Small Concentration Asymptotics and Instrumental Variables Inference
D. S. Poskitt and C. L. Skeels
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.
Keywords: IV estimator, concentration parameter, small concentration
asymptotics, hypothesis testing, confidence region construction, valid inference.
