Caveats for Causal Reasoning with Equilibrium Models

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Counterfactual reasoning and learning systems: the example of computational advertising (2012, background): “Quantities measured when a feedback causal system reaches equilibrium often display conditional independence patterns that cannot be represented with directed acyclic graphs (Lauritzen and Richardson, 2002; Dash, 2003).”
Network inference using steady-state data and Goldbeter-Koshland kinetics (2012, background): “The chemical reaction that gives product Xi from substrate X0i is known as phosphorylation and is catalysed by kinases XE (E ∈ Ei).”
Learning Why Things Change: The Difference-Based Causality Learner (2010, methodology): “Dash [2003, 2005] shows that some dynamic systems do not obey Equilibration-Manipulation Commutabil-ity (EMC), i.e., the causal graph that results when an equilibrium model is manipulated can be diﬀerent from the (true) graph that results when the dynamic model is manipulated and then equilibrated.”