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Strong Consistency of the Least-Squares Estimator in Simple Regression Models with Stochastic Regressors

Author

Listed:
  • Norbert Christopeit

    (University of Bonn)

  • Michael Massmann

    (VU University Amsterdam)

Abstract

Strong consistency of least squares estimators of the slope parameter in simple linear regression models is established for predetermined stochastic regressors. The main result covers a class of models which falls outside the applicability of what is presently available in the literature. An application to the identification of economic models with adaptive learning is discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20120109
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    File URL: https://papers.tinbergen.nl/12109.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. Norbert Christopeit & Michael Massmann, 2010. "Consistent Estimation of Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 10-077/4, Tinbergen Institute.
    3. Lucas, Robert E, Jr, 1973. "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review, American Economic Association, vol. 63(3), pages 326-334, June.
    4. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    5. 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.
    6. 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.
    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.
    Full references (including those not matched with items 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.
    4. Norbert Christopeit & Michael Massmann, 2018. "Strong consistency of the least squares estimator in regression models with adaptive learning," Tinbergen Institute Discussion Papers 18-045/III, Tinbergen Institute.

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    More about this item

    Keywords

    linear regression; least-squares; consistency; stochastic regressors; adaptive learning; decreasing gain;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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