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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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Suggested Citation

  • 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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    References listed on IDEAS

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    1. Binder, Michael & Hsiao, Cheng & Pesaran, M. Hashem, 2005. "Estimation And Inference In Short Panel Vector Autoregressions With Unit Roots And Cointegration," Econometric Theory, Cambridge University Press, vol. 21(04), pages 795-837, August.
    2. Kazuhiko Hayakawa & M. Hashem Pesaran, 2012. "Robust Standard Errors in Transformed Likelihood Estimation of Dynamic Panel Data Models," Working Paper series 38_12, Rimini Centre for Economic Analysis.
    3. Geert Dhaene & Koen Jochmans, 2011. "An Adjusted profile likelihood for non-stationary panel data models with fixed effects," Working Papers hal-01073732, HAL.
    4. Kruiniger, Hugo, 2013. "Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions," Journal of Econometrics, Elsevier, vol. 173(2), pages 175-188.
    5. Maddala, G S, 1971. "The Use of Variance Components Models in Pooling Cross Section and Time Series Data," Econometrica, Econometric Society, vol. 39(2), pages 341-358, March.
    6. Arturas Juodis, 2013. "First Difference Transformation in Panel VAR models: Robustness, Estimation and Inference," UvA-Econometrics Working Papers 13-06, Universiteit van Amsterdam, Dept. of Econometrics.
    7. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 277-297.
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    Cited by:

    1. 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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