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t Test in a Structural Equation

Kimio Morimune

Abstract

Properties of t ratios associated with the LIML, TSLS, and OLS estimators in a structural form estimation are studied in this paper. The existence of moments of these t ratios including the LIML form is proved first. Second, Monte Carlo simulations are performed to find out real sizes of the t test and the likelihood ratio test. Third, asymptotic expansions of the distributions of t ratios are derived under the null hypothesis to find out deviations of real sizes from nominal sizes theoretically. The asymptotic power functions are also derived, and t ratios associated with the LIML and TSLS estimators are proved asymptotically as powerful as the likelihood ratio test.