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Improved inference for the partially identified instrumental variables regression model

It is now well known that standard asymptotic inference techniques for instrumental variable estimation perform very poorly in the presence of weak instruments. Specifically, standard asymptotic techniques give spuriously small standard errors, leading investigators to apparently tight confidence regions which may be very far from the true parameter of interest. While much research has been done on inference in models with one right-hand-side endogenous variable, not much is known about inference on individual coefficients in models with multiple right-hand-side endogenous variables. In this paper we systematically investigate inference on individual structural coefficients in instrumental variables regression models with multiple right-hand-side endogenous variables. We focus on the cases where instruments may be weak for all coefficients or only for a subset of coefficients. We evaluate existing techniques for performing inference on individual coefficients using Staiger and Stock's weak instrument asymptotics, and perform extensive finite sample analyses using Monte Carlo simulations.