Consistent estimation of discrete-choice models for panel data with multiplicative effects

This paper presents an extension to the fixed-effect Logit for panel-data discrete-choice models, where the error component structure is multiplicative (individual effects multiplied by time effects). In linear models with such an error-component structure as investigated by Ahn, Lee and Schmidt (2001), usual fixed-effect estimators are generally inconsistent. We propose a conditional Logit estimator based on a different sufficient statistic, for the case where multiplicative time effects are known. When not the case, we discuss the implementation of the Modified Profile Likelihood based on a transformation of incidental parameters. The last estimator is an extension of Honoré and Lewbel (2000) semiparametric estimator. We investigate small sample properties of these estimators with a Monte Carlo experiment.