Testing the quantity–quality model of fertility: Estimation using unrestricted family size models

We examine the relationship between child quantity and quality. Motivated by the theoretical ambiguity regarding the sign of the marginal effects of additional siblings on children's outcomes, our empirical model allows for an unrestricted relationship between family size and child outcomes. We find that the conclusion in Black, Devereux, and Salvanes (2005) of no family size effect does not hold after relaxing their linear specification in family size. We find nonzero effects of family size in ordinary least squares estimation with controls for confounding characteristics like birth order and in instrumental variables estimation instrumenting family size with twin births. Estimation using a unrestricted specification for the quality–quantity relationship yields substantial family size effects. This finding suggests that social policies that provide incentives for fertility should account for spillover effects on existing children.