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

TL;DR

This paper develops a robust method for inference on average treatment effects that remains valid even when the number of covariates exceeds observations, using model selection techniques like group lasso.

Contribution

It introduces a doubly-robust estimator with valid confidence intervals under high-dimensional covariate settings, combining data-driven selection with economic theory.

Findings

Estimator attains semiparametric efficiency bound.

Performs well in finite samples in simulations.

Yields accurate estimates and tight confidence intervals on real data.

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, which is particularly well-suited to treatment effects data, and derive new 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.