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Two-step estimation in linear regressions with adaptive learning

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  • 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.

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  • 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
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    References listed on IDEAS

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    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.
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