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Annual Review of Economics

Volume 10, 2018

Fixed Effects Estimation of Large-Panel Data Models

Abstract

This article reviews recent advances in fixed effects estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable, conditional on covariates and unobserved effects, is specified parametrically while the distribution of the unobserved effects is left unrestricted. In contrast to existing reviews on long panels, we discuss models with both individual and time effects, split-panel jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects are our main focuses, and the unifying theme is that the order of this bias is given by the simple formula / for all models discussed, with being the number of estimated parameters and the total sample size.

Keyword(s): bias correction, fixed effects, incidental parameter problem, JEL C23, JEL C33, nonlinear models, panel data, unobserved heterogeneity
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2018-08-02
2024-04-25
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Literature Cited

  1. Altonji JG, Matzkin RL 2005. Cross section and panel data estimators for nonseparable models with endogenous regressors. Econometrica 73:1053–102
     [Google Scholar]
  2. Alvarez J, Arellano M 2003. The time series and cross-section asymptotics of dynamic panel data estimators. Econometrica 71:1121–59
     [Google Scholar]
  3. Andersen E 1970. Asymptotic properties of conditional maximum-likelihood estimators. J. R. Stat. Soc. Ser. B 32:283–301
     [Google Scholar]
  4. Anderson JE, van Wincoop E 2003. Gravity with gravitas: a solution to the border puzzle. Am. Econ. Rev. 93:170–92
     [Google Scholar]
  5. Arellano M 2003.a Discrete choices with panel data. Invest. Econ. 27:423–58
     [Google Scholar]
  6. Arellano M 2003.b Panel Data Econometrics Oxford, UK: Oxford Univ. Press
  7. Arellano M, Bond S 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Rev. Econ. Stud. 58:277–97
     [Google Scholar]
  8. Arellano M, Bonhomme S 2011. Nonlinear panel data analysis. Annu. Rev. Econ. 3:395–424
     [Google Scholar]
  9. Arellano M, Bonhomme S 2017. Nonlinear panel data methods for dynamic heterogeneous agent models. Annu. Rev. Econ. 9:471–96
     [Google Scholar]
  10. Arellano M, Carrasco R 2003. Binary choice panel data models with predetermined variables. J. Econom. 115:125–57
     [Google Scholar]
  11. Arellano M, Hahn J 2007. Understanding bias in nonlinear panel models: some recent developments. Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress R Blundell, W Newey, T Persson 381–409 Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  12. Arellano M, Hahn J 2016. A likelihood-based approximate solution to the incidental parameter problem in dynamic nonlinear models with multiple effects. Glob. Econ. Rev. 45:251–74
     [Google Scholar]
  13. Arellano M, Honoré B 2001. Panel data models: some recent developments. Handbook of Econometrics 5 JJ Heckman, E Learner 3229–96 Amsterdam: Elsevier
     [Google Scholar]
  14. Arellano M, Weidner M 2017. Instrumental variable quantile regressions in large panels with fixed effects Unpublished manuscript, Cent. Monet. Financ. Stud., Madrid/Univ. Coll. London
  15. Bai J 2009. Panel data models with interactive fixed effects. Econometrica 77:1229–79
     [Google Scholar]
  16. Bai J, Wang P 2016. Econometric analysis of large factor models. Annu. Rev. Econ. 8:53–80
     [Google Scholar]
  17. Baltagi B 2008. Econometric Analysis of Panel Data Hoboken, NJ: Wiley
  18. Bester CA, Hansen C 2009. A penalty function approach to bias reduction in nonlinear panel models with fixed effects. J. Bus. Econ. Stat. 27:131–48
     [Google Scholar]
  19. Blundell R, Griffith R, Windmeijer F 1999. Individual effects and dynamics in count data models Work. Pap. W99/3 Inst. Fisc. Stud London:
  20. Blundell R, Griffith R, Windmeijer F 2002. Individual effects and dynamics in count data models. J. Econom. 108:113–31
     [Google Scholar]
  21. Boneva L, Linton O 2017. A discrete-choice model for large heterogeneous panels with interactive fixed effects with an application to the determinants of corporate bond issuance. J. Appl. Econom. 32:1226–43
     [Google Scholar]
  22. Bonhomme S 2012. Functional differencing. Econometrica 80:1337–85
     [Google Scholar]
  23. Bonhomme S, Lamadon T, Manresa E 2017. Discretizing unobserved heterogeneity Unpublished manuscript, Univ. Chicago/N. Y. Univ.
