Graphical Models for Structural Vector Autoregressions

In this paper a method to identify the causal structure associated with a VAR model is proposed. The structure is described by means of a graph, which provides a rigorous language to analyze the statistical and logical properties of causal relations. Under some general assumptions, causal relations are associated with a set of vanishing partial correlations among the variables that constitute them. In order to infer the causal structure among the contemporaneous variable, tests on vanishing partial correlations among the estimated residuals of a VAR are used, jointly with background knowledge. This method is applied to an updated version of the King et al. (1991) dataset and it allows to obtain an orthogonalization of the residuals coherent with the causal structure among the contemporaneous variables and alternative to the standard one, which is based on the Choleski factorization of the covariance matrix of the residuals. The impulse response functions calculated, with the method proposed here, for the King et al. (1991) model confirm their results about the fact that US macroeconomic data do not support the hypothesis that real permanent shocks are the dominant source of business-cycle fluctuations.