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Testing Mechanisms

Soonwoo Kwon, Jonathan Roth

Abstract

Economists are often interested in the mechanisms by which a treatment affects an outcome. We develop tests for the "sharp null of full mediation" that a treatment $D$ affects an outcome $Y$ only through a particular mechanism (or set of mechanisms) $M$. Our approach exploits connections between mediation analysis and the econometric literature on testing instrument validity. We also provide tools for quantifying the magnitude of alternative mechanisms when the sharp null is rejected: we derive sharp lower bounds on the fraction of individuals whose outcome is affected by the treatment despite having the same value of $M$ under both treatments (``always-takers''), as well as sharp bounds on the average effect of the treatment for such always-takers. 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. We illustrate our methodology in two empirical applications.

Testing Mechanisms

Abstract

Economists are often interested in the mechanisms by which a treatment affects an outcome. We develop tests for the "sharp null of full mediation" that a treatment affects an outcome only through a particular mechanism (or set of mechanisms) . Our approach exploits connections between mediation analysis and the econometric literature on testing instrument validity. We also provide tools for quantifying the magnitude of alternative mechanisms when the sharp null is rejected: we derive sharp lower bounds on the fraction of individuals whose outcome is affected by the treatment despite having the same value of under both treatments (``always-takers''), as well as sharp bounds on the average effect of the treatment for such always-takers. An advantage of our approach relative to existing tools for mediation analysis is that it does not require stringent assumptions about how is assigned. We illustrate our methodology in two empirical applications.
Paper Structure (52 sections, 10 theorems, 103 equations, 4 figures, 7 tables)

This paper contains 52 sections, 10 theorems, 103 equations, 4 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related literature.
  3. Set-up and notation.
  4. Special Case: Binary Mediator
  5. Theory: General Case
  6. Intuition.
  7. Computation of bounds.
  8. Inference
  9. Monte Carlo
  10. Treatment, outcome, and mediator.
  11. Sample sizes.
  12. Description of DGP.
  13. Methods used.
  14. Simulation results.
  15. Choice of bins.
  16. ...and 37 more sections

Key Result

Proposition 3.1

Figures (4)

  • Figure 1: Illustration of Testable Implications in bursztyn_misperceived_2020
  • Figure 1: Illustration of Testable Implications in bursztyn_misperceived_2020 Using Full Sample
  • Figure 2: Illustration of partial identification of type shares
  • Figure 3: Testable Implications of the Sharp Null for the Grandmother Mediator in baranov_maternal_2020

Theorems & Definitions (29)

  • Example 1: Monotonicity and relaxations thereof
  • Example 2: Elementwise monotonicity
  • Example 3: Bounded effect of $D$ on $M$
  • Example 4: No restrictions
  • Proposition 3.1
  • Corollary 3.1: Testable implications of sharp null
  • Remark 1: Closed-form solution with fully-ordered, monotone $M$
  • Remark 2: Identifying power
  • Remark 3: Binning values of $M$
  • Remark 4: Functions of the $\nu_k$
  • ...and 19 more