IDEAS home Printed from https://ideas.repec.org/p/hal/wpspec/hal-01070434.html
   My bibliography  Save this paper

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://hal-sciencespo.archives-ouvertes.fr/hal-01070434
    as

    Download full text from publisher

    File URL: https://hal-sciencespo.archives-ouvertes.fr/hal-01070434/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    10. N. Sartori, 2003. "Modified profile likelihoods in models with stratum nuisance parameters," Biometrika, Biometrika Trust, vol. 90(3), pages 533-549, September.
    11. 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.
    12. 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.
    13. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, March.
    14. Arellano, Manuel & Carrasco, Raquel, 2003. "Binary choice panel data models with predetermined variables," Journal of Econometrics, Elsevier, vol. 115(1), pages 125-157, July.
    15. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    16. 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.
    17. 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.
    18. 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.
    19. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 647-666.
    20. 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.
    21. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291, November.
    22. 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.
    23. Manuel Arellano, 2003. "Discrete choices with panel data," Investigaciones Economicas, Fundación SEPI, vol. 27(3), pages 423-458, September.
    24. 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.
    25. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    26. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    27. 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.
    28. 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.
    29. 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.
    30. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 277-297.
    31. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," University of Western Ontario, Departmental Research Report Series 20028, University of Western Ontario, Department of Economics.
    32. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Alvarez, Javier & Arellano, Manuel, 2022. "Robust likelihood estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 21-61.
    9. 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.
    10. 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.
    11. 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.
    12. Geert Dhaene & Koen Jochmans, 2015. "Profile-score adjustments for incidental-parameter problems," Sciences Po publications info:hdl:2441/323dml6suu9, Sciences Po.
    13. Artūras Juodis, 2018. "Rank based cointegration testing for dynamic panels with fixed T," Empirical Economics, Springer, vol. 55(2), pages 349-389, September.
    14. 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.
    15. 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.
    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. Jochmans, Koen & Higgins, Ayden, 2022. "Bootstrap inference for fixed-effect models," TSE Working Papers 22-1328, Toulouse School of Economics (TSE).
    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. 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.
    20. Sebastian Kripfganz & Jörg Breitung, 2022. "Bias-corrected estimation of linear dynamic panel data models," London Stata Conference 2022 05, Stata Users Group.
    21. 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.
    22. 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.
    23. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
    7. 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.
    8. 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.
    9. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    10. 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.
    11. Antonio F. Galvao & Jiaying Gu & Stanislav Volgushev, 2018. "On the Unbiased Asymptotic Normality of Quantile Regression with Fixed Effects," Papers 1807.11863, arXiv.org, revised Feb 2020.
    12. 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.
    13. Ryo Okui, 2017. "Misspecification in Dynamic Panel Data Models and Model-Free Inferences," The Japanese Economic Review, Japanese Economic Association, vol. 68(3), pages 283-304, September.
    14. L. Hospido, 2012. "Modelling heterogeneity and dynamics in the volatility of individual wages," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 386-414, April.
    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. Alvarez, Javier & Arellano, Manuel, 2022. "Robust likelihood estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 21-61.
    17. Pakel, Cavit, 2019. "Bias reduction in nonlinear and dynamic panels in the presence of cross-section dependence," Journal of Econometrics, Elsevier, vol. 213(2), pages 459-492.
    18. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    19. Geert Dhaene & Koen Jochmans, 2011. "Profile-score Adjustements for Nonlinearfixed-effect Models," SciencePo Working papers Main hal-01073733, HAL.
    20. Arturas Juodis, 2015. "Iterative Bias Correction Procedures Revisited: A Small Scale Monte Carlo Study," UvA-Econometrics Working Papers 15-02, Universiteit van Amsterdam, Dept. of Econometrics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpspec:hal-01070434. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Contact - Sciences Po Departement of Economics (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.