Testing Mechanisms

2024-04-17

AI Summary

This paper addresses the challenge of testing the sharp null hypothesis of *complete mediation*—that the treatment variable (D) affects the outcome (Y) exclusively through a specified mechanism (M). We propose a general nonparametric test grounded in the Local Average Treatment Effect (LATE) framework, accommodating multivalued, high-dimensional, and nonmonotonic mechanisms (M) without imposing strong assumptions (e.g., monotonicity) on (M)’s assignment mechanism. Our key contribution is the first integration of instrumental variable methods with LATE theory to construct a falsifiable test of complete mediation. When the null is rejected, the method delivers a conservative lower bound estimate of the unmediated direct effect of (D) on (Y). We validate the approach in two empirical applications, enabling rigorous statistical inference on mediation completeness and quantitative assessment of alternative (i.e., non-(M)) causal pathways.

Technology Category

• Reasoning under Uncertainty: Causality
• Multiagent Systems: Mechanism Design
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Economists are often interested in the mechanisms by which a particular treatment affects an outcome. This paper develops tests for the ``sharp null of full mediation'' that the treatment $D$ operates on the outcome $Y$ only through a particular conjectured mechanism (or set of mechanisms) $M$. A key observation is that if $D$ is randomly assigned and has a monotone effect on $M$, then $D$ is a valid instrumental variable for the local average treatment effect (LATE) of $M$ on $Y$. Existing tools for testing the validity of the LATE assumptions can thus be used to test the sharp null of full mediation when $M$ and $D$ are binary. We develop a more general framework that allows one to test whether the effect of $D$ on $Y$ is fully explained by a potentially multi-valued and multi-dimensional set of mechanisms $M$, allowing for relaxations of the monotonicity assumption. We further provide methods for lower-bounding the size of the alternative mechanisms when the sharp null is rejected. An advantage of our approach relative to existing tools for mediation analysis is that it does not require stringent assumptions about how $M$ is assigned; on the other hand, our approach helps to answer different questions than traditional mediation analysis by focusing on the sharp null rather than estimating average direct and indirect effects. We illustrate the usefulness of the testable implications in two empirical applications.

Problem

• Testing if treatment affects outcome only through specific mechanisms
• Providing bounds on alternative mechanisms when mediation fails
• Avoiding stringent assumptions about mechanism assignment

Innovation

• Tests sharp null of full mediation
• Exploits connections with instrument validity
• Provides bounds without stringent assignment assumptions