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Fixed‐Smoothing Asymptotics in a Two‐Step Generalized Method of Moments Framework

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  • Yixiao Sun

Abstract

This paper develops the fixed‐smoothing asymptotics in a two‐step generalized method of moments (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 Lagrange multiplier statistic remain asymptotically pivotal. It is shown that critical values from the fixed‐smoothing asymptotic distribution are high order correct under the conventional increasing‐smoothing 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 statistical tests based on the new fixed‐smoothing approximation are much more accurate in size than existing tests.

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  • Yixiao Sun, 2014. "Fixed‐Smoothing Asymptotics in a Two‐Step Generalized Method of Moments Framework," Econometrica, Econometric Society, vol. 82, pages 2327-2370, November.
    • Handle: RePEc:wly:emetrp:v:82:y:2014:i::p:2327-2370
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    Cited by:

    1. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    2. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    3. Pierre Perron & Eduardo Zorita & Timothy J. Vogelsang & Nasreen Nawaz, 2017. "Estimation and Inference of Linear Trend Slope Ratios With an Application to Global Temperature Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 640-667, September.
    4. Matei Demetrescu & Robinson Kruse-Becher, 2021. "Is U.S. real output growth really non-normal? Testing distributional assumptions in time-varying location-scale models," CREATES Research Papers 2021-07, Department of Economics and Business Economics, Aarhus University.
    5. Pellatt , Daniel & Sun, Yixiao, 2020. "Asymptotic F test in Regressions with Observations Collected at High Frequency over Long Span," University of California at San Diego, Economics Working Paper Series qt19f0d9wz, Department of Economics, UC San Diego.
    6. Li, Kunpeng & Cui, Guowei & Lu, Lina, 2020. "Efficient estimation of heterogeneous coefficients in panel data models with common shocks," Journal of Econometrics, Elsevier, vol. 216(2), pages 327-353.
    7. Hanck, Christoph & Demetrescu, Matei & Kruse, Robinson, 2015. "Fixed-b Asymptotics for t-Statistics in the Presence of Time-Varying Volatility," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112916, Verein für Socialpolitik / German Economic Association.
    8. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    9. Demetrescu, Matei & Kruse, Robinson, 2015. "Testing heteroskedastic time series for normality," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113221, Verein für Socialpolitik / German Economic Association.
    10. Pellatt, Daniel F. & Sun, Yixiao, 2023. "Asymptotic F test in regressions with observations collected at high frequency over long span," Journal of Econometrics, Elsevier, vol. 235(2), pages 1281-1309.
    11. Jungbin Hwang & Gonzalo Valdés, 2020. "Finite-sample Corrected Inference for Two-step GMM in Time Series," Working papers 2020-02, University of Connecticut, Department of Economics.
    12. Laurini, Márcio Poletti & Ohashi, Alberto, 2015. "A noisy principal component analysis for forward rate curves," European Journal of Operational Research, Elsevier, vol. 246(1), pages 140-153.
    13. Gangzheng Guo & Yixiao Sun & Shaoping Wang, 2019. "Testing for moderate explosiveness," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 73-95.
    14. Sokbae Lee & Yuan Liao & Myung Hwan Seo & Youngki Shin, 2022. "Fast Inference for Quantile Regression with Tens of Millions of Observations," Papers 2209.14502, arXiv.org, revised Oct 2023.
    15. Hwang, Jungbin & Valdés, Gonzalo, 2023. "Finite-sample corrected inference for two-step GMM in time series," Journal of Econometrics, Elsevier, vol. 234(1), pages 327-352.
    16. Guo, Gangzheng & Wang, Shaoping & Sun, Yixiao, 2018. "Testing for Moderate Explosiveness in the Presence of Drift," University of California at San Diego, Economics Working Paper Series qt2k26h10n, Department of Economics, UC San Diego.

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