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Asymptotic F and t tests in an efficient GMM setting

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  • Hwang, Jungbin
  • Sun, Yixiao

Abstract

This paper considers two-step efficient GMM estimation and inference where the weighting matrix and asymptotic variance matrix are based on the series long run variance estimator. We propose a simple and easy-to-implement modification to the trinity of test statistics in the two-step efficient GMM setting and show that the modified test statistics are all asymptotically F distributed under the so-called fixed-smoothing asymptotics. The modification is multiplicative and involves the J statistic for testing over-identifying restrictions. This leads to convenient asymptotic F tests whose critical values, i.e., the standard F critical values, are readily available from standard statistical tables and programming environments. For testing a single restriction with a one-sided alternative, an asymptotic t test theory using the standard t distribution as the reference distribution is also developed.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:198:y:2017:i:2:p:277-295
    DOI: 10.1016/j.jeconom.2017.02.003
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    19. Preinerstorfer, David & Pötscher, Benedikt M., 2016. "On Size And Power Of Heteroskedasticity And Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 32(2), pages 261-358, April.
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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, revised Aug 2020.
    2. Martínez-Iriarte, Julián & Sun, Yixiao & Wang, Xuexin, 2019. "Asymptotic F Tests under Possibly Weak Identification," University of California at San Diego, Economics Working Paper Series qt6qk200q8, Department of Economics, UC San Diego.
    3. Liu, Cheng & Sun, Yixiao, 2019. "A simple and trustworthy asymptotic t test in difference-in-differences regressions," Journal of Econometrics, Elsevier, vol. 210(2), pages 327-362.
    4. Xiaoqing Ye & Yixiao Sun, 2018. "Heteroskedasticity- and autocorrelation-robust F and t tests in Stata," Stata Journal, StataCorp LP, vol. 18(4), pages 951-980, December.
    5. Hwang, Jungbin & Sun, Yixiao, 2018. "SIMPLE, ROBUST, AND ACCURATE F AND t TESTS IN COINTEGRATED SYSTEMS," Econometric Theory, Cambridge University Press, vol. 34(5), pages 949-984, October.
    6. Martínez-Iriarte, Julián & Sun, Yixiao & Wang, Xuexin, 2020. "Asymptotic F tests under possibly weak identification," Journal of Econometrics, Elsevier, vol. 218(1), pages 140-177.

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    More about this item

    Keywords

    Efficient GMM; F distribution; Fixed-smoothing asymptotics; Heteroskedasticity and autocorrelation robust; t distribution; Two-step GMM;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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