Modified Profile Likelihood for Fixed-Effects Panel Data Models

We show how modified profile likelihood methods, developed in the statistical literature, may be effectively applied to estimate the structural parameters of econometric models for panel data, with a remarkable reduction of bias with respect to ordinary likelihood methods. Initially, the implementation of these methods is illustrated for general models for panel data including individual-specific fixed effects and then, in more detail, for the truncated linear regression model and dynamic regression models for binary data formulated along with different specifications. Simulation studies show the good behavior of the inference based on the modified profile likelihood, even when compared to an ideal, although infeasible, procedure (in which the fixed effects are known) and also to alternative estimators existing in the econometric literature. The proposed estimation methods are implemented in an R package that we make available to the reader.

[1]  D. Cox,et al.  Inference and Asymptotics , 1994 .

[2]  Bo E. Honoré,et al.  Panel Data Discrete Choice Models with Lagged Dependent Variables , 2000 .

[3]  F. Bartolucci,et al.  A Dynamic Model for Binary Panel Data With Unobserved Heterogeneity Admitting a Root-N Consistent Conditional Estimator , 2007 .

[4]  Nicola Sartori,et al.  Modified profile likelihoods in models with stratum nuisance parameters , 2003 .

[5]  Thomas J. DiCiccio,et al.  Information Bias and Adjusted Profile Likelihoods , 1996 .

[6]  D. Cox,et al.  Parameter Orthogonality and Approximate Conditional Inference , 1987 .

[7]  Jesus M. Carro.  Estimating Dynamic Panel Data Discrete Choice Models with Fixed Effects , 2003 .

[8]  Luigi Pace,et al.  Adjustments of the profile likelihood from a new perspective , 2006 .

[9]  Ivan Fernandez-Val,et al.  Fixed effects estimation of structural parameters and marginal effects in panel probit models , 2007 .

[10]  Jinyong Hahn,et al.  Understanding Bias in Nonlinear Panel Models: Some Recent Developments ∗ , 2005 .

[11]  Iván Fernández�?Val,et al.  Bias Corrections for Two-Step Fixed Effects Panel Data Estimators , 2007, SSRN Electronic Journal.

[12]  Nicola Sartori,et al.  Practical Use of Modified Maximum Likelihoods for Stratified Data , 2006, Biometrical journal. Biometrische Zeitschrift.

[13]  Ruggero Bellio,et al.  Effects of the reference set on frequentist inferences , 2006 .

[14]  David R. Cox,et al.  A time series illustration of approximate conditional likelihood , 1989 .

[15]  J. Hanfelt,et al.  Robust modified profile estimating function with application to the generalized estimating equation , 2008 .

[16]  Thomas A. Severini,et al.  An approximation to the modified profile likelihood function , 1998 .

[17]  W. Greene,et al.  The Behaviour of the Maximum Likelihood Estimator of Limited Dependent Variable Models in the Presence of Fixed Effects , 2004 .

[18]  Vassilis A. Hajivassiliou,et al.  Some Practical Issues in Maximum Simulated Likelihood , 1997 .

[19]  T. Severini.  Modified estimating functions , 2002 .

[20]  Thomas A. Severini,et al.  An empirical adjustment to the likelihood ratio statistic , 1999 .

[21]  Jinyong Hahn,et al.  BIAS REDUCTION FOR DYNAMIC NONLINEAR PANEL MODELS WITH FIXED EFFECTS , 2011, Econometric Theory.

[22]  Francesco Bartolucci,et al.  Pseudo Conditional Maximum Likelihood Estimation of the Dynamic Logit Model for Binary Panel Data , 2009 .

[23]  O. Barndorff-Nielsen.  On a formula for the distribution of the maximum likelihood estimator , 1983 .

[24]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[25]  T. Severini.  Likelihood Methods in Statistics , 2001 .

[26]  Christian Hansen,et al.  A Penalty Function Approach to Bias Reduction in Non-Linear Panel Models with Fixed Effects , 2005 .

[27]  Tony Lancaster,et al.  Orthogonal Parameters and Panel Data , 2002 .