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

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.

arXiv comment48 pages, 1 figure, 1 table

References in corpus (16)

• Simultaneous analysis of Lasso and Dantzig selector
• On asymptotically optimal confidence regions and tests for high-dimensional models
• On the conditions used to prove oracle results for the Lasso
• Consistency of the group Lasso and multiple kernel learning
• Least squares after model selection in high-dimensional sparse models
• Valid post-selection inference
• High-dimensional generalized linear models and the lasso
• Support union recovery in high-dimensional multivariate regression
• Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator
• Semiparametric efficiency in GMM models with auxiliary data
• Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak Conditions
• Consistent group selection in high-dimensional linear regression
• Union Support Recovery in Multi-task Learning
• Confidence Sets Based on Sparse Estimators Are Necessarily Large
• Post-Selection Inference for Generalized Linear Models with Many Controls
• On the Distribution of Penalized Maximum Likelihood Estimators: The LASSO, SCAD, and Thresholding

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