of A Bootstrap Method for Identifying and Evaluating a Structural Vector AutoregressionGraph-theoretic methods of causal search based in the ideas of Pearl (2000), Spirtes, Glymour, and Scheines (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 autoregression (SVAR), 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, since 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 procedures. These methods exploit patterns of conditional independence in the data. In cases in which unique identification is not possible, they may nonetheless reduce the class of admissible identifying assumptions considerably. 1 Demiralp and Hoover (2003) provide
KeywordsMonte Carlo evidence that, provided signal-to-noise ratios are high enough, these graphtheoretic methods can recover effectively the true contemporaneous structure of SVARs.Monte Carlo results are too often specific to particular simulations and do not necessarily provide generic guidance. To remedy this problem, we develop a bootstrap method that 3 allows one to assess the reliability of a data-based identification scheme for arbitrary structures. We show that this technique allows us, in cases in which we do not know the true underlying structure, to present simulation evidence that closely mimics Monte Carlo simulations for which we know the underlying structure ex hypothesi. It therefore allows us to give reasonable assessments of the reliability of data-based, graph-theoretic identifications of SVARs.The SVAR can be written as: (2) is easily estimated, the covariance matrix, Λ = E(UU′) in general will not be diagonal, so that it will be impossible to evaluate the effects of shocks to particular variables. The identification problem reduces to this: if we know A 0 , then it is easy to recover equation (1) from our estimates of (2); but how do we know A 0 ?Identification schemes typically start with the property that Σ, the covariance matrix of E t , is diagonal. True identification would permit us to transform equation (2) into (1) and recover the diagonal Σ. There are a large number of N × N matrices, P i such that the covariance matrix ) )' ( ( There are, in general, n! such matrices, each corresponding to one Wold-or recursive causal ordering of the variables in Y.We too restrict ourselves ...