, January.
    17. Blume, Lawrence E. & Easley, David, 1984. "Rational expectations equilibrium: An alternative approach," Journal of Economic Theory, Elsevier, vol. 34(1), pages 116-129, October.
    18. 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.
    19. Fuchs, Gerard, 1979. "Is error learning behaviour stabilizing?," Journal of Economic Theory, Elsevier, vol. 20(3), pages 300-317, June.
    20. Lettau, M. & Van Zandt, T., 1995. "Robustness of Adaptive Expections as an Equilibrium Selection Device," Papers 9598, Tilburg - Center for Economic Research.
    21. Saari, Donald G. & Williams, Steven R., 1986. "On the local convergence of economic mechanisms," Journal of Economic Theory, Elsevier, vol. 40(1), pages 152-167, October.
    22. Coulson, N Edward & Robins, Russell P, 1987. "A Test of the First Difference Transformation in Time Series Models," The Review of Economics and Statistics, MIT Press, vol. 69(4), pages 723-726, November.
    23. TILLMANN, Georg, 1983. "Stability in a simple pure consumption loan model," CORE Discussion Papers RP 615, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    24. Spear, Stephen E. & Srivastava, Sanjay, 1986. "Markov rational expectations equilibria in an overlapping generations model," Journal of Economic Theory, Elsevier, vol. 38(1), pages 35-62, February.
    25. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
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    Cited by:

    1. Shurojit Chatterji & Ignacio N. Lobato, 2010. "Transformations of the state variable and learning dynamics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(4), pages 385-403.
    2. 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.

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