  We study efficiency improvements in randomized experiments for estimating a
vector of potential outcome means using regression adjustment (RA) when there
are more than two treatment levels. We show that linear RA which estimates
separate slopes for each assignment level is never worse, asymptotically, than
using the subsample averages. We also show that separate RA improves over
pooled RA except in the obvious case where slope parameters in the linear
projections are identical across the different assignment levels. We further
characterize the class of nonlinear RA methods that preserve consistency of the
potential outcome means despite arbitrary misspecification of the conditional
mean functions. Finally, we apply these regression adjustment techniques to
efficiently estimate the lower bound mean willingness to pay for an oil spill
prevention program in California.
