Topic: Contributions on nonstationary time series and panels Title: Estimating structural parameters in regression models with adaptive learning Authors:  Norbert Christopeit - University of Bonn (Germany)
Michael Massmann - WHU - Otto Beisheim School of Management (Germany) [presenting]
Abstract: The ordinary least squares (OLS) estimator of the structural parameters is examined in a class of stylised macroeconomic models in which agents are boundedly rational and use an adaptive learning rule to form expectations of the endogenous variable. The popularity of this type of model has recently increased amongst applied economists and policy makers who seek to estimate it empirically. Two prominent learning algorithms are considered, namely constant gain and decreasing gain learning. For each of the two learning rules, the analysis proceeds in two stages. First, we derive the asymptotic properties of agents' expectations. At the second stage, we derive the asymptotics of OLS in the structural model, taken the first stage learning dynamics as given. In the case of constant gain learning, the structural model effectively amounts to a static, cointegrating or co-explosiveness regression. With decreasing gain learning, the regressors are asymptotically collinear such that OLS does not satisfy, in general, the Grenander conditions for consistent estimability. Nevertheless, we show that the OLS estimator remains consistent in all models considered. We also show, however, that its asymptotic distribution, and hence any inference based upon it, may be non-standard.