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Graphical Models for Structural Vector Autoregressions

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  • Alessio Moneta

Abstract

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.

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Bibliographic Info

Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2003/07.

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Date of creation: 09 Dec 2003
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Handle: RePEc:ssa:lemwps:2003/07

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Keywords: Causality; Directed Acyclic Graphs; Identification Problem; Residuals Orthogonalization; Impulse Response Functions.;

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References

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  1. Jon Faust & Eric M. Leeper, 1994. "When do long-run identifying restrictions give reliable results?," International Finance Discussion Papers 462, Board of Governors of the Federal Reserve System (U.S.).
  2. Bessler, David A. & Yang, Jian, 2003. "The structure of interdependence in international stock markets," Journal of International Money and Finance, Elsevier, vol. 22(2), pages 261-287, April.
  3. Kevin Hoover & Selva Demiralp, 2003. "Searching for the Causal Structure of a Vector Autoregression," Working Papers 33, University of California, Davis, Department of Economics.
  4. Haigh, Michael S. & Bessler, David A., 2002. "Causality And Price Discovery: An Application Of Directed Acyclic Graphs," 2002 Conference, April 22-23, 2002, St. Louis, Missouri 19057, NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
  5. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  6. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  7. 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.
  8. Glymour, Clark & Spirtes, Peter, 1988. "Latent variables, causal models and overidentifying constraints," Journal of Econometrics, Elsevier, vol. 39(1-2), pages 175-198.
  9. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September.
  10. Granger, C. W. J., 1988. "Some recent development in a concept of causality," Journal of Econometrics, Elsevier, vol. 39(1-2), pages 199-211.
  11. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  12. Gilli, Manfred, 1992. "Causal Ordering and Beyond," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(4), pages 957-71, November.
  13. Alessio Moneta, 2004. "Identification of Monetary Policy Shocks: A graphical causal approach," Notas Económicas, Faculdade de Economia, Universidade de Coimbra, issue 20, pages 39-62, December.
  14. Titus O. Awokuse & David A. Bessler, 2003. "Vector Autoregressions, Policy Analysis, and Directed Acyclic Graphs: An Application to the U.S. Economy," Journal of Applied Economics, Universidad del CEMA, vol. 0, pages 1-24, May.
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Cited by:
  1. 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.
  2. Alessio Moneta, 2008. "Graphical causal models and VARs: an empirical assessment of the real business cycles hypothesis," Empirical Economics, Springer, vol. 35(2), pages 275-300, September.

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