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The Causal Impact of Credit Lines on Spending Distributions
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Extends DR, IPW and DML causal estimators to distribution-valued outcomes in Wasserstein space with multiple treatments, using a neural functional regression net (NFR Net), and applies them to estimate the effect of credit lines on e-commerce spending distributions.
Problem
Causal effects of credit lines on consumer spending are usually measured with scalar summaries (e.g., average spending), discarding the information in the full spending distribution; classical causal inference assumes scalar outcomes and single-valued treatments.
Approach
Defines a causal effect map in Wasserstein space (difference of quantile functions of Wasserstein barycenters across multiple treatment levels), proposes DR, IPW and cross-fitted DML estimators for it, and a neural functional regression network (NFR Net) that maps (treatment, covariates) to a quantile function via a basis expansion.
Key results
- In the synthetic experiment, NFR Net with DML achieves average MAE 0.034 ± 0.026, the best among compared methods (Ridge DML 0.034 ± 0.027, D/DML 0.037).
- On real data, spending at the 90% quantile rises from 381.0 (Low) to 1020.3 (High) credit lines (about 167.8% increase), while the 10% quantile rises only about 9.3% (28.0 to 30.6).
- Credit lines increase spending at all nine reported quantiles (Low→Middle and Low→High causal effect maps are positive everywhere), with larger effects at higher quantiles.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use NFR instead of the strongest listed linear baseline (Ridge) for DR | Synthetic causal effect estimation · Synthetic experiment | MAE: 0.118 ± 0.050 -> 0.052 ± 0.027 | Helped |
| Use NFR instead of Lasso for IPW | Synthetic causal effect estimation · Synthetic experiment | MAE: 0.044 ± 0.021 -> 0.044 ± 0.021 | No clear effect |
| Use NFR instead of Ridge for DML | Synthetic causal effect estimation · Synthetic experiment | MAE: 0.034 ± 0.027 -> 0.034 ± 0.026 | No clear effect |
| Increase credit line from Low to High | E-commerce users' spending distributions · E-commerce users, 10% quantile | spending: 28.0 -> 30.6; 9.29%↑ | Helped |
| Increase credit line from Low to High | E-commerce users' spending distributions · E-commerce users, 90% quantile | spending: 381.0 -> 1020.3; 167.80%↑ | Helped |
Surprising findings
- Under the DR estimator, NFR Net's MAE at Q=30% (0.104) is worse than the Lasso and Ridge baselines (0.064 and 0.075), so NFR Net is not uniformly best across quantiles.
- IPW results are nearly identical across all methods because the same random forest propensity model is used, so the IPW comparison is not informative about the outcome model.
Limitations
- Credit line is treated as discrete (Low/Middle/High) rather than continuous; continuous treatment is left to future work.
- Real-data ground truth is unavailable, so evaluation relies on a synthetic simulation; the empirical dataset is proprietary and not released.
- Consistency results depend on several convergence assumptions and rates for nuisance estimators (e.g., alpha_N, nu_N = o(N^-1/2)).
Experimental setup
Datasets: synthetic data from a data generation process e-commerce platform spending and credit line data (4,043 users)
Benchmarks: synthetic causal effect map simulation real e-commerce credit line dataset
Metrics: mean absolute error (MAE) mean and 95% CI of quantile causal map
Baselines: Lasso Ridge Elastic net MCP D/DML
Builds on: Double machine learning Inverse propensity weighting Wasserstein barycenter Functional regression
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