Transformations of the state variable and learning dynamics

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.