  24. Bonhomme S, Manresa E 2015. Grouped patterns of heterogeneity in panel data. Econometrica 83:1147–84
     [Google Scholar]
  25. Botosaru I, Muris C 2017. Binarization for panel models with fixed effects Work. Pap. CWP31/17 Cent. Microdata Methods Pract London:
  26. Bun MJ, Kiviet JF 2003. On the diminishing returns of higher-order terms in asymptotic expansions of bias. Econ. Lett. 79:145–52
     [Google Scholar]
  27. Candelaria LE 2016. A semiparametric network formation model with multiple linear fixed effects Unpublished manuscript, Duke Univ Durham, NC:
  28. Carro J 2007. Estimating dynamic panel data discrete choice models with fixed effects. J. Econom. 140:503–28
     [Google Scholar]
  29. Chamberlain G 1980. Analysis of covariance with qualitative data. Rev. Econ. Stud. 47:225–38
     [Google Scholar]
  30. Chamberlain G 1984. Panel data. Handbook of Econometrics 2 Z Griliches, MD Intriligator 1247–318 Amsterdam: Elsevier
     [Google Scholar]
  31. Chamberlain G 2010. Binary response models for panel data: identification and information. Econometrica 78:159–68
     [Google Scholar]
  32. Charbonneau KB 2014. Multiple fixed effects in binary response panel data models. Econom. J. 20:S1–S13
     [Google Scholar]
  33. Chen M 2016. Estimation of nonlinear panel models with multiple unobserved effects Econ. Res. Pap. 1120 Warwick Univ Coventry, UK:
  34. Chen M, Fernandez-Val I, Weidner M 2014. Nonlinear panel models with interactive effects. arXiv1412.5647 [stat.ME]
  35. Chernozhukov V, Fernández-Val I, Hahn J, Newey W 2013. Average and quantile effects in nonseparable panel models. Econometrica 81:535–80
     [Google Scholar]
  36. Chernozhukov V, Fernández-Val I, Hoderlein S, Holzmann H, Newey W 2015. Nonparametric identification in panels using quantiles. J. Econom. 188:378–92
     [Google Scholar]
  37. Chernozhukov V, Fernández-Val I, Newey W 2017.a Nonseparable multinomial choice models in cross-section and panel data. arXiv1706.08418 [stat.ME]
  38. Chernozhukov V, Fernández-Val I, Weidner M 2017.b Network and panel quantile effects via distribution regression Work. Pap. CWP21/18 Cent. Microdata Methods Pract London:
  39. Chudik A, Pesaran MH 2015.a Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors. J. Econom. 188:393–420
     [Google Scholar]
  40. Chudik A, Pesaran MH 2015.b Large panel data models with cross-sectional dependence: a survey. The Oxford Handbook of Panel Data BH Baltagi 3–45 Oxford, UK: Oxford Univ. Press
     [Google Scholar]
  41. Chudik A, Pesaran MH, Yang JC 2016. Half-panel jackknife fixed effects estimation of panels with weakly exogenous regressor Work. Pap. 281, Glob. Monet. Policy Inst., Fed. Reserve Bank Dallas
  42. Cox DR 1958. The regression analysis of binary sequences. J. R. Stat. Soc. Ser. B 20:215–42
     [Google Scholar]
  43. Cox DR, Reid N 1987. Parameter orthogonality and approximate conditional inference. J. R. Stat. Soc. Ser. B 49:1–39
     [Google Scholar]
  44. Cruz-González M, Fernández-Val I, Weidner M 2017. Bias corrections for probit and logit models with two-way fixed effects. Stata J 17:517–45
     [Google Scholar]
  45. Dhaene G, Jochmans K 2015.a Profile-score adjustments for incidental-parameter problems Work. Pap., Sci. Po, Paris
  46. Dhaene G, Jochmans K 2015.b Split-panel jackknife estimation of fixed-effect models. Rev. Econ. Stud. 82:991–1030
     [Google Scholar]
  47. Dhaene G, Jochmans K 2016. Likelihood inference in an autoregression with fixed effects. Econom. Theory 32:1178–215
     [Google Scholar]
