Small Concentration Asymptotics and Instrumental Variables Inference

Poskitt and Skeels (2003) provide a new approximation to the sampling distribution of the IV estimator in a simultaneous equations model, the approximation is appropriate when the concentration parameter associated with the reduced form model is small. A basic purpose of this paper is to provide the practitioner with easily implemented inferential tools based upon extensions to these small concentration asymptotic results. We present various approximations to the sampling distribution of functions of the IV estimator based upon small concentration asymptotics, and investigate hypothesis testing procedures and confidence region construction using these approximations. It is shown that the test statistics advanced are asymptotically pivotal and that the associated critical regions generate locally uniformly most powerful invariant tests. The confidence regions are also shown to be valid. The small-concentration asymptotic approximations lead to a non-standard application of standard distributions, facilitating numerical implementation using commonly available software. Some key words: IV estimator, concentration parameter, small concentration asymptotics, hypothesis testing, confidence region construction, valid inference. JEL Subject classifications: C12, C16, C30, C50. Small Concentration Parameter Inference 1