  Regression on observational data can fail to capture a causal relationship in
the presence of unobserved confounding. Confounding strength measures this
mismatch, but estimating it requires itself additional assumptions. A common
assumption is the independence of causal mechanisms, which relies on
concentration phenomena in high dimensions. While high dimensions enable the
estimation of confounding strength, they also necessitate adapted estimators.
In this paper, we derive the asymptotic behavior of the confounding strength
estimator by Janzing and Sch\"olkopf (2018) and show that it is generally not
consistent. We then use tools from random matrix theory to derive an adapted,
consistent estimator.
