The Rouwenhorst method of approximating stationary AR(1) processes has been overlooked by much of the literature despite having many desirable properties unmatched by other methods. In particular, we prove that it can match the conditional and unconditional mean and variance, and the first-order autocorrelation of any stationary AR(1) process. These properties makes the Rouwenhorst method more reliable than others in approximating highly persistent processes and generating accurate model solutions. To illustrate this, we compare the performances of the Rouwenhorst method and four others in solving the stochastic growth model and an income fluctuation problem. We find that (i) the choice of approximation method can have a large impact on the computed model solutions, and (ii) the Rouwenhorst method is more robust than others with respect to variation in the persistence of the process, the number of points used in the discrete approximation and the procedure used to generate model statistics.

We consider a life-cycle model with idiosyncratic risk in earnings, out-of-pocket medical and nursing home expenses, and survival. Partial insurance is available through welfare, Medicaid, and social security. Calibrating the model to the United States we show that savings for old-age, out-of-pocket expenses account for 13.5 percent of aggregate wealth, half of which is due to nursing home expenses; cross-sectional out-of-pocket nursing home risk accounts for 3 percent of aggregate wealth and substantially slows down wealth decumulation at older ages; and all newborns would benefit if social insurance for nursing home stays was made more generous. (JEL D91, E21, E62, H51, I13, I18, I38, J14)

Poor heath, large acute and long-term care medical expenses and spousal death are significant drivers of impoverishment among retirees. We document these facts and build a rich overlapping generations model that reproduces them. We use the model to assess the incentive and welfare effects of U.S. Social Security and means-tested social insurance programs, such as Medicaid and food stamp programs, for the aged. We find that U.S. means-tested social insurance programs for retirees provide significant welfare benefits for all newborn. Moreover, when means-tested social insurance benefits are of the scale in the U.S., all newborn prefer that Social Security be removed. Finally, we find that the current scale of means-tested social insurance in the U.S. is about right in the following sense. If we condition on the current Social Security program, the benefits of increasing means-tested social insurance are small or negative.

A model with leisure production and endogenous retirement is used to explain declining labor force participation rates of elderly males. The model is calibrated to cross-sectional data on labor force participation rates of U.S. males by age, their drop in consumption, and leisure good expenditure share in 2000. Running the calibrated model for the period 1850-2000, a prediction of the evolution of the cross-section is obtained. The model accounts for more than 87% of the increase in retirement of men over 65. The increase in retirement is driven by rising wages and falling prices of leisure goods.

We consider a life-cycle model with idiosyncratic risk in labor earnings, out-of-pocket medical and nursing home expenses, and survival. Partial insurance is available through welfare, Medicaid, and social security. Calibrating the model to the United States, we find that 12 percent of aggregate savings is accumulated to finance and self-insure against old-age health expenses given the absence of complete public health care for the elderly and that nursing home expenses play an important role in the savings of the wealthy and on aggregate. Moreover, we find that the aggregate and distributional effects of public health care provision are highly dependent on the availability of other programs making up the social insurance system. JEL classification: E21, H31, H53, I18, I38