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Asymptotically Unbiased Estimation Of Autocovariances And Autocorrelations With Long Panel Data

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  • Okui, Ryo

Abstract

An important reason for analyzing panel data is to observe the dynamic nature of an economic variable separately from its time-invariant unobserved heterogeneity. This paper examines how to estimate the autocovariances of a variable separately from its time-invariant unobserved heterogeneity. When both cross-sectional and time series sample sizes tend to infinity, we show that the within-group autocovariances are consistent, although they are severely biased when the time series length is short. The biases have the leading term that converges to the long-run variance of the individual dynamics. This paper develops methods to estimate the long-run variance in panel data settings and to alleviate the biases of the within-group autocovariances based on the proposed long-run variance estimators. Monte Carlo simulations reveal that the procedures developed in this paper effectively reduce the biases of the estimators for small samples.

Suggested Citation

  • Okui, Ryo, 2010. "Asymptotically Unbiased Estimation Of Autocovariances And Autocorrelations With Long Panel Data," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1263-1304, October.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:05:p:1263-1304_99
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    Cited by:

    1. 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.
    2. Chengwang Liao & Ziwei Mei & Zhentao Shi, 2024. "Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions," Papers 2410.09825, arXiv.org.
    3. 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.
    4. Okui, Ryo & Yanagi, Takahide, 2019. "Panel data analysis with heterogeneous dynamics," Journal of Econometrics, Elsevier, vol. 212(2), pages 451-475.
    5. Jungmo Yoon & Antonio F. Galvao, 2020. "Cluster robust covariance matrix estimation in panel quantile regression with individual fixed effects," Quantitative Economics, Econometric Society, vol. 11(2), pages 579-608, May.
    6. Lee, Yoon-Jin & Okui, Ryo & Shintani, Mototsugu, 2018. "Asymptotic inference for dynamic panel estimators of infinite order autoregressive processes," Journal of Econometrics, Elsevier, vol. 204(2), pages 147-158.
    7. 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 129-181, July.
    8. 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.
    9. Ziwei Mei & Liugang Sheng & Zhentao Shi, 2023. "Nickell Bias in Panel Local Projection: Financial Crises Are Worse Than You Think," Papers 2302.13455, arXiv.org, revised Oct 2023.
    10. Yifan Li & Yao Rao, 2021. "A simple nearly unbiased estimator of cross‐covariances," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 240-266, March.
    11. 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.
    12. 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.
    13. Yang, Jingjing & Vogelsang, Timothy J., 2018. "Finite sample performance of a long run variance estimator based on exactly (almost) unbiased autocovariance estimators," Economics Letters, Elsevier, vol. 165(C), pages 21-27.

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