Forecasted Treatment Effects

TL;DR

This paper introduces a method for estimating treatment effects without a control group by using unbiased forecasts of counterfactual outcomes based on pre-treatment data, emphasizing forecast unbiasedness over accuracy.

Contribution

It provides unbiased estimators for individual and average treatment effects using simple basis function regressions, avoiding the need for control groups and reducing model misspecification risk.

Findings

The estimator is unbiased and asymptotically normal.

Simple basis functions ensure forecast unbiasedness across various data processes.

The method can replicate previous findings without a control group.

Abstract

We consider estimation and inference of the effects of a policy in the absence of an untreated or 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, across individuals, the difference between observed post-treatment outcomes and unbiased forecasts of their 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. In contrast, forecasting based on a specific parametric model 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 it does so without using an untreated or control group.