Identification of Child Penalties

TL;DR

This paper formalizes the Normalized Triple Differences (NTD) framework for estimating child penalties, reveals its limitations under certain assumptions, and proposes a new estimand to better measure gender earnings impacts of parenthood.

Contribution

It introduces the NTD framework, analyzes its identification issues, and proposes a new estimand for more accurate measurement of child penalties in labor earnings.

Findings

NTD does not identify the conventional estimand when parallel trends are violated.

Higher-ability individuals delay childbirth, causing underestimation of early-childhood penalties.

A new estimand targeting the gender earnings ratio is identified under NTD.

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.