A Comparison Of Discrete And Parametric Methods For Continuous-State Dynamic Programming Problems

This paper presents a dynamic model of the joint labor/leisure and consumption/saving decision over the life cycle. Such a dynamic model provides a framework for considering the important policy experiments related to the reforms in Social Security. We address the role of labor supply in a life cyle utility maximization model formally, building upon recent work by Low (1998), and extending the classical optimal lifetime consumption problem under uncertainty first formalized in Phelps (1962) and later in Hakansson (1970). We begin by solving the finite horizon consumption/saving problem analytically and numerically and compare the two solutions. We also simulate this benchmark model. Once the labor choice is considered, the stochastic dynamic programming utility maximization problem of the individual is solved numerically, since analytical solutions are infeasible when the individual is maximizing utility over consumption and leisure, given non-linear marginal utility. We show how such a model captures changes in labor supply over the life cycle and that simulated consumption and wealth accumulation paths are consistent with empirical evidence. We also present a model of endogenously determined annuities in a consumption/saving framework under capital uncertainty and in the presence of bequest motives.