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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. Garry Phillips & Emma Iglesias, 2004. "Simultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances," Econometric Society 2004 Far Eastern Meetings 567, Econometric Society.
  2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  3. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  4. 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.
  5. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
  6. West, Kenneth D., 2002. "Efficient GMM estimation of weak AR processes," Economics Letters, Elsevier, vol. 75(3), pages 415-418, May.
  7. Sentana, E. & Fiorentini, G., 1997. "Identification, Estimation and Testing of Conditionally Heteroskedastic Factor Model," Papers 9709, Centro de Estudios Monetarios Y Financieros-.
  8. 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.
  9. 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, vol. 96(1), pages 116-31, February.
  10. Roberto Rigobon, 2001. "The Curse of Non-Investment Grade Countries," NBER Working Papers 8636, National Bureau of Economic Research, Inc.
  11. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  12. Arthur Lewbel, 2010. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80, December.
  13. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(01), pages 17-43, March.
  14. Todd Prono, 2009. "Market proxies, correlation, and relative mean-variance efficiency: still living with the roll critique," Risk and Policy Analysis Unit Working Paper QAU09-3, Federal Reserve Bank of Boston.
  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. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  17. 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, vol. 65(5), pages 1201-1214, September.
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Citations

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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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