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Asymptotic F Tests under Possibly Weak Identification

Author

Listed:
  • Julian Martinez-Iriarte
  • Yixiao Sun
  • Xuexin Wang
Abstract
This paper develops asymptotic F tests robust to weak identification and temporal dependence. The test statistics are modified versions of the S statistic of Stock and Wright (2000) and the K statistic of Kleibergen (2005), both of which are based on the continuous updating generalized method of moments. In the former case, the modification involves only a multiplicative degree-of-freedom adjustment. In the latter case, the modification involves an additional multiplicative adjustment that uses a J statistic for testing overidentification. By adopting fixed-smoothing asymptotics, we show that both the modified S statistic and the modified K statistic are asymptotically F-distributed. The asymptotic F theory accounts for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators, which the asymptotic chi-squared theory ignores. Monte Carlo simulations show that the F approximations are much more accurate than the corresponding chi-squared approximations in finite samples.

Suggested Citation

  • Julian Martinez-Iriarte & Yixiao Sun & Xuexin Wang, 2019. "Asymptotic F Tests under Possibly Weak Identification," Working Papers 2019-03-12, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    • Handle: RePEc:wyi:wpaper:002400
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    References listed on IDEAS

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    Cited by:

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    2. Ulrich K. Müller & Mark W. Watson, 2020. "Low-Frequency Analysis of Economic Time Series," Working Papers 2020-13, Princeton University. Economics Department..
    3. Manuel Denzer & Constantin Weiser, 2021. "Beyond F-statistic - A General Approach for Assessing Weak Identification," Working Papers 2107, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
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    More about this item

    Keywords

    Heteroskedasticity and autocorrelation robust variance; continuous updating GMM; F distribution; fixed-smoothing asymptotics; weak identification;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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