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Data-Driven Selection of Instrumental Variables for Additive Nonlinear, Constant Effects Models
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Proposes the CAT (Cross Auxiliary-based independent Test) condition and a distance-correlation-based algorithm to select valid instrumental variable sets under additive nonlinear, constant effects models.
Problem
Selecting valid instrumental variable sets from observational data when the structural relations are nonlinear and the instruments may violate exclusion restriction (C2) and exogeneity (C3), where prior methods assume additive linear models.
Approach
Tests cross-independence between auxiliary variables (outcome minus the IV-based causal effect times treatment) and the other candidate IV; shows this CAT condition is necessary and, under an algebraic equation condition, sufficient for valid IV sets, and implements selection by minimizing summed distance correlations.
Key results
- On synthetic ANICE data across four cases and sample sizes 1k-5k (100 repetitions), CAT consistently yields causal-effect estimates closest to the true beta=1 with minimal variance, outperforming NAIVE, MR-Egger, TSHT, CIIV, sisVIVE, and IV-tetrad.
- On the Colonial Origins data, the candidate set {Mor, Euro} is not rejected as valid (p-values 0.21 and 0.25), consistent with Acemoglu et al. (2001).
- On the Angrist & Evans data, the smallest distance correlation (0.022) is for {boys2, girls2}, consistent with prior findings that these are valid IVs.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the CAT algorithm instead of the comparison methods | causal-effect estimation in the ANICE model · Synthetic data, Cases 1–4 | causal-effect estimate accuracy | Helped |
| apply the CAT condition to {Mor, Euro}, conditioning on Lat | Ins → Ed in Colonial Origins Data · Colonial Origins Data | IV-set validity test: 0.21; 0.25 | No clear effect |
| apply CAT with K = 2 to the candidate IVs | morekids → weeksm1 · Children and Mothers’ Labor Supply | distance correlation: 0.022 | Helped |
Surprising findings
- Linear-model baselines such as MR-Egger perform poorly even in the nonlinear setting, and the NAIVE estimator is badly biased due to unmeasured confounders.
Limitations
- Assumes the causal effect beta is constant; nonlinear causal effects are left for future work.
- Requires at least two valid IVs and the algebraic equation condition (Assumption 1) for sufficiency; second-order moment conditions can miss some invalid sets.
- Requires the user to specify K (number of valid IVs), and exhaustive subset search scales combinatorially with the number of candidates.
Experimental setup
Datasets: Colonial Origins Data (Acemoglu et al., 2001) Children and Mothers' Labor Supply Data (Angrist & Evans, 1996)
Benchmarks: synthetic ANICE simulations (four cases) Colonial Origins Data Children and Mothers' Labor Supply Data
Metrics: estimated causal effect beta_hat (true beta=1) distance correlation p-values
Baselines: NAIVE MR-Egger TSHT CIIV sisVIVE IV-tetrad
Builds on: Silva & Shimizu IV-tetrad rank-faithfulness AIT condition IV-GIN TSHT MR-Egger
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