**Frank Kleibergen**, University of Amsterdam
Efficient Size Correct Subset Inference in Linear Instrumental Variables Regression __Abstract__ : We show that Moreira's (2003) conditional critical value function for the likelihood ratio statistic that tests the structural parameter in the iid linear instrumental variables regression model with one included endogenous variable provides a bounding distribution for the subset likelihood ratio statistic that tests one structural parameter in an iid linear instrumental variables regression model with several included endogenous variables. The only adjustment concerns the usual degrees of freedom correction for subset tests of the involved χ² distributed random variables. The conditional critical value function makes the subset likelihood ratio test size correct under weak identification of the structural parameters and efficient under strong identification. When the hypothesized value of the parameter of interest is distant from the true one, the subset Anderson-Rubin and likelihood ratio statistics are invariant with respect to the parameter of interest and equal statistics that test the identification of all structural parameters. Thus, the values of the statistic that result when testing a distant value of different structural parameters are all identical. All results extend to tests on the parameters of the included exogenous variables.
Homepage |