Pseudo Conditional Maximum Likelihood Estimation of the Dynamic Logit Model for Binary Panel Data

Abstract

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator for the structural parameters of the dynamic logit model which is very simple to compute. Asymptotic properties of this estimator are derived. Simulation results show that the estimator is competitive in terms of efficiency with estimators very recently proposed in the econometric literature. We also show how the approach may be exploited to construct a Wald-type test for state dependence.

Keywords: log-linear models, longitudinal data, pseudo likelihood inference, quadratic exponential distribution

JEL Classification: C12, C13, C23, C25