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Should We Go One Step Further? Â An Accurate Comparison of One-step and Two-step Procedures in a Generalized Method of Moments Framework

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  • Hwang, Jungbin
  • Sun, Yixiao

Abstract

According to the conventional asymptotic theory, the two-step Generalized Method of Moments (GMM) estimator and test perform as least as well as the one-step estimator and test in large samples. The conventional asymptotic theory, as elegant and convenient as it is, completely ignores the estimation uncertainty in the weighting matrix, and as a result it may not reflect finite sample situations well. In this paper, we employ the fixed-smoothing asymptotic theory that accounts for the estimation uncertainty, and compare the performance of the one-step and two-step procedures in this more accurate asymptotic framework. We show the two-step procedure outperforms the one-step procedure only when the benefit of using the optimal weighting matrix outweighs the cost of estimating it. This qualitative message applies to both the asymptotic variance comparison and power comparison of the associated tests. A Monte Carlo study lends support to our asymptotic results.

Suggested Citation

  • Hwang, Jungbin & Sun, Yixiao, 2015. "Should We Go One Step Further? Â An Accurate Comparison of One-step and Two-step Procedures in a Generalized Method of Moments Framework," University of California at San Diego, Economics Working Paper Series qt58r2z98m, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt58r2z98m
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    References listed on IDEAS

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    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
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    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Yixiao Sun, 2013. "A heteroskedasticity and autocorrelation robust F test using an orthonormal series variance estimator," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-26, February.
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    8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
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    Citations

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    Cited by:

    1. Jungbin Hwang, 2017. "Simple and Trustworthy Cluster-Robust GMM Inference," Working papers 2017-19, University of Connecticut, Department of Economics.
    2. Luciano de Castro & Antonio F. Galvao & David M. Kaplan & Xin Liu, 2017. "Smoothed GMM for quantile models," Working Papers 1803, Department of Economics, University of Missouri, revised 28 Feb 2018.
    3. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(01), pages 105-157, February.
    4. repec:eee:econom:v:198:y:2017:i:2:p:277-295 is not listed on IDEAS
    5. repec:eee:streco:v:45:y:2018:i:c:p:84-93 is not listed on IDEAS
    6. Luciano de Castro & Antonio F. Galvao & David M. Kaplan & Xin Liu, 2017. "Smoothed GMM for quantile models," Working Papers 1803, Department of Economics, University of Missouri, revised 28 Feb 2018.
    7. Hwang, Jungbin & Sun, Yixiao, 2017. "Asymptotic F and t tests in an efficient GMM setting," Journal of Econometrics, Elsevier, vol. 198(2), pages 277-295.

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