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

arXiv: https://arxiv.org/abs/1309.4686 · HTML: https://mlsanity.com/paper/1309.4686/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2013.

## Built on by (most cited first, 30 of 38)

- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Falsification before Extrapolation in Causal Effect Estimation](https://mlsanity.com/paper/2209.13708/) (2022)
- [β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap](https://mlsanity.com/paper/2110.05225/) (2021)
- [Neural Score Matching for High-Dimensional Causal Inference](https://mlsanity.com/paper/2203.00554/) (2022)
- [Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation](https://mlsanity.com/paper/2402.14264/) (2024)
- [A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond](https://mlsanity.com/paper/2205.10198/) (2022)
- [Double Robust Semi-Supervised Inference for the Mean: Selection Bias under MAR Labeling with Decaying Overlap](https://mlsanity.com/paper/2104.06667/) (2021)
- [Doubly Robust Interval Estimation for Optimal Policy Evaluation in Online Learning](https://mlsanity.com/paper/2110.15501/) (2021)
- [Double Robust Bayesian Inference on Average Treatment Effects](https://mlsanity.com/paper/2211.16298/) (2022)
- [Variable Importance Matching for Causal Inference](https://mlsanity.com/paper/2302.11715/) (2023)
- [Causal-StoNet: Causal Inference for High-Dimensional Complex Data](https://mlsanity.com/paper/2403.18994/) (2024)
- [Optimally taming biases in black-box models for efficient semiparametric estimation](https://mlsanity.com/paper/2606.06368/) (2026)
- [Robust Causal Learning for the Estimation of Average Treatment Effects](https://mlsanity.com/paper/2209.01805/) (2022)
- [Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators](https://mlsanity.com/paper/2306.10590/) (2023)
- [Unveiling the Potential of Robustness in Selecting Conditional Average Treatment Effect Estimators](https://mlsanity.com/paper/2402.18392/) (2024)
- [Calibrating doubly-robust estimators with unbalanced treatment assignment](https://mlsanity.com/paper/2403.01585/) (2024)
- [Causal inference through multi-stage learning and doubly robust deep neural networks](https://mlsanity.com/paper/2407.08560/) (2024)
- [Factor Informed Double Deep Learning For Average Treatment Effect Estimation](https://mlsanity.com/paper/2508.17136/) (2025)
- [Causal Inference in Possibly Nonlinear Factor Models](https://mlsanity.com/paper/2008.13651/) (2020)
- [Normalized Augmented Inverse Probability Weighting with Neural Network Predictions](https://mlsanity.com/paper/2108.01768/) (2021)
- [Moderately-Balanced Representation Learning for Treatment Effects with Orthogonality Information](https://mlsanity.com/paper/2209.01956/) (2022)
- [Convolutional neural networks for valid and efficient causal inference](https://mlsanity.com/paper/2301.11732/) (2023)
- [Active and Passive Causal Inference Learning](https://mlsanity.com/paper/2308.09248/) (2023)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Dynamic covariate balancing: estimating treatment effects over time with potential local projections](https://mlsanity.com/paper/2103.01280/) (2021)
- [Generalized Linear Models with Structured Sparsity Estimators](https://mlsanity.com/paper/2104.14371/) (2021)
- [An Interpretable Neural Network for Parameter Inference](https://mlsanity.com/paper/2106.05536/) (2021)
- [Heterogeneous Treatment Effect Bounds under Sample Selection with an Application to the Effects of Social Media on Political Polarization](https://mlsanity.com/paper/2209.04329/) (2022)
- [Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap](https://mlsanity.com/paper/2301.05703/) (2023)

## Abstract (arXiv)

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.