A comparison of alternative methods to model endogeneity in count mod- els. An application to the demand for health care and health insurance choice

Several estimators have been suggested to tackle the problem of endogenous regressors and selectivity in count regression models. They differ in the structure and the degree of parameterization of the underlying models. The estimation of health services utilization conditional on the choice of different forms of health insurance provides a classical example of such problems. In Switzerland, basic health insurance is mandatory and each individual is insured separately. The insurance premium varies by region of residence but is independent of income and risk. The insured face a minimal annual deductible. Annually, they are given a choice of higher deductibles to reduce their insurance premium by a regulated percentage. The choice of a higher deductible sets incentives for a more cautious utilization of health services. Clearly, the choice is made based on expected health service utilization. The effect of the choice of a higher than the minimal deductible on the number of physician visits is analyzed. A matching estimator, a GMM estimator, two-stage method of moments estimators which account for selectivity and endogenous switching count regression models are applied to data from the 1997 Swiss Health Survey. Incentive-induced behavioral changes are disentangled from selection effects. The main finding is that most of the observed lower utilization for individuals with a high insurance deductible is caused by self-selection of individuals into the respective insurance contracts which either differ in their preferences or are healthier in unobserved aspects of their health status.