The causal impact of children? Rethinking the identification and estimation of child penalties

A fast-growing literature estimates child penalties -the impact of parenthood on the labor market outcomes of mothers relative to fathers -using event study design. This paper clarifies the identification assumption underlying the most commonly used specification with event time, year, and age fixed effects, and shows that this approach is prone to bias in the presence of heterogeneity by age and calendar year, even under valid identification. I then propose an unbiased estimator, using the same identification framework. Applied to French administrative data, my estimates for mothers are 27% smaller than those using the standard approach. The paper also discusses identification under an alternative parallel trend assumption, that is, when controlling for individual unobserved heterogeneity, and highlights key trade-offs in defining counterfactuals, as one cannot simultaneously absorb individual heterogeneity, age, age at birth, and event time. I provide a framework to build an estimator step-by-step, which is easily adaptable depending on which comparisons researchers assess most appropriate. Finally, I document substantial heterogeneity by age at childbirth for both mothers and fathers. By eight years after the birth of their first child, mothers aged 20-25 at birth lose 50% compared to their counterfactual earnings, compared to 12-20% for older mothers. Fathers aged 20-25 at first birth earn on average 26% less eight years later, while effects for older fathers are close to zero. These findings have important implications for both policy and applied research using event study designs to estimate the causal impact of children.