Partial Identification under Stratified Randomization

TL;DR

This paper introduces a comprehensive framework for partial identification and inference in stratified experiments with attrition, providing new methods for equal and heterogeneous treatment shares, with improved variance estimation and bounds.

Contribution

It develops a unified approach for partial identification in stratified experiments, including new variance estimators and bounds for both equal and heterogeneous treatment shares.

Findings

Closed-form variance estimators for equal-share designs

Tighter confidence intervals compared to conventional methods

Valid bounds under heterogeneous treatment shares

Abstract

This paper develops a unified framework for partial identification and inference in stratified experiments with attrition, accommodating both equal and heterogeneous treatment shares across strata. For equal-share designs, we apply recent theory for finely stratified experiments to Lee bounds, yielding closed-form, design-consistent variance estimators and properly sized confidence intervals. Simulations show that the conventional formula can overstate uncertainty, while our approach delivers tighter intervals. When treatment shares differ across strata, we propose a new strategy, which combines inverse probability weighting and global trimming to construct valid bounds even when strata are small or unbalanced. We establish identification, introduce a moment estimator, and extend existing inference results to stratified designs with heterogeneous shares, covering a broad class of moment-based estimators which includes the one we formulate. We also generalize our results to designs in which strata are defined solely by observed labels.