  A common assumption in causal inference from observational data is that there
is no hidden confounding. Yet it is, in general, impossible to verify this
assumption from a single dataset. Under the assumption of independent causal
mechanisms underlying the data-generating process, we demonstrate a way to
detect unobserved confounders when having multiple observational datasets
coming from different environments. We present a theory for testable
conditional independencies that are only absent when there is hidden
confounding and examine cases where we violate its assumptions: degenerate &
dependent mechanisms, and faithfulness violations. Additionally, we propose a
procedure to test these independencies and study its empirical finite-sample
behavior using simulation studies and semi-synthetic data based on a real-world
dataset. In most cases, the proposed procedure correctly predicts the presence
of hidden confounding, particularly when the confounding bias is large.
