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A Note on an Estimation Problem in Models with Adaptive Learning

Author

Listed:
  • Norbert Christopeit

    (University of Bonn, Germany)

  • Michael Massmann

    (VU University Amsterdam)

Abstract

This paper provides an example of a linear regression model with predetermined stochastic regressors for which the sufficient condition for strong consistency of the ordinary least squares estimator by Lai & Wei (1982, Annals of Statistics) is not met. Nevertheless, the estimator is strongly consistent, as shown in a companion paper, cf. Christopeit & Massmann (2013b). This is intriguing because the Lai & Wei condition is the best currently available and is referred to as “in some sense the weakest possible”. Moreover, the example discussed in this paper arises naturally in a class of macroeconomic models with adaptive learning, the estimation of which has recently gained popularity amongst researchers and policy makers.

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20130151
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    File URL: https://papers.tinbergen.nl/13151.pdf
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    References listed on IDEAS

    as
    1. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    2. DRYGAS, Hilmar, 1976. "Weak and strong consistency of the least squares estimators in regression models," LIDAM Reprints CORE 236, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Norbert Christopeit & Michael Massmann, 2013. "Estimating Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-111/III, Tinbergen Institute.
    4. Norbert Christopeit & Michael Massmann, 2012. "Strong Consistency of the Least-Squares Estimator in Simple Regression Models with Stochastic Regressors," Tinbergen Institute Discussion Papers 12-109/III, Tinbergen Institute.
    5. Chevillon, Guillaume & Massmann, Michael & Mavroeidis, Sophocles, 2010. "Inference in models with adaptive learning," Journal of Monetary Economics, Elsevier, vol. 57(3), pages 341-351, April.
    6. Lai, T. L. & Wei, C. Z., 1982. "Asymptotic properties of projections with applications to stochastic regression problems," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 346-370, September.
    7. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
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    Cited by:

    1. Norbert Christopeit & Michael Massmann, 2013. "Estimating Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-111/III, Tinbergen Institute.
    2. Norbert Christopeit & Michael Massmann, 2012. "Strong Consistency of the Least-Squares Estimator in Simple Regression Models with Stochastic Regressors," Tinbergen Institute Discussion Papers 12-109/III, Tinbergen Institute.

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    More about this item

    Keywords

    least-squares regression; stochastic regressors; strong consistency; minimal sufficient condition; adaptive learning;
    All these keywords.

    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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