Pensions with heterogenous individuals and endogenous fertility

We study the design of pension schemes when fertility is endogenous and parents differ in ability to raise children. Pay-as-you-go schemes require, under perfect information, a marginal subsidy on fertility to correct for the externality they create, equal pensions, and contributions that increase or decrease with the number of children. Under asymmetric information, incentive-related distortions supplement the Pigouvian subsidy. These require an additional subsidy or an offsetting tax depending on whether the redistribution is towards people with more or with less children. In the former case, pensions are decreasing in the number of children; otherwise, they are increasing.