The size of adverse selection and moral hazard effects in health insurance markets has important policy implications. For example, if adverse selection effects are small while moral hazard effects are large, conventional remedies for inefficiencies created by adverse selection (e.g., mandatory insurance enrolment) may lead to substantial increases in health care spending. Unfortunately, there is no consensus on the magnitudes of adverse selection vs. moral hazard. This paper sheds new light on this While both adverse selection and moral hazard effects of Medigap have been studied separately, this is the first paper to estimate both in an unified econometric framework. We develop an econometric model of insurance demand and health care expenditure, where adverse selection is measured by sensitivity of insurance demand to expected expenditure. The model allows for correlation between unobserved determinants of expenditure and insurance demand, and for heterogeneity in the size of moral hazard effects. Inference relies on an MCMC algorithm with data augmentation. Our results suggest there is adverse selection into Medigap, but the effect is small. A one standard deviation increase in expenditure risk raises the probability of insurance purchase by 0.037. In contrast, our estimate of the moral hazard effect is much larger. On average, Medigap coverage increases health care expenditure by 32%.