The Impact of the Correlation between Health Expenditure and Survival Probability on the Demand for Insurance

This paper studies the effects of health shocks on the demand for health insurance and annuities, along with precautionary saving in a dynamic life-cycle model. I argue that when the health shock can simultaneously increase health expenses and reduce longevity, rational agents would neither fully insure their uncertain health expenses nor fully annuitize their wealth because the correlation between health expenses and longevity provides a self-insurance channel for both uncertainties. That is, when the agent is hit by a health shock (which simultaneously increases health expenses and reduces longevity), she can use the resources originally saved for consumption in the reduced period of life to pay for the increased health expenses. Since the two uncertainties partially offset each other, the precautionary saving generated in the model should be smaller than in a standard model without the correlation between health expenses and longevity. In a quantitative life-cycle model calibrated using the Medical Expenditure Panel Survey dataset, I find that the health expenses are highly correlated with the survival probabilities, and this correlation significantly reduces the demand for actuarially fair health insurance, while its impact on the demand for annuities and precautionary saving is relatively small