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Almost Unbiased Variance Estimation in Simultaneous Equation Models

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Abstract

While a good deal of research in simultaneous equation models has been conducted to examine the small sample properties of coefficient estimators there has not been a corresponding interest in the properties of estimators for the associated variances. In this paper we build on Kiviet and Phillips (2000) and explore the biases in variance estimators. This is done for the 2SLS and the MLIML estimators.The approximations to the bias are then used to develop less biased estimators whose properties are examined and compared in a number of simulation experiments. In addition, a bootstrap estimator is included which is found to perform especially well. The experiments also consider coverage probabilities/test sizes and test powers of the t-tests where it is shown that tests based on 2SLS are generally oversized while test sizes based on MLIML are closer to nominal levels. In both cases test statistics based on the corrected variance estimates generally have a higher power than standard procedures.

Suggested Citation

  • Phillip, Garry & Xu, Yongdeng, 2016. "Almost Unbiased Variance Estimation in Simultaneous Equation Models," Cardiff Economics Working Papers E2016/10, Cardiff University, Cardiff Business School, Economics Section.
  • Handle: RePEc:cdf:wpaper:2016/10
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    1. Russell Davidson & James G. MacKinnon, 2006. "The case against JIVE," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 827-833, September.
    2. 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.
    3. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    4. Kiviet, Jan F. & Phillips, Garry D.A., 2014. "Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 424-448.
    5. Phillips, Garry D. A., 2000. "An alternative approach to obtaining Nagar-type moment approximations in simultaneous equation models," Journal of Econometrics, Elsevier, vol. 97(2), pages 345-364, August.
    6. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-737, September.
    7. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
    8. Sargan, J D, 1974. "The Validity of Nagar's Expansion for the Moments of Econometric Estimators," Econometrica, Econometric Society, vol. 42(1), pages 169-176, January.
    9. Smith, Murray D., 1994. "Exact densities for variance estimators of the structural disturbances in simultaneous equations models," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 157-180.
    10. Iglesias, Emma M. & Phillips, Garry D.A., 2010. "The bias to order T-Â 2 for the general k-class estimator in a simultaneous equation model," Economics Letters, Elsevier, vol. 109(1), pages 42-45, October.
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    1. New Year's Reading
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2016-12-31 20:20:00

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    More about this item

    Keywords

    Simultaneous equation models; 2SLS and Fuller's estimators; Bias corrected variance estimation; Inference and bias corrected variance;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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