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Mortality Risk and Bequests

Michael D. Hurd

Abstract

I analyze and estimate an extended life cycle model of consumption in which utility depends on the path of consumption and bequests. The theoretical section gives conditions under which consumption and wealth will decline with age. An important determinant is a boundary condition on the consumption path caused by annuities. Using panel data from the Retirement History Survey on the wealth of the retired elderly, I estimate the parameters of the model, which are the degree of mortality risk aversion, the subjective time rate of discount, and the marginal utility of bequests. The estimation method involves solving for the optimal consumption trajectory from the first-order conditions of the dynamic optimization, and from the boundary conditions. The results indicate that the consumption path is sensitive to variations in mortality rates, meaning that mortality risk aversion is moderate, and certainly much smaller than what is typically assumed in the literature. The marginal utility of bequests is small; therefore, desired bequests, which are estimated from model simulations, are small on average. Apparently most bequests are accidental, the result of uncertainty about the date of death. The parameter estimates imply that although consumption and wealth paths may rise at early ages, eventually they will fall as mortality rates become large. Falling wealth with age is confirmed in the raw data: average wealth holdings of the elderly decline with age, and the majority of individuals dissave as they age.