Partially Identified Heterogeneous Treatment Effect with Selection: An Application to Gender Gaps

TL;DR

This paper develops a robust method to bound and analyze the gender gap considering sample selection bias and heterogeneity, revealing how different population types contribute to gender disparities over time.

Contribution

It introduces a new bounding approach under sample selection with an exclusion restriction, allowing segmentation of the population into types for detailed gender gap analysis.

Findings

Increasing proportion of always-working individuals over time

Gender gap bounds vary across types and over time

Persistent gaps for certain types despite assumptions

Abstract

This paper addresses the sample selection model within the context of the gender gap problem, where even random treatment assignment is affected by selection bias. By offering a robust alternative free from distributional or specification assumptions, we bound the treatment effect under the sample selection model with an exclusion restriction, an assumption whose validity is tested in the literature. This exclusion restriction allows for further segmentation of the population into distinct types based on observed and unobserved characteristics. For each type, we derive the proportions and bound the gender gap accordingly. Notably, trends in type proportions and gender gap bounds reveal an increasing proportion of always-working individuals over time, alongside variations in bounds, including a general decline across time and consistently higher bounds for those in high-potential wage groups. Further analysis, considering additional assumptions, highlights persistent gender gaps for some types, while other types exhibit differing or inconclusive trends. This underscores the necessity of separating individuals by type to understand the heterogeneous nature of the gender gap.