Title: Designing an Intergenerational Welfare State when Fertility is Endogenous
Authors: J.Ignacio Conde-Ruiz (Universitat Pompeu Fabra and FEDEA ), Eduardo L. Gimenez (Universidade de Vigo) and Miguel Perez-Nievas (Universidade de Santiago)
In an overlapping generation model with endogenous fertility and incomplete markets for investment in human capital we design a set of intergenerational welfare transfers which are able to replicate in a decentralized way the set of centralized efficiency allocations (static and dynamic). The intergenerational transfers that we propose are simply public education and social security systems. The idea is to link both systems in order to replicate the set of efficiency allocations. As in Montes and Boldrin (2000) this “efficiency link” is captured by equalizing the rate of return of the public education (implicitly characterized by the levels of both transfers programs) and the market rate of return of the physical capital. Contrary to the previous authors, we prove that in our context with endogenous fertility the return of investment of human capital (the pension system) should take into account not only the investment in education (quality of human capital) but also the cost of bearing children (quantity of human capital). In this context, the pension that an individual receives when old, can be re-interpreted as the return of the investment on human capital in the next generation according to a two-part tariff system: a fix part (positive or negative depending on how much the parents value the children) for each descendant (quantity) and a variable part for the amount of resources invested on them (quality). Finally, it is interesting to point out that the results of this model may recommend to pay more pension to individuals with more descendants, but contrary to other papers, we justify this policy in terms of efficiency (normative), instead of a way to encourage the birth rate (positive).