This dissertation consists of two essays examining formal and informal long term health insurance markets. The first essay analyzes heterogeneity of Long-Term Care Insurance policyholders in their lapse decision, and how their ex-ante and ex-post subjective beliefs about the probability of needing Long-Term Care affect their lapse decisions. In this essay, I develop a model of lapse decision in a two-period insurance framework with a Bayesian learning process and implement several empirical specifications of the model using longitudinal data from the Health and Retirement Study. The results show that policyholders\u27 ex- ante point predictions of their probabilities and their uncertainties about them have a persistent but declining impact on lapse decisions. Those who believe that their risk is higher are indeed more likely to remain insured. However, as their uncertainties surrounding their ex-ante point predictions increase, their chances of lapsing increase regardless of their initial perception biases. These results are heterogeneous across cohorts and policyholders and, in particular, show that those in the older group near the average age of Nursing Home entry have a precise prediction of their risk levels compared to the younger cohort. Policy simulations show that a more informed initial purchase decision reduces the chance of lapsing down the road.
The second essay examines the extent to which informal risk sharing arrangement provides insurance against health shocks. I develop a comprehensive model of informal risk sharing contract with two-sided limited commitment which extends the standard model to a regime with the following features. Information regarding the nature of realized health shocks is imperfect and individuals\u27 health capital stock serves as a storage technology and is a factor of production. The theoretical results show that, in such a regime, Pareto optimal allocations are history dependent even if participation constraints do not bind. I perform numerical analysis to show that risk sharing against health shock is less likely to be sustainable among non-altruistic individuals with different levels of biological survival rates and health capital productivity. The results also show that optimal allocations vary depending on the set of information available to individuals. Using panel data of households from villages in rural Ethiopia, I test the main predictions of the theoretical model. While there is negative history dependence in transfers among non-altruistic partners, history dependence is positive when risk sharing is along bloodline and kinship. However, neither short-term nor long-term health shocks are insured through informal risk sharing arrangements among non-altruistic individuals