Primary Submission Category: Instrumental Variables
Estimation of a Common Local Average Treatment Effect with Multiple Instruments
Authors: Aniruddhan Ganesaraman, Patrick Lopatto, P. M. Aronow,
Presenting Author: Aniruddhan Ganesaraman*
Recently, Ghosh and Rothenhäusler (2025) have proposed an assumption-robust approach to causal inference for the average treatment effect (ATE) in the presence of multiple plausible adjustment sets. When it is unclear which candidate set satisfies ignorability, they construct a reweighted target population, as close as possible to the original one in KL divergence, such that the estimands obtained from the different adjustment sets agree. If at least one adjustment set is valid, this common estimand equals the ATE in the reweighted population, yielding a single asymptotically valid confidence interval for the reweighted-population ATE.
Building on the work of Ghosh and Rothenhäusler, we propose an assumption-robust approach to inference with multiple instrumental variables. Different instruments may identify local average treatment effects (LATEs) for distinct complier subpopulations, and disagreement among instrument-specific Wald estimates is generically attributable to treatment effect heterogeneity, instrument invalidity, or both. We propose to estimate the LATE in a reweighted population, which is constructed to guarantee causal identifiability when at least one of the instruments is valid. The corresponding estimator is doubly robust, $sqrt{n}$-consistent, and asymptotically normal. Our theoretical results are illustrated with a simulation study.