  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.
