  Standard estimators of the global average treatment effect can be biased in
the presence of interference. This paper proposes regression adjustment
estimators for removing bias due to interference in Bernoulli randomized
experiments. We use a fitted model to predict the counterfactual outcomes of
global control and global treatment. Our work differs from standard regression
adjustments in that the adjustment variables are constructed from functions of
the treatment assignment vector, and that we allow the researcher to use a
collection of any functions correlated with the response, turning the problem
of detecting interference into a feature engineering problem. We characterize
the distribution of the proposed estimator in a linear model setting and
connect the results to the standard theory of regression adjustments under
SUTVA. We then propose an estimator that allows for flexible machine learning
estimators to be used for fitting a nonlinear interference functional form. We
propose conducting statistical inference via bootstrap and resampling methods,
which allow us to sidestep the complicated dependences implied by interference
and instead rely on empirical covariance structures. Such variance estimation
relies on an exogeneity assumption akin to the standard unconfoundedness
assumption invoked in observational studies. In simulation experiments, our
methods are better at debiasing estimates than existing inverse propensity
weighted estimators based on neighborhood exposure modeling. We use our method
to reanalyze an experiment concerning weather insurance adoption conducted on a
collection of villages in rural China.
