This paper develops the Finite Mixture Roy model for count variables and uses this semiparametric model to analyze the effect of supplemental Medigap private insurance on the demand for prescription drugs for the U.S. elderly unemployed Medicare population. The model is an extension of the Count Roy model, which produces unrealistic treatment effects when observed count patterns are consistent with finite mixtures. To estimate the numbers of components in the mixtures for individuals with and without Medigap, this paper adopts the random permutation sampler. The considered application motivates two additional features of the model. Specifically, the smoothly mixing regression approach is utilized to model the probabilities of the components, and a continuous instrumental variable is allowed to enter the treatment equation nonparametrically. Strong evidence is found that there are two components both in the treated and untreated states. These lower and higher utilization components are interpreted as relatively healthy and unhealthy groups. The estimated treatment effects show that Medigap insurance provides incentives to increase prescription drug utilization by 2%. The results are consistent with adverse selection.
