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Finite sample performance of the robust Wald test in simultaneous equation systems

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  • Calzolari, Giorgio
  • Panattoni, Lorenzo

Abstract

The estimator of the coefficient covariance matrix proposed in White (1982) can be used to robustify the classical Wald test. Sampling experiments recently performed on linear regressions and simultaneous equation models, however, suggest that such an estimator tends to underestimate the covariance matrix if the model is correctly specified. In the classical framework of simultaneous equation systems, this paper aims at investigating the consequences of the use of robust covariance matrix estimator in the Wald test, when there is no misspecification.

Suggested Citation

  • Calzolari, Giorgio & Panattoni, Lorenzo, 1987. "Finite sample performance of the robust Wald test in simultaneous equation systems," MPRA Paper 22557, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:22557
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    File URL: https://mpra.ub.uni-muenchen.de/24847/1/MPRA_paper_24847.pdf
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    References listed on IDEAS

    as
    1. Berndt, Ernst R & Savin, N Eugene, 1977. "Conflict among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model," Econometrica, Econometric Society, vol. 45(5), pages 1263-1277, July.
    2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    3. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    4. Calzolari, Giorgio & Panattoni, Lorenzo & Weihs, Claus, 1987. "Computational efficiency of FIML estimation," Journal of Econometrics, Elsevier, vol. 36(3), pages 299-310, November.
    5. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    6. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    7. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826, Elsevier.
    8. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October.
    9. Davidson, Russel & MacKinnon, James G., 1983. "Small sample properties of alternative forms of the Lagrange Multiplier test," Economics Letters, Elsevier, vol. 12(3-4), pages 269-275.
    10. Alok Bhargava, 2006. "Wald Tests And Systems Of Stochastic Equations," World Scientific Book Chapters, in: Econometrics, Statistics And Computational Approaches In Food And Health Sciences, chapter 2, pages 29-48, World Scientific Publishing Co. Pte. Ltd..
    11. Calzolari, Giorgio & Panattoni, Lorenzo, 1988. "Alternative Estimators of FIML Covariance Matrix: A Monte Carlo Stud y," Econometrica, Econometric Society, vol. 56(3), pages 701-714, May.
    12. Calzolari, Giorgio & Panattoni, Lorenzo, 1984. "A Simulation Study on FIML Covariance Matrix," MPRA Paper 28804, University Library of Munich, Germany.
    13. Breusch, T S, 1979. "Conflict among Criteria for Testing Hypotheses: Extensions and Comments," Econometrica, Econometric Society, vol. 47(1), pages 203-207, January.
    14. Belsley, David A., 1980. "On the efficient computation of the nonlinear full-information maximum-likelihood estimator," Journal of Econometrics, Elsevier, vol. 14(2), pages 203-225, October.
    15. Evans, G B A & Savin, N E, 1982. "Conflict among the Criteria Revisited: The W, LR and LM Tests," Econometrica, Econometric Society, vol. 50(3), pages 737-748, May.
    16. Davidson, Russell & MacKinnon, James G., 1981. "Efficient estimation of tail-area probabilities in sampling experiments," Economics Letters, Elsevier, vol. 8(1), pages 73-77.
    17. Savin, N Eugene, 1976. "Conflict among Testing Procedures in a Linear Regression Model with Autoregressive Disturbances," Econometrica, Econometric Society, vol. 44(6), pages 1303-1315, November.
    18. Amemiya, Takeshi, 1977. "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model," Econometrica, Econometric Society, vol. 45(4), pages 955-968, May.
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    More about this item

    Keywords

    Simultaneous equations; Wald test; robust covariance matrix estimator; Monte Carlo;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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