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Asymptotically Unbiased Estimation of Autocovariances and Autocorrelations with Panel Data in the Presence of Individual and Time Effects

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  • Okui Ryo

    (Institute of Economic Research, Kyoto University, Yoshida-Hommachi, Sakyo, Kyoto, Kyoto, 606-8501, Japan)

Abstract

This article proposes asymptotically unbiased estimators of autocovariances and autocorrelations for panel data with both individual and time effects. We show that the conventional autocovariance estimators suffer from the bias caused by the elimination of individual and time effects. The bias related to individual effects is proportional to the long-run variance, and it related to time effects is proportional to the value of the estimated autocovariance. For the conventional autocorrelation estimators, the elimination of time effects does not cause a bias while the elimination of individual effects does. We develop methods to estimate the long-run variance and propose bias-corrected estimators based on the proposed long-run variance estimator. We also consider the half-panel jackknife estimation for bias correction. The theoretical results are given by employing double asymptotics under which both the number of observations and the length of the time series tend to infinity. Monte Carlo simulations show that the asymptotic theory provides a good approximation to the actual bias and that the proposed bias-correction methods work well.

Suggested Citation

  • Okui Ryo, 2014. "Asymptotically Unbiased Estimation of Autocovariances and Autocorrelations with Panel Data in the Presence of Individual and Time Effects," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 1-53, July.
    • Handle: RePEc:bpj:jtsmet:v:6:y:2014:i:2:p:53:n:4
    DOI: 10.1515/jtse-2013-0017
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    References listed on IDEAS

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    9. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
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    11. Okui, Ryo, 2009. "Testing serial correlation in fixed effects regression models based on asymptotically unbiased autocorrelation estimators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2897-2909.
    12. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
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    14. Okui, Ryo, 2011. "Asymptotically unbiased estimation of autocovariances and autocorrelations for panel data with incidental trends," Economics Letters, Elsevier, vol. 112(1), pages 49-52, July.
    15. Hayakawa, Kazuhiko, 2009. "A SIMPLE EFFICIENT INSTRUMENTAL VARIABLE ESTIMATOR FOR PANEL AR(p) MODELS WHEN BOTH N AND T ARE LARGE," Econometric Theory, Cambridge University Press, vol. 25(3), pages 873-890, June.
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    Cited by:

    1. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    2. Andreas Joseph, 2019. "Parametric inference with universal function approximators," Papers 1903.04209, arXiv.org, revised Oct 2020.
    3. Timothy J. Vogelsang & Jingjing Yang, 2016. "Exactly/Nearly Unbiased Estimation of Autocovariances of a Univariate Time Series With Unknown Mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 723-740, November.
    4. Okui, Ryo & Yanagi, Takahide, 2019. "Panel data analysis with heterogeneous dynamics," Journal of Econometrics, Elsevier, vol. 212(2), pages 451-475.
    5. Ryo Okui, 2017. "Misspecification in Dynamic Panel Data Models and Model-Free Inferences," The Japanese Economic Review, Japanese Economic Association, vol. 68(3), pages 283-304, September.
    6. Ryo Okui & Takahide Yanagi, 2020. "Kernel estimation for panel data with heterogeneous dynamics [Econometric tools for analyzing market outcomes]," The Econometrics Journal, Royal Economic Society, vol. 23(1), pages 156-175.
    7. Haruo Iwakura & Ryo Okui, 2014. "Asymptotic Efficiency in Factor Models and Dynamic Panel Data Models," KIER Working Papers 887, Kyoto University, Institute of Economic Research.

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