July 2, 2004
Sven H. Sinclair and Kent A. Smetters
A new explanation is offered for the thin private market for individual annuities in the United States. Individuals face a risk of health shocks which simultaneously cause large uninsured expenses and shorten the life expectancy. The value of a life annuity then decreases at the same time as the need for cash increases, undermining its effectiveness in providing financial security. When the risk of such health shocks is substantial, it is no longer optimal for risk-averse individuals with uncertain life spans to hold all of their wealth in life annuity form, even if annuity contracts are reversible, and bequest motives, transaction costs and adverse selection are absent.
A dynamic programming model is used to compute the demand for annuities, under conditions involving health shocks, in an overlapping-generations setting calibrated to resemble the United States economy. The model is used to estimate the demand for life annuities and the relative significance of the factors that affect the demand: health shocks, Social Security, bequest motives and premium loads. It is useful for understanding various modes of drawing down retirement savings, measuring the extent of uninsured health-related risks (particularly long-term care expenses) and providing a consistent framework for analysis of various approaches to insure such risks.