Directed Cyclic Graphical Representations of Feedback Models
This work addresses the representation of feedback models in economic processes, offering a generalization of DAG-based methods, but it appears incremental as it builds on existing graphical model frameworks.
The paper tackles the problem of representing non-recursive structural equation models, such as those used in economics, by developing directed cyclic graphs with independent errors, and it generalizes this to systems with dependent errors and provides a sufficient condition for conditional independence in non-linear systems.
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.