Efficient size correct subset inference in homoskedastic linear instrumental variables regression

We show that Moreira’s (2003) conditional critical value function for likelihood ratio (LR) tests on the structural parameter in homoskedastic linear instrumental variables (IV) regression provides a bounding critical value function for subset LR tests on one structural parameter of several for general homoskedastic linear IV regression. The resulting subset LR test is size correct under weak identification and efficient under strong identification. A power study shows that it outperforms the subset Anderson–Rubin test with conditional critical values from Guggenberger et al. (2019a) when the structural parameters are reasonably identified and has slightly less power when identification is weak.