Estimating Structural Parameters in Regression Models with Adaptive Learning

Norbert Christopeit and Michael Massmann
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Norbert Christopeit: University of Bonn, Germany

No 15-106/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This 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 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, 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.

Keywords: adaptive learning; non-stationary regression; ordinary least squares; consistency; asymptotic distribution (search for similar items in EconPapers)
JEL-codes: C22 C51 D83 (search for similar items in EconPapers)
Date: 2015-09-02
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (1)

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Related works:
Working Paper: Estimating Structural Parameters in Regression Models with Adaptive Learning (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20150106

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