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Journal of Time Series Econometrics

Editor-in-Chief: Hidalgo, Javier

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Mathematical Citation Quotient (MCQ) 2016: 0.10

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On Identifying Structural VAR Models via ARCH Effects

George Milunovich / Minxian Yang
Published Online: 2013-05-03 | DOI: https://doi.org/10.1515/jtse-2013-0010

Abstract: We consider the local identification of parameters in structural VAR models with ARCH type errors. By establishing a mapping between the structural and reduced-form models, we provide a set of sufficient conditions for the joint identification of all parameters. Under these conditions, as the structural parameters are identified, various restrictions on the parameters can be tested in a standard manner. For example, the significance test for the ARCH effect in the usual GARCH formulation for a structural shock does not suffer the complications caused by a lack of identification encountered in univariate GARCH models.

Keywords: structural vector autoregression; SVAR; ARCH; GARCH; local identification


  • Abadir, K. M., and J. R. Magnus. 2005, Matrix Algebra (Econometric Exercises, Vol. 1). New York, USA: Cambridge University Press.Google Scholar

  • Bernanke, B. 1986. “Alternative Explorations of the Money–Income Correlation.” Carnegie-Rochester Series on Public Policy 25:49–99.Google Scholar

  • Blanchard, O. J., and P. Diamond. 1989. “The Beveridge Curve.” Brookings Papers on Economic Activity 20:1–76.CrossrefGoogle Scholar

  • Blanchard, O. J., and D. Quah. 1989. “The Dynamic Effects of Aggregate Demand and Supply Disturbances.” American Economic Review 79:655–73.Google Scholar

  • Bollerslev, T., R. F. Engle, and D. B. Nelson. 1994. “ARCH Models.” In Handbook of Econometrics, Vol. IV, edited by R. F. Engle and D. L. McFadden, 2959–3038. Amsterdam, The Netherlands: Elsevier Science.Google Scholar

  • Caporale, G. M., A. Cipollini, and P. O. Demetriades.2005. “Monetary Policy and the Exchange rate During the Asian Crisis: Identification through Heteroscedasticity.” Journal of International Money and Finance 24:39–53.Web of ScienceGoogle Scholar

  • Dungey, M., G. Milunovich, and S. Thorp. 2010. “Unobservable Shocks as Carriers of Contagion: A Dynamic Analysis Using Identified Structural GARCH.” Journal of Banking and Finance 34:1008–21.Google Scholar

  • Engle, R. F., and K. F. Kroner. 1995. “Multivariate Simultaneous Generalized ARCH.” Econometric Theory 11:122–50.CrossrefGoogle Scholar

  • Klein, R., and F. Vella. 2010. “Estimating a Class of Triangular Simultaneous Equations Models without Exclusion Restrictions.” Journal of Econometrics 154:154–64.Web of ScienceGoogle Scholar

  • Lanne, M., H. Lutkepohl, and K. Maciejowska. 2010. “Structural Vector Autoregressions with Markov Switching.” Journal of Economic Dynamics and Control 34:121–31.Web of ScienceGoogle Scholar

  • Lewbel, A. 2010. “Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models.” Boston College Working Papers in Economics 587, revised 15 Dec 2010.Google Scholar

  • Normandin, M., and L. Phaneuf. 2004. “Monetary Policy Shocks: Testing Identification Conditions Under Time-Varying Conditional Volatility.” Journal of Monetary Economics 51:1217–43.CrossrefGoogle Scholar

  • Prono, T. 2008. “GARCH-Based Identification and Estimation of Triangular Systems.” Federal Reserve Bank of Boston Working Paper QAU 08–4.Google Scholar

  • Rigobon, R. 2003. “Identification through Heteroskedasticity.” The Review of Economics and Statistics 85:777–92.Google Scholar

  • Rigobon, R., and B. Sack. 2003. “Spillovers across U.S. Financial Markets.” Finance and Economics Discussion Series 2003–13, Board of Governors of the Federal Reserve System (U.S.).Google Scholar

  • Rothenberg, T. J. 1971. “Identification in Parametric Models.” Econometrica 39:577–91.Google Scholar

  • Sentana, E., and G. Fiorentini. 2001. “Identification, Estimation and Testing of Conditionally Heteroskedastic Factor Models”. Journal of Econometrics 102:143–64.Google Scholar

  • Sims, C. A. 1980 “Macroeconomics and Reality.” Econometrica 48:1–48.Google Scholar

  • Wright, P. G. 1928. The Tariff on Animal and Vegetable Oils. New York: Macmillan.Google Scholar

About the article

Published Online: 2013-05-03

Identification via constraints placed on variances was first considered by Wright (1928).

See for example Rigobon and Sack (2003), Caporale, Cipollini, and Demetriades (2005), and Dungey, Milunovich, and Thorp (2010).

Sentana and Fiorentini (2001) use a two-step estimation approach. Based on the unconditional variance, their first step provides an estimator of the matrix, which is used as input for the second step that produces the estimators of the conditional variance parameters. They acknowledge that, when the factor dimension is greater than or equal to two, “…the two-step estimator of (parameters in the conditional variance) will be inconsistent” (see paragraph 2, 150).

Although is lower triangular (not symmetric), we still use vech() to denote its lower triangular elements when no confusions can arise.

Citation Information: Journal of Time Series Econometrics, Volume 5, Issue 2, Pages 117–131, ISSN (Online) 1941-1928, ISSN (Print) 2194-6507, DOI: https://doi.org/10.1515/jtse-2013-0010.

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