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

2024-07-16

AI Summary

This paper addresses the identification and estimation of the average treatment effect (ATE) in $2^K$ factorial experiments with noncompliance. Moving beyond conventional approaches that rely on strong monotonicity or exclusion restrictions, we derive tight bounds for the complier average treatment effect (CATE) under milder, empirically plausible noncompliance assumptions. Methodologically, we integrate the instrumental variable framework, extremal optimization, and the potential outcomes model to derive falsifiable theoretical bounds for CATE, rigorously establishing their identifiability under bounded outcomes. Simulation results demonstrate that our bounds substantially narrow the estimation interval compared to existing methods. Our key contribution is the first robust causal bounding procedure for multi-factorial designs that dispenses with stringent exogeneity constraints—achieving both theoretical rigor and practical applicability.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Bounds causal effects in factorial experiments with non-compliance
• Identifies treatment effects under mild non-compliance assumptions
• Addresses limitations of strong assumptions in previous studies

Innovation

• Bounds complier effects in factorial experiments
• Uses instrumental variables approach
• Relaxes strong non-compliance assumptions