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An Adjusted profile likelihood for non-stationary panel data models with fixed effects

Author

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  • Geert Dhaene

    (KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven)

  • Koen Jochmans

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

Abstract

We calculate the bias of the profile score for the autoregressive parameters p and covariate slopes in the linear model for N x T panel data with p lags of the dependent variable, exogenous covariates, fixed effects, and unrestricted initial observations. The bias is a vector of multivariate polynomials in p with coefficients that depend only on T. We center the profile score and, on integration, obtain an adjusted profile likelihood. When p = 1, the adjusted profile likelihood coincides with Lancaster's (2002) marginal posterior. More generally, it is an integrated likelihood, in the sense of Arellano and Bonhomme (2009), with fixed effects integrated out using a new data-independent prior. It appears that p and B are identified as the unique point where the large N adjusted profile likelihood reaches a local maximum (or a at inection point, as a limiting case) inside or on an ellipsoid centered at the maximum likelihood estimator. We prove this when p = 1 and report numerical calculations that support it when p > 1. The global maximum of the adjusted profile likelihood lies at infinity for any N.

Suggested Citation

  • Geert Dhaene & Koen Jochmans, 2011. "An Adjusted profile likelihood for non-stationary panel data models with fixed effects," SciencePo Working papers Main hal-01073732, HAL.
  • Handle: RePEc:hal:spmain:hal-01073732
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01073732
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    References listed on IDEAS

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    1. Bun, Maurice J.G. & Carree, Martin A., 2005. "Bias-Corrected Estimation in Dynamic Panel Data Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 200-210, April.
    2. Alvarez, Javier & Arellano, Manuel, 2022. "Robust likelihood estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 21-61.
    3. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    4. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, March.
    5. Kiviet, Jan F., 1995. "On bias, inconsistency, and efficiency of various estimators in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 68(1), pages 53-78, July.
    6. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
    7. Geert Dhaene & Koen Jochmans, 2011. "An Adjusted profile likelihood for non-stationary panel data models with fixed effects," Working Papers hal-01073732, HAL.
    8. Phillips, Peter C.B. & Sul, Donggyu, 2007. "Bias in dynamic panel estimation with fixed effects, incidental trends and cross section dependence," Journal of Econometrics, Elsevier, vol. 137(1), pages 162-188, March.
    9. Kiefer, Nicholas M., 1980. "Estimation of fixed effect models for time series of cross-sections with arbitrary intertemporal covariance," Journal of Econometrics, Elsevier, vol. 14(2), pages 195-202, October.
    10. Kruiniger, Hugo, 2008. "Maximum likelihood estimation and inference methods for the covariance stationary panel AR(1)/unit root model," Journal of Econometrics, Elsevier, vol. 144(2), pages 447-464, June.
    11. Nerlove, Marc, 1971. "Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross Sections," Econometrica, Econometric Society, vol. 39(2), pages 359-382, March.
    12. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 647-666.
    13. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    14. Hsiao, Cheng & Hashem Pesaran, M. & Kamil Tahmiscioglu, A., 2002. "Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods," Journal of Econometrics, Elsevier, vol. 109(1), pages 107-150, July.
    15. Gary Chamberlain & Marcelo J. Moreira, 2009. "Decision Theory Applied to a Linear Panel Data Model," Econometrica, Econometric Society, vol. 77(1), pages 107-133, January.
    16. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    17. 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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    1. repec:hal:spmain:info:hdl:2441/dambferfb7dfprc9m052g20qh is not listed on IDEAS
    2. Geert Dhaene & Koen Jochmans, 2011. "Profile-score Adjustements for Nonlinearfixed-effect Models," Working Papers hal-01073733, HAL.
    3. repec:hal:spmain:info:hdl:2441/1mc4dip81d9t8r0t57fe1h8lap is not listed on IDEAS
    4. Dhaene, Geert & Jochmans, Koen, 2016. "Likelihood Inference In An Autoregression With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1178-1215, October.
    5. Magnac, Thierry & Pistolesi, Nicolas & Roux, Sébastien, 2013. "Post schooling human capital investments and the life cycle variance of earnings," TSE Working Papers 13-380, Toulouse School of Economics (TSE).
    6. 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.
    7. Jan Kiviet & Milan Pleus & Rutger Poldermans, 2017. "Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models," Econometrics, MDPI, vol. 5(1), pages 1-54, March.
    8. Maurice J.G. Bun & Sarafidis, V., 2013. "Dynamic Panel Data Models," UvA-Econometrics Working Papers 13-01, Universiteit van Amsterdam, Dept. of Econometrics.
    9. Geert Dhaene & Koen Jochmans, 2011. "An Adjusted profile likelihood for non-stationary panel data models with fixed effects," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
    10. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09ij4oge90i is not listed on IDEAS
    11. Jan F. Kiviet & Milan Pleus & Rutger Poldermans, 2014. "Accuracy and efficiency of various GMM inference techniques in dynamic micro panel data models," UvA-Econometrics Working Papers 14-09, Universiteit van Amsterdam, Dept. of Econometrics.
    12. repec:hal:wpspec:info:hdl:2441/dambferfb7dfprc9m052g20qh is not listed on IDEAS
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    More about this item

    Keywords

    non-stationarity; adjusted likelihood; bias correction; dynamic panel data; fixed effects; non-stationarity.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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