  This paper examines finely stratified designs for the efficient estimation of
treatment effect parameters in randomized experiments. In such designs, units
are divided into groups of fixed size, with a proportion within each group
randomly assigned to a binary treatment. We focus on parameters defined using
moment conditions constructed from known functions of the observed data. We
establish that the naive method of moments estimator under a finely stratified
design achieves the same asymptotic variance as that obtained using ex post
covariate adjustment in i.i.d. designs, and further that this variance achieves
the efficiency bound in a large class of designs.
