Bootstrap Inference with Many Instruments or Weak Instruments


Day & Time
25th December 2015, 15:00-
Room C816, Building of the Faculty of Science Graduate school of Science
Presentation Title
Bootstrap Inference with Many Instruments or Weak Instruments
Wang and Kaffo (2015, conditionally accepted by JoE) analyze the application of bootstrap methods to instrumental variable models when the available instruments may be weak and the number of instruments goes to infinity with the sample size. We demonstrate that the standard residual-based bootstrap procedure cannot consistently estimate the distribution of the limited information maximum likelihood estimator or Fuller (1977) estimator under many/many weak instrument sequence. The primary reason is that the bootstrap procedure fails to capture the instrument strength in the sample adequately. We propose modified bootstrap procedures that provide a valid distributional approximation for the two estimators with many/many weak instruments. Furthermore, Wang and Doko Tchakota (2015) study subset hypothesis testing in linear structural models in which instrumental variables (IVs) can be arbitrarily weak. We investigate the validity of the bootstrap for Anderson-Rubin (AR) type tests of hypotheses specified on a subset of structural parameters (i.e., subset AR test), with or without identification. We show that when identification is strong and the number of instruments is fixed, the bootstrap provides a higher-order approximation of the null limiting distribution of the subset AR test statistic. However, the bootstrap is inconsistent when instruments are weak. This result contrasts with bootstrapping the AR statistic of the null hypothesis specified on the full vector of structural parameters, which remains valid even when identification is weak.