Identification of Child Penalties

TL;DR

This paper formalizes Normalized Triple Differences (NTD) as the identification framework underlying normalized event studies used to estimate the child penalty, showing that the conventional gender-gap-in-normalized-effects estimand is not identified when parallel-trends in levels fail. It introduces a new estimand, the effect of parenthood on the gender earnings ratio $\Delta\rho(d,a)$, which is identified under NTD, and provides an estimator with valid inference. Using Israeli administrative data, the author demonstrates that parallel-trends violations are likely—especially for early birth groups—leading to substantial underestimation of penalties in conventional estimates, and that the new estimand can yield different magnitudes and a clear decomposition of the gender gap. An open-source R package is provided to facilitate replication and application across settings and outcomes.

Abstract

A growing body of research estimates child penalties, the gender gap in the effect of parenthood on labor market earnings, using event studies that normalize treatment effects by counterfactual earnings. I formalize the identification framework underlying this approach, which I term Normalized Triple Differences (NTD), and show it does not identify the conventional target estimand when the parallel trends assumption in levels is violated. Insights from human capital theory suggest such violations are likely: higher-ability individuals delay childbirth and have steeper earnings growth, a mechanism that causes conventional estimates to understate child penalties for early-treated parents. Using Israeli administrative data, a bias-bounding exercise suggests substantial understatement for early groups. As a solution, I propose targeting the effect of parenthood on the gender earnings ratio and show this new estimand is identified under NTD.

Figures (11)

• Figure 1: Selection and Age at Birth of First Child
• Figure 2: Bias-Bounding Diagnostic: Conventional vs Bias-Corrected Estimates
• Figure 3: Validation Tests by Treatment-Control Pairs
• Figure 4: Observed Gender Earnings Ratios Before Childbirth
• Figure 5: Estimates of the Effect of Parenthood on the Gender Earnings Ratio

Theorems & Definitions (20)

• Proposition 1
• Theorem 1
• Proposition 2
• Theorem 2
• Lemma 1
• proof : Proof of Lemma \ref{['lemma:desc_tie_cause']}
• proof : Proof of Proposition \ref{['prop:cp_ident_ass']}
• proof : Proof of Theorem \ref{['thm:cp_iden_res']}
• Lemma 2
• proof