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

TL;DR

This paper introduces a partial identification framework for causal stress testing with continuous treatments and no control group, addressing confounding bias and providing finite-sample uncertainty quantification.

Contribution

It develops a novel envelope-based approach with interpretable sensitivity parameters and combines it with conformal prediction for robust inference.

Findings

Standard models are causally biased and under-cover in stress testing.

The proposed framework achieves near-nominal coverage in semi-synthetic experiments.

Recursive estimation is preferable under certain conditions.

Abstract

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.