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Abstract for:

Second-order refinements for t-ratios with many instruments

Yukitoshi  Matsushita,  Taisuke  Otsu,  May 2020
Paper No' EM 612: | Full paper (pdf)
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Keywords: simultaneous equation; many instrumental variables; higher order expansion

JEL Classification: C12; C26

Is hard copy/paper copy available? YES - Paper Copy Still In Print.
This Paper is published under the following series: Econometrics
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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.