There is a rich literature on the methods and techniques that focusing

on measuring the income inequality. We found that four Different methods have

been developed to decompose income inequality in the literature. The first

method have been developed by Mincer (1958 and 1970) Becker (1964) and Oxaaca

(1973) which concerns with estimating

the differences in the means. The second method deals with decomposing

inequality within-subgroups and between-groups ingredients (Pyatt, 1976; Shorrocks,

1984; Fields, 2000; Almeida dos Reis and de Barros; 1991, Cowell and Jenkins

1995; and Morduch and Sicular, 2002). The third method concerns with applying

linear regression approach on income functions ( Morduch and Sicular; 2002, Fields;

2003, and Rani et al.; 2017). The fourth method is based on the factor

ingredients ( Fei et al. 1978; Pyatt et al. 1980, and Shorrocks 1982).

Inequality is decomposed by subgroups, income source and

demographic sources. Fields (2000) and Morduch and Sicular (2002) use

regression-based decomposition method. The proportional contribution of an

income source in inequality is the coefficient of that source from the

regression equation of income multiplied by a factor of adjusted weighted mean

of income by sources to mean income. Standard errors of source contributions

are also computed. Fields (2003) propose different method which is applicable

to the changes in income inequality, and it is useful any index of inequality. He

used standard semi-logarithmic regression model of income in order to obtain

the contributions of different indicators to the change and the level in

inequality. The benefit from his approach that it can integrate several indicator

types in the regression model. Moreover it can include nonlinear effects and controlling

for endogeneity. Rani et al. (2017) used Fields (2003) and Bigotta et

al. (2015) to decompose income inequality in India. The primary points of

interest of this method is the likelihood of including quantitative and also qualitative

variables as contributing factors and its possibility to apply to the measures

of inequality.

The Gini coefficient is the most widely measure of inequality.

Giles (2004) estimates the Gini coefficient and its standard deviations using

linear regression, while the assumption of the ordinary least square method are

violated. Davidson (2009) used an asymptotic approach primarily based on the

natural estimator of the cumulative distribution. Lubrano and Ndoye (2016)

showed that the distribution of log-normal is suitable for modeling the

distribution of income. They decompose inequality within-subgroups and

between-groups ingredients by applying a finite mixture of log-normal

distributions using Bayesian methods and Gibbs sampling. Moreover, the strong

prior information indicates that Bayesian standard deviations of the Gini

coefficient are somewhat low compared with those found in Davidson (2009) and

much lower than those found in Giles (2004).

Inequality can also be decomposed at different levels. At the

national level, it can be decomposed into within-subgroup and between-subgroup

components (Heshmati, 2004).

Statistical inference on inequality and its dimensions is proposed

by Van de gaer, Funnell and McCarthy (1999),

where they name two ways of inference with measures of inequality or of functions

of inequality: Bootstrapped standard errors or large-sample distributions’

standard errors. Biewen, M. (2002) showed that a

bootstrapping simulation and provided an evidence that this method is better

than asymptotic methods.