Summary Indices in Treatment Effect Estimation
Abstract
This paper studies the practice of combining multiple outcomes into a summary index to estimate a causal effect. For common estimators and index constructions, the estimate equals a weighted sum of the estimated effects on the components, with weights that are implicit and rarely reported. The paper derives the weights and shows that, for inverse-covariance-weighted indices, they can be negative and unrestricted in magnitude, so the index effect can have the opposite sign to every component effect. The paper proposes two procedures for valid inference on the index effect: a variance estimator that accounts for the data-dependent weights, and a shifted t-test that requires no such correction. Conventional t-tests of the null of no effect remain valid. Contrary to common claims, summary indices do not generally improve power. Three published studies illustrate the results.
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BibTeX
@misc{fedchenko2026summary,
title = {{Summary Indices in Treatment Effect Estimation}},
author = {Danil Fedchenko},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21393},
eprint = {2609.21393},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21393},
}
RIS
TY - UNPB
TI - Summary Indices in Treatment Effect Estimation
AU - Danil Fedchenko
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21393
UR - https://arxiv.org/abs/2609.21393
AB - This paper studies the practice of combining multiple outcomes into a summary index to estimate a causal effect. For common estimators and index constructions, the estimate equals a weighted sum of the estimated effects on the components, with weights that are implicit and rarely reported. The paper derives the weights and shows that, for inverse-covariance-weighted indices, they can be negative and unrestricted in magnitude, so the index effect can have the opposite sign to every component effect. The paper proposes two procedures for valid inference on the index effect: a variance estimator that accounts for the data-dependent weights, and a shifted t-test that requires no such correction. Conventional t-tests of the null of no effect remain valid. Contrary to common claims, summary indices do not generally improve power. Three published studies illustrate the results.
ER -