  48. Dzemski A 2017. An empirical model of dyadic link formation in a network with unobserved heterogeneity Work. Pap. Econ. 698 Univ. Gothenburg Swed.:
  49. Evdokimov K 2010. Identification and estimation of a nonparametric panel data model with unobserved heterogeneity Unpublished manuscript, Dept. Econ., Princeton Univ. Princeton, NJ:
  50. Fernández-Val I 2009. Fixed effects estimation of structural parameters and marginal effects in panel probit models. J. Econom. 150:71–85
     [Google Scholar]
  51. Fernández-Val I, Lee J 2013. Panel data models with nonadditive unobserved heterogeneity: estimation and inference. Quant. Econ. 4:453–81
     [Google Scholar]
  52. Fernández-Val I, Vella F 2011. Bias corrections for two-step fixed effects panel data estimators. J. Econom. 163:144–62
     [Google Scholar]
  53. Fernández-Val I, Weidner M 2016. Individual and time effects in nonlinear panel models with large N, T. J. Econom. 192:291–312
     [Google Scholar]
  54. Freyberger J 2018. Nonparametric panel data models with interactive fixed effects. Rev. Econ. Stud. In press
  55. Galvao A, Kato K 2016. Smoothed quantile regression for panel data. J. Econom. 193:92–112
     [Google Scholar]
  56. Galvao AF, Kato K 2018. Quantile regression methods for longitudinal data. Handbook of Quantile Regression R Koenker, V Chernozhukov, X He, L Peng pp. 363–80. Boca Raton, FL: CRC Press:
     [Google Scholar]
  57. Gonçalves S, Kaffo M 2015. Bootstrap inference for linear dynamic panel data models with individual fixed effects. J. Econom. 186:407–26
     [Google Scholar]
  58. Graham BS 2017. An econometric model of link formation with degree heterogeneity. Econometrica 85:1033–63
     [Google Scholar]
  59. Graham BS, Powell JL 2012. Identification and estimation of average partial effects in irregular correlated random coefficient panel data models. Econometrica 80:2105–52
     [Google Scholar]
  60. Greene W 2004. The behavior of the fixed effects estimator in nonlinear models. Econom. J. 7:98–119
     [Google Scholar]
  61. Hahn J, Kuersteiner G 2002. Asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and T are large. Econometrica 70:1639–57
     [Google Scholar]
  62. Hahn J, Kuersteiner G 2007. Bandwidth choice for bias estimators in dynamic nonlinear panel models Unpublished manuscript, Univ. Calif Los Angeles/Davis:
  63. Hahn J, Kuersteiner G 2011. Bias reduction for dynamic nonlinear panel models with fixed effects. Econom. Theory 27:1152–91
     [Google Scholar]
  64. Hahn J, Moon HR 2006. Reducing bias of MLE in a dynamic panel model. Econom. Theory 22:499–512
     [Google Scholar]
  65. Hahn J, Moon HR 2010. Panel data models with finite number of multiple equilibria. Econom. Theory 26:863–81
     [Google Scholar]
  66. Hahn J, Newey W 2004. Jackknife and analytical bias reduction for nonlinear panel models. Econometrica 72:1295–319
     [Google Scholar]
  67. Harrigan J 1996. Openness to trade in manufactures in the OECD. J. Int. Econ. 40:23–39
     [Google Scholar]
  68. Hausman J, Hall BH, Griliches Z 1984. Econometric models for count data with an application to the patents-R & D relationship. Econometrica 52:909–38
     [Google Scholar]
  69. Helpman E, Melitz M, Rubinstein Y 2008. Estimating trade flows: trading partners and trading volumes. Q. J. Econ. 123:441–87
     [Google Scholar]
  70. Hirji KF, Mehta CR, Patel NR 1987. Computing distributions for exact logistic regression. J. Am. Stat. Assoc. 82:1110–17
     [Google Scholar]
  71. Hoderlein S, White H 2012. Nonparametric identification in nonseparable panel data models with generalized fixed effects. J. Econom. 168:300–14
