# Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap

arXiv: https://arxiv.org/abs/2301.05703 · HTML: https://mlsanity.com/paper/2301.05703/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 172 references that are in the map.
- First posted on arXiv 13 Jan 2023.

## Builds on (most cited first, 30 of 49)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Orthogonal Random Forest for Causal Inference](https://mlsanity.com/paper/1806.03467/) (2018)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [Augmented Minimax Linear Estimation](https://mlsanity.com/paper/1712.00038/) (2017)
- [Program Evaluation and Causal Inference with High-Dimensional Data](https://mlsanity.com/paper/1311.2645/) (2013)
- [Orthogonal Machine Learning: Power and Limitations](https://mlsanity.com/paper/1711.00342/) (2017)
- [Bayesian Causal Inference: A Critical Review](https://mlsanity.com/paper/2206.15460/) (2022)
- [Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations](https://mlsanity.com/paper/1705.00998/) (2017)
- [Robust Inference Using Inverse Probability Weighting](https://mlsanity.com/paper/1810.11397/) (2018)
- [Selective inference for effect modification via the lasso](https://mlsanity.com/paper/1705.08020/) (2017)
- [Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score](https://mlsanity.com/paper/1812.08683/) (2018)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness](https://mlsanity.com/paper/1712.04594/) (2017)
- [Debiased Inverse Propensity Score Weighting for Estimation of Average Treatment Effects with High-Dimensional Confounders](https://mlsanity.com/paper/2011.08661/) (2020)
- [Randomization Inference for Treatment Effect Variation](https://mlsanity.com/paper/1412.5000/) (2014)
- [Propensity score weighting under limited overlap and model misspecification](https://mlsanity.com/paper/2006.04038/) (2020)
- [Doubly Robust Uniform Confidence Band for the Conditional Average Treatment Effect Function](https://mlsanity.com/paper/1601.02801/) (2016)
- [Adaptive normalization for IPW estimation](https://mlsanity.com/paper/2106.07695/) (2021)

## Abstract (arXiv)

In this paper, I try to tame "Basu's elephants" (data with extreme selection on observables). I propose new practical large-sample and finite-sample methods for estimating and inferring heterogeneous causal effects (under unconfoundedness) in the empirically relevant context of limited overlap. I develop a general principle called "Stable Probability Weighting" (SPW) that can be used as an alternative to the widely used Inverse Probability Weighting (IPW) technique, which relies on strong overlap. I show that IPW (or its augmented version), when valid, is a special case of the more general SPW (or its doubly robust version), which adjusts for the extremeness of the conditional probabilities of the treatment states. The SPW principle can be implemented using several existing large-sample parametric, semiparametric, and nonparametric procedures for conditional moment models. In addition, I provide new finite-sample results that apply when unconfoundedness is plausible within fine strata. Since IPW estimation relies on the problematic reciprocal of the estimated propensity score, I develop a "Finite-Sample Stable Probability Weighting" (FPW) set-estimator that is unbiased in a sense. I also propose new finite-sample inference methods for testing a general class of weak null hypotheses. The associated computationally convenient methods, which can be used to construct valid confidence sets and to bound the finite-sample confidence distribution, are of independent interest. My large-sample and finite-sample frameworks extend to the setting of multivalued treatments.