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Randomization-based confidence sets for the local average treatment effect

P. M. Aronow, Haoge Chang, Patrick Lopatto

TL;DR

This paper develops a randomization-based approach for constructing confidence sets for the Local Average Treatment Effect ($LATE$) in randomized experiments with noncompliance. It refines the Imbens–Rosenbaum framework by employing a studentized Anderson–Rubin statistic, ensuring finite-sample exactness under constant additive effects and asymptotic validity under heterogeneity, with a uniform guarantee over instrument strength. The authors extend the method to regression-adjusted settings, provide efficient Monte Carlo algorithms to compute the confidence sets exactly, and demonstrate favorable finite-sample performance in simulations and GOTV data applications. The resulting inference avoids reliance on large-sample normal approximations even with weak instruments and offers practical, robust tools for applied work in randomized experiments with noncompliance.

Abstract

We consider the problem of generating confidence sets in randomized experiments with noncompliance. We show that a refinement of a randomization-based procedure proposed by Imbens and Rosenbaum (2005) has desirable properties. Namely, we show that using a studentized Anderson--Rubin-type statistic as a test statistic yields confidence sets that are finite-sample exact under treatment effect homogeneity, and remain asymptotically valid for the Local Average Treatment Effect when the treatment effect is heterogeneous. We provide a uniform analysis of this procedure and efficient algorithms to construct the confidence set.

Randomization-based confidence sets for the local average treatment effect

TL;DR

This paper develops a randomization-based approach for constructing confidence sets for the Local Average Treatment Effect () in randomized experiments with noncompliance. It refines the Imbens–Rosenbaum framework by employing a studentized Anderson–Rubin statistic, ensuring finite-sample exactness under constant additive effects and asymptotic validity under heterogeneity, with a uniform guarantee over instrument strength. The authors extend the method to regression-adjusted settings, provide efficient Monte Carlo algorithms to compute the confidence sets exactly, and demonstrate favorable finite-sample performance in simulations and GOTV data applications. The resulting inference avoids reliance on large-sample normal approximations even with weak instruments and offers practical, robust tools for applied work in randomized experiments with noncompliance.

Abstract

We consider the problem of generating confidence sets in randomized experiments with noncompliance. We show that a refinement of a randomization-based procedure proposed by Imbens and Rosenbaum (2005) has desirable properties. Namely, we show that using a studentized Anderson--Rubin-type statistic as a test statistic yields confidence sets that are finite-sample exact under treatment effect homogeneity, and remain asymptotically valid for the Local Average Treatment Effect when the treatment effect is heterogeneous. We provide a uniform analysis of this procedure and efficient algorithms to construct the confidence set.
Paper Structure (45 sections, 27 theorems, 204 equations, 1 figure, 3 tables)

This paper contains 45 sections, 27 theorems, 204 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Organization
  4. Acknowledgments
  5. Basic Setup
  6. Notation and Identification Assumptions
  7. Experimental Design and Data Environment
  8. Statistical Framework
  9. Confidence Sets Without Regression Adjustment
  10. Studentized Estimator
  11. Critical Values and Confidence Sets
  12. Theoretical Guarantees
  13. Confidence Sets With Regression Adjustment
  14. Notation and Assumptions
  15. Studentized Estimators
  16. ...and 30 more sections

Key Result

Theorem 3.3

Fix $\alpha, \delta \in (0,1)$, $r \in (0,1/2]$, and $A > 0$. Let $\Theta_n(\delta,r,A)$ be the parameter space of models that satisfy Assumptions a:exclusion, a:monotonicity, d:theta, and a:cr with these constants. We have

Figures (1)

  • Figure 1: A figure illustrating Algorithm \ref{['alg:2.1']} and Algorithm \ref{['alg:2.2']}. The dashed lines are the AR functions from simulated assignments. The dot-dashed line is the AR function from the observed data. The solid curve is the quantile function. We use 4 simulated assignments and the 75th percentile for the illustration. The vertical lines denote the intersections of the simulated AR functions.

Theorems & Definitions (55)

  • Remark 3.1
  • Remark 3.2
  • Theorem 3.3
  • Remark 4.1
  • Theorem 4.2
  • Remark 5.1
  • Remark 5.2
  • Lemma 5.3
  • proof
  • Theorem 5.4
  • ...and 45 more