A note on the correctness of the causal ordering algorithm

In this paper we examine in detail the algorithm of Simon [H.A. Simon, Causal ordering and identifiability, in: W.C. Hood, T.C. Koopmans (Eds.), Studies in Econometric Method. Cowles Commission for Research in Economics, Monograph No. 14, John Wiley & Sons, Inc., New York, 1953, pp. 49-74, Chapter III], called the causal ordering algorithm (COA), used for constructing the ''causal ordering'' of a system given a complete specification of the system in terms of a set of ''structural'' equations that govern the variables in the system. This algorithm constructs a graphical characterization of the model in a form that we call a partial causal graph. Simon argued in [H.A. Simon, Causal ordering and identifiability, in: W.C. Hood, T.C. Koopmans (Eds.), Studies in Econometric Method. Cowles Commission for Research in Economics, Monograph No. 14, John Wiley & Sons, Inc., New York, 1953, pp. 49-74, Chapter III] and subsequent papers that a graph so generated explicates causal structure among variables in the model. We formalize this claim further by proving that any causal model based on a one-to-one correspondence between equations and variables must be consistent with the COA.

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