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Likelihood inference in an Autoregression with fixed effects

Author

Listed:
  • 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 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," SciencePo Working papers hal-01070434, HAL.
    • Handle: RePEc:hal:wpspec:hal-01070434
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01070434
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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. Haihong Li & Bruce G. Lindsay & Richard P. Waterman, 2003. "Efficiency of projected score methods in rectangular array asymptotics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 191-208, February.
    4. Javier Alvarez & Manuel Arellano, 2003. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Econometrica, Econometric Society, vol. 71(4), pages 1121-1159, July.
    5. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    6. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    7. Blundell, Richard & Bond, Stephen, 1998. "Initial conditions and moment restrictions in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 87(1), pages 115-143, August.
    8. N. Sartori, 2003. "Modified profile likelihoods in models with stratum nuisance parameters," Biometrika, Biometrika Trust, vol. 90(3), pages 533-549, September.
    9. Gagliardini, Patrick & Gourieroux, Christian, 2014. "Efficiency In Large Dynamic Panel Models With Common Factors," Econometric Theory, Cambridge University Press, vol. 30(5), pages 961-1020, October.
    10. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    11. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, March.
    12. Arellano, Manuel & Carrasco, Raquel, 2003. "Binary choice panel data models with predetermined variables," Journal of Econometrics, Elsevier, vol. 115(1), pages 125-157, July.
    13. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    14. Manuel Arellano & Jinyong Hahn, 2016. "A likelihood-Based Approximate Solution to the Incidental Parameter Problem in Dynamic Nonlinear Models with Multiple Effects," Global Economic Review, Taylor & Francis Journals, vol. 45(3), pages 251-274, July.
    15. 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.
    16. 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.
    17. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 647-666.
    18. Tiemen Woutersen & Marcel Voia, 2002. "Adaptive Estimation of the Dynamic Linear Model with Fixed Effects," University of Western Ontario, Departmental Research Report Series 200210, University of Western Ontario, Department of Economics.
    19. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    20. Manuel Arellano, 2003. "Discrete choices with panel data," Investigaciones Economicas, Fundación SEPI, vol. 27(3), pages 423-458, September.
    21. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    22. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    23. Hahn, Jinyong & Kuersteiner, Guido, 2011. "Bias Reduction For Dynamic Nonlinear Panel Models With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1152-1191, December.
    24. Bester, C. Alan & Hansen, Christian, 2009. "A Penalty Function Approach to Bias Reduction in Nonlinear Panel Models with Fixed Effects," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 131-148.
    25. 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.
    26. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," University of Western Ontario, Departmental Research Report Series 20028, University of Western Ontario, Department of Economics.
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    Cited by:

    1. Alvarez, Javier & Arellano, Manuel, 2022. "Robust likelihood estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 21-61.
    2. Sebastian Kripfganz & Jörg Breitung, 2022. "Bias-corrected estimation of linear dynamic panel data models," London Stata Conference 2022 05, Stata Users Group.
    3. repec:spo:wpecon:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    4. 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.
    5. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    6. Geert Dhaene & Koen Jochmans, 2015. "Profile-score adjustments for incidental-parameter problems," Working Papers hal-03460016, HAL.
    7. 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.
    8. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    9. 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.
    10. 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.
    11. 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.
    12. Ayden Higgins & Koen Jochmans, 2022. "Bootstrap inference for fixed-effect models," Papers 2201.11156, arXiv.org.
    13. Hayakawa, Kazuhiko, 2024. "Recent development of covariance structure analysis in economics," Econometrics and Statistics, Elsevier, vol. 29(C), pages 31-48.
    14. 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.
    15. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Artūras Juodis, 2018. "Rank based cointegration testing for dynamic panels with fixed T," Empirical Economics, Springer, vol. 55(2), pages 349-389, September.
    21. 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.
    22. 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.
    23. 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.
    24. repec:spo:wpmain:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    25. 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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