Econometrica: Nov, 1989, Volume 57, Issue 6

t Test in a Structural Equation

https://doi.org/0012-9682(198911)57:6<1341:TTIASE>2.0.CO;2-5
p. 1341-1360

Kimio Morimune

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.