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Fixed-smoothing Asymptotics in a Two-step GMM Framework

  • Sun, Yixiao

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.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt64x4z265.

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Date of creation: 01 Jun 2013
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Handle: RePEc:cdl:ucsdec:qt64x4z265
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  1. Phillips, Peter C.B. & Sun, Yixiao & Jin, Sainan, 2004. "Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation," University of California at San Diego, Economics Working Paper Series qt6mf9q2rt, Department of Economics, UC San Diego.
  2. Yixiao Sun & Peter C.B. Phillips & Sainan Jin, 2010. "Power Maximization and Size Control in Heteroskedasticity and Autocorrelation Robust Tests with Exponentiated Kernels," Cowles Foundation Discussion Papers 1749, Cowles Foundation for Research in Economics, Yale University.
  3. Xiaofeng Shao, 2010. "A self-normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366.
  4. Min Seong Kim & Yixiao Sun, 2012. "Asymptotic F Test in a GMM Framework with Cross Sectional Dependence," Working Papers 032, Ryerson University, Department of Economics.
  5. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  6. 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.
  7. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, 05.
  8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  9. Gonçalves, Sílvia & Vogelsang, Timothy J., 2011. "Block Bootstrap Hac Robust Tests: The Sophistication Of The Naive Bootstrap," Econometric Theory, Cambridge University Press, vol. 27(04), pages 745-791, August.
  10. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation for Research in Economics, Yale University.
  11. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2006. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Cowles Foundation Discussion Papers 1545, Cowles Foundation for Research in Economics, Yale University.
  12. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1350-1366, December.
  13. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B., 2011. "Inference with dependent data using cluster covariance estimators," Journal of Econometrics, Elsevier, vol. 165(2), pages 137-151.
  14. 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, 02.
  15. 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.
  16. Ibragimov, Rustam & Müller, Ulrich K., 2010. "t-Statistic Based Correlation and Heterogeneity Robust Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 453-468.
  17. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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