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Likelihood Inference In An Autoregression With Fixed Effects

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  • Dhaene, Geert
  • Jochmans, Koen

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.

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  • 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.
    • Handle: RePEc:cup:etheor:v:32:y:2016:i:05:p:1178-1215_00
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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. 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.
    3. 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 110375, University Library of Munich, Germany, revised 15 Aug 2021.
    4. 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.
    5. 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.
    6. Alvarez, Javier & Arellano, Manuel, 2022. "Robust likelihood estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 21-61.
    7. 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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    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. Geert Dhaene & Koen Jochmans, 2015. "Profile-score adjustments for incidental-parameter problems," Sciences Po publications info:hdl:2441/323dml6suu9, Sciences Po.
    11. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    12. Artūras Juodis, 2018. "Rank based cointegration testing for dynamic panels with fixed T," Empirical Economics, Springer, vol. 55(2), pages 349-389, September.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Jochmans, Koen & Higgins, Ayden, 2022. "Bootstrap inference for fixed-effect models," TSE Working Papers 22-1328, Toulouse School of Economics (TSE), revised Dec 2023.
    18. 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.
    19. repec:hal:spmain:info:hdl:2441/323dml6suu9mb9otmuenjljv9a is not listed on IDEAS
    20. 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.
    21. Sebastian Kripfganz & Jörg Breitung, 2022. "Bias-corrected estimation of linear dynamic panel data models," London Stata Conference 2022 05, Stata Users Group.
    22. 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.
    23. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09ij4j0h0h1 is not listed on IDEAS
    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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