# Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score

arXiv: https://arxiv.org/abs/1812.08683 · HTML: https://mlsanity.com/paper/1812.08683/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2018.

## Built on by (most cited first, 12 of 12)

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- [Estimating Average Treatment Effects with Support Vector Machines](https://mlsanity.com/paper/2102.11926/) (2021)
- [Calibrated and Conformal Propensity Scores for Causal Effect Estimation](https://mlsanity.com/paper/2306.00382/) (2023)
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- [Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Model](https://mlsanity.com/paper/2405.11377/) (2024)
- [Towards Representation Learning for Weighting Problems in Design-Based Causal Inference](https://mlsanity.com/paper/2409.16407/) (2024)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Optimal use of a black-box learner in semiparametric estimation](https://mlsanity.com/paper/2607.21541/) (2026)
- [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)
- [Incorporating External Controls for Estimating the Average Treatment Effect on the Treated with High-Dimensional Data: Retaining Double Robustness and Ensuring Double Safety](https://mlsanity.com/paper/2509.20586/) (2025)
- [Data-Poisoning Audits for Causal Effect Estimation](https://mlsanity.com/paper/2607.19692/) (2026)

## Abstract (arXiv)

In this paper, we propose a robust method to estimate the average treatment effects in observational studies when the number of potential confounders is possibly much greater than the sample size. We first use a class of penalized M-estimators for the propensity score and outcome models. We then calibrate the initial estimate of the propensity score by balancing a carefully selected subset of covariates that are predictive of the outcome. Finally, the estimated propensity score is used to construct the inverse probability weighting estimator. We prove that the proposed estimator, which has the sample boundedness property, is root-n consistent, asymptotically normal, and semiparametrically efficient when the propensity score model is correctly specified and the outcome model is linear in covariates. More importantly, we show that our estimator remains root-n consistent and asymptotically normal so long as either the propensity score model or the outcome model is correctly specified. We provide valid confidence intervals in both cases and further extend these results to the case where the outcome model is a generalized linear model. In simulation studies, we find that the proposed methodology often estimates the average treatment effect more accurately than the existing methods. We also present an empirical application, in which we estimate the average causal effect of college attendance on adulthood political participation. Open-source software is available for implementing the proposed methodology.