Precautionary Saving and Accidental Bequests

This paper presents a simple general equilibrium model of precautionary saving and accidental bequests. This model is used to analyze the implications of individual lifetime uncertainty for aggregate consumption and capital accumulation. A precautionary demand for saving arises because an individual consumer does not know in advance the date at which he will die, and he wants to avoid low levels of consumption in the event that he lives longer than expected. An implication of this precautionary saving is that when death does occur, the consumer is generally holding some wealth, which is then passed on to his heirs in the form of an accidental bequest. Even if all consumers have the same ex ante mortality probabilities, there will be some intracohort variation in the date of death; consequently there will be a nondegenerate distribution of bequests left by consumers in a cohort. This nondegenerate distribution of bequests left by one generation induces variation in the distributions of wealth, consumption, and bequests of subsequent generations. The importance of bequests in aggregate saving has been established by Laurence Kotlikoff and Lawrence Summers (1981) who reported that 80 percent of U.S. household wealth is inherited wealth. One interpretation of this finding is that the simple life cycle model without bequest motives is an inadequate description of saving behavior in the United States, but the model I present demonstrates that accidental bequests by selfish consumers can account for a potentially sizeable fraction of aggregate wealth. Although some part of bequests, especially by the wealthy, undoubtedly results from an explicit bequest motive, accidental bequests also play a role in the intergenerational transfer of wealth as well as in the intragenerational variation in wealth. In order to focus on the role of accidental bequests, I purposely exclude a bequest motive from the specification of the utility function. ' The effects of lifetime uncertainty on individual consumption behavior were first examined formally in a seminal paper by Menachem Yaari (1965). Yaari's model provided the basic framework for virtually all subsequent work on uncertain lifetimes including well-known papers by Nils Hakansson (1969), Stanley Fischer (1973), Robert Barro and James Friedman (1977), David Levhari and Leonard Mirman (1977), and Kotlikoff and Avia Spivak (1981). However, all of these papers focused on the consumption decision of an individual and ignored the effect of accidental bequests on the behavior of the recipients of these accidental bequests.2 As will be shown at various points in this paper, changes in the economic environment can have effects on aggregate behavior which differ sharply from the effects on individual behavior because of the endogenous adjustment of bequests. The effects of *Department of Economics, Harvard University, Cambridge, MA 02138. This paper is a revised version of "Bequests and Social Security with Uncertain Lifetimes," NBER Working Paper No. 1372, June 1984. I thank Olivier Blanchard, John Burbidge, Christopher Cavanagh, Robert Clower, Stanley Fischer, Benjamin Friedman, Elhanan Helpman, Mervyn King, Nobuhiro Kiyotaki, Laurence Kotlikoff, Robert McDonald, James Pesando, Julio Rotemberg, Lawrence Summers, Lars Svensson, Mark Watson, and Jeffrey Wolcowitz for valuable conversations and correspondence. I also thank the participants in seminars at Boston University, Columbia University, Cornell University, Federal Reserve Board, Harvard University, University of Iowa, MIT, University of Minnesota, University of Montreal, National Bureau of Economic Research, North Carolina State University, the Wharton School, and Yale University, and two anonymous referees for their helpful comments. I also thank the National Science Foundation for financial support. 1 In the presence of perfect annuity and life insurance markets, there may or may not be bequests (depending on the presence or absence of a bequest motive), but there would be no accidental bequests. 2 Kotlikoff and Spivak focus on the role of the family in providing an (incomplete) annuities market, but stop short of a full-scale overlapping generations model in which the distribution of bequests is determined endogenously.