Inequality factor decomposition under uniform additions property with applications to Cameroonian rural data

Abstract

In this article, we generalize and extend the Morduch and Sicular's (2002) Coefficient of Variation (CV)-squared decomposition approach. This leads to a class of decomposition methods which satisfy the uniform additions principle, especially in the case of the Gini index. The regression-based method using the new formulations of component contributions is carried out. An application using Cameroonian data is provided to support the appropriateness of the procedure and to contrast our results to those of Morduch and Sicular.

Keywords:

• inequality factor decomposition
• uniform additions property
• regression-based decomposition
• Cameroon

JEL Classification:

• O15
• C43
• D63

Notes

¹ In many empirical works, total expenditure or consumption is used rather than total income because of data availability.

² In this article, the m variables and the residual are treated in the same manner. Note that other approaches, as found in Wan (2002), propose that the constant and the residual terms are treated separately.

³ In fact, this is just an approximation of the SEs computation. The correct SEs are very quite complicated to compute as they require the use of bootstrap or the nontrivial asymptotic distribution (Cowell and Fiorio, 2005).

⁴ We suppose that the total consumption is a good proxy of total income.

⁵ It is no surprise that the alternative decomposition rule of the CV squared (with α = μ) is in concordance with the natural decomposition of the Theil's T index. As we have already mentioned, the former coincides with the natural decomposition of the entropy index with θ = 2, while the latter is the natural decomposition of the entropy index with θ = 1.