Graphical models for structural vector autoregressions

The identification of a VAR requires differentiating between correlation and causation. This paper presents a method to deal with this problem. Graphical models, which provide a rigorous language to analyze the statistical and logical properties of causal relations, associate a particular set of vanishing partial correlations to every possible causal structure. The structural form is described by a directed graph and from the analysis of the partial correlations of the residuals the set of acceptable causal structures is derived. This procedure is applied to an updated version of the King et al. (American Economic Review, 81, (1991), 819) data set and it yields an orthogonalization of the residuals consistent with the causal structure among contemporaneous variables and alternative to the standard one, based on a Choleski factorization of the covariance matrix of the residuals.