Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract 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 * An older and less complete version of this paper was previously circulated under the title "Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles". We thank for helpful comments and suggestions Terms of use: Documents in EconStor may

Using data from the Health and Retirement Survey and the Assets and Health Dynamics of the Oldest Old survey, we estimate the stochastic process that determines both the distribution and dynamics of health care costs. We find that the data generating process for log health costs is well represented as the sum of a white noise process and a highly persistent AR(1) process. We also find that the innovations to this process can be modelled with a normal distribution that has been adjusted to capture the risk of catastrophic health care costs. Simulating this model, we find that in any given year 0.1% of households receive a health cost shock with a present value of at least $125,000.

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.