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Graph-Based Search Procedure for Vector Autoregressive Models

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  • Alessio Moneta
  • Peter Spirtes

Abstract

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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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 2005/14.

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Date of creation: 12 Jun 2005
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Handle: RePEc:ssa:lemwps:2005/14

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Keywords: VARs; Problem of Identification; Causal Graphs; Structural Shocks;

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  1. 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.
  2. Haigh, Michael S. & Bessler, David A., 2002. "Causality And Price Discovery: An Application Of Directed Acyclic Graphs," Working Papers 28588, University of Maryland, Department of Agricultural and Resource Economics.
  3. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
  4. Glymour, Clark & Spirtes, Peter, 1988. "Latent variables, causal models and overidentifying constraints," Journal of Econometrics, Elsevier, vol. 39(1-2), pages 175-198.
  5. Kevin Hoover & Selva Demiralp, 2003. "Searching for the Causal Structure of a Vector Autoregression," Working Papers 33, University of California, Davis, Department of Economics.
  6. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  7. 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.
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