  In an influential critique of empirical practice, Freedman (2008) showed that
the linear regression estimator was biased for the analysis of randomized
controlled trials under the randomization model. Under Freedman's assumptions,
we derive exact closed-form bias corrections for the linear regression
estimator with and without treatment-by-covariate interactions. We show that
the limiting distribution of the bias corrected estimator is identical to the
uncorrected estimator, implying that the asymptotic gains from adjustment can
be attained without introducing any risk of bias. Taken together with results
from Lin (2013), our results show that Freedman's theoretical arguments against
the use of regression adjustment can be completely resolved with minor
modifications to practice.
