Annuities and Individual Welfare

Thomas Davidoff, Jeffrey Brown and Peter Diamond


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.

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