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The Accuracy of the Higher Order Bias Approximation for the 2SLS Estimator

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  • Hadri, K.
  • Phillips, G.D.A.

Abstract

Mikhail (1972a) found that estimated 2SLS biases, obtained through simulation using antithetic variables and control variate methods, were closer to each other than to Nagar's bias approximation to order T-1. As remarked by Kiviet and Phillips (1996), this result represents one of a very small number of higher order approximations in the econometric literature yet there is no published evidence of its accuracy. In this paper the accuracy of the approximation is explored in the context of a framework similar to that chosen by Mikhail (1972a) and it is found that the higher order approximation is clearly superior. In cases where the bias is severe, the results support the belief that, when the first order approximation is poor but not terrible, the higher order approximation mops up most of the error.

Suggested Citation

  • Hadri, K. & Phillips, G.D.A., 1999. "The Accuracy of the Higher Order Bias Approximation for the 2SLS Estimator," Discussion Papers 9906, University of Exeter, Department of Economics.
    • Handle: RePEc:exe:wpaper:9906
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    References listed on IDEAS

    as
    1. Sawa, Takamitsu, 1972. "Finite-Sample Properties of the k-Class Estimators," Econometrica, Econometric Society, vol. 40(4), pages 653-680, July.
    2. Phillips, G. D. A. & Harvey, A. C., 1984. "A note on estimating and testing exogenous variable coefficient estimators in simultaneous equation models," Economics Letters, Elsevier, vol. 15(3-4), pages 301-307.
    3. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
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    Cited by:

    1. Kaddour Hadri & Yao Rao, 2008. "Panel Stationarity Test with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(2), pages 245-269, April.
    2. Yao Rao & Kaddour Hadri & Ruijun Bu, 2010. "Testing For Stationarity In Heterogeneous Panel Data In The Case Of Model Misspecification," Bulletin of Economic Research, Wiley Blackwell, vol. 62(3), pages 209-225, July.
    3. Kiviet, Jan F. & Phillips, Garry D.A., 2012. "Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3705-3729.
    4. Badi Baltagi & Seuck Heun Song & Byoung Cheol Jung, 2002. "Simple Lm Tests For The Unbalanced Nested Error Component Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 167-187.
    5. 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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    More about this item

    Keywords

    TIME SERIES ; STATISTICAL ANALYSIS ; ECONOMETRICS;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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