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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. Hanck, Christoph & Demetrescu, Matei & Kruse, Robinson, 2015. "Fixed-b Asymptotics for t-Statistics in the Presence of Time-Varying Volatility," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112916, Verein für Socialpolitik / German Economic Association.
    2. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    3. Demetrescu, Matei & Kruse, Robinson, 2015. "Testing heteroskedastic time series for normality," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113221, Verein für Socialpolitik / German Economic Association.
    4. 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.
    5. 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.
    6. repec:bla:jtsera:v:38:y:2017:i:5:p:640-667 is not listed on IDEAS

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