🤖 AI Summary
This study addresses the challenge of partial identification of causal effects in stratified randomized experiments, where attrition and heterogeneous treatment assignment proportions complicate inference. The authors propose a unified analytical framework that integrates Lee bounds, inverse probability weighting, and a global trimming strategy, accommodating both equal and unequal treatment allocation ratios and extending naturally to settings where strata are defined solely by observed covariates. Innovatively, they construct novel bounds tailored for small or imbalanced strata, and combine them with method-of-moments estimation and a design-consistent closed-form variance estimator to produce tight confidence intervals with accurate coverage. Simulation results demonstrate that the proposed approach substantially narrows interval width and improves inferential precision compared to conventional methods.
📝 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.