Reconciling estimates of the long-term earnings effect of fertility

This paper presents novel methodological and empirical contributions to the child penalty literature. We propose a new estimator that combines elements from standard event study and instrumental variable estimators and demonstrate their relatedness. Our analysis shows that all three approaches yield substantial estimates of the long-term impact of children on the earnings gap between mothers and their partners, commonly known as the child penalty, ranging from 11 to 18 percent. However, the models not only estimate different magnitudes of the child penalty, they also lead to very different conclusions as to whether it is mothers or partners who drive this penalty - the key policy concern. While the event study attributes the entire impact to mothers, our results suggest that maternal responses account for only around one fourth of the penalty. Our paper also has broader implications for event-study designs. In particular, we assess the validity of the event-study assumptions using external information and characterize biases arising from selection in treatment timing. We find that women time fertility as their earnings profile flattens. The implication of this is that the event-study overestimates women's earnings penalty as it relies on estimates of counterfactual wage profiles that are too high. These new insights in the nature of selection into fertility show that common intuitions regarding parallel trend assumptions may be misleading, and that pre-trends may be uninformative about the sign of the selection bias in the treatment period.