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Simultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances

Author

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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

Suggested Citation

  • Garry Phillips & Emma Iglesias, 2004. "Simultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances," Econometric Society 2004 Far Eastern Meetings 567, Econometric Society.
  • Handle: RePEc:ecm:feam04:567
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    File URL: http://repec.org/esFEAM04/up.15622.1080053485.pdf
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    References listed on IDEAS

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    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    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. 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.
    4. 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.
    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. 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, June.
    7. 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.
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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. 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.

    More about this item

    Keywords

    Simultaneous Equations; conditionally heteroscedastic disturbances;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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