Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations

86 Pages Posted: 19 Sep 2013 Last revised: 3 Apr 2015

See all articles by Max Farrell

Max Farrell

University of Chicago - Booth School of Business - Econometrics and Statistics

Date Written: March 27, 2015

Abstract

This paper concerns robust inference on average treatment effects following model selection. In the selection on observables framework, we show how to construct confidence intervals based on a doubly-robust estimator that are robust to model selection errors and prove that they are valid uniformly over a large class of treatment effect models. The class allows for multivalued treatments with heterogeneous effects (in observables), general heteroskedasticity, and selection amongst (possibly) more covariates than observations. Our estimator attains the semiparametric efficiency bound under appropriate conditions. Precise conditions are given for any model selector to yield these results, and we show how to combine data-driven selection with economic theory. For implementation, we give a specific proposal for selection based on the group lasso and derive new technical results for high-dimensional, sparse multinomial logistic regression. A simulation study shows our estimator performs very well in finite samples over a wide range of models. Revisiting the National Supported Work demonstration data, our method yields accurate estimates and tight confidence intervals.

Keywords: High-dimensional sparse model, heterogeneous treatment effects, uniform inference, model selection, doubly-robust estimator, unconfoundedness

JEL Classification: C1, C21, C51

Suggested Citation

Farrell, Max, Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations (March 27, 2015). Available at SSRN: https://ssrn.com/abstract=2324292 or http://dx.doi.org/10.2139/ssrn.2324292

Max Farrell (Contact Author)

University of Chicago - Booth School of Business - Econometrics and Statistics ( email )

Chicago, IL 60637
United States

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