# How Wrong Can Your Counterfactual Be? Quantifying Confounding Bias for Continuous Treatments without a Control Group

arXiv: https://arxiv.org/abs/2603.07438 · HTML: https://mlsanity.com/paper/2603.07438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 26 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders](https://mlsanity.com/paper/1902.00450/) (2019)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Sensitivity to Unobserved Confounding in Studies with Factor-structured Outcomes](https://mlsanity.com/paper/2208.06552/) (2022)
- [Causal Data Science for Financial Stress Testing](https://mlsanity.com/paper/1703.03076/) (2017)

## Abstract (arXiv)

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.