Estimating Structural Parameters in Regression Models with Adaptive Learning

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis paper examines the ordinary least squares (OLS) estimator of the structural parameters 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, the paper derives the asymptotic properties of agents' expectations. At the second stage, the paper derives the asymptotics of OLS in the structural model, taken the rst stage learning dynamics as given. In the case of constant gain learning, the structural model eectively 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, this paper shows that the OLS estimator remains consistent in all models considered. It also shows, however, that its asymptotic distribution, and hence any inference based upon it, may be non-standard.

A Note on an Estimation Problem in Models with Adaptive Learning

“…This is the quantity whose behaviour turns out crucial for the consistency of the OLS estimator of δ and β, see Christopeit & Massmann (2013a). By virtue of (12),…”

“…It is shown in Christopeit & Massmann (2013a) that a T → α with probability one. Therefore, p T and r T in (6)- (7) satisfy, with probability one,…”

“…The asymptotic properties of this system are analysed in detail in two companion papers, viz. Christopeit & Massmann (2013a, 2013b). The properties turn out to depend crucially on c = γ (1 − β) .…”

“…Christopeit & Massmann (2013a). Investigation of the boundary case c = 1/2 is left to future research.…”