Bounds on causal effects in $2^{K}$ factorial experiments with non-compliance

TL;DR

This paper develops methods to bound causal effects in factorial experiments with non-compliance, using instrumental variables under weaker assumptions, thus enabling more robust inference in social and biomedical studies.

Contribution

It introduces bounds on causal effects in $2^{K}$ factorial experiments with non-compliance, relaxing strong assumptions required by previous identification approaches.

Findings

Provides bounds for causal effects under mild assumptions

Applicable to bounded outcomes in factorial experiments

Enhances robustness of causal inference in non-compliance scenarios

Abstract

Factorial experiments are ubiquitous in the social and biomedical sciences, but when units fail to comply with each assigned factors, identification and estimation of the average treatment effects become impossible without strong assumptions. Leveraging an instrumental variables approach, previous studies have shown how to identify and estimate the causal effect of treatment uptake among respondents who comply with treatment. A major caveat is that these identification results rely on strong assumptions on the effect of randomization on treatment uptake. This paper shows how to bound these complier average treatment effects for bounded outcomes under more mild assumptions on non-compliance.