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 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
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).
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.