A Common Thread Linking the Design of Guarantee and Non-Escalating Payments of Public Annuities

Motivated by Diamond (2004) and the experiences in economies adopting the defined-contribution pension system, we study public annuities in the presence of survival probability heterogeneity. It is found that the annuitization-weighted average of survival probabilities is a useful measure of the severity of adverse selection. We then examine public annuities with a guarantee feature which bundles annuity income and bequeathable wealth components. We show that when the heterogeneity in survival probability is limited, the magnitude of guarantee proportion is irrelevant. On the other hand, an increase in the guarantee proportion mitigates adverse selection when the extent of heterogeneity is sufficiently large, because the share of annuity purchase by retirees with lower (resp. higher) survival probabilities is increased (resp. decreased). We also obtain a similar set of results for public annuities with non-escalating payments. Our results are useful in policy design regarding the number and form of public annuities: the decision about introducing public annuities or not is more important than the precise number of public annuity plans introduced; and the public annuity plan with survival-contingent payments only may be less preferred when compared with weaker alternatives with guarantee payments