Conditional likelihood ratio test with many weak instruments

Ayyar, Sree, Matsushita, Yukitoshi and Otsu, Taisuke ORCID: 0000-0002-2307-143X (2025) Conditional likelihood ratio test with many weak instruments. Econometric Theory. ISSN 0266-4666 (In Press)

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Abstract

This paper extends the validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003) 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). A simulation study illustrates the desirable finite sample properties of our test.

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Economics
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics H Social Sciences > HA Statistics
Date Deposited:	07 Mar 2025 09:27
Last Modified:	07 Mar 2025 10:00
URI:	http://eprints.lse.ac.uk/id/eprint/127520

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