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

Naoya Hashimoto, Yuta Kawakami, Jin Tian
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:2085-2118, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-hashimoto26a, title = {Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information}, author = {Hashimoto, Naoya and Kawakami, Yuta and Tian, Jin}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {2085--2118}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/hashimoto26a/hashimoto26a.pdf}, url = {https://proceedings.mlr.press/v337/hashimoto26a.html}, 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.} }
Endnote
%0 Conference Paper %T Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information %A Naoya Hashimoto %A Yuta Kawakami %A Jin Tian %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-hashimoto26a %I PMLR %P 2085--2118 %U https://proceedings.mlr.press/v337/hashimoto26a.html %V 337 %X 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.
APA
Hashimoto, N., Kawakami, Y. & Tian, J.. (2026). Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:2085-2118 Available from https://proceedings.mlr.press/v337/hashimoto26a.html.

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