Improved Inference in Weakly Identified Instrumental Variables Regression

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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 t oa pparently tight confidence regions which may be very far from the true parameter of interest. Whilemuch 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 righthand-side endogenous variables. We focus on the cases where instruments may be weak for all coefficients or only for a subset of coefficients. We introduce a new test statistic, the S-statistic, which has good properties under weak identification. We then 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. It is now well known that standard asymptotic inference techniques for instrumental variable (IV) estimation perform very poorly in the presence of weak instruments. The failure is of the worst kind – false results are accompanied by reported confidence intervals which lend an appearance of great precision. That point estimates of coefficients do a poor job of telling us the true values of those coefficients is probably irremediable, after all if an equation is poorly identified then the data do not tell us much about the parameters of the system. In this paper we uncover test statistics and related confidence intervals that work quite well in the sense that they lead to reasonably accurate inference when instruments are poor and that are essentially identical to the usual asymptotic IV test statistics and confidence intervals when the instruments are good. This sort of performance under weak and strong identification respectively is important as it discourages practitioners’ natural tendency to cling to traditional methods which may give (spuriously) tight confidence bounds and erroneous inference. We make two contributions to inference when instruments are weak. First, we introduce a new test statistic, the S-statistic and associated confidence intervals. Second,