Precautionary Saving and Accidental Bequests
Precautionary Saving and Accidental Bequests
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预防性储蓄和意外遗赠
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发表时间：
1985
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通讯作者：
Andrew B. Abel
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作者：
Andrew B. Abel
本文建立了一个简单的预防性储蓄和意外遗赠的一般均衡模型。这个模型被用来分析个人一生的不确定性对总消费和资本积累的影响。预防性储蓄需求的产生是因为个人消费者事先不知道自己的死亡日期，如果他的寿命比预期的长，他希望避免低水平的消费。这种预防性储蓄的一个含义是，当死亡确实发生时，消费者通常持有一些财富，然后以意外遗赠的形式传给他的继承人。即使所有的消费者都有相同的事前死亡概率，也会有一些死亡日期的内部变化;因此，消费者在一个队列中留下的遗赠会有一个非退化分布。这一代人留下的遗产的非退化分布导致了后代财富、消费和遗产分配的变化。劳伦斯·科特利科夫（Laurence Kotlikoff）和劳伦斯·萨默斯（Lawrence Summers）（1981）在报告中指出，美国家庭财富的80%是继承财富。对这一发现的一种解释是，没有遗赠动机的简单生命周期模型并不足以描述美国的储蓄行为，但我提出的模型表明，自私消费者的意外遗赠可以占总财富的一个潜在的相当大的比例。虽然遗产的一部分，特别是富人的遗产，无疑是一个明确的遗赠动机的结果，偶然的遗产也发挥了作用，在代际转移的财富，以及在代内的财富变化。为了集中讨论意外遗赠的作用，我特意从效用函数的说明中排除了遗赠动机。寿命不确定性对个人消费行为的影响最早是在Menachem Yaari（1965）的一篇开创性论文中正式研究的。Yaari的模型为几乎所有后续关于不确定寿命的工作提供了基本框架，包括Nils Hakansson（1969）、Stanley Fischer（1973）、Robert巴罗和James Friedman（1977）、大卫·莱夫哈里（David Levhari）和伦纳德·米尔曼（Leonard Mirman）（1977）以及科特利科夫（Kotlikoff）和阿维亚·斯皮瓦克（Avia Spivak）（1981）的著名论文。然而，所有这些论文都集中在个人的消费决策上，而忽略了意外遗赠对这些意外遗赠的接受者行为的影响。[2]正如本文将在不同的地方展示的那样，经济环境的变化会对总体行为产生影响，这与对个人行为的影响截然不同，因为遗赠会进行内生调整。* 经济学系，哈佛大学，剑桥，MA 02138。本文是“不确定寿命的遗产和社会保障”的修订版，NBER工作文件第1372号，1984年6月。我感谢奥利维耶·布兰查德、约翰·伯比奇、克里斯托弗·卡瓦纳、罗伯特·克洛、斯坦利·菲舍尔、本杰明·弗里德曼、埃尔哈南·赫尔普曼、默文·金、清泷信弘、劳伦斯·科特利科夫、罗伯特·麦克唐纳、詹姆斯·佩桑多、胡里奥·罗滕贝格、劳伦斯·萨默斯、拉尔斯·斯文森、马克·沃森和杰弗里·沃尔克维茨，感谢他们与我进行了宝贵的交谈和通信。我还要感谢在波士顿大学、哥伦比亚大学、康奈尔大学、联邦储备委员会、哈佛大学、爱荷华州大学、麻省理工学院、明尼苏达大学、蒙特利尔大学、国家经济研究局、北卡罗来纳州州立大学、沃顿商学院和耶鲁大学举办的研讨会的与会者，以及两位匿名推荐人，感谢他们提出的有益意见。我还要感谢国家科学基金会的财政支持。[1]在完美的年金和人寿保险市场中，可能存在也可能不存在遗赠（取决于遗赠动机的存在与否），但不会存在意外遗赠。[2]科特利科夫和斯皮瓦克关注的是家庭在提供（不完全）年金市场方面的作用，但没有建立一个完整的世代重叠模型，在这个模型中，遗赠的分配是内生决定的。
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.