Properties of estimators of count data model with endogenous switching

We examine properties of estimators of count data model with endogenous switching. The estimation of the count data model that accommodates endogenous switching can be accomplished by Full Information Maximum Likelihood (FIML). However, FIML estimation requires fully and correctly specified model and is computationally burdensome. Alternative estimation methods do not require fully specified model have been proposed. The typical methods are Two Stage Method of moments (TSM) and Nonlinear Weighted Least Squares (NWLS). The properties of these estimators have never been studied so far. In this paper, we compared the finite sample properties of these estimators under correct and incorrect model specifications using Monte Carlo experiments. We find that FIML estimator has the smallest standard deviation and TSM estimator has the largest when the model is correctly specified. This property also holds under incorrect model specification. An important point to emphasize is the large standard deviation of the estimate of endogeneity suggests that TSM and NWLS estimations result in an anomalous estimate of endogeneity very frequent even under the correct specification.