Transformations of the State Variable and Learning Dynamics

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.Temporary equilibrium, Ordinary least squares learning, Globally stable formulations

Transformations of the State Variable and Learning Dynamics

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.

Local coordination and market equilibria

We reformulate the local stability analysis of market equilibria in a competitive market as a local coordination problem in a market game, where the map associating market prices to best-responses of all traders is common knowledge and well-defined both in and out of equilibrium. Initial expectations over market variables differ from their equilibrium values and are not common knowledge. This results in a coordination problem as traders use the structure of the market game to converge back to equilibrium. We analyse a simultaneous move and a sequential move version of the market game and explore the link with local rationalizability