Estimation of Treatment Effects with High-Dimensional Controls

• Activity Number: 269
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: JBES-Journal of Business & Economic Statistics
• Author(s): Alexandre Belloni*+ and Victor Chernozhukov and Christian Hansen
• Companies: Duke University and Massachusetts Institute of Technology and The University of Chicago

Abstract

We propose methods for inference on the effect of a treatment on a scalar outcome in the presence of very many controls. Our setting is a partially linear regression model containing the treatment/policy variable and a large number p of controls or series terms. We allow p to be much larger than the sample size n but impose that only s < n controls or series terms whose identities are unknown are needed to approximate the regression function accurately. The latter condition makes it possible to estimate the entire regression function as well as the treatment effect by selecting approximately the right set of controls. We develop estimation and inference methods for the average treatment effect in this setting, proposing a novel "post-double-selection" method that provides attractive inferential and estimation properties. In our analysis, we expressly allow for imperfect selection of the controls and account for the impact of selection errors on estimation and inference. In order to cover typical applications in economics, we present methods that allow for non-Gaussian and heteroskedastic disturbances. We illustrate the use of the developed methods with numerical simulations and an application to the effect of abortion on crime rates.