A Bootstrap Method for Identifying and Evaluating a Structural Vector AutoregressionÅ

Graph-theoretic methods of causal search based on the ideas of Pearl (2000), Spirtes et al. (2000), and others have been applied by a number of researchers to economic data, particularly by Swanson and Granger (1997) to the problem of finding a data-based contemporaneous causal order for the structural vector autoregression, rather than, as is typically done, assuming a weakly justified Choleski order. Demiralp and Hoover (2003) provided Monte Carlo evidence that such methods were effective, provided that signal strengths were sufficiently high. Unfortunately, in applications to actual data, such Monte Carlo simulations are of limited value, as the causal structure of the true data-generating process is necessarily unknown. In this paper, we present a bootstrap procedure that can be applied to actual data (i.e. without knowledge of the true causal structure). We show with an applied example and a simulation study that the procedure is an effective tool for assessing our confidence in causal orders identified by graph-theoretic search algorithms. I. Identification of the structural vector autoregression The structural vector autoregression (SVAR) has become a workhorse of empirical macroeconomics. The main hurdle to using the SVAR is to identify the system so that *We thank Katarina Juselius, Søren Johansen, David Hendry, the participants in seminars at the University of Copenhagen and Oxford University, and two anonymous referees for comments on an earlier draft. JEL Classification numbers: C30, C32, C51.