A Conceptual Framework For Retirement Products: Risk Sharing Arrangements Between Providers And Retirees has been decreasing during the last decade, suggesting improved efficiency of the market. The WE of annuities for a 65 years old man, with no pre-annuitized wealth and different assumptions on real interest rate, risk aversion and if utilty is considered pre or after-tax, is between 60% and 70% of non annuitized wealth in a world with certain inflation. The same measure is between 70% and 80% when consumers have 50% of wealth preannuitized. The same figures are slightly higher in a world of uncertain inflation.

Brown _et al_ . (2001) use the MWR and AEW measures to valuate nominal and real (retail-price indexed) single premium, immediate, life annuities in the UK, as well as real<sup>25</sup> and variable annuities in the US. Differently from Mitchell _et al_ . (1999), the authors use cohort mortality tables for the population as a whole and report always pretax valuations. They find that: 1) similarly to the Mitchell _et al_ . (1999) for the US, there exists a substantial variation in the annuity benefits paid by different insurers; 2) for 65 years old male in the UK, nominal annuities with average payouts are valued at 91% of the annuity premium, while real annuities are valued at 85% of the annuity premium; 3) for a 65 years old male in the US, nominal annuities with average payouts are valued at 86% of the annuity premium,<sup>26</sup> while ILONA real annuities are valued at 70% of the annuity premium, a good 15 percentage points lower than in the UK. The AEW for a 65 years old man in the US, with no pre-annuitized wealth and different assumptions on risk aversion, is between 150% and 200% of annuitized wealth, for real annuities, and 145% and 160% for nominal annuities. The same measures are between 133% and 181%, and 130% and 157%, respectively, when consumers have 50% of wealth pre-annuitized in real terms.

Finkelstein and Poterba (2002) evaluate the MWR of three types of monthly, single life annuity products in the UK: 1) nominal; 2) real; and 3) 5% escalating annnuities. By using population mortality tables and annuities with average payouts, the authors report that for a 65 years old male, the average MWR is 90.1%, 82.2%, and 85.4% respectively for nominal, real and 5% escalating annuities in the compulsory annuity market. In the voluntary annuity market the same MWRs are 86.1%, 79.1% and 80.7%, respectively.

The results by Mitchell _et al_ . (1999) indicate that despite a 65 years old man would expect to receive, in present value terms, between 81% and 93% of paid premiums for an annuity, his risk aversion make him value the insurance contract so much that he would be prepared to forego up to 40% of initial wealth to have access to the annuity market. The results by Brown _et al_ . (2001) are complementary as they show that the same individual would need non-annuitized wealth starting in the neighborhood of 145% of his annuitized wealth to attain the same level of utility. Finally, the higher the level of risk aversion the lower the WE (the higher the AEW) generally needed to attain the same level of utility.

The review of the literature on the value of annuities, similarly to the theoretical literature based on the life cycle hypothesis, seems to indicate that consumers would be ready to pay a substantial premium to own these assets. Alternatively, that these assets

> 25 The real annuities valued in Brown _et al_ .  (2001) are a CPI-indexed annuity sold by the Irish Life Company of North America (ILONA).

> 26 Similarly, Poterba and Warshawsky (2001) report that in 1998 the average MWR for a 65 years old male was 84%, using population mortality tables.

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