Identification and Bounding of Joint Expectation over Potential Outcomes
Abstract
The joint expectation of functions of potential outcomes (Y1,Y0) is a fundamental quantity in causal inference, particularly when investigating the variation or heterogeneity of causal effects. This paper provides novel assumptions for their identification: comonotonicity and countercomonotonicity. These assumptions offer a unified framework for their identification across discrete, continuous, and mixed outcome variables. In the absence of these assumptions, we derive sharp bounds for two broad classes of functions, yielding new results for bounding moments of individual causal effects, which are central to measuring effect heterogeneity. We present corresponding estimation methods and illustrate them in simulation studies and real-world datasets.
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BibTeX
@misc{kawakami2026identification,
title = {{Identification and Bounding of Joint Expectation over Potential Outcomes}},
author = {Yuta Kawakami and Jin Tian},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07536},
eprint = {2611.07536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07536},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Identification and Bounding of Joint Expectation over Potential Outcomes
AU - Yuta Kawakami
AU - Jin Tian
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07536
UR - https://arxiv.org/abs/2611.07536
AB - The joint expectation of functions of potential outcomes (Y_1,Y_0) is a fundamental quantity in causal inference, particularly when investigating the variation or heterogeneity of causal effects. This paper provides novel assumptions for their identification: comonotonicity and countercomonotonicity. These assumptions offer a unified framework for their identification across discrete, continuous, and mixed outcome variables. In the absence of these assumptions, we derive sharp bounds for two broad classes of functions, yielding new results for bounding moments of individual causal effects, which are central to measuring effect heterogeneity. We present corresponding estimation methods and illustrate them in simulation studies and real-world datasets.
ER -