Bias correction for inequality measures: an application to China and Kenya

Abstract

An analytical bias correction technique for inequality measures is applied to income data from China and Kenya. The coefficient of variation squared is used and it is illustrated how the bias is downward for positively skewed distributions. The analytical bias correction technique is then compared to a jackknife estimator in a simulation exercise. The bias will be important, even for moderately large sample sizes.

Small Sample Bias Corrections for Entropy Inequality Measures

“…For example, these measures satisfy the decomposability axiom, particularly useful for territorial comparisons, as it allows to decompose the total inequality into the part due to inequality within areas and the part due to differences between areas. A few papers propose a small sample correction for those measures (see [1,[3][4][5]), and only in the simple random sample context. Regarding the small sample bias correction for simple random sample, Breunig [3] focuses on one entropy measure, the coefficient of variation squared ( )…”

“…Breunig [4] applies that corrected estimator for the coefficient of variation squared to income data for Cina and Kenya, and compare that estimator to an alternative bias-corrected estimator,  2 , jkn CV obtained using the leave-one-out jackknife estimator. Through a simulation study he shows that, when the sample is small or moderately large and the skewness coefficient is greater than…”

Estimating Standard Errors for the Parks Model: Can Jackknifing Help?

“…On the face of it, jackknifing would appear to be a promising avenue. As a result of increased computer processing speeds, jackknifing has become increasingly feasible (Breunig, 2002;Sunil, 2002). Further, it has been shown to reliably estimate coefficient standard errors in a variety of settings (Schucany and Sheather, 1989;Jennrich, 2008).…”

Estimating Standard Errors for the Parks Model: Can Jackknifing Help?

“…On the face of it, jackknifing would appear to be a promising avenue. As a result of increased computer processing speeds, jackknifing has become increasingly feasible (Breunig, 2002;Sunil, 2002). Further, it has been shown to reliably estimate coefficient standard errors in a variety of settings (Schucany and Sheather, 1989;Jennrich, 2008).…”