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Simultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances

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  • Garry Phillips
  • Emma Iglesias

Abstract

In this paper we extend the setting analysed in Hahn and Hausman (2002a) by allowing for conditionally heteroscedastic disturbances. We start by considering the type of conditional variance-covariance matrices proposed by Engle and Kroner (1995) and we show that, when we impose a GARCH specification in the structural model, some conditions are needed to have a GARCH process of the same order in the reduced form equations. Later, we propose a modified-2SLS and a modified-3SLS procedures where the conditional heteroscedasticity is taken into account, that are more asymptotically efficient than the traditional 2SLS and 3SLS estimators. We recommend to use these modified-2SLS and 3SLS procedures in practice instead of alternative estimators like LIML/FIML, where the non-existence of moments leads to extreme values (in case we are interested in the structural form). We show theoretically and with simulation that in some occasions 2SLS, 3SLS and our proposed 2SLS and 3SLS procedures can have very severe biases, and we present the bias correction mechanisms to apply in practice

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 Far Eastern Meetings with number 567.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:feam04:567

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Keywords: Simultaneous Equations; conditionally heteroscedastic disturbances;

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References

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  1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  2. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
  3. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06.
  4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  5. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January.
  6. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448 Elsevier.
  7. Jinyong Hahn & Jerry Hausman, 2003. "Weak Instruments: Diagnosis and Cures in Empirical Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 118-125, May.
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Cited by:
  1. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Risk and Policy Analysis Unit Working Paper QAU08-4, Federal Reserve Bank of Boston.
  2. 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.
  3. Todd, Prono, 2009. "GARCH-Based Identification and Estimation of Triangular Systems," MPRA Paper 20032, University Library of Munich, Germany.

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