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The Robustness of the Higher-Order 2SLS and General k-Class Bias Approximations to Non-Normal Disturbances

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In a seminal paper Nagar (1959) obtained first and second moment approximations for the k-class of estimators in a general static simultaneous equation model under the assumption that the structural disturbances were i.i.d and normally distributed. Later Mikhail (1972) obtained a higher-order bias approximation for 2SLS under the same assumptions as Nagar while Iglesias and Phillips (2010) obtained the higher order approximation for the general k-class of estimators. These approximations show that the higher order biases can be important especially in highly overidentified cases. In this paper we show that Mikhail.s higher order bias approximation for 2SLS continues to be valid under symmetric, but not necessarily normal, disturbances with an arbitrary degree of kurtosis but not when the disturbances are asymmetric. A modified approximation for the 2SLS bias is then obtained which includes the case of asymmetric disturbances. The results are then extended to the general k-class of estimators.

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  • Phillips, Garry D.A. & Liu-Evans, Gareth, 2011. "The Robustness of the Higher-Order 2SLS and General k-Class Bias Approximations to Non-Normal Disturbances," Cardiff Economics Working Papers E2011/20, Cardiff University, Cardiff Business School, Economics Section.
    • Handle: RePEc:cdf:wpaper:2011/20
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    1. Knight, John L., 1985. "The moments of ols and 2sls when the disturbances are non-normal," Journal of Econometrics, Elsevier, vol. 27(1), pages 39-60, January.
    2. 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.
    3. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 505-520, June.
    4. 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.
    5. Anderson, T. W. & Kunitomo, Naoto & Morimune, Kimio, 1986. "Comparing Single-Equation Estimators in a Simultaneous Equation System," Econometric Theory, Cambridge University Press, vol. 2(1), pages 1-32, April.
    6. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    7. 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.
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    1. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 505-520, June.
    2. Liu-Evans, Gareth & Phillips, Garry D.A., 2018. "On the use of higher order bias approximations for 2SLS and k-class estimators with non-normal disturbances and many instruments," Econometrics and Statistics, Elsevier, vol. 6(C), pages 90-105.

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