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Transformations of the state variable and learning dynamics
Author(s) -
Chatterji Shurojit,
Lobato Ignacio N.
Publication year - 2010
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2010.00142.x
Subject(s) - variable (mathematics) , state variable , class (philosophy) , mathematical economics , stability (learning theory) , state (computer science) , economics , set (abstract data type) , ordinary least squares , econometrics , transformation (genetics) , mathematics , regular polygon , dynamics (music) , computer science , artificial intelligence , mathematical analysis , biochemistry , chemistry , physics , geometry , algorithm , machine learning , gene , thermodynamics , programming language , acoustics
This article examines dynamics in a model where agents forecast a one dimensional state variable through ordinary least squares regressions on the lagged values of the state variable. We study the stability properties of alternative transformations of the state variable, such as taking logarithms, which the agent can endogenously set forth. Surprisingly, for the considered class of economies, we found that the transformations that an econometrician would attempt 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 who in an attempt to improve forecasting transforms the state variable using standard transformations, is more likely to deviate from the steady state than a passive agent.