By Ben Heijdra, Jochen Mierau and Laurie Rijnders
We construct a tractable discrete-time overlapping generations model of a closed economy and use it to study government redistribution of accidental bequests and private annuities in general equilibrium. Individuals face longevity risk as there is a positive probability of passing away before the retirement period. We find non-pathological cases where it is better for long-run welfare to waste accidental bequests than to give them to the elderly. Next we study the introduction of a perfectly competitive life insurance market offering actuarially fair annuities. There exists a tragedy of annuitization: although full annuitization of assets is privately optimal it is not socially beneficial due to adverse general equilibrium repercussions.
My intuition was that annuities are privately beneficial but underused because of lack of knowledge about them and some innate fears people have about wasting savings if they die early, that is, annuities should be encouraged. This paper shows that we should discourage them. The reason is that the presence of annuities discourages savings, and the government is then better off throwing away accidental bequests.