Asymptotic Properties of the Hahn–Hausman Test for Weak-Instruments

This paper provides weak-instrument asymptotic representations of tests for instrument validity by Hahn and Hausman's (HH) [Hahn, J., Hausman, J., 2002. A new specification test for the validity of instrumental variables. Econometrica 70, 163–189.], and uses these representations to compute asymptotic power against weak or irrelevant instruments. The HH tests were proposed as pretests, and the asymptotic properties of post-test inferences, conditional on the tests failing to reject instrument validity, are also examined.