Searching for the Causal Structure of a Vector Autoregression

Vector autoregressions (VARs) are economically interpretable only when identified by being transformed into a structural form (the SVAR) in which the contemporaneous variables stand in a well-defined causal order. These identifying transformations are not unique. It is widely believed that practitioners must choose among them using a priori theory or other criteria not rooted in the data under analysis. We show how to apply graph-theoretic methods of searching for causal structure based on relations of conditional independence to select among the possible causal orders – or at least to reduce the admissible causal orders to a narrow equivalence class. The graph-theoretic approaches were developed by computer scientists and philosophers (Pearl, Glymour, Spirtes among others) and applied to cross-sectional data. We provide an accessible introduction to this work. Then building on the work of Swanson and Granger (1997), we show how to apply it to searching for the causal order of an SVAR. We present simulation results to show how the efficacy of the search method algorithm varies with signal strength for realistic sample lengths. Our findings suggest that graph-theoretic methods may prove to be a useful tool in the analysis of SVARs.