Gregorio Impavido, Craig Thorburn, Mike Wadsworth should occupy a larger portion in household wealth than what is observed empirically. The next section attempts to reconcile these statements with country specific factual evidence and by considering possible relaxations of the assumptions made in Yaari (1965).

# **_I.D Is low annuity demand really a puzzle?_**

The prediction of the lifecycle model that full annuitization is optimal in the absence of a bequest motive relies on a series of strong assumptions. One possible reaction to the so called “puzzle” is to posit that the assumptions in Yaari (1965) are too strong for the prediction to be plausible. However, attempts to relax these assumptions have not provided a definite answer to the issue either. The literature summarized in this section provides very ambiguous answers on whether the annuity puzzle exists or not.

Various reasons not necessarily independent from one another have been identified for the low demand for annuities. Among these are low subjective life expectancy or myopia, adverse selection and high load factors, incomplete markets, pre-annuitized wealth, precautionary savings, and bequest motives.

The retirement risk survey conducted by the Society of Actuaries (SOA 2001) finds that men tend to underestimate average life expectancy at age 65, currently 81 to 83 years of age depending on the population projected. Women estimate their life expectancy only slightly better than men. Roughly half the women in the sample underestimate the average 65-year-old female’s life expectancy, which is 85 to 86 years of age. In general, only about one-third of retirees and pre-retirees are on target or err on the side of overestimating average life expectancy at age 65. Retirees and those nearing retirement age (age 45 and over) underestimate the life expectancy of the average 65 year old.

Adverse selection and loads are factors explaining money’s worth ratios below unity and are also considered to explain the annuity puzzle. The source of adverse selection lies in the difference between annuitant and population average mortality tables. Annuitants as a group tend to live longer than the population average. The presence of asymmetric information in insurance markets implies that individuals self select themselves on the basis of private information about their longevity. This form of adverse selection can explain the high load factors in certain markets. For instance, Fong (2002) finds that in Singapore, adverse selection explains around 13% of the cost of longevity insurance and she concludes that a policy option would be to mandate annuitization to avoid the adverse selection problem. Murthi _et al_ . (1999), in their price analysis of UK annuities conclude that the main source of reduction in annuity yields in that market is given by adverse selection that however, are not translated in high load factors. Finkelstein and Poterba (2002) find that private information not only affects the decision to participate in the insurance market, but also affects the choice of annuity products. For instance, annuitants who tend to live longer, also tend to select backloaded products. Finally Warshwsky (1988) finds that an average load factor of 29 cents applies to the US annuity market but however, he concludes that this would not be sufficient to prevent individuals from buying annuities and that the low level of demand should be explained by other factors like bequest motives.

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