Research map / Probabilistic and scientific modeling / Treatment effects
Beyond the Average: Distributional Causal Inference under Imperfect Compliance
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Proposes a regression-adjusted, Neyman-orthogonal estimator of local distributional treatment effects (LDTE) for compliers under covariate-adaptive randomization with noncompliance, proves asymptotic normality and semiparametric efficiency, and applies it to the Oregon Health Insurance Experiment.
Problem
Estimating distributional treatment effects for compliers in randomized experiments with covariate-adaptive randomization and imperfect compliance, where standard methods only handle average effects or full compliance.
Approach
Combines instrumental-variable identification of the complier outcome CDF difference (LDTE) with distribution regression nuisance functions, AIPW-style Neyman-orthogonal moments, and cross-fitting, under stratified/CAR designs with heterogeneous assignment probabilities.
Key results
- In simulations, ML-adjusted (gradient boosting) LDTE estimator reduces RMSE by up to 50% relative to the unadjusted estimator, while linear adjustment yields 1-10% gains.
- On the Oregon experiment, regression adjustment reduces LDTE standard errors by about 0.5-15% and LPTE standard errors by about 3.5-26.5% across most of the distribution.
- The regression-adjusted analysis finds the probability of zero ED visits decreases by 9 percentage points (SE 4.2 pp) among compliers.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add linear regression adjustment | LDTE estimator · Nonlinear high-dimensional simulation (quantiles 0.1–0.9) | RMSE: 1–10% | Helped |
| Add gradient boosting regression adjustment with 2-fold cross-fitting | LDTE estimator · Nonlinear high-dimensional simulation (quantiles 0.1–0.9) | RMSE: up to 50% | Helped |
| Use gradient boosting regression adjustment with 2-fold cross-fitting instead of no adjustment | LDTE estimator · Nonlinear high-dimensional simulation (quantiles 0.1–0.9) | 95% CI length | Helped |
| Use gradient boosting regression adjustment with 2-fold cross-fitting instead of no adjustment | LDTE estimator · Nonlinear high-dimensional simulation (quantiles 0.1–0.9) | Empirical coverage: up to 0.98–1.00 | Mixed |
| Add regression adjustment using 28 pre-treatment covariates | LDTE estimator · Oregon Health Insurance Experiment (ED visits) | Standard error: 0.5–15% | Helped |
| Add regression adjustment using 28 pre-treatment covariates | LPTE estimator · Oregon Health Insurance Experiment (ED visits) | Standard error: 3.5–26.5% | Mixed |
| Add insurance coverage | Compliers in the Oregon Health Insurance Experiment · ED visits; zero visits | LPTE: decreases by 9 percentage points (pp) | Helped |
| Add insurance coverage | Compliers in the Oregon Health Insurance Experiment · ED visits; five visits | LPTE: increase of approximately 1.7 pp | Mixed |
Surprising findings
- ML adjustment shows slight over-coverage (up to 0.98-1.00) in simulations, indicating conservative intervals.
- Regression adjustment slightly increases standard errors for LPTE at y in {0,1,2,3} in the Oregon application.
Limitations
- Relies on standard IV assumptions (monotonicity, exclusion restriction) and binary treatment only.
- Finite-sample performance depends on quality of nuisance estimation.
- Conservative coverage with ML adjustment in simulations.
Experimental setup
Datasets: Oregon Health Insurance Experiment simulated data (n=500, 1000, 5000)
Benchmarks: Oregon Health Insurance Experiment (ED visits, n=17,021) simulation study
Metrics: RMSE average 95% CI length empirical coverage standard error reduction
Baselines: unadjusted LDTE estimator linear regression-adjusted LDTE estimator
Builds on: local average treatment effect (LATE) augmented inverse propensity weighting cross-fitting (double machine learning) Neyman orthogonality
Closest papers by meaning
- On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization (ICML 2025 · similarity 0.92)
- Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reduction (ICML 2024 · similarity 0.89)
- Impossibility of Distribution-Free Predictive Inference for Individual Treatment Effects (NeurIPS 2026 · similarity 0.89)
- Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data (NeurIPS 2024 · similarity 0.87)
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- Optimistic Algorithms for Adaptive Estimation of the Average Treatment Effect (ICML 2025 · similarity 0.87)
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