Second-order refinements for t-ratios with many instruments

Yukitoshi Matsushita and Taisuke Otsu

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: This paper studies second-order properties of the many instruments robust t-ratios based on the limited information maximum likelihood and Fuller estimators for instrumental variable regression models under the many instruments asymptotics, where the number of instruments may increase proportionally with the sample size n, and proposes second-order refinements to the t-ratios to improve the size and power properties. Based on asymptotic expansions of the null and non-null distributions of the t-ratios derived under the many instruments asymptotics, we show that the second order terms of those expansions may have non-trivial impacts on the size as well as the power properties. Furthermore, we propose adjusted t-ratios whose approximation errors for the null rejection probabilities are of order O(n^{-1}) in contrast to the ones for the unadjusted t-ratios of order O(n^{-1/2}), and show that these adjustments induce some desirable power properties in terms of the local maximinity.

Keywords: simultaneous equation; many instrumental variables; higher order expansion (search for similar items in EconPapers)
JEL-codes: C12 C26 (search for similar items in EconPapers)
Date: 2020-05
New Economics Papers: this item is included in nep-ecm and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:612

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