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Likelihood inference in an Autoregression with fixed effects

Author

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  • Geert Dhaene

    (KU Leuven)

  • Koen Jochmans

    (Département d'économie)

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. We argue that the parameters are local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.

Suggested Citation

  • Geert Dhaene & Koen Jochmans, 2013. "Likelihood inference in an Autoregression with fixed effects," Sciences Po publications 2013-07, Sciences Po.
  • Handle: RePEc:spo:wpmain:info:hdl:2441/dambferfb7dfprc9m052g20qh
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    Cited by:

    1. Iván Fernández-Val & Martin Weidner, 2018. "Fixed Effects Estimation of Large-TPanel Data Models," Annual Review of Economics, Annual Reviews, vol. 10(1), pages 109-138, August.
    2. Barbosa, José Diogo Valadares Moreira & Moreira, Marcelo J., 2017. "Likelihood inference and the role of initial conditions for the dynamic panel data model," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 788, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    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. Artūras Juodis, 2018. "Rank based cointegration testing for dynamic panels with fixed T," Empirical Economics, Springer, vol. 55(2), pages 349-389, September.
    5. 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.
    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. 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.
    9. 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.
    10. Maurice J. G. Bun & Frank Kleibergen, 2021. "Identification robust inference for moments based analysis of linear dynamic panel data models," Papers 2105.08346, arXiv.org.
    11. 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.
    12. Wendong Zhang & Sergio H. Lence & Todd Kuethe, 2020. "Are Expert Opinions Accurate? Panel Data Evidence from the Iowa Land Value Survey," Center for Agricultural and Rural Development (CARD) Publications 20-wp612, Center for Agricultural and Rural Development (CARD) at Iowa State University.
    13. Alexander Chudik & M. Hashem Pesaran & Jui-Chung Yang, 2016. "Half-panel jackknife fixed effects estimation of panels with weakly exogenous regressor," Globalization Institute Working Papers 281, Federal Reserve Bank of Dallas.
    14. 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.
    15. 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.
    16. 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.
    17. Geert Dhaene & Koen Jochmans, 2015. "Profile-score adjustments for incidental-parameter problems," Sciences Po publications info:hdl:2441/323dml6suu9, Sciences Po.

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    Keywords

    adjusted likelihood; autoregression; incidental parameters; local maximizer; recentered estimating equation;
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