     [Google Scholar]
  72. Honoré BE 1992. Trimmed LAD and least squares estimation of truncated and censored regression models with fixed effects. Econometrica 60:533–65
     [Google Scholar]
  73. Honoré BE 2002. Nonlinear models with panel data. Port. Econ. J. 1:163–79
     [Google Scholar]
  74. Honoré BE, Kyriazidou E 2000. Panel data discrete choice models with lagged dependent variables. Econometrica 68:839–74
     [Google Scholar]
  75. Honoré BE, Tamer E 2006. Bounds on parameters in panel dynamic discrete choice models. Econometrica 74:611–29
     [Google Scholar]
  76. Horowitz JL 1992. A smoothed maximum score estimator for the binary response model. Econometrica 60:505–31
     [Google Scholar]
  77. Hsiao C 2014. Analysis of Panel Data Cambridge, UK: Cambridge Univ. Press
  78. Jochmans K 2017. Two-way models for gravity. Rev. Econ. Stat. 99:478–85
     [Google Scholar]
  79. Jochmans K 2018. Semiparametric analysis of network formation. J. Bus. Econ. Stat. In press
  80. Jochmans K, Otsu T 2018. Likelihood corrections for two-way models Work. Pap., Suntory Toyota Int. Cent. Econ. Relat. Disc., London School Econ.
  81. Kato K, Galvao AF, Montes-Rojas GV 2012. Asymptotics for panel quantile regression models with individual effects. J. Econom. 170:76–91
     [Google Scholar]
  82. Kim MS, Sun Y 2016. Bootstrap and k-step bootstrap bias corrections for the fixed effects estimator in nonlinear panel data models. Econom. Theory 32:1523–68
     [Google Scholar]
  83. Kiviet JF 1995. On bias, inconsistency, and efficiency of various estimators in dynamic panel data models. J. Econom. 68:53–78
     [Google Scholar]
  84. Koenker R 2004. Quantile regression for longitudinal data. J. Multivar. Anal. 91:74–89
     [Google Scholar]
  85. Kyriazidou E 1997. Estimation of a panel data sample selection model. Econometrica 65:1335–64
     [Google Scholar]
  86. Kyriazidou E 2001. Estimation of dynamic panel data sample selection models. Rev. Econ. Stud. 68:543–72
     [Google Scholar]
  87. Lancaster T 2000. The incidental parameter problem since 1948. J. Econom. 95:391–413
     [Google Scholar]
  88. Lancaster T 2002. Orthogonal parameters and panel data. Rev. Econ. Stud. 69:647–66
     [Google Scholar]
  89. Li H, Lindsay BG, Waterman RP 2003. Efficiency of projected score methods in rectangular array asymptotics. J. R. Stat. Soc. Ser. B 65:191–208
     [Google Scholar]
  90. Manski C 1987. Semiparametric analysis of random effects linear models from binary panel data. Econometrica 55:357–62
     [Google Scholar]
  91. Matzkin RL 2007. Nonparametric identification. Handbook of Econometrics 6B J Heckman, E Learner 5307–68 Amsterdam: Elsevier
     [Google Scholar]
  92. Matzkin RL 2013. Nonparametric identification in structural economic models. Annu. Rev. Econ. 5:457–86
     [Google Scholar]
  93. Moon HR, Weidner M 2017. Dynamic linear panel regression models with interactive fixed effects. Econom. Theory 33:158–95
     [Google Scholar]
  94. Moreira MJ 2009. A maximum likelihood method for the incidental parameter problem. Ann. Stat. 37:3660–96
     [Google Scholar]
  95. Mundlak Y 1978. On the pooling of time series and cross section data. Econometrica 46:69–85
     [Google Scholar]
  96. Muris C 2017. Estimation in the fixed-effects ordered logit model. Rev. Econ. Stat. 99:465–77
     [Google Scholar]
  97. Neyman J, Scott E 1948. Consistent estimates based on partially consistent observations. Econometrica 16:1–32
     [Google Scholar]
