Treatment effects without a control group

Abstract

We propose a method for estimating the effect of a program or policy when all individuals in a population are treated. We show how individual pre-treatment information - even from very short panels - can be exploited to forecast individual counterfactuals, which can then be used to estimate the average treatment effect. We propose a simple estimator based on local polynomial regressions, which does not require correct specification of the individual forecast model or a long pre- treatment history. Our first contribution is to show that this estimator is unbiased and asymptotically normal for a broad class of data-generating processes (DGPs) that express the individual potential outcomes as the sum of (possibly) three un- observed components: a stationary process, a unit root process, and a polynomial time trend. Simulation results suggest that the choice of a larger polynomial order could mitigate the bias due to a "non-stationary" initial condition in short panels. (with I. Botosaru and M. Weidner)