IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2204.05298.html
   My bibliography  Save this paper

Two-step estimation in linear regressions with adaptive learning

Author

Listed:
  • Alexander Mayer

Abstract

Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares from an auxiliary model. The singular limiting distribution of the two-step estimator is normal and in general affected by the sampling uncertainty from the first step. However, this `generated-regressor' issue disappears for certain parameter combinations.

Suggested Citation

  • Alexander Mayer, 2022. "Two-step estimation in linear regressions with adaptive learning," Papers 2204.05298, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2204.05298
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2204.05298
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christopeit, Norbert & Massmann, Michael, 2018. "Estimating Structural Parameters In Regression Models With Adaptive Learning," Econometric Theory, Cambridge University Press, vol. 34(1), pages 68-111, February.
    2. Chevillon, Guillaume & Mavroeidis, Sophocles, 2017. "Learning can generate long memory," Journal of Econometrics, Elsevier, vol. 198(1), pages 1-9.
    3. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    4. Malmendier, Ulrike & Nagel, Stefan & Yan, Zhen, 2021. "The making of hawks and doves," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 19-42.
    5. Ulrike Malmendier & Stefan Nagel, 2016. "Learning from Inflation Experiences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 53-87.
    6. Milani, Fabio, 2007. "Expectations, learning and macroeconomic persistence," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2065-2082, October.
    7. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    8. Chan, Nigel & Wang, Qiying, 2015. "Nonlinear regressions with nonstationary time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 182-195.
    9. Markiewicz, Agnieszka & Pick, Andreas, 2014. "Adaptive learning and survey data," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PB), pages 685-707.
    10. 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.
    11. Mustafa Salamh & Liqun Wang, 2021. "Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors," Econometrics, MDPI, vol. 9(4), pages 1-17, November.
    12. Wang, Qiying, 2021. "Least Squares Estimation For Nonlinear Regression Models With Heteroscedasticity," Econometric Theory, Cambridge University Press, vol. 37(6), pages 1267-1289, December.
    13. 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.
    14. Davidson, James, 1993. "The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case," Econometric Theory, Cambridge University Press, vol. 9(3), pages 402-412, June.
    Full references (including those not matched with items on IDEAS)

    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. Mayer, Alexander, 2023. "Two-step estimation in linear regressions with adaptive learning," Statistics & Probability Letters, Elsevier, vol. 195(C).
    2. 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.
    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. Jaqueson K. Galimberti, 2020. "Information weighting under least squares learning," CAMA Working Papers 2020-46, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    5. Chevillon, Guillaume & Mavroeidis, Sophocles, 2018. "Perpetual learning and apparent long memory," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 343-365.
    6. Cole, Stephen J. & Milani, Fabio, 2021. "Heterogeneity in individual expectations, sentiment, and constant-gain learning," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 627-650.
    7. Peter Andrebriq & Carlo Pizzinelli & Christopher Roth & Johannes Wohlfart, 2022. "Subjective Models of the Macroeconomy: Evidence From Experts and Representative Samples [Rationally Confused: On the Aggregate Implications of Information Provision Policies]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 2958-2991.
    8. Galimberti, Jaqueson K., 2019. "An approximation of the distribution of learning estimates in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 29-43.
    9. Berardi, Michele & Galimberti, Jaqueson K., 2017. "Empirical calibration of adaptive learning," Journal of Economic Behavior & Organization, Elsevier, vol. 144(C), pages 219-237.
    10. Evans, David & Evans, George W. & McGough, Bruce, 2022. "The RPEs of RBCs and other DSGEs," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    11. Patrick Pintus & Jacek Suda, 2019. "Learning Financial Shocks and the Great Recession," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 31, pages 123-146, January.
    12. Dave, Chetan & Malik, Samreen, 2017. "A tale of fat tails," European Economic Review, Elsevier, vol. 100(C), pages 293-317.
    13. Michele Berardi, 2020. "A probabilistic interpretation of the constant gain learning algorithm," Bulletin of Economic Research, Wiley Blackwell, vol. 72(4), pages 393-403, October.
    14. Koursaros, Demetris, 2019. "Learning expectations using multi-period forecasts," Journal of Economics and Business, Elsevier, vol. 102(C), pages 1-25.
    15. Audzei, Volha, 2023. "Learning and cross-country correlations in a multi-country DSGE model," Economic Modelling, Elsevier, vol. 120(C).
    16. 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.
    17. Evans, George W & McGough, Bruce, 2018. "Equilibrium selection, observability and backward-stable solutions," Journal of Monetary Economics, Elsevier, vol. 98(C), pages 1-10.
    18. Chevillon, Guillaume & Mavroeidis, Sophocles, 2017. "Learning can generate long memory," Journal of Econometrics, Elsevier, vol. 198(1), pages 1-9.
    19. Orphanides, Athanasios & Williams, John C., 2008. "Learning, expectations formation, and the pitfalls of optimal control monetary policy," Journal of Monetary Economics, Elsevier, vol. 55(Supplemen), pages 80-96, October.
    20. Martin Geiger & Johann Scharler, 2021. "How Do People Interpret Macroeconomic Shocks? Evidence from U.S. Survey Data," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(4), pages 813-843, June.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2204.05298. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.