There has been much recent interest by econometricians in analyzing the unsatisfactory performance of instrumental variables (IV) estimators when the instruments used are only weakly correlated with the endogenous variable. This dissertation applies the bootstrap method to provide alternative solutions to the problems caused by the presence of weak instruments and unifies two of the existing lines of research in the literature.
The first chapter of the dissertation proposes the use of a bias reduction technique based on the bootstrap to attenuate the finite sample bias of the two-stage least squares (TSLS) estimator that is exacerbated in the presence of weak instruments. In addition, several robust-to-weak-instruments (RWI) estimators are compared through Monte Carlo techniques. The results indicate that the proposed bias-corrected estimator is successful in reducing the bias of the TSLS estimator, and also outperforms other RWI estimators under several model specifications considered.
The second chapter compares several tests for instrument relevance proposed in the literature using Monte Carlo techniques. None of the tests are found to perform satisfactorily when different model specifications are con¬sidered. Therefore, a new approach to test instrument relevance based on the use of bootstrap confidence intervals (BCIs) is proposed. This new approach appears successful as judged from the simulation results.
The last chapter unifies the two different lines of research in the previous chapters. Here, we consider the use of tests for instrument relevance as a means for choosing an IV estimation method, either conventional or RWI methods. By using simulation methods, we compare this methodology with other estimators, which enables us to suggest practical guidelines to applied researchers.