How Wrong Can Your Counterfactual Be? Quantifying Confounding Bias for Continuous Treatments without a Control Group
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917504436142080 |
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| author | Wang, Yu Liu, Xiangchen Li, Siguang |
| author_facet | Wang, Yu Liu, Xiangchen Li, Siguang |
| contents | Stress testing poses a causal question: how would portfolio credit losses change if the macroeconomy followed an adverse counterfactual path? Yet standard practice remains predictive and might be therefore vulnerable to omitted-variable bias. We propose a partial identification framework for causal stress testing in panel data with a continuous common treatment and no control group. By assuming that the unobserved confounder affects outcome and macro variables additively, we derive a closed-form confounding envelope parameterized by two interpretable sensitivity parameters. We further analyze two practical estimators -- recursive rollout and direct multi-horizon prediction -- derive non-asymptotic error bounds, and characterize when recursive compounding makes direct estimation preferable. For inference, we combine the identification envelope with importance-weighted conformal prediction, yielding finite-sample intervals that separate estimation uncertainty from identification uncertainty under covariate shift. In semi-synthetic experiments built from real U.S. unemployment paths, standard high-accuracy predictive models remain causally biased and substantially under-cover, whereas the proposed framework achieves near-nominal coverage across stress horizons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07438 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | How Wrong Can Your Counterfactual Be? Quantifying Confounding Bias for Continuous Treatments without a Control Group Wang, Yu Liu, Xiangchen Li, Siguang Artificial Intelligence Stress testing poses a causal question: how would portfolio credit losses change if the macroeconomy followed an adverse counterfactual path? Yet standard practice remains predictive and might be therefore vulnerable to omitted-variable bias. We propose a partial identification framework for causal stress testing in panel data with a continuous common treatment and no control group. By assuming that the unobserved confounder affects outcome and macro variables additively, we derive a closed-form confounding envelope parameterized by two interpretable sensitivity parameters. We further analyze two practical estimators -- recursive rollout and direct multi-horizon prediction -- derive non-asymptotic error bounds, and characterize when recursive compounding makes direct estimation preferable. For inference, we combine the identification envelope with importance-weighted conformal prediction, yielding finite-sample intervals that separate estimation uncertainty from identification uncertainty under covariate shift. In semi-synthetic experiments built from real U.S. unemployment paths, standard high-accuracy predictive models remain causally biased and substantially under-cover, whereas the proposed framework achieves near-nominal coverage across stress horizons. |
| title | How Wrong Can Your Counterfactual Be? Quantifying Confounding Bias for Continuous Treatments without a Control Group |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2603.07438 |