  Causal questions are omnipresent in many scientific problems. While much
progress has been made in the analysis of causal relationships between random
variables, these methods are not well suited if the causal mechanisms only
manifest themselves in extremes. This work aims to connect the two fields of
causal inference and extreme value theory. We define the causal tail
coefficient that captures asymmetries in the extremal dependence of two random
variables. In the population case, the causal tail coefficient is shown to
reveal the causal structure if the distribution follows a linear structural
causal model. This holds even in the presence of latent common causes that have
the same tail index as the observed variables. Based on a consistent estimator
of the causal tail coefficient, we propose a computationally highly efficient
algorithm that estimates the causal structure. We prove that our method
consistently recovers the causal order and we compare it to other
well-established and non-extremal approaches in causal discovery on synthetic
and real data. The code is available as an open-access R package.
