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- W2102592823 abstract "This paper studies the properties of t-ratios associated with the limited information maximum likelihood (LIML) estimators in a structural form estimation when the number of instrumental variables is large. Asymptotic expansions are made of the distributions of the LIML estimator and t-ratio statistic under large K asymptotics. A modified t-ratio statistic is proposed from the asymptotic expansion. It is shown that when the number of instruments is large, the null distribution of the standard t-ratio is skewed and extremely deviated from the normal distribution. The null distribution of the large K t-ratio is closer to the normal distribution than the standard t-ratio, but still skewed and the size distortion can be large for the one-sided test. The null distribution of the modified large K t-ratio is closest to the standard normal distribution. In addition, the power of the large K t-ratio test is shown to dominate the AR test, the K-test by Kleibergen (2002), and the conditional LR test by Moreira (2003); and the difference can be substantial when the instruments are weak. When we know the sign of the parameter from the economic theory, the use of the modified large K t-ratio statistic is recommended as a more accurate test procedure." @default.
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- W2102592823 date "2006-01-01" @default.
- W2102592823 modified "2023-09-27" @default.
- W2102592823 title "t-Tests in a Structural Equation with Many Instruments" @default.
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