Modified Profile Likelihood for 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 the ordinary likelihood methods. The implementation of these methods is illustrated in detail for certain static and dynamic models which are commonly used in economic applications. We consider, in particular, the truncated linear regression model, the first order autoregressive model, the (static and dynamic) logit model, and the (static and dynamic) probit model. Differently from static models, dynamic models include the lagged response variable among the regressors. For each of these models, we report the results of simulation studies showing the good behaviour of the proposed estimation methods, even with respect to an ideal, although infeasible, procedure. The methods are made available through an R package.

Keywords: autoregressive models, bias reduction, dynamic models, incidental parameter problem, logit model, probit model, truncated regression

JEL Classification: C10, C13, C23