Estimating Average Treatment Effects with Projected Instrumental Variables
Abstract
In this paper, we develop a projected instrumental variable framework that relaxes conventional assumptions for causal identification with instrumental variables. Building on the interpretation of conditional expectation as an orthogonal projection in a Hilbert space, the framework replaces the conditional expectation operator with a general projection operator. We provide an alternative inverse problem formulation based on the Riesz representation. Drawing on semiparametric efficiency theory, we further develop debiased and adaptive machine learning methods for estimation and inference. The proposed framework connects invalid instrumental variables to instrumented difference-in-differences. We also examine invalid projected instrumental variables and discuss their relationship to existing methods. Simulation studies and real data analysis demonstrate that the proposed methods perform favorably compared with existing approaches.
Related
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- Imputation is all you need: double robustness, semiparametric efficiency, and automatic covariate balance for estimating the average treatment effect
- Estimating the average treatment effect under limited overlap via Polynomial Approximation and Extrapolation
- Estimating Group Average Treatment Effects in High-Risk Populations with Unobserved Target Membership
- Distribution-free predictive inference with instrumental variables
BibTeX
@misc{chen2026estimating,
title = {{Estimating Average Treatment Effects with Projected Instrumental Variables}},
author = {Shuyuan Chen and Yifan Cui},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00705},
eprint = {2611.00705},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00705},
}
RIS
TY - UNPB
TI - Estimating Average Treatment Effects with Projected Instrumental Variables
AU - Shuyuan Chen
AU - Yifan Cui
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00705
UR - https://arxiv.org/abs/2611.00705
AB - In this paper, we develop a projected instrumental variable framework that relaxes conventional assumptions for causal identification with instrumental variables. Building on the interpretation of conditional expectation as an orthogonal projection in a Hilbert space, the framework replaces the conditional expectation operator with a general projection operator. We provide an alternative inverse problem formulation based on the Riesz representation. Drawing on semiparametric efficiency theory, we further develop debiased and adaptive machine learning methods for estimation and inference. The proposed framework connects invalid instrumental variables to instrumented difference-in-differences. We also examine invalid projected instrumental variables and discuss their relationship to existing methods. Simulation studies and real data analysis demonstrate that the proposed methods perform favorably compared with existing approaches.
ER -