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On Maximum Likelihood Estimation of Dynamic Panel Data Models

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  • Maurice J.G. Bun
  • Martin A. Carree
  • Artūras Juodis

Abstract

We analyze the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider Transformed Maximum Likelihood (TML) and Random effects Maximum Likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first-order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual specific effects. We consider different approaches taking into account the non-negativity restriction for the variance. We show that these approaches may lead to a boundary solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this boundary solution issue is non-negligible for small values of T and that different approaches might lead to substantially different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log-likelihood function. We illustrate these issues modeling U.S. state level unemployment dynamics.
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  • Maurice J.G. Bun & Martin A. Carree & Artūras Juodis, 2017. "On Maximum Likelihood Estimation of Dynamic Panel Data Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(4), pages 463-494, August.
  • Handle: RePEc:bla:obuest:v:79:y:2017:i:4:p:463-494
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    File URL: http://hdl.handle.net/10.1111/obes.12156
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    Cited by:

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    2. Arturas Juodis, 2015. "Iterative Bias Correction Procedures Revisited: A Small Scale Monte Carlo Study," UvA-Econometrics Working Papers 15-02, Universiteit van Amsterdam, Dept. of Econometrics.
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    5. Mehic, Adrian, 2020. "Half-panel jackknife estimation for dynamic panel models," Economics Letters, Elsevier, vol. 190(C).
    6. Artūras Juodis, 2018. "Rank based cointegration testing for dynamic panels with fixed T," Empirical Economics, Springer, vol. 55(2), pages 349-389, September.
    7. Adrian Mehic, 2021. "FDML versus GMM for Dynamic Panel Models with Roots Near Unity," JRFM, MDPI, vol. 14(9), pages 1-9, August.
    8. Breitung, Jörg & Kripfganz, Sebastian & Hayakawa, Kazuhiko, 2022. "Bias-corrected method of moments estimators for dynamic panel data models," Econometrics and Statistics, Elsevier, vol. 24(C), pages 116-132.
    9. Badi H. Baltagi & Georges Bresson & Anoop Chaturvedi & Guy Lacroix, 2023. "Robust dynamic space–time panel data models using $$\varepsilon $$ ε -contamination: an application to crop yields and climate change," Empirical Economics, Springer, vol. 64(6), pages 2475-2509, June.
    10. Juodis, Artūras & Poldermans, Rutger W., 2021. "Backward mean transformation in unit root panel data models," Economics Letters, Elsevier, vol. 201(C).

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