The Causal Effect of Fertility on Female Labor Supply: Evidence from Taiwanese Son Preference

Abstract

Economic models of home production predict a tradeoff between a mother's fertility and her labor supply. Recent empirical work suggests that while these outcomes are correlated, the causal impact is negligible when estimated through Instrumental Variables (sex preference, twinning). I find that in Taiwan, intense son preference produces 2SLS estimates of a mother's labor response that are larger than OLS estimates, suggesting that previous IV analyses may focus on mothers with lower than average costs to childbearing. I present a model of a mother's joint determination of fertility and labor supply allowing for unobserved heterogeneity in both the benefits and costs of children. The model predicts that IV estimates will rise in proportion to the intensity of the instrument, and provides a framework for assessing the bias in OLS and IV estimators. Estimation of the structural model predicts that the average causal effect of a third child on a mother's probability of working is -10 percent in Taiwan and -12 percent in the United States for mothers between 34 and 36 years of age. The results imply that the IV estimate for the US (-7 percent) is lower than the average causal effect, but the IV estimate in Taiwan (-11 percent) is slightly larger than the average causal effect. I present a set of simulations to consider how IV estimates derived from simulated data change when the strength of the instrument varies, and find that in both Taiwan and the US, weaker instruments provide estimates lower than the average causal effect, and stronger instruments yield estimates closer to the average causal effect.