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Conditional likelihood ratio test with many weak instruments

Author

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  • Ayyar, Sree
  • Matsushita, Yukitoshi
  • Otsu, Taisuke

Abstract

This article extends the validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003, Econometrica 71(4), 1027-–1048) to instrumental variable regression models with unknown homoskedastic error variance and many weak instruments. We argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid in this setting. We propose a modified critical value function for the likelihood ratio (LR) statistic with estimated error variance, and prove that our modified test achieves asymptotic validity under many weak instruments asymptotics. Our critical value function is constructed by representing the LR using four statistics, instead of two as in Moreira (2003, Econometrica 71(4), 1027-–1048). A simulation study illustrates the desirable finite sample properties of our test.

Suggested Citation

  • Ayyar, Sree & Matsushita, Yukitoshi & Otsu, Taisuke, 2025. "Conditional likelihood ratio test with many weak instruments," LSE Research Online Documents on Economics 127520, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:127520
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    File URL: https://researchonline.lse.ac.uk/id/eprint/127520/
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    References listed on IDEAS

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    1. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    2. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    3. Isaiah Andrews & James H. Stock & Liyang Sun, 2019. "Weak Instruments in Instrumental Variables Regression: Theory and Practice," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 727-753, August.
    4. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2010. "On the asymptotic optimality of the LIML estimator with possibly many instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 191-204, August.
    5. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    6. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    7. 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.
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    Cited by:

    1. Doko Tchatoka, Firmin & Ma, Yuguo, 2025. "Inference with many instruments: When is Anderson–Rubin test still useful?," Economics Letters, Elsevier, vol. 257(C).

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    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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