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Transformations of the State Variable and Learning Dynamics

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  • Shurojit Chatterji

    ()
    (Singapore Management University)

  • Ignacio Lobato

    ()
    (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))

Abstract

This article studies dynamics in a model where agents forecast a one dimensional state 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 attempt, such as differencing, detrending, or taking instantaneous concave transformations, such as logarithms. Surprisingly, 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, in an attempt to improve forecasting, transforms the state variable using the standard transformations, is more likely to deviate from the steady state than a passive agent.

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Bibliographic Info

Paper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0902.

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Length: 36 pages
Date of creation: Jan 2009
Date of revision:
Handle: RePEc:cie:wpaper:0902

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  1. Lobato, Ignacio N, 2003. "Testing for Nonlinear Autoregression," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 164-73, January.
  2. 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 652-68, September.
  3. Chatterji, Shurojit & Ghosal, Sayantan, 2004. "Local coordination and market equilibria," Journal of Economic Theory, Elsevier, vol. 114(2), pages 255-279, February.
  4. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
  5. 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.
  6. 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.
  7. George W. Evans & Seppo Honkapohja, . "Economic Dynamics with Learning: New Stability Results," Computing in Economics and Finance 1997 51, Society for Computational Economics.
  8. Spear, Stephen E., 1985. "Rational expectations in the overlapping generations model," Journal of Economic Theory, Elsevier, vol. 35(2), pages 251-275, August.
  9. Shurojit Chatterji, 1995. "Temporary Eq'Uilibrium Dynamics With Bayesian Learning," Working Papers. Serie AD 1995-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Lettau, Martin & Van Zandt, Timothy, 2001. "Robustness of Adaptive Expectations as an Equilibrium Selection Device," CEPR Discussion Papers 2882, C.E.P.R. Discussion Papers.
  11. 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.
  12. 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.
  13. 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.
  14. 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 723-26, November.
  15. Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
  16. Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, vol. 59(4), pages S401-26, October.
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