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ESTIMATING STRUCTURAL PARAMETERS IN REGRESSION MODELS WITH ADAPTIVE LEARNING

Published online by Cambridge University Press:  09 January 2017

Norbert Christopeit  and
Michael Massmann
Norbert Christopeit
Affiliation:
University of Bonn
Michael Massmann*
Affiliation:
WHU – Otto Beisheim School of Management and Vrije Universiteit Amsterdam
*
*Address correspondence to Michael Massmann, WHU – Otto Beisheim School of Management, Burgplatz 2, 56179 Vallendar, Germany; e-mail: michael.massmann@whu.edu.
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Abstract

This paper examines the ordinary least squares (OLS) estimator of the structural parameters in a simple macroeconomic model in which agents are boundedly rational and use an adaptive learning rule to form expectations of the endogenous variable. The popularity of learning models has recently increased amongst applied economists and policy makers who seek to estimate them empirically. Yet the econometrics of learning models is largely uncharted territory. We consider two prominent learning algorithms, namely constant gain and decreasing gain learning. For each of the two learning rules, our 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, taking the first stage learning dynamics as given. In the case of constant gain learning, the structural model effectively amounts to a stationary, 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 nonstandard.

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ARTICLES
Information
Econometric Theory , Volume 34 , Issue 1 , February 2018 , pp. 68 - 111
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

This paper replaces and extends Christopeit and Massmann (2010, 2013). The authors would like to thank seminar participants at the Universities of Cologne, Oxford, St. Andrews and Birmingham, at the Tinbergen Institutes in Amsterdam and Rotterdam, at ESEM 2013 and at CFE 2015. In particular, the discussions with and suggestions of Karim Abadir, Klaus Adam, Jörg Breitung, George Evans, Cars Hommes, Offer Lieberman, Tassos Magdalinos, Roderick McCrorie, Kaushik Mitra and Bent Nielsen are greatly appreciated. All remaining errors are of course ours.

References

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