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Fixed-smoothing Asymptotics in a Two-step GMM Framework

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  • Sun, Yixiao

Abstract

The paper develops the Öxed-smoothing asymptotics in a two-step GMM framework. Under this type of asymptotics, the weighting matrix in the second-step GMM criterion function converges weakly to a random matrix and the two-step GMM estimator is asymptotically mixed normal. Nevertheless, the Wald statistic, the GMM criterion function statistic and the LM statistic remain asymptotically pivotal. It is shown that critical values from the fixedsmoothing asymptotic distribution are high order correct under the conventional increasingsmoothing asymptotics. When an orthonormal series covariance estimator is used, the critical values can be approximated very well by the quantiles of a noncentral F distribution. A simulation study shows that the new statistical tests based on the fixed-smoothing critical values are much more accurate in size than the conventional chi-square test.

Suggested Citation

  • Sun, Yixiao, 2013. "Fixed-smoothing Asymptotics in a Two-step GMM Framework," University of California at San Diego, Economics Working Paper Series qt64x4z265, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt64x4z265
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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(1), pages 116-142, February.
    2. 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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    5. Sun, Yixiao, 2011. "Robust trend inference with series variance estimator and testing-optimal smoothing parameter," Journal of Econometrics, Elsevier, vol. 164(2), pages 345-366, October.
    6. Sun, Yixiao & Phillips, Peter C.B. & Jin, Sainan, 2011. "Power Maximization And Size Control In Heteroskedasticity And Autocorrelation Robust Tests With Exponentiated Kernels," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1320-1368, December.
    7. Sun, Yixiao & Kaplan, David M., 2011. "A New Asymptotic Theory for Vector Autoregressive Long-run Variance Estimation and Autocorrelation Robust Testing," University of California at San Diego, Economics Working Paper Series qt8cx0t4gc, Department of Economics, UC San Diego.
    8. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    9. Peter C. B. Phillips & Yixiao Sun & Sainan Jin, 2006. "Spectral Density Estimation And Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 837-894, August.
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    Cited by:

    1. Cheol-Keun Cho & Timothy J. Vogelsang, 2016. "Fixed- b Inference for Testing Structural Change in a Time Series Regression," Econometrics, MDPI, vol. 5(1), pages 1-26, December.
    2. Yixiao Sun, 2014. "Fixed-smoothing Asymptotics and AsymptoticFandtTests in the Presence of Strong Autocorrelation," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 14, pages 23-63, Emerald Group Publishing Limited.
    3. Xianyang Zhang & Xiaofeng Shao, 2016. "On the coverage bound problem of empirical likelihood methods for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 395-421, March.

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