June 2022 Evidence factors from multiple, possibly invalid, instrumental variables
Anqi Zhao, Youjin Lee, Dylan S. Small, Bikram Karmakar
Author Affiliations +
Ann. Statist. 50(3): 1266-1296 (June 2022). DOI: 10.1214/21-AOS2148


Valid instrumental variables enable treatment effect inference even when selection into treatment is biased by unobserved confounders. When multiple candidate instruments are available, but some of them are possibly invalid, the previously proposed reinforced design enables one or more nearly independent valid analyses that depend on very different assumptions. That is, we can perform evidence factor analysis. However, the validity of the reinforced design depends crucially on the order in which multiple instrumental variable analyses are conducted. Motivated by the orthogonality of balanced factorial designs, we propose a balanced block design to offset the possible violation of the exclusion restriction by balancing the instruments against each other in the design, and demonstrate its utility for constructing approximate evidence factors under multiple analysis strategies free of the order imposition. We also propose a novel stratification method using multiple, nested candidate instruments, in which case the balanced block design is not applicable. We apply our proposed methods to evaluate (a) the effect of education on future earnings using instrumental variables arising from the disruption of education during World War II via the balanced block design, and (b) the causal effect of malaria on stunting among children in Western Kenya using three nested instruments.

Funding Statement

Anqi Zhao was supported by the National University of Singapore Start-Up Grant R-155-000-216-133, and Bikram Karmakar was supported by NSF Grant DMS-2015250.


Download Citation

Anqi Zhao. Youjin Lee. Dylan S. Small. Bikram Karmakar. "Evidence factors from multiple, possibly invalid, instrumental variables." Ann. Statist. 50 (3) 1266 - 1296, June 2022. https://doi.org/10.1214/21-AOS2148


Received: 1 February 2021; Revised: 1 October 2021; Published: June 2022
First available in Project Euclid: 16 June 2022

MathSciNet: MR4441120
zbMATH: 07547930
Digital Object Identifier: 10.1214/21-AOS2148

Primary: 62G10
Secondary: 62K10

Keywords: Bias in observational studies , Causal inference , exclusion restriction , nonparametric tests , replication , sensitivity analysis

Rights: Copyright © 2022 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.50 • No. 3 • June 2022
Back to Top