COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1250

On the Number of Bootstrap Repetitions for BC_a Confidence Intervals

Donald W. K. Andrews and Moshe Buchinsky

December 1997
Revised: November 1999
February 2000

This paper considers the problem of choosing the number bootstrap repetitions B to use with the BC_a bootstrap confidence intervals introduced by Efron (1987). Because the simulated random variables are ancillary, we seek a choice of B that yields a confidence interval that is close to the ideal bootstrap confidence interval for which B = infinity. We specifiy a three-step method of choosing B that ensures that the lower and upper lengths of the confidence interval deviate from those of the ideal bootstrap confidence interval by at most a small percentage with high probability.