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Graph-Based Search Procedure for Vector Autoregressive Models


  • Alessio Moneta
  • Peter Spirtes


Vector Autoregressions (VARs) are a class of time series models commonly used in econometrics to study the dynamic effect of exogenous shocks to the economy. While the estimation of a VAR is straightforward, there is a problem of finding the transformation of the estimated model consistent with the causal relations among the contemporaneous variables. Such problem, which is a version of what is called in econometrics “the problem of identification,” is faced in this paper using a semi-automated search procedure. The unobserved causal relations of the structural form, to be identified, are represented by a directed graph. Discovery algorithms are developed to infer features of the causal graph from tests on vanishing partial correlations among the VAR residuals. Such tests cannot be based on the usual tests of conditional independence, because of sampling problems due to the time series nature of the data. This paper proposes consistent tests on vanishing partial correlations based on the asymptotic distribution of the estimated VAR residuals. Two different types of search algorithm are considered. A first algorithm restricts the analysis to direct causation among the contemporaneous variables, a second algorithm allows the possibility of cycles (feedback loops) and common shocks among contemporaneous variables. Recovering the causal structure allows a reliable transformation of the estimated vector autoregressive model which is very useful for macroeconomic empirical investigations, such as comparing the effects of different shocks (real vs. nominal) on the economy and finding a measure of the monetary policy shock.

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  • Alessio Moneta & Peter Spirtes, 2005. "Graph-Based Search Procedure for Vector Autoregressive Models," LEM Papers Series 2005/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  • Handle: RePEc:ssa:lemwps:2005/14

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    References listed on IDEAS

    1. Alessio Moneta, 2003. "Graphical Models for Structural Vector Autoregressions," LEM Papers Series 2003/07, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    2. Glymour, Clark & Spirtes, Peter, 1988. "Latent variables, causal models and overidentifying constraints," Journal of Econometrics, Elsevier, vol. 39(1-2), pages 175-198.
    3. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    4. Bernanke, Ben S., 1986. "Alternative explanations of the money-income correlation," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 49-99, January.
    5. Michael S. Haigh & David A. Bessler, 2004. "Causality and Price Discovery: An Application of Directed Acyclic Graphs," The Journal of Business, University of Chicago Press, vol. 77(4), pages 1099-1121, October.
    6. Selva Demiralp & Kevin D. Hoover, 2003. "Searching for the Causal Structure of a Vector Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 745-767, December.
    7. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
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    VARs; Problem of Identification; Causal Graphs; Structural Shocks;

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