  Recursive max-linear structural equation models with regularly varying noise
variables are considered. Their causal structure is represented by a directed
acyclic graph (DAG). The problem of identifying a recursive max-linear model
and its associated DAG from its matrix of pairwise tail dependence coefficients
is discussed. For example, it is shown that if a causal ordering of the
associated DAG is additionally known, then the minimum DAG representing the
recursive structural equations can be recovered from the tail dependence
matrix. For the relevant subclass of recursive max-linear models,
identifiability of the associated minimum DAG from the tail dependence matrix
and the initial nodes is shown. Algorithms find the associated minimum DAG for
the different situations. Furthermore, given a tail dependence matrix, an
algorithm outputs all compatible recursive max-linear models and their
associated minimum DAGs.
