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Multiply-Robust Causal Change Attribution
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Proposes a multiply-robust estimator for causal change attribution that combines nested regression and re-weighting over a causal DAG, with asymptotic normality results and Shapley/path attribution extensions.
Problem
Attributing the change in an outcome distribution between two samples to each causal mechanism in a known causal DAG, which requires estimating counterfactual distributions that are not directly observed.
Approach
A multiply-robust estimating equation that combines sequentially nested regressions with RN-derivative (re-weighting) debiasing terms, so each causal mechanism needs either a correct regression or correct weights; the estimator is plugged into Shapley values and path-based attribution with valid inference.
Key results
- In Monte Carlo Design 1 with correctly specified parametric learners, the multiply-robust estimator performs statistically indistinguishable from the best of regression-only or re-weighting-only methods.
- When either regression or weights are misspecified (quadratic terms omitted), the MR estimator performs as well as the correctly specified method while the misspecified single method has much higher error.
- In the CPS 2015 application, the contribution of P(wage | occupation, education) is the largest Shapley component, with education positive and significant and occupation given education negative and significant, in a gender wage gap of $7.91/hour.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Combine regression and re-weighting in the multiply-robust estimator instead of using regression or re-weighting alone | Causal change attribution, Design 1 with correctly specified parametric learners · Monte Carlo Design 1 | MAE | No clear effect |
| Use the multiply-robust estimator when either the regression or the weights are misspecified and the other component is correctly specified | Causal change attribution, Design 1 · Monte Carlo Design 1 | MAE | Helped |
| Use the multiply-robust estimator with misspecified parametric regression and weights | Causal change attribution, Design 1 · Monte Carlo Design 1 | Shapley value error | Mixed |
| Use the multiply-robust estimator with neural-network or gradient-boosting learners instead of regression-only or re-weighting-only methods | Causal change attribution, Design 1 · Monte Carlo Design 1 | MAE | Helped |
| Use the multiply-robust estimator instead of regression-only or re-weighting-only methods | Causal change attribution, Design 2 · Monte Carlo Design 2 | worst-case absolute error | Helped |
| Shift the education mechanism in the gender wage-gap attribution | Multiply-Robust Causal Change Attribution · CPS 2015 gender wage gap | Shapley value | Helped |
| Shift the occupation distribution conditional on education in the gender wage-gap attribution | Multiply-Robust Causal Change Attribution · CPS 2015 gender wage gap | Shapley value | Hurt |
Limitations
- Requires a known causal DAG (or causal ordering) and no unobserved confounding of the mediators/outcome by T.
- Asymptotic guarantees rely on overlap and product-rate conditions on regression and weight estimation.
- Shapley computation requires 2^(K+1) counterfactual estimates.
Experimental setup
Datasets: Current Population Survey 2015
Benchmarks: Monte Carlo simulations CPS 2015 gender wage gap
Metrics: mean absolute error absolute error of PATH estimates
Baselines: regression-only estimator re-weighting-only estimator do-Shapley values
Builds on: double/debiased machine learning doubly robust mediation estimation Shapley values Oaxaca-Blinder decomposition
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