Endogenous treatment effects for count data models with endogenous participation or sample selection

We propose an estimator for models in which an endogenous dichotomous treatment affects a count outcome in the presence of either sample selection or endogenous participation using maximum simulated likelihood. We allow for the treatment to have an effect on both the participation or the sample selection rule and on the main outcome. Applications of this model are frequent in-but not limited to-health economics. We show an application of the model using data from Kenkel (Kenkel and Terza, 2001, Journal of Applied Econometrics 16: 165-184), who investigated the effect of physician advice on the amount of alcohol consumption. Our estimates suggest that in these data, a) neglecting treatment endogeneity leads to a wrongly signed effect of physician advice on drinking intensity, b) accounting for treatment endogeneity but neglecting endogenous participation leads to an upwardly biased estimate of the treatment effect, and c) advice affects only the drinking-intensive margin but not drinking prevalence.