NATIONAL BUREAU OF ECONOMIC RESEARCH

# A Score Based Approach to Wild Bootstrap Inference

## Patrick M. Kline, Andres Santos

NBER Working Paper No. 16127
Issued in June 2010, Revised in December 2011
NBER Program(s):Technical Working Papers, Labor Studies

We propose a generalization of the wild bootstrap of Wu (1986) and Liu (1988) based upon perturbing the scores of M-estimators. This "score bootstrap" procedure avoids recomputing the estimator in each bootstrap iteration, making it substantially less costly to compute than the conventional nonparametric bootstrap, particularly in complex nonlinear models. Despite this computational advantage, in the linear model, the score bootstrap studentized test statistic is equivalent to that of the conventional wild bootstrap up to order O_p(n^(-1)). We establish the consistency of the procedure for Wald and Lagrange Multiplier type tests and tests of moment restrictions for a wide class of M-estimators under clustering and potential misspecification. In an extensive series of Monte Carlo experiments we find that the performance of the score bootstrap is comparable to competing approaches despite its computational savings.

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Document Object Identifier (DOI): 10.3386/w16127

Published: Kline Patrick & Santos Andres, 2012. "A Score Based Approach to Wild Bootstrap Inference," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 23-41, August. citation courtesy of

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