Before revision:  We show thatthis bias-corrected estimator is uncorrelated with the benchmark estimator that only uses the experimental data, and can thus be combined with the benchmark estimator to improve efficiency. Under a common experimental design that randomly assigns units into the experimental group, our method can reduce the variance by up to 50\% , so that only half of the experimental sample is required to attain the same accuracy.
After revision:  We show thatthis bias-corrected estimator is uncorrelated with the benchmark estimator that only uses the experimental data, improve estimation efficiency. I outline three estimators (weighting, shrinkage, or GMM) for implementing this strategy, and show that my methods can reduce variance by up to 50\% , so that only half of the experimental sample is required to attain the same accuracy.