# Moments of Causal Effects

arXiv: https://arxiv.org/abs/2505.04971 · HTML: https://mlsanity.com/paper/2505.04971/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 64 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 13 of 13)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Machine Learning Methods Economists Should Know About](https://mlsanity.com/paper/1903.10075/) (2019)
- [Semiparametric counterfactual density estimation](https://mlsanity.com/paper/2102.12034/) (2021)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Causal effects based on distributional distances](https://mlsanity.com/paper/1806.02935/) (2018)
- [Causal Inference on Distribution Functions](https://mlsanity.com/paper/2101.01599/) (2021)
- [Optimal Treatment Allocation for Efficient Policy Evaluation in Sequential Decision Making](https://mlsanity.com/paper/2311.02532/) (2023)
- [Probabilities of Causation for Continuous and Vector Variables](https://mlsanity.com/paper/2405.20487/) (2024)
- [Marginal and dependence uncertainty: bounds, optimal transport, and sharpness](https://mlsanity.com/paper/1709.00641/) (2017)
- [Identification and Estimation of Conditional Average Partial Causal Effects via Instrumental Variable](https://mlsanity.com/paper/2401.11130/) (2024)

## Built on by (most cited first, 3 of 3)

- [Estimating Aleatoric Uncertainty in the Causal Treatment Effect](https://mlsanity.com/paper/2602.08461/) (2026)
- [Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions](https://mlsanity.com/paper/2602.18762/) (2026)
- [Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information](https://mlsanity.com/paper/2607.04957/) (2026)

## Abstract (arXiv)

The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments, including covariance and correlation, reveal the relationships between multiple random variables. On the other hand, the primary focus of causal inference is the evaluation of causal effects, which are defined as the difference between two potential outcomes. While traditional causal effect assessment focuses on the average causal effect, this work provides definitions, identification theorems, and bounds for moments and product moments of causal effects to analyze their distribution and relationships. We conduct experiments to illustrate the estimation of the moments of causal effects from finite samples and demonstrate their practical application using a real-world medical dataset.