Detecting Weak Identification by Bootstrap

This paper suggests bootstrap resampling for detecting weak instruments in the instrumental variable regression. When instruments are not weak, the bootstrap distribution of the standardized Two-Stage-Least-Squares estimator is close to the standard normal distribution. In contrast, a substantial difference between these two distributions indicates the existence of weak instruments. A bootstrap-based test for evaluating the strength of instruments is developed. Monte Carlo simulations show that the test has good size and power. The test is illustrated by an application taken from Card, where the return to schooling is significantly positive under a strong instrument, but insignificant under a weak one.