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A Non-parametric Direct Learning Approach to Heterogeneous Treatment Effect Estimation under Unmeasured Confounding
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Proposes IV-DL, a direct-learning framework that estimates CATE under unmeasured confounding by regressing an IV-weighted Wald-type pseudo-outcome, plus residualized robust variants (IV-RDL1/IV-RDL2) evaluated in simulations and a census labor-force example.
Problem
Estimating conditional average treatment effects (CATE) when unmeasured confounding invalidates the standard no-unmeasured-confounding assumption, in observational studies or RCTs with non-compliance.
Approach
Identifies CATE as a conditional Wald ratio using a binary instrumental variable and turns it into a weighted least squares regression on an IV-weighted pseudo-outcome (direct learning under IV), then residualizes the outcome by conditional mean estimates to gain efficiency and multiple robustness.
Key results
- In simulation Setting 1, IV-RDL1 achieved MSE 40.5 (x10^-2) versus 89.6 for causal forest and 55.5 for IV-DL, with the best AR (84.6) and Value (89.9).
- In Setting 2 (nonlinear CATE), IV-RDL1 attained MSE 140 versus 149 for causal forest, and AR 77.9 versus 70.1 for causal forest.
- The census analysis found older mothers and mothers with low-income fathers show differing effects of a third child on employment, with five subgroups identified by a regression tree on estimated CATE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Residualize the outcome using a function of covariates instead of using unresidualized IV-DL (ablation) | IV-DL · Simulation Setting 1 | MSE: 55.5(3.8) -> 40.5(2.9) | Helped |
| Residualize the outcome using a function of covariates instead of using unresidualized IV-DL (ablation) | IV-DL · Simulation Setting 1 | AR: 81.4(1) -> 84.6(0.8) | Helped |
| Residualize the outcome using a function of covariates instead of using unresidualized IV-DL (ablation) | IV-DL · Simulation Setting 1 | Value: 87.1(1) -> 89.9(0.9) | Helped |
| Residualize the outcome using a function of covariates instead of using unresidualized IV-DL (ablation) | IV-DL · Simulation Setting 2 | MSE: 164(8.9) -> 140(7.7) | Helped |
| Residualize the outcome using a function of covariates instead of using unresidualized IV-DL (ablation) | IV-DL · Simulation Setting 2 | AR: 77.1(0.9) -> 77.9(0.8) | Helped |
| Residualize the outcome using a function of covariates instead of using unresidualized IV-DL (ablation) | IV-DL · Simulation Setting 2 | Value: 89.9(1) -> 90.6(0.9) | Helped |
| Use IV-RDL1 rather than the strongest non-proposed baseline | CATE and ITR methods · Simulation Setting 1 | MSE: 66.3(2.3) -> 40.5(2.9) | Helped |
| Use IV-RDL1 rather than the strongest non-proposed baseline | CATE and ITR methods · Simulation Setting 1 | Value: 85.4(0.7) -> 89.9(0.9) | Helped |
| Use IV-RDL1 rather than the strongest non-proposed baseline | CATE and ITR methods · Simulation Setting 2 | AR: 70.1(1) -> 77.9(0.8) | Helped |
| Use IV-RDL1 rather than the strongest non-proposed baseline | CATE and ITR methods · Simulation Setting 2 | Value: 83.5(1.2) -> 90.6(0.9) | Helped |
| Use IV-RDL1 rather than IV-RDL2 residualization (ablation) | IV-DL · Simulation Setting 1 | MSE: 42.5(3.3) -> 40.5(2.9) | Helped |
| Use IV-RDL1 rather than IV-RDL2 residualization (ablation) | IV-DL · Simulation Setting 2 | MSE: 142(7.4) -> 140(7.7) | No clear effect |
Surprising findings
- The unresidualized IV-DL outperformed most competitors, and in some settings IV-DL had larger MSE than causal forest (e.g., Setting 2 MSE 164 vs 149), showing residualization matters for the estimator's efficiency.
Limitations
- Extreme inverse propensity weights can cause instability and biased results.
- Requires a valid binary instrument and assumptions (e.g., no additive interaction between U and Z in predicting A); only binary treatment and binary IV considered.
- Robustness relies on correct specification in some scenarios; delta must be consistently estimated.
Experimental setup
Datasets: simulated data (5 uniform covariates, binary IV, Bridge-distributed confounder) 1980 US census 80PUMS married mothers with two or more children
Benchmarks: simulation settings 1-4 with MSE, AR and Value metrics 1980 census 80PUMS data analysis
Metrics: MSE AR (correct ITR classification rate) Value
Baselines: BART RD IPW-MR Causal forest with IV MRIV IV-DL (unresidualized)
Builds on: Direct Learning Robust Direct Learning Multiply robust IV estimation (Wang and Tchetgen Tchetgen) Causal Forest with IV (GRF) Bridge distribution for IV models
Closest papers by meaning
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