This paper considers the problem of finding the “best” estimator among a class that includes most of the commonly used limited information estimators in simultaneous equation systems. Concentration comparisons, based on the Edgeworth expansion of the distribution of these estimators, lead to selection rules of sufficient simplicity to be useful in applied econometric research.

This paper is concerned with the refined asymptotic properties of several tests for the admissibility of a subset of (overidentifying) instrumental variables. It derives maximum likelihood and linearized maximum likelihood tests and calculates size corrections to the order 1/T. The local power function of the size-corrected tests is the same to the order 1/T, irrespectively of the form of the test statistic or the limited information estimator used in its computation. Futher, it compares these tests with two previously proposed tests. The size and the power of the original and the size-corrected tests are compared by Monte Carlo experiments.