Family size, birth order, and tests of the quantity-quality model

Recent empirical studies challenge the quantity-quality (Q-Q) trade-off of children modeled by Becker and Lewis. In the ordinary least squares (OLS) estimates, the effect of family size on child outcomes is frequently estimated with birth order controls. In a group of instrumental variable (IV) estimates, the family size effect is estimated only for low-parity children. We show that existing studies using the above two specifications do not identify the family size effect on average child quality and do not contradict the Becker-Lewis Q-Q theory.