Improved Inference for the Instrumental Variables Estimator

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 accept apparently tight confidence regions which unfortunately may be very far from the true parameter of interest. We present an improved technique for inference on structural parameters based on reduced form estimates. The `S-statistic' produces confidence regions based on a joint test of the structural hypothesis and the identification condition. The S-statistic converges to the standard asymptotic Wald statistic as identification becomes certain, has much better size properties when the instruments are weak, and may be inverted in closed form to conveniently compute confidence regions. In addition to providing improved inference for instrumental variable estimation, the technique suggested here may be useful in other applications where weak identification is important.