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Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data
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Combines confounded observational data with a weak-instrument IV study by first estimating biased CATEs from observational data, then correcting the bias via compliance-weighted regression on IV data (parametric or shared-representation variants), with consistency rates and simulation/401(k) experiments.
Problem
Estimating heterogeneous treatment effects (CATEs) from observational data is biased by unobserved confounding, while IV-based CATE estimates have high variance or are undefined where instrument compliance is low or zero.
Approach
A two-stage framework: learn a confounded CATE from observational data, then estimate its bias via weighted ERM on IV data using compliance-times-instrument-variance weights, so zero-compliance regions are extrapolated from covariate-level bias structure (parametric basis or learned shared representation).
Key results
- In simulations with 5,000-sample datasets, the corrected CATE from the parametric method is approximately unbiased with low variance across covariates, while the IV-only CATE has high variance in low-compliance regions and the observational CATE is biased.
- Theorems give consistency with rate O_p(r_gamma + r_pi + r_tauO + 1/sqrt(n_E)) for the parametric estimator and an extra 1/sqrt(n_O) term for the shared-representation estimator.
- On 401(k) data, the corrected CATE closely matches the IV CATE estimate, while the observational estimate is upwardly biased, even with artificially induced non-compliance for individuals with under 12 years of education.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| combine observational CATE estimates with compliance-weighted IV correction using parametric extrapolation | CATE estimation with Random Forest learners · Synthetic simulation | CATE bias | Helped |
| combine observational CATE estimates with compliance-weighted IV correction using parametric extrapolation | CATE estimation with Random Forest learners · Synthetic simulation | CATE variance | Helped |
| combine observational CATE estimates with IV data using a shared learned representation | CATE estimation with neural network learners · Synthetic simulation | CATE bias | Helped |
| combine observational CATE estimates with IV data using a shared learned representation | CATE estimation with neural network learners · Synthetic simulation | CATE variance | Helped |
| combine observational data with IV data using parametric extrapolation | 401(k) CATE estimation · 401(k) participation and financial wealth | CATE agreement with IV estimate | Helped |
Surprising findings
- Observational treatment effect estimates on 401(k) data are upwardly biased, plausibly due to unobserved financial literacy.
Limitations
- Consistency relies on realizability of the bias function in the chosen class; misspecification yields asymptotic bias.
- Requires unconfounded compliance and nonzero compliance on a set of positive measure; clipping of compliance scores is needed in practice.
- Neural-network representation rates scale poorly with network size for over-parameterized models.
Experimental setup
Datasets: simulated observational and IV datasets 1991 Survey of Income and Program Participation (401(k))
Benchmarks: synthetic DGP simulation (100 runs) 401(k) SIPP real-data case study
Metrics: mean and standard error of CATE estimates across simulations agreement with IV CATE without artificial non-compliance
Baselines: observational CATE estimate (confounded) IV CATE estimate without weighting
Builds on: two-stage least squares Wald / LATE ratio estimator T-learner generalized least squares
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