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Conditional Likelihood Ratio Test with Many Weak Instruments

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  • Sreevidya Ayyar
  • Yukitoshi Matsushita
  • Taisuke Otsu

Abstract

This paper extends validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003) to instrumental variable regression models with unknown error variance and many weak instruments. In this setting, we argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid. We propose a modified critical value function for the likelihood ratio (LR) statistic with estimated error variance, and prove that this modified test achieves asymptotic validity under many weak instrument asymptotics. Our critical value function is constructed by representing the LR using four statistics, instead of two as in Moreira (2003). A simulation study illustrates the desirable properties of our test.

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  • Sreevidya Ayyar & Yukitoshi Matsushita & Taisuke Otsu, 2022. "Conditional Likelihood Ratio Test with Many Weak Instruments," Papers 2210.07680, arXiv.org.
    • Handle: RePEc:arx:papers:2210.07680
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    References listed on IDEAS

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    1. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    2. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    3. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    4. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
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    Cited by:

    1. Anna Mikusheva & Liyang Sun, 2023. "Weak Identification with Many Instruments," Papers 2308.09535, arXiv.org, revised Jan 2024.

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