Forecasted treatment effects

We consider estimation and inference about 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 effects, based on forecasting counterfactuals using a short time series of pre-treatment data. We show that the focus should be on forecast unbiasedness rather than accuracy. Correct specification of the forecasting model is not necessary to obtain unbiased estimates of the individual treatment effects. Instead, simple basis function (e.g., polynomial time trends) regressions deliver unbiasedness under a broad class of data-generating processes for the individual counterfactuals. Basing the forecasts on a model can introduce misspecification bias and does not necessarily improve performance even under correct specification. Consistency and asymptotic normality of the Forecasted Average Treatment effects (FAT) estimator attains under an additional assumption that rules out common and unforecastable shocks occurring between the treatment date and the date at which the effect is calculated.