There Fields, 2000; Almeida dos Reis and de Barros;

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.

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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.