This paper studies the effects of health shocks on the demand for health insurance and annuities, precautionary saving, and the welfare implications of public policies in a simple life-cycle model. I show that when the health shock simultaneously increases health expenses and reduces longevity, the following results can be obtained via closed-form solutions. First, utility-maximizing agents would neither fully insure their uncertain health expenses nor fully annuitize their wealth, even in the absence of market frictions and bequest motives. Second, the effect of uncertain health expenses on precautionary saving may be smaller than what has been found in previous studies. Under certain conditions, uncertain health expenses may even reduce precautionary saving. Third, mandatory health insurance (e.g. public health insurance) tends to benefit the poor more, while mandatory annuitization (e.g. public pen- sion) is more likely to favor the rich. A simple numerical application of the model to the US long term care (LTC) insurance market suggests that the simultaneous effect of health shock on health expenses and longevity is a quantitatively important reason why agents (especially the rich) do not purchase more private LTC insurance.
Saving Annuities Health Insurance Social Security Medicare