Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects

Count data regression models are extended to account for endogenous switching and its two most common incarnations, viz., endogenous dummy variables (treatment effects) and sample selection. Fully parametric and partially parametric versions of the extended model are discussed. In the parametric version of the model, a full information maximum likelihood (FIML) approach to estimation is introduced. Under the correct model specification the FIML estimator is efficient but computationally burdensome. For the relatively robust partially parametric version of the model I develop a two-stage method of moments (TSM) estimator. The TSM estimator is a nonlinear least-squares analog to the popular Heckman (1976, 1979) estimator and therefore avoids the computational requirements of FIML estimation. A nonlinear weighted least-squares (NWLS) estimator is offered for the fully parametric case. The NWLS estimator is computationally efficient relative to FIML estimation, and statistically efficient relative to the TSM estimator. For illustrative purposes the TSM and NWLS estimators are applied to the estimation of a regression model with household trip frequency as the dependent variable and a potentially endogenous dummy variable indicating vehicle ownership among the regressors.