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CONDITIONAL LIKELIHOOD RATIO TEST WITH MANY WEAK INSTRUMENTS

Published online by Cambridge University Press:  15 April 2025

Sreevidya Ayyar ,
Yukitoshi Matsushita  and
Taisuke Otsu
Sreevidya Ayyar
Affiliation:
London School of Economics
Yukitoshi Matsushita
Affiliation:
Hitotsubashi University
Taisuke Otsu*
Affiliation:
London School of Economics
*
Address correspondence to Department of Economics, London School of Economics, London, WC2A 2AE, UK, e-mail: [email protected]
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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.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 27
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

We are grateful to Naoto Kunitomo, Anna Mikusheva, Peter Phillips, and anonymous referees for helpful comments. Y.M. acknowledges financial support from the JSPS KAKENHI (23K01331).

References

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