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.
"Sharp bounds on the variance in randomized experiments." Ann. Statist. 42 (3) 850 - 871, June 2014. https://doi.org/10.1214/13-AOS1200