Testing Subsets of Structural Parameters in the Instrumental Variables

We develop Lagrange multiplier and likelihood ratio statistics to test hypotheses on subsets of the structural parameters in an instrumental variables regression model. The asymptotic distributions of these statistics are robust to instrument quality. A key assumption is, however, that the instruments are valid for the remaining endogenous variables. We show that the statistics lead to 95% confidence sets for the return on education in data from Card (1995) that are considerably different from the confidence sets that result from the 2SLS Wald statistic, which is the common statistic used in the literature.