Identification and inference in a simultaneous equation under alternative information sets and sampling schemes

In simple static linear simultaneous equation models the empirical distributions ofIV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. It is demonstrated why in this context the limiting distribution of a consistent estimator is not a¤ected by conditioning on exogenous regressors, whereas that of an inconsistent estimator is. The asymptotic variance and the simulated actual variance of the inconsistent OLS estimator are shown to diminish by extending the set of exogenous variables kept fixed in sampling, whereas such an extension disrupts the distribution of consistent IV estimation and deteriorates the accuracy of its standard asymptotic approximation, not only when instruments are weak. Against this background the consequences for the identification of the parameters of interest are examined for a setting in which (in practice often incredible) assumptions regarding the zero correlation between instruments and disturbances are replaced by (generally more credible) interval assumptions on the correlation between endogenous regressors and disturbances. This leads to a feasible procedure for constructing purely OLS-based robust confidence intervals, which yield conservative coverage probabilities in finite samples, and often outperform IV-based intervals regarding their length.