We consider the K-statistic, Kleibergen's (2002, Econometrica 70, 1781–1803)
adaptation of the Anderson–Rubin (AR) statistic in instrumental
variables regression. Whereas Kleibergen (2002) especially analyzes the asymptotic behavior
of the statistic, we focus on finite-sample properties in a Gaussian
framework. The AR statistic then has an F-distribution. The
finite-sample distribution of the K-statistic is, however, affected by
nuisance parameters. We consider two extreme cases for the nuisance
parameters, which provide tight bounds for the exact distribution. The
first case amounts to perfect identification—which is similar to
the asymptotic case—where the statistic has an
F-distribution. In the other extreme case there is total
underidentification. For the latter case we show how to compute the
exact distribution. We thus provide tight bounds for exact confidence
sets based on the K-statistic. Asymptotically the two bounds converge,
except when there is a large number of redundant instruments.The authors' research documented in this
paper has been funded by the NWO Vernieuwingsimpuls research grant
“Empirical Comparison of Economic Models.”