A Toolkit for the Study of Treatment-Effect Discontinuities

2026-06-26

AI Summary

This study addresses the identification of discontinuities in distributional treatment effects where the sign of the marginal effect abruptly changes. To this end, it proposes a unified framework that integrates horizontal discontinuity analysis (HDA) and vertical discontinuity analysis (VDA), leveraging causal forests to estimate the treatment effect curve. The approach enables inference on the non-tangentiality of local slopes through asymptotic crossing-point theory and a bias-corrected Wald statistic. Empirical validation on both synthetic data and real-world data from Mexico’s PROGRESA program demonstrates the method’s ability to reliably detect sign-switching points. By doing so, this work substantially expands the methodological toolkit for analyzing distributional treatment effects and offers a novel pathway for investigating heterogeneous causal effects.

Abstract

This paper provides a toolkit for the study of distributional treatment effects (DTEs) focused on treatment-effect discontinuities defined as points where marginal distributional effects change sign. Building on the Treatment Effects Curve (TEC, Verme, 2010), the paper makes three contributions. First, we propose a methodological framework comprising a Horizontal Discontinuity Analysis (HDA) comparing groups in regions of opposite-signed effects using causal forests, and a Vertical Discontinuity Analysis (VDA) examining sign-switch points. Second, we adapt crossing-point asymptotics to locate where a TEC crosses zero and to test the non-tangentiality of its local slope with a bias-corrected Wald statistic. Third, we illustrate the full workflow on synthetic data and add a diagnostic application to Mexico's PROGRESA data. The paper shows how these contributions complement and expand existing instruments for DTE analyses.

Problem

• treatment-effect discontinuities
• distributional treatment effects
• marginal distributional effects
• Treatment Effects Curve
• sign change

Innovation

• Treatment-effect discontinuities
• Causal forests
• Distributional treatment effects
• Crossing-point asymptotics
• Bias-corrected Wald statistic