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

arXiv: https://arxiv.org/abs/2607.04957 · HTML: https://mlsanity.com/paper/2607.04957/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Structural Causal Models Are (Solvable by) Credal Networks](https://mlsanity.com/paper/2008.00463/) (2020)
- [Efficient Computation of Counterfactual Bounds](https://mlsanity.com/paper/2307.08304/) (2023)
- [Scalable Computation of Causal Bounds](https://mlsanity.com/paper/2308.02709/) (2023)
- [Moments of Causal Effects](https://mlsanity.com/paper/2505.04971/) (2025)
- [Multilinear and Linear Programs for Partially Identifiable Queries in Quasi-Markovian Structural Causal Models](https://mlsanity.com/paper/2509.03548/) (2025)
- [Beyond Conditional Averages: Estimating The Individual Causal Effect Distribution](https://mlsanity.com/paper/2210.16563/) (2022)
- [Adding covariates to bounds: What is the question?](https://mlsanity.com/paper/2502.03156/) (2025)
- [Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions](https://mlsanity.com/paper/2602.18762/) (2026)

## Abstract (arXiv)

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.