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

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.