Individual and Time Effects in Nonlinear Panel Data Models with Large N, T

Fixed effects estimators of panel models can be severely biased because of the well-known incidental parameters problem. We develop analytical and jackknife bias corrections for nonlinear models with both individual and time effects. Under asymptotics where the time-dimension (T ) grows with the cross-sectional dimension (N), the time effects introduce additional incidental parameter bias. As the existing bias expressions apply to models with only individual effects, we derive the appropriate corrections. The basis for the corrections are asymptotic expansions of fixed effects estimators with incidental parameters in multiple dimensions. These expansions apply to M-estimators with concave objective functions, which cover fixed effects estimators of the most popular limited dependent variable models such as logit, probit, Tobit and Poisson models. We consider specifications with additive or interactive individual and time effects, therefore extending the use of large-T bias adjustments to an important class of models.

[1]  P. Phillips,et al.  Linear Regression Limit Theory for Nonstationary Panel Data , 1999 .

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

[3]  W. Greene,et al.  The Behavior of the Fixed Effects Estimator in Nonlinear Models, , 2002 .

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

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

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

[7]  Z. Griliches,et al.  Econometric Models for Count Data with an Application to the Patents-R&D Relationship , 1984 .

[8]  R. Olsen,et al.  Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model , 1978 .

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

[10]  J. Kadane.  Structural Analysis of Discrete Data with Econometric Applications , 1984 .

[11]  J. Pratt.  Concavity of the Log Likelihood , 1981 .

[12]  Tiemen Woutersen.  Robustness against Incidental Parameters , 2002 .

[13]  Karyne B. Charbonneau.  Multiple Fixed Effects in Nonlinear Panel Data Models Theory and Evidence , 2012 .

[14]  J. Bai,et al.  Panel Data Models With Interactive Fixed Effects , 2009 .

[15]  Jinyong Hahn,et al.  Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects When Both N and T are Large , 2000 .

[16]  Hyungsik Roger Moon,et al.  REDUCING BIAS OF MLE IN A DYNAMIC PANEL MODEL , 2005, Econometric Theory.

[17]  T. Lancaster.  The incidental parameter problem since 1948 , 2000 .

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

[19]  Jinyong Hahn,et al.  JACKKNIFE AND ANALYTICAL BIAS REDUCTION FOR NONLINEAR PANEL MODELS , 2003 .