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Meier, Volker; Wrede, Matthias (2005): Pension, fertility, and education. CESifo Working Paper, 1521
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A pay-as-you-go pension scheme is associated with positive externalities of having children and providing them with human capital. In a framework with heterogeneity in productivity, and stochastic and endogenous investment in fertility and education, we discuss internalization policies associated with child benefits in the pension formula. The second-best scheme displays both a benefit contingent on the contributions of children and a purely fertility-related component.

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