Efficient Bias Correction for Cross-section and Panel Data

TL;DR

This paper demonstrates that various bias correction methods, including bootstrap, jackknife, and analytical approaches, have equivalent higher-order variance when estimating semiparametrically efficient estimators, with some methods like split-sample jackknife increasing variance.

Contribution

It establishes the asymptotic equivalence of bias correction methods' higher-order variance for efficient estimators and highlights the inefficiency of split-sample jackknife in finite samples.

Findings

Bootstrap bias correction matches analytical and jackknife methods in higher-order variance.

Split-sample jackknife results in larger higher-order variance than leave-one-out jackknife.

Bias correction methods with asymptotically linear bias estimates do not affect the estimator's higher-order variance.

Abstract

Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher-order variance of semiparametrically efficient parametric estimators, so long as the estimate of the bias is asymptotically linear. It is also shown that bootstrap, jackknife, and analytical bias estimates are asymptotically linear for estimators with higher-order expansions of a standard form. In particular, we find that for a variety of estimators the straightforward bootstrap bias correction gives the same higher-order variance as more complicated analytical or jackknife bias corrections. In contrast, bias corrections that do not estimate the bias at the parametric rate, such as the split-sample jackknife, result in larger higher-order variances in the i.i.d. setting we focus on. For both a cross-sectional MLE and a panel model with individual fixed effects, we show that the split-sample jackknife has a higher-order variance term that is twice as large as that of the `leave-one-out' jackknife.