A Note on the Efficient Semiparametric Estimation of Some Exponential Panel Models

This paper investigates the semiparametric efficiency of the conditional maximum likelihood estimation in some panel models. The nonparametric component of the model is the unknown distribution of the fixed effect. For the exponential panel model, there exists a complete sufficient statistic for the fixed effect. When the complete sufficient statistic does not depend on the parameter of interest, the conditional maximum likelihood estimator (CMLE) achieves the semiparametric efficiency bound. In particular, the CMLE is semiparametrically efficient for the panel Poisson regression model and the panel negative binomial model.