Bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models

Abstract

This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method provides a finite-sample bound on the difference between the true and nominal probabilities of rejecting a correct null hypothesis. The method is a non-Studentized version of the S test of Stock and Wright (2000) but is implemented and analyzed differently. It does not require restrictive distributional assumptions, linearity of the estimated model, simultaneous equations, or information about whether the instruments are strong or weak. It can be applied to quantile IV models that may be nonlinear and can be used to test a parametric IV model against a nonparametric alternative. It provides information about the relation between the “degree of weakness” of the instruments and the power of the test. The bound presented here holds in finite samples, regardless of the strength of the instruments.