Forecasted Treatment Effects (2309.05639v3)

Abstract: 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.