We examine the effects of introducing actuarially fair annuity markets into an overlapping generations model of endogenous growth. The complete annuitisation of agents' wealth is not, in general, dynamically optimal; the degree of annuitisation that is dynamically optimal depends nonmonotonically on the expected length of retirement and on the pay-as-you-go social security tax rate. The government has an incentive to restrict the availability of actuarially fair annuities contracts, and can often move the economy from a pay-as-you-go to a fully-funded social security system via voluntary contributions to a government sponsored, actuarially fair pension today accompanied by reductions in social security taxes tomorrow.
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Pecchenino et al. (1997) studied this question.