The Asymptotic Variance Bound for Instrumental Variables Estimators

The paper derives the asymptotic variance bound for instrumental variables (IV) estimators, and extends the Gauss-Markov theorem for the regressions with correlated regressors and regression errors. For some special class of models, the usual IV estimator attains the lower bound and becomes the best linear consistent estimator (BLCE). In general, however, the IV estimator has asymptotic variance strictly larger than the lower bound that we obtained. Out lower bound can be consistently estimated, so that we may compute the asymptotic relative efficiency (ARE) of the IV estimator. The notion of ARE can be used to evaluate th IV practice. This is illustrated with an application of our method to the Klein's simultaneous equations model.