Sharp bounds on the variance in randomized experiments

TL;DR

This paper introduces a consistent method for estimating sharp bounds on the variance of the difference-in-means estimator in randomized experiments, improving confidence interval precision in causal inference.

Contribution

It generalizes previous work to provide sharp variance bounds, addressing a key identification problem in causal inference and enabling narrower confidence intervals.

Findings

Provides a consistent estimator for sharp variance bounds.

Facilitates asymptotically narrow conservative confidence intervals.

Applicable to randomized controlled and clinical trials.

Abstract

We propose a consistent estimator of sharp bounds on the variance of the difference-in-means estimator in completely randomized experiments. Generalizing Robins [Stat. Med. 7 (1988) 773-785], our results resolve a well-known identification problem in causal inference posed by Neyman [Statist. Sci. 5 (1990) 465-472. Reprint of the original 1923 paper]. A practical implication of our results is that the upper bound estimator facilitates the asymptotically narrowest conservative Wald-type confidence intervals, with applications in randomized controlled and clinical trials.