Fast Iterated Bootstrap Mean Bias Correction

Abstract: The article proposes a computationally efficient procedure for bias adjustment in the iterated bootstrap. The new technique replaces the need for successive levels of bootstrap resampling by proposing an approximation for the double bootstrap “calibrating coefficient” using only one draw from the second level probability distribution. Extensive Monte Carlo evidence suggest that the proposed approximation performs better than the ordinary bootstrap bias correction. The article evaluates the usefulness of the bootstrap and fast bootstrap in reducing the bias of generalized method of moments estimators under weak instruments. In identified models, this fast bootstrap bias correction leads to estimators with lower variance than those based on the double bootstrap. The proposed fast iterated bootstrap performs better than the double bootstrap in all scenarios and especially when the model has the weakest instrument relevance and the highest degree of endogeneity. However, when the estimators have no finite moments and the instruments are weak, the bootstrap does not work well and iterating it makes things worse.