Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information

2026-07-06

AI Summary

This study addresses the identification and bounding of central moments of individual causal effect distributions under the constraint that only marginal central moments of potential outcomes are known, thereby characterizing treatment effect heterogeneity. The work proposes a novel framework for identification and inference that relies solely on marginal moments rather than full distributional information. By integrating moment-constrained optimization, causal inference theory, and inequality analysis, the authors establish sharp identifiability conditions and tight bounds for higher-order central moments. This approach substantially reduces data requirements compared to existing methods, and its validity and practical utility are demonstrated through empirical applications.

Abstract

Evaluating the causal effect of a treatment on an outcome is a central objective in causal inference. While the average causal effect summarizes the mean impact of treatment, the central moments of the individual causal effect (ICE) characterize the shape of the ICE distribution, thereby revealing the extent and structure of treatment effect heterogeneity across individuals. This paper investigates the identification and bounding of the central moments of the ICE using only the marginal central moments of each potential outcome (PO). Compared with existing approaches that require knowledge of the full marginal distributions of the POs, marginal moment information is often substantially easier to obtain in empirical applications. Finally, we illustrate the practical relevance of our results through two empirical case studies.

Problem

• causal inference
• individual causal effect
• central moments
• marginal moments
• treatment effect heterogeneity

Innovation

• central moments
• causal inference
• individual causal effect
• marginal moments
• treatment effect heterogeneity