Evaluation of a three-step method for choosing the number of bootstrap repetitions

This paper provides a variety of Monte Carlo simulations that evaluate the finite-sample performance of the three-step method for choosing the number of bootstrap repetitions, suggested by Andrews and Buchinsky (Econometrica 67 (2000) 23–51). The simulations cover bootstrap standard errors, confidence intervals, tests, and p-values. Three commonly used econometric applications are considered: linear regression, binary probit, and quantile regression. In brief, we find that the three-step method works very well in all of the contexts examined here. We also find that the number of bootstrap repetitions commonly used in econometric applications is much less than needed to achieve accurate bootstrap quantities.