Adverse Selection, Moral Hazard and the Demand for Medigap Insurance

This paper studies selection and moral hazard in the US Medigap health insurance market. It develops an econometric model for insurance demand and health care expenditure, in which the degree of selection is measured by the sensitivity of insurance demand to expected expenditure in uninsured state, conditional on other variables. The model allows for correlation between unobserved determinants of health care expenditure and the demand for insurance. To capture the complex shape of the distribution of the expenditure, a smooth mixture of Tobit models is employed (a generalization of the smoothly mixing regressions framework of Geweke and Keane (2007)). The model is estimated using a MCMC algorithm with data augmentation. The results suggest that conditionally on income, education, risk attitudes, cognitive ability, Financial planning horizon and longevity expectations there is an adverse selection into Medigap insurance, but the effect is small: a one standard deviation increase in the expected expenditure in uninsured state increases the probability of buying insurance by 0.01. The model allows estimation of the sample distribution of the moral hazard effect of Medigap on health care expenditure. On average, an insured individual spends about $1,600 more on health care than her uninsured counterpart and the size of this effect is lower for healthier individuals as well as for blacks and hispanics. The smooth mixture of Tobits model developed in this paper predicts the conditional expectation of health care expenditure in our data better than the five standard models selected for comparison, and also correctly captures the complex shape of the expenditure distribution.