GMM-Estimation of Nonlinear Models on Panel Data

We show that the Generalized Method of Moments (GMM) methodology is a useful tool to obtain the asymptotic properties of some existing estimators for nonlinear panel data models as well as to construct new ones. Many non-linear panel data models imply conditional moments, which do not depend on parameters from the off-diagonal part of the intertemporal covariance matrix of the error terms. The pooled maximum likelihood estimator, the sequential ML estimator based on minimum distance estimation in the second step, and previously suggested alternative GMM estimators are based on these moments. Although the pooled ML estimator is asymptotically the least efficient of the estimators considered, the Monte Carlo study indicates that it may have good small sample properties. We use a low dimensional approximation of the optimal instrument matrix to obtain an estimator, which appeared to be nearly as efficient as FIML. However, GMM estimators are easier to compute and also possess desirable sm..