Identification of Child Penalties

This paper formalizes the identification framework underlying common child penalty triple difference estimators that normalize by counterfactual earnings. I reverse-engineer the identification assumptions from the validation tests used in applied practice and term this framework Normalized Triple Differences (NTD). I show that the conventional estimator is biased for its target causal estimand, even when NTD holds, if the parallel trends assumption is violated. I propose a new target, the effect of parenthood on the gender earnings ratio, and show it is point identified under NTD. Applying the framework to Israeli administrative data, a bias-bounding exercise suggests the conventional estimator is substantially biased for early treatment groups. Using the new estimator, I find that the contribution of parenthood to gender earnings inequality is heterogeneous across treatment groups.