Comment on Kotlikoff, Shoven, and Spivak

In the absence of perfect annuity markets, individual consumers generally undertake precautionary saving to provide resources for their future consumption in the event that they live longer than expected. Kotlikoff, Shoven, and Spivak (in this issue) (hereafter KSS) have provided us with a well-conceived and well-executed study of the effects of various annuity arrangements on individual and aggregate saving in the presence of lifetime uncertainty. Each of these authors has had a long-standing interest in this area, and their current paper reflects their accumulated expertise. Their results indicate that a potentially sizable fraction of U.S. household wealth represents precautionary saving resulting from the absence of perfect annuity markets. The strategy of the KSS paper is to develop simple models of individual saving behavior on the basis of utility maximization and then to aggregate the behavior of individuals both intraand intertemporally. By comparing the results of models that differ in the specification of bequest motives and opportunities for creating annuities, KSS provide insights about the effects of various annuity arrangements on saving and capital accumulation. Although the models are all conceptually simple, analytic solutions cannot be obtained in many cases. Therefore, KSS provide numerical solutions to their models. In addition, because the models are conceptually