Modified Profile Likelihood for Fixed-Effects Panel Data Models

Abstract

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.

Keywords:

• Autoregressive models
• Bias reduction
• Dynamic logit model
• Dynamic probit model
• Incidental parameter problem
• Truncated regression

JEL Classification:

• C13 (Estimation: General)
• C23 (Panel Data Models - Spatio-temporal Models)

ACKNOWLEDGMENT

Francesco Bartolucci acknowledges the financial support from the “Einaudi Institute for Economics and Finance” EIEF (Rome, IT) and the Italian Government (FIRB, “Futuro in Ricerca”). Nicola Sartori was supported by the Cariparo Foundation Excellence grant 2011/2012. Ruggero Bellio, Alessandra Salvan, and Nicola Sartori were supported by MIUR PRIN 2008. We thank the reviewers for their constructive comments.