Stochastic Fertility, Moral Hazard, and the Design of Pay-As-You-Go Pension Plans

This article models a two-period overlapping generations economy in the steady state
where the realization of the quantity/quality number of children depends on an initial investment
in children and on a random shock. It shows that the implementation of the first-best
allocation, in which the effort level is publicly observable, requires a subsidy on the investment
in children. There should also be full insurance with respect to second-period consumption
and pensions must be invariant to the number of children. On the other hand, when investment is unobservable and one cannot subsidize it, the full insurance property
goes away. In this case, pensions must be linked positively to the number of children.