We often see that the F test is applied to testing significance of a subset of coefficients even in a structural equation. This is obviously a doubtful method because the sum of squared errors is not distributed as x^2 in a simultaneous equation system. It is known, however, that the likelihood ratio test is asymptotically distributed as x^2 with proper degrees of freedom. We analyze the asymptotic properties of these two kinds of test statistics. We find the likelihood ratio method associated with limited information maximum likelihood estimation is reliable in practice.