Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations (1309.4686v3)

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.

• The paper introduces a doubly robust estimator for average treatment effects that remains valid even when covariates outnumber observations.
• It employs group lasso for efficient covariate selection and derives uniform confidence intervals under approximate sparsity conditions.
• Empirical tests, including simulations and an application to the NSW data, confirm the estimator’s reliability across diverse high-dimensional scenarios.

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

This paper by Max H. Farrell addresses the challenges associated with estimating average treatment effects (ATEs) in settings where the number of covariates may exceed the number of observations, a situation often encountered in modern empirical studies. The principal contribution is the development of a robust inference methodology that remains valid despite model selection uncertainty, especially in high-dimensional contexts.

Methodological Contributions

The paper proposes a doubly-robust estimator for ATEs, capable of handling model selection errors and variability in covariate estimation. This estimator is consistent if either the treatment model or the outcome regression model is specified correctly, thus providing robustness against misspecification common in empirical applications with high-dimensional data. The introduction of the group lasso for covariate selection is a novel approach for managing multivalued treatments with grouping structures, improving estimation accuracy and interpretability.

In terms of statistical guarantees, the paper offers detailed asymptotic results, proving the uniform validity of confidence intervals for ATEs across a wide range of potential data-generating processes. This is accomplished by showing that certain first-stage convergence rates for the covariate selection and estimation steps are sufficient to attain reliable inference. The conditions demonstrated are more nuanced than the classical $n^{1/4}$ rate, leveraging the properties of the doubly-robust estimator to enforce milder assumptions.

Theoretical Implications

The theoretical results hinge on the concept of approximate sparsity in high-dimensional models, where only a small subset of covariates or transformed covariates are influential for determining treatment effects. This notion of sparsity allows for the development of model selection techniques, such as the group lasso, that can efficiently handle a vast number of potential covariates by concentrating on the most informative ones.

Furthermore, the paper explores the challenging aspects of post-selection inference, providing non-asymptotic bounds and detailed mathematical derivations to support model selection outcomes via group lasso in both the multinomial logistic and linear regression settings. The analytical treatment extends to proofs of consistency and asymptotic normality for the proposed estimators, ensuring that reliable statistical inference is achievable in practice.

Practical Applications and Further Research

Empirically, the methodology is applied to the National Supported Work (NSW) demonstration data, revisiting previously established results with a focus on the objectivity and robustness of model selection. The simulation studies complement this empirical application, illustrating the estimator's robustness across a variety of settings with differing sparsity levels and signal strengths.

The research foresees several potential avenues for further exploration, including but not limited to optimal penalty parameter selection for the lasso methods employed and extending the results to dynamic treatment regimes and more complex decision-making scenarios. Additionally, the treatment of high-dimensional models in longitudinal or panel data contexts offers a promising domain for expanding the application of these robust inference techniques.

In conclusion, Farrell's work represents a significant step forward in the field of econometrics and causal inference, offering a comprehensive framework for dealing with the intricacies of high-dimensional data while ensuring reliable inference for average treatment effects.