How much does one learn about the state of inequality in a developing country by looking exclusively at the Gini coefficient

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Anar Bakhshaliyev

How much does one learn about the state of inequality in a developing country by looking exclusively at the Gini coefficient?

        Introduction

There has been considerable interest in inequality recently, due mainly to the fact that there seems to be positive relationship between equality and future growth (Persson & Tablellini [1994]). I have attempted to show in this essay what one can learn about the state of inequality in a developing country by looking at a measure of inequality – Gini coefficient. This work concentrates mainly on Gini coefficient measured in income space. This does not mean other spaces are not equally important; income is only part of the broader inequality problem. Indeed I stress the fact that ignoring other variables limits our understanding of the problem. Two factors seem to make income as an attractive variable to use for inequality analysis:

  1. Much easier to measure compared to other variables
  2. Having big impact on peoples well-being

Societies have differing values, which in turn means they attach different weights to possible inequality variables. One has to thoroughly address these weights when examining the state of inequality in a developing country. This, as we will see later limit the benefits of cross country comparisons when Gini coefficient measured in a particular space is used.

If we choose Economic inequality to be more relevant then I suggest consumption is a better variable than income for measuring the Gini coefficient. However lack of data for this variable limits in-depth analysis.

After analyzing the measure I come to the conclusion that the Gini index is a good measure of inequality as it satisfies properties that are of fundamental importance. Of course it is not perfect, as no other measure is, as it has few problems associated with it, which I address.

        Gini coefficient

Gini coefficient was named after an Italian statistician and demographer Corrado Gini who pioneered studies of the measurable characteristics of populations. In this essay I will be mostly concentrating on distribution of income among citizens of a country. However it is worth mentioning at this stage that Gini can be used to measure distribution of other variables such as employment, healthcare, education, etc. And the population does not have to comprise of all the citizens. For example we could be interested in the inequality of healthcare among black population. However it is best to use other measures of inequality like coefficient of variation for variables such as age, years of schooling etc, which do not have diminishing marginal utility. Also it is not very useful for measuring variables not measured on a ratio scale, e.g. occupational prestige.

The Gini coefficient is best explained using Lorenz Curve. The cumulative percentages of population are plotted against cumulative percentages of the income (or some other resource); these can also be quintiles (Figure 1). Lorenz curve is a graphical representation of the degree of inequality of a frequency distribution.

Figure 1

Lorenz Curve

It is the convex curve starting at F and ending at J. The 45° line FJ represents the state of perfect equality, where everybody receives the same level of income. On the other hand, in perfect inequality one person receives all the income in the country, represented by FHJ. Since there is no country with any of these two extreme states of equality/inequality the Lorenz curve will typically lie between the 45° line FJ and FHJ. Higher level of convexity implies greater state of inequality.

Gini coefficient is the ratio of the shaded area A to the area below the 45° line - the triangle FHJ.

        

The above formula implies the value of Gini will lie between 0 and 1. Values 0 and 1 are states of perfect equality and inequality I mentioned above. The area A becomes zero when perfect equality prevails. Plugging this in the above formula gives 0. On the other hand in state of perfect inequality one person receives all the income making area B zero. Substitution yields value of 1 for Gini. It gives a neat and well-defined measure, and it is not hard to see why it has been so widely used in the empirical literature on inequality.

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Gini has many attractive features:

  • The most attractive feature of the index is that it satisfies the Pigou-Dalton Transfer Principle, which requires that a transfer of income from the poor to the rich should increase inequality measure and vice verse. This is the least one should expect from any income inequality measure.
  • It is sensitive to transfers, but this depends on ranking of individuals as opposed to their numeric scores. Gini is most sensitive to transfers around the middle of the distribution and least sensitive among the richest and the poorest. Gini is particularly appealing to someone concerned ...

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