On divergent dynamics with ordinary least squares learning

• Learning may lead to divergent paths where forecasts do not improve.
• Agents are likely to question the validity of their model and may modify aspects of it.
• We study stability properties of a divergent economy where the agent transforms the state variable.
• Differencing and detrending the data do not help to achieve stability.
• Inverting the data may have a stabilizing effect.

This article addresses the stability properties of a simple economy (characterized by a one-dimensional state variable) when the representative agent, confronted by trajectories that are divergent from the steady state, performs transformations in that variable in order to improve forecasts. We find that instability continues to be a robust outcome for transformations such as differencing and detrending the data, the two most typical approaches in econometrics to handle nonstationary time series data. We also find that inverting the data, a transformation that can be motivated by the agent reversing the time direction in an attempt to improve her forecasts, may lead the dynamics to a perfect-foresight path.