Exiting the health insurance market as a rational choice: Demand for health insurance in a learning model

It is widely believed that individuals exit the insurance market due to adverse shock to their income, insurance premium or both. This paper studies the role of imperfect information and subsequent learning about health endowment on individuals’ decisions to continue health insurance coverage. We show that rational individuals may exit the insurance market even in the absence of adverse shocks to income and/or insurance premium. We assume that unknown health endowment and age are the only determinants of losses due to expenditures on medical care. Individuals receive noisy signals about their endowment by observing these losses as they advance in age. Following Jovanovic (1982), we develop a model in which individuals incorporate this new information in the decision making process by using Bayesian Learning to update their beliefs about their health. Favorable new information diminishes the valuation of continuing insurance coverage; similarly, unfavorable new information increases its valuation. As individuals grow older, they accumulate additional information, which increases the precision of their beliefs. Beliefs that are more precise react imperceptibly to new information. Therefore, new information influences the beliefs of young people more than of old. Moreover, for a given belief, increased precision induces a mean preserving decrease in risk, reducing the demand for health insurance. Since precision increases as individuals age, we call it the learning effect of age. The other effect of growing older is the biological depreciation of health, which increases the size of loss. This increases the demand for health insurance and we call it the aging effect of age. Consequently, there is a continuous trade off between the gain in precision and increase in loss as individuals grow older. Bayesian Learning implies that the learning effect weakens with age. However, biological depreciation strengthens with age. Hence, we expect that the aging effect will override the learning effect at a unique point over the life span of an individual. Thus, unlike previous studies, we predict that controlling for changes in income, premium and new information, middle-aged individuals are least likely to renew insurance coverage. In the second part of the paper, we use a panel component of MEPS data for 1997-2000 to test our model. We select individuals who are single, non-elderly, ineligible for public insurance and privately insured in the reference period and estimate their probability of insuring in the subsequent period. We construct a measure for new information and find that the likelihood of continuing coverage increases for adverse surprises. This relationship between new information and continuing coverage is stronger for young people than for old. We find that for the young, the probability of continuing coverage increases by 5.33 % points (95%CI 0.39, 13.60 % points) and for the old by 0.37 %points (CI -1.62, 1.20 % points), when new information is changed from 5th percentile to 95th percentile. We also find that the impact of age on the likelihood of continuing insurance coverage is non-monotonic. It decreases until 37 years of age (95%CI 34, 39 years of age), and then increases, as predicted by the theoretical model. Thus, we find some empirical evidence that unanticipated new information affects the demand for insurance and the interaction between learning and biological depreciation as individuals age.