Directed Cyclic Graphical Representations of Feedback Models
  The use of directed acyclic graphs (DAGs) to represent conditional
independence relations among random variables has proved fruitful in a variety
of ways. Recursive structural equation models are one kind of DAG model.
However, non-recursive structural equation models of the kinds used to model
economic processes are naturally represented by directed cyclic graphs with
independent errors, a characterization of conditional independence errors, a
characterization of conditional independence constraints is obtained, and it is
shown that the result generalizes in a natural way to systems in which the
error variables or noises are statistically dependent. For non-linear systems
with independent errors a sufficient condition for conditional independence of
variables in associated distributions is obtained.
