IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20120109.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/12109.pdf
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    4. 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.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, Decembrie.
    6. 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.
    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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, 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.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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, 2010. "Consistent Estimation of Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 10-077/4, Tinbergen Institute.
    3. 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.
    4. Berardi, Michele & Galimberti, Jaqueson K., 2017. "Empirical calibration of adaptive learning," Journal of Economic Behavior & Organization, Elsevier, vol. 144(C), pages 219-237.
    5. 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.
    6. Alexander Mayer, 2022. "Estimation and inference in adaptive learning models with slowly decreasing gains," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 720-749, September.
    7. Demery, David & Duck, Nigel W., 2007. "The theory of rational expectations and the interpretation of macroeconomic data," Journal of Macroeconomics, Elsevier, vol. 29(1), pages 1-18, March.
    8. Gerunov, Anton, 2014. "Критичен Преглед На Основните Подходи За Моделиране На Икономическите Очаквания [A Critical Review of Major Approaches for Modeling Economic Expectations]," MPRA Paper 68797, University Library of Munich, Germany.
    9. Berardi, Michele & Galimberti, Jaqueson K., 2017. "On the initialization of adaptive learning in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 26-53.
    10. Chryssi Giannitsarou, 2003. "Heterogeneous Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 885-906, October.
    11. 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.
    12. Tarlok Singh, 2007. "Intertemporal Optimizing Models Of Trade And Current Account Balance: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 25-64, February.
    13. repec:ebl:ecbull:v:4:y:2006:i:36:p:1-7 is not listed on IDEAS
    14. Sidney Martins Caetano & Guilherme Valle Moura, 2011. "Reajuste Informacionalno Brasil: uma aplicação da curva de Phillips sobrigidez de informação," Anais do XXXVII Encontro Nacional de Economia [Proceedings of the 37th Brazilian Economics Meeting] 54, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    15. Agnieszka Markiewicz, 2012. "Model Uncertainty And Exchange Rate Volatility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 815-844, August.
    16. Gaballo, Gaetano, 2014. "Sequential coordination, higher-order belief dynamics and the E-stability principle," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 270-279.
    17. Lahiri, Kajal & Sheng, Xuguang, 2008. "Evolution of forecast disagreement in a Bayesian learning model," Journal of Econometrics, Elsevier, vol. 144(2), pages 325-340, June.
    18. Seppo Honkapohja & Kaushik Mitra, 2006. "Learning Stability in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 284-309, April.
    19. Alexander Mayer, 2022. "Two-step estimation in linear regressions with adaptive learning," Papers 2204.05298, arXiv.org, revised Nov 2022.
    20. Evans, George W & McGough, Bruce, 2018. "Equilibrium selection, observability and backward-stable solutions," Journal of Monetary Economics, Elsevier, vol. 98(C), pages 1-10.
    21. 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.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20120109. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.