We develop a general equilibrium stochastic OLG model with heterogenous households. Households differ with respect to their productivity. Productivity depends stochastically on parents' unobservable investment in their child's human capital and an aggregate productivity shock. We introduce a PAYG social security system that conditions benefits on the aggregate wage sum and on the wage of one's child. We analyze the effects of such a social security system on the endogenous distribution of human capital and compare it to real world systems, which typically do not condition benefits on the wages of one's children. We decompose the effects of social security on the investment in human capital into an incentive effect, an insurance effect, a redistributive effect and a general equilibrium effect. Furthermore, we discuss the effects of social security on the long run distribution of human capital. Our approach suggests a novel role for a well-designed social security system: it can foster human capital accumulation and act as intragenerational insurance against human capital risk.