  98. Nickell SJ 1981. Biases in dynamic models with fixed effects. Econometrica 49:1417–26
     [Google Scholar]
  99. Pakel C 2014. Bias reduction in nonlinear and dynamic panels in the presence of cross-section dependence Unpublished manuscript, Bilkent Univ Ankara:
  100. Pakes A, Porter J 2013. Moment inequalities for semiparametric multinomial choice with fixed effects Work. Pap Harvard Univ Cambridge, MA:
  101. Palmgren J 1981. The Fisher information matrix for log linear models arguing conditionally on observed explanatory variable. Biometrika 68:563–66
     [Google Scholar]
  102. Pesaran MH 2006. Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74:967–1012
     [Google Scholar]
  103. Phillips PCB, Moon H 1999. Linear regression limit theory for nonstationary panel data. Econometrica 67:1057–111
     [Google Scholar]
  104. Quenouille MH 1949. Approximate tests of correlation in time-series. J. R. Stat. Soc. Ser. B 11:68–84
     [Google Scholar]
  105. Quenouille MH 1956. Notes on bias in estimation. Biometrika 43:353–60
     [Google Scholar]
  106. Rasch G 1960. Probabilistic Models for Some Intelligence and Achievement Tests Copenhagen: Dan. Inst. Educ. Res.
  107. Santos Silva J, Tenreyro S 2006. The log of gravity. Rev. Econ. Stat. 88:641–58
     [Google Scholar]
  108. Shao J, Tu D 1995. The Jackknife and Bootstrap New York: Springer
  109. Shi X, Shum M, Song W 2014. Estimating multinomial choice models using cyclic monotonicity Soc. Sci. Work. Pap. 1397 Calif. Inst. Technol Pasadena:
  110. Shi Z, Chen X 2016. A structural pairwise network model with individual heterogeneity Unpublished manuscript, Chin. Univ. Hong Kong/Yale Univ New Haven, CT:
  111. Stammann A, Heiß F, McFadden D 2016. Estimating fixed effects logit models with large panel data Unpublished manuscript Ger. Econ. Assoc Berlin:
  112. Sun Y 2016.a Likelihood-based inference for nonlinear models with both individual and time effects Discuss. Pap. 16.07 Kathol. Univ. Leuven Belg.:
  113. Sun Y 2016.b Second-order corrected likelihood for nonlinear models with fixed effects Discuss. Pap. 16.06 Kathol. Univ. Leuven Belg.:
  114. Sun Y 2016.c Xtspj: Split-panel jackknife estimation for nonlinear fixed-effect models Unpublished manuscript Kathol. Univ. Leuven Belg.:
  115. Torgovitsky A 2016. Nonparametric inference on state dependence with applications to employment dynamics Unpublished manuscript, Univ. Chicago
  116. Tukey JW 1958. Bias and confidence in not-quite large samples. Ann. Math. Statist. 29:614
     [Google Scholar]
  117. Wang F 2017. Maximum likelihood estimation and inference for high dimensional nonlinear factor models Work. Pap. 09-2017, Cent. Econom. Anal., Cass Bus. School London:
  118. Westerlund J 2018. CCE in panels with general unknown factors. Econom. J. In press
  119. Wooldridge JM 2010. Econometric Analysis of Cross Section and Panel Data Cambridge, MA: MIT Press, 2nd ed..
  120. Woutersen T 2002. Robustness against incidental parameters Res. Rep. 2002-8, Univ. West. Ontario, London, Can.
  121. Yan T, Jiang B, Fienberg SE, Leng C 2016. Statistical inference in a directed network model with covariates. arXiv:1609.04558 [stat.ME]
/content/journals/10.1146/annurev-economics-080217-053542
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Fixed Effects Estimation of Large-TPanel Data Models
Annual Review of Economics 10, 109 (2018); https://doi.org/10.1146/annurev-economics-080217-053542
/content/journals/10.1146/annurev-economics-080217-053542
/content/journals/10.1146/annurev-economics-080217-053542
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