Transformations of the State Variable and Learning Dynamics
AbstractThis 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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Bibliographic InfoPaper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0708.
Length: 35 pages
Date of creation: Dec 2007
Date of revision:
Temporary equilibrium; Ordinary least squares learning; Globally stable formulations;
Other versions of this item:
- 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.
- Shurojit Chatterji & Ignacio Lobato, 2009. "Transformations of the State Variable and Learning Dynamics," Working Papers 0902, Centro de Investigacion Economica, ITAM.
- NEP-ALL-2008-05-17 (All new papers)
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