Sampling Variation, Monotone Instrumental Variables and the Bootstrap Bias Correction

This paper discusses the finite sample bias of analogue bounds under the monotone instrumental variables assumption. By analyzing the bias function, we first propose a conservative estimator which is biased downwards (upwards) when the analogue estimator is biased upwards (downwards). Using the bias function, we then show the mechanism of the parametric bootstrap correction procedure, which can reduce but not eliminate the bias, and there is also a possibility of overcorrection.This motivates us to propose a simultaneous multi-level bootstrap procedure so as to further correct the remaining bias. The procedure is justified under the assumption that the bias function can be well approximated by a polynomial. Our multi-level bootstrap algorithm is feasible and does not suffer from the curse of dimensionality. Monte Carlo evidence supports the usefulness of this approach and we apply it to the disability misreporting problem studied by Kreider and Pepper (2007).