Undersmoothing and Bias Corrected

Abstract:     
There are many important examples of -consistently estimable functionals that are interesting in econometrics, such as average derivatives and nonparametric consumer surplus. Corresponding estimators may require undersmoothing to achieve -consistency, due to first order bias in the expected influence function. We give a general bias correction that can be added to a plug-in estimator to remove the need for undersmoothing and improve its higher order properties. We also describe a bootstrap smoothing correction for the nonparametric estimator that achieves analogous results for the plug-in estimator and show that idempotent transformations of the empirical distribution need not require undersmoothing for -consistency. We find that this bias correction can lead to large efficiency improvements and lower sensitivity to bandwidth choice.

JEL Classification: C13, C14

working papers series