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Estimating Structural Parameters in Regression Models with Adaptive Learning

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  • Norbert Christopeit

    (University of Bonn, Germany)

  • Michael Massmann

    (VU University Amsterdam)

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.

Suggested Citation

  • Norbert Christopeit & Michael Massmann, 2013. "Estimating Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-111/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20130111
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    References listed on IDEAS

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    Cited by:

    1. Norbert Christopeit & Michael Massmann, 2013. "A Note on an Estimation Problem in Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-151/III, Tinbergen Institute.
    2. Norbert Christopeit & Michael Massmann, 2013. "Estimating Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-111/III, Tinbergen Institute.
    3. Norbert Christopeit & Michael Massmann, 2017. "Strong consistency of the least squares estimator in regression models with adaptive learning," WHU Working Paper Series - Economics Group 17-07, WHU - Otto Beisheim School of Management.

    More about this item

    Keywords

    adaptive learning; non-stationary regression; ordinary least squares; consistency; asymptotic distribution;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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