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GARCH-Based Identification and Estimation of Triangular Systems

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  • Todd, Prono

Abstract

The diagonal GARCH(1,1) model is shown to support identification of the triangular system and is argued as a higher moment analog to traditional exclusion restrictions. Estimators for this result include QML and GMM. For the GMM estimator, only partial parameterization of the conditional covariance matrix is required. An alternative weighting matrix for the GMM estimator is also proposed.

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File URL: http://mpra.ub.uni-muenchen.de/27482/
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File URL: http://mpra.ub.uni-muenchen.de/30996/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 20032.

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Date of creation: Sep 2009
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Handle: RePEc:pra:mprapa:20032

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Related research

Keywords: Triangular Systems; Endogeneity; Identification; Heteroskedasticity; Quasi Maximum Likelihood; Generalized Method of Moments; GARCH; QML; GMM;

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References

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  1. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1201-1214, September.
  2. Garry Phillips & Emma Iglesias, 2004. "Simultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances," Econometric Society 2004 Far Eastern Meetings, Econometric Society 567, Econometric Society.
  3. Roberto Rigobon, 2001. "The Curse of Non-Investment Grade Countries," NBER Working Papers 8636, National Bureau of Economic Research, Inc.
  4. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers, Tilburg - Center for Economic Research 9240, Tilburg - Center for Economic Research.
  5. Gabriele Fiorentini & Enrique Sentana Iváñez, 1997. "Identification, estimation and testing of conditionally heteroskedastic factor models," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 1997-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Todd Prono, 2009. "Market proxies, correlation, and relative mean-variance efficiency: still living with the roll critique," Risk and Policy Analysis Unit Working Paper, Federal Reserve Bank of Boston QAU09-3, Federal Reserve Bank of Boston.
  7. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 64(4), pages 891-916, July.
  8. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(01), pages 122-150, February.
  9. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, Econometric Society, vol. 64(3), pages 575-96, May.
  10. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
  11. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-87, October.
  12. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 6(01), pages 17-43, March.
  13. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(1), pages 116-31, February.
  14. Arthur Lewbel, 2003. "Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Boston College Working Papers in Economics, Boston College Department of Economics 587, Boston College Department of Economics, revised 15 Dec 2010.
  15. Todd, Prono, 2009. "Market Proxies, Correlation, and Relative Mean-Variance Efficiency: Still Living with the Roll Critique," MPRA Paper 20031, University Library of Munich, Germany.
  16. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
  17. West, Kenneth D., 2002. "Efficient GMM estimation of weak AR processes," Economics Letters, Elsevier, Elsevier, vol. 75(3), pages 415-418, May.
  18. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  19. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
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Cited by:
  1. Todd, Prono, 2009. "Market Proxies, Correlation, and Relative Mean-Variance Efficiency: Still Living with the Roll Critique," MPRA Paper 20031, University Library of Munich, Germany.
  2. Prono, Todd, 2011. "When A Factor Is Measured with Error: The Role of Conditional Heteroskedasticity in Identifying and Estimating Linear Factor Models," MPRA Paper 33593, University Library of Munich, Germany.

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