  We consider estimation and inference of the effects of a policy in the
absence of a control group. We obtain unbiased estimators of individual
(heterogeneous) treatment effects and a consistent and asymptotically normal
estimator of the average treatment effect. Our estimator averages over unbiased
forecasts of individual counterfactuals, based on a (short) time series of
pre-treatment data. The paper emphasizes the importance of focusing on forecast
unbiasedness rather than accuracy when the end goal is estimation of average
treatment effects. We show that simple basis function regressions ensure
forecast unbiasedness for a broad class of data-generating processes for the
counterfactuals, even in short panels. In contrast, model-based forecasting
requires stronger assumptions and is prone to misspecification and estimation
bias. We show that our method can replicate the findings of some previous
empirical studies, but without using a control group.
