Univariate Income Inequality

might represent a persistent trend in export volumes (Deaton, 1999). Therefore, he applies different measures of inequality, such as the GINI Index, the proportion of the highest and lowest earners in the economy using the top and bottom 10% and 20% respectively. The empirical results must be interpreted with caution, despite multiple robustness checks. One of the results implies that an increase in the value raises the price and creates economic diversification from the economy. It is found that coffee prices have a strong negative effect on income inequality between the top 20% and the bottom 20% in the economy. Intuitively, the ratio of incomes is measure of income inequality, since coffee prices are more directly related to income than

According to Patton (2006), it has also been found that related price series may show asymmetric dependence, which is an indicator of multivariate non normality.
Based on the Sklar’s (1959) theorem, an n dimensional joint distribution characterizing dependence of n economic variables can be decomposed into n univariate distributions and a copula function. The latter fully describes the dependence structure between the variables under study. In other words, copula functions allow a flexible dependence structure between the n random variables and are specially suited when no obvious choice for the multivariate density exists (Serra and Gil, 2012).
Here, we will present the methodological tool of copula for a two dimensional and bivariate case .
Let be a random vector with distribution function , where are the marginal distribution functions of (i=1,2). Utilizing the Sklar’s (1959) theorem, there exists a copula function , such that for all it holds that (1)
As long as the marginal distributions are continuous, there is a unique copula function , where are the inverse distribution functions and they are quantiles (probabilities) of the uniform distribution function

Rewriting the previous relationship, (2), we have that (3)
In general, a joint probability density function of two random variables (X1 and X2) contains information on the marginal behavior of these variables and, moreover, on the dependence between them. In each random variable is fed on its own distribution function. As a result, all information contained in the marginal distribution functions is swept away and what is left in c and C is pure joint information about X1 and X2.
Hence, form relationship (3) we derive that the copula function fully characterizes the co movement (dependence structure) of the random variables by capturing the information missing from the marginal distributions to complete the joint distribution (Meucci, 2011, Emmanouilides et al, 2014).
The inverse of Sklar’s (1959) theorem holds and it means that given H1 and H2 and any copula function C, the function H of relationship (1) defines a valid joint distribution function with margins H1 and H2.
The next step is to define the appropriate measures for dependence. A standard rank based measure of functional dependence is Kendall’s tau, defined