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Likelihood Inference in an Autoregression with Fixed Effects

Author

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  • Geert Dhaene

    (UCL - Université Catholique de Louvain = Catholic University of Louvain)

  • 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 regression coefficients in a multistratum autoregressive model with stratum-specific intercepts. The bias is free of incidental parameters. Centering the profile score delivers an unbiased estimating equation and, upon integration, an adjusted profile likelihood. A variety of other approaches to constructing modified profile likelihoods are shown to yield equivalent results. However, the global maximizer of the adjusted likelihood lies at infinity for any sample size, and the adjusted profile score has multiple zeros. Consistent parameter estimates are obtained as local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.

Suggested Citation

  • Geert Dhaene & Koen Jochmans, 2016. "Likelihood Inference in an Autoregression with Fixed Effects," SciencePo Working papers Main hal-03391995, HAL.
  • Handle: RePEc:hal:spmain:hal-03391995
    DOI: 10.1017/S0266466615000146
    Note: View the original document on HAL open archive server: https://hal-sciencespo.archives-ouvertes.fr/hal-03391995
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    Cited by:

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    2. Barbosa, José Diogo & Moreira, Marcelo J., 2021. "Likelihood inference and the role of initial conditions for the dynamic panel data model," Journal of Econometrics, Elsevier, vol. 221(1), pages 160-179.
    3. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    4. Alvarez, Javier & Arellano, Manuel, 2022. "Robust likelihood estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 21-61.
    5. Kruiniger, Hugo, 2018. "A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions," MPRA Paper 88623, University Library of Munich, Germany.
    6. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    7. Artūras Juodis, 2018. "Rank based cointegration testing for dynamic panels with fixed T," Empirical Economics, Springer, vol. 55(2), pages 349-389, September.
    8. Norkutė, Milda & Westerlund, Joakim, 2021. "The factor analytical approach in near unit root interactive effects panels," Journal of Econometrics, Elsevier, vol. 221(2), pages 569-590.
    9. Geert Dhaene & Koen Jochmans, 2015. "Profile-score adjustments for incidental-parameter problems," Sciences Po publications info:hdl:2441/323dml6suu9, Sciences Po.
    10. 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.
    11. Jose Diogo Barbosa & Marcelo Moreira, 2017. "Likelihood inference and the role of initial conditions for the dynamic panel data model," CeMMAP working papers 04/17, Institute for Fiscal Studies.
    12. 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.
    13. Guangjie Li, 2015. "Consistency in Estimation and Model Selection of Dynamic Panel Data Models with Fixed Effects," Econometrics, MDPI, vol. 3(3), pages 1-31, July.
    14. Jochmans, Koen & Higgins, Ayden, 2022. "Bootstrap inference for fixed-effect models," TSE Working Papers 22-1328, Toulouse School of Economics (TSE), revised Dec 2023.
    15. repec:hal:spmain:info:hdl:2441/323dml6suu9mb9otmuenjljv9a is not listed on IDEAS
    16. Wendong Zhang & Sergio H. Lence & Todd Kuethe, 2021. "Are Expert Opinions Accurate? Panel Data Evidence from the Iowa Land Value Survey," Land Economics, University of Wisconsin Press, vol. 97(4), pages 875-892.
    17. Schumann, Martin & Severini, Thomas A. & Tripathi, Gautam, 2021. "Integrated likelihood based inference for nonlinear panel data models with unobserved effects," Journal of Econometrics, Elsevier, vol. 223(1), pages 73-95.
    18. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09ij4j0h0h1 is not listed on IDEAS
    19. Bun, Maurice J.G. & Kleibergen, Frank, 2022. "Identification Robust Inference For Moments-Based Analysis Of Linear Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 38(4), pages 689-751, August.
    20. Dhaene, Geert & Sun, Yutao, 2021. "Second-order corrected likelihood for nonlinear panel models with fixed effects," Journal of Econometrics, Elsevier, vol. 220(2), pages 227-252.
    21. Alexander Chudik & M. Hashem Pesaran & Jui‐Chung Yang, 2018. "Half‐panel jackknife fixed‐effects estimation of linear panels with weakly exogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(6), pages 816-836, September.
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    23. Sebastian Kripfganz & Jörg Breitung, 2022. "Bias-corrected estimation of linear dynamic panel data models," London Stata Conference 2022 05, Stata Users Group.
    24. 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.

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