Gregorio Impavido, Craig Thorburn, Mike Wadsworth efficient intergenerational risk sharing arrangements in the presence of incomplete insurance markets. According to the authors, by promising old age support, children are in practice selling an annuity to their parents, the price of which is the bequest.

Empirical studies on the savings behavior of the elderly are central to the explanation of the role of bequests in annuity demand. The life cycle hypothesis predicts rapid dissaving of assets during retirement. However, Bernheim (1987) argues that while bequeathable assets tend to decrease after retirement, more general measures of wealth that include also annuitized wealth (from pensions) tend to remain constant. Annuitized wealth can be used to compensate the decrease in bequeathable assets thus supporting the assumption of the bequest motive. Indeed, Bernheim (1991) presents empirical evidence that savings during retirement age is affected by the wish to leave bequests. Hurd (1992) concludes that it is not necessary to invoke the bequest motive to justify slow dissaving during retirement age. In fact dissaving during old age is found to be similar among parents and non-parents providing no support for the bequest motive. The author argues that the absence of private annuity markets can explain slow dissaving in the face of longevity risk.

Laitner and Juster (1996) find substantial evidence of intergenerational altruism in a sample of TIAA-CREF annuitants, which represent relatively high income households. Kotlikoff and Summers (1981) also find high evidence of bequest motivated savings. However, Hurd (1986 and 1989) finds little evidence of intergenerational altruism. Altonji _et al_ . (1992) also test the relevance of the altruistic model that predicts that the distribution of consumption among different generations in the dynasty should be independent of the distribution of wealth. By using the panel study of income dynamics on parents and their children in the US, the authors strongly reject the prediction of the altruistic model. Despite observing that a selection bias may exist in the data as wealthier families (more likely to be altruistic and leave bequests) are excluded from the database, they conclude that altruism does not affect consumption, and hence savings, during the old age.<sup>28</sup> However, similar conclusions regarding the relevance of the altruistic model in explaining bequests motives are reached by Wilhelm (1996) by using the Estate Income Tax Match database. This covers only the wealthiest households in the United States and therefore excludes those households unlikely to be altruistic.

Finally, two papers, that attempt a direct relaxation of the Yaari (1965) assumptions are here considered.

Petrova (2002) considers the possibilities that status dependent utility may affect the demand for annuity and that individuals systematically overestimate their life expectancy.<sup>29</sup> The author, using the Health Retirement Study for the US, finds that

> 28 Notice that this is not a rejection of the hypothesis of altruistic transfers among households but only  a rejection that the altruistic motives affect savings behavior and hence bequests during old age.  In fact, altruistic transfers can take the form of intravivos transfers, like support for education and other in kind transfers earlier in the life of heirs, aimed at offsetting liquidity constraints among heirs (Cox (1990) and Cox and Jappelli (1990)).  However, Altonji _et al_ .  (1997) focus on the more general altruistic assumption and do not find any evidence of altruism in the PSID data.

> 29 Petrova’s (2002) argument being that, given asymmetries of information between annuity providers and buyers regarding lifespan, a positive bias in individuals’ subjective life expectancy would increase private annuity demand.

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