This paper constructs a rich model of saving for retired single people. Our framework allows for bequest motives and heterogeneity in medical expenses and life expectancies. We estimate the model using AHEAD data and the method of simulated moments. The data show that out-of-pocket medical expenses rise quickly with both age and permanent income. For many elderly people the risk of living long and requiring expensive medical care is a more important driver of old age saving than the desire to leave bequests. Social insurance programs such as Medicaid rationalize the low asset holdings of the poorest. These government programs, however, also benefit the rich because they insure them against their worst nightmares about their very old age: either not being able to afford the medical care that they need, or being left destitute by huge medical bills.
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