Is full annuitization socially optimal

A seminal result Yaari holds that all pension savings should be in life-annuities. Annuities offer a higher return than standard assets and diversify mortality risk and therefore it is individually optimal to save in annuities only. This is a cornerstone result in the pensions literature where many attempts have been made to explain that individual savings in annuities is very low, the socalled annuity puzzle. But is the result that all pension savings should be in life-annuities also socially optimal? We show in a standard setting with fair annuities and dynamic efficiency that full annutization of all pensions saving is not socially optimal. Less than full annutization implies unintentional bequests and thus transfers from the old to the young, which is welfare improving under dynamic efficiency. Further, we show that no annutization can implement the Golden Rule capital stock level and analyse whether some annutization is socially optimal using a numerical analysis, which shows that it is the case under a wide range of parameter constellations.