Partial Identification of Distributional Treatment Effects in Panel Data using Copula Equality Assumptions

TL;DR

This paper develops a method to partially identify distributional treatment effects in panel data by using copula equality assumptions, accommodating multiple treatment switches and heterogeneity across groups.

Contribution

It introduces two copula equality assumptions for bounding unknown joint distributions, enhancing DTE identification in panel data with treatment switching.

Findings

Improved bounds on distributional treatment effects compared to existing methods.

Method applied to assess exercise impact on adult body weight.

Testable assumptions with empirical validation.

Abstract

This paper aims to partially identify the distributional treatment effects (DTEs) that depend on the unknown joint distribution of treated and untreated potential outcomes. We construct the DTE bounds using panel data and allow individuals to switch between the treated and untreated states more than once over time. Individuals are grouped based on their past treatment history, and DTEs are allowed to be heterogeneous across different groups. We provide two alternative group-wise copula equality assumptions to bound the unknown joint and the DTEs, both of which leverage information from the past observations. Testability of these two assumptions are also discussed, and test results are presented. We apply this method to study the treatment effect heterogeneity of exercising on the adults' body weight. These results demonstrate that our method improves the identification power of the DTE bounds compared to the existing methods.