**DISCUSSION PAPER PI-0307**

**Annuities and Individual Welfare**

*Thomas Davidoff, Jeffrey Brown and Peter Diamond*

**ABSTRACT**

This paper advances the theory of annuity demand. First, we derive

sufficient conditions under which complete annuitization is optimal,

showing that this well-known result holds true in a more general setting

than in Yaari (1965). Specifically, when markets are complete, sufficient

conditions need not impose exponential discounting, intertemporal separability

or the expected utility axioms; nor need annuities be actuarilly fair, nor
longevity

risk be the only source of consumption uncertainty. All that is required is
that

consumers have no bequest motive and that annuitites pay a rate of return
for

survivors greater than those of otherwise matching conventional assets, net
of

administrative costs. Second, we show that full annuitization may not be optimal

when markets are incomplete. Some annuitization is optimal as long as conventional

asset markets are complete. The incompleteness of markets can lead to zero

annuitization but the conditions on both annuity and bond markets are stringent.

Third, we extend the simulation literature that calculates the utility gains
from

annuitization by considering consumers whose utility depends both on present

consumption and a "standard-of-living" to which they have become accustomed.

The value of annuitization hinges critcally on the size of the initial standard-of-living

relative to wealth.