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Asymptotic F tests under possibly weak identification

Julián Martínez-Iriarte, Yixiao Sun and Xuexin Wang

Journal of Econometrics, 2020, vol. 218, issue 1, 140-177

Abstract: This paper develops asymptotic F tests robust to weak identification and temporal dependence. The test statistics we focus on are modified versions of the S statistic of Stock and Wright (2000) and the K statistic of Kleibergen (2005). In the former case, the modification involves only a multiplicative degree-of-freedom adjustment, and the modified S statistic is asymptotically F distributed under fixed-smoothing asymptotics regardless of the strength of the model identification. In the latter case, the modification involves an additional multiplicative adjustment that uses a J statistic for testing overidentification. We show that the modified K statistic is asymptotically F-distributed when the model parameters are completely unidentified or nearly-weakly identified. When the model parameters are weakly identified, the F approximation for the K statistic can be justified under the conventional asymptotics. The F approximations account for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators, which the chi-squared approximations ignore. Monte Carlo simulations show that the F approximations are much more accurate than the corresponding chi-squared approximations in finite samples.

Keywords: Heteroskedasticity and autocorrelation robust variance; Continuous updating GMM; F distribution; Fixed-smoothing asymptotics; Weak identification (search for similar items in EconPapers)
JEL-codes: C12 C14 C32 C36 (search for similar items in EconPapers)
Date: 2020
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Working Paper: Asymptotic F Tests under Possibly Weak Identification (2019) Downloads
Working Paper: Asymptotic F Tests under Possibly Weak Identification (2019) Downloads
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DOI: 10.1016/j.jeconom.2019.10.011

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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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