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A THREE-STEP METHOD FOR CHOOSING THE NUMBER OF BOOTSTRAP REPETITIONS



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A THREE STEP METHOD FOR CHOOSING THE NUMBER OF BOOTSTRAP REPETITIONS BY DONALD W K ANDREWS and MOSHE BUSHINSKY COWLES FOUNDATION PAPER NO 1001 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven Connecticut 06520 8281 2000 http cowles econ yale edu Econometrica Vol 68 No 1 January 2000 23 51 A THREE STEP METHOD FOR CHOOSING THE NUMBER OF BOOTSTRAP REPETITIONS BY DONALD W K ANDREWS AND MOSHE BUCHINSKY 1 This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors confidence intervals confidence regions hypothesis tests p values and bias correction For each of these problems the paper provides a three step method for choosing B to achieve a desired level of accuracy Accuracy is measured by the percentage deviation of the bootstrap standard error estimate confidence interval length test s critical value test s p value or bias corrected estimate based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B s The results apply quite generally to parametric semiparametric and nonparametric models with independent and dependent data The results apply to the standard nonparametric iid bootstrap moving block bootstraps for time series data parametric and semiparametric bootstraps and bootstraps for regression models based on bootstrapping residuals Monte Carlo simulations show that the proposed methods work very well KEYWORDS Bias correction bootstrap bootstrap repetitions confidence interval hypothesis test p value simulation standard error estimate 1 INTRODUCTION BOOTSTRAP METHODS HAVE GAINED a great deal of popularity in empirical research Although the methods are easy to apply determining the number of bootstrap repetitions B to employ is a common problem in the existing literature Typically this number is determined in a somewhat ad hoc manner This is problematic because one can obtain a different answer from the same data merely by using different



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