Gini Coefficient How To Read

[Jkobe Peoples]

Ineconomics, the Gini coefficient (/ˈdʒiːni/ JEE-nee), also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality, the wealth inequality, or the consumption inequality[3] within a nation or a social group. It was developed by Italian statistician and sociologist Corrado Gini.

The Gini coefficient measures the inequality among the values of a frequency distribution, such as levels of income. A Gini coefficient of 0 reflects perfect equality, where all income or wealth values are the same, while a Gini coefficient of 1 (or 100%) reflects maximal inequality among values, a situation where a single individual has all the income while all others have none.[4][5]

There are some issues in interpreting a Gini coefficient, as the same value may result from many different distribution curves. To mitigate this, the demographic structure should be taken into account. Countries with an aging population, or those with an increased birth rate, experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Many scholars have devised over a dozen variants of the Gini coefficient.[14][15][16]

The Gini coefficient was developed by the Italian statistician Corrado Gini and published in his 1912 paper Variabilit e mutabilit (English: variability and mutability).[17][18] Building on the work of American economist Max Lorenz, Gini proposed that the difference between the hypothetical straight line depicting perfect equality, and the actual line depicting people's incomes, be used as a measure of inequality.[19] In this paper, he introduced the concept of simple mean difference as a measure of variability.

He then applied the simple mean difference of observed variables to income and wealth inequality in his work On the measurement of concentration and variability of characters in 1914. Here, he presented the concentration ratio, which further developed in the Gini coefficient used today. Secondly, Gini observed that his proposed ratio can be also achieved by improving methods already introduced by Lorenz, Chatelain, or Sailles.

The Gini coefficient is an index for the degree of inequality in the distribution of income/wealth, used to estimate how far a country's wealth or income distribution deviates from an equal distribution.[22]

Assuming non-negative income or wealth for all, the Gini coefficient's theoretical range is from 0 (total equality) to 1 (absolute inequality). This measure is often rendered as a percentage, spanning 0 to 100. However, if negative values are factored in, as in cases of debt, the Gini index could exceed 1. Typically, we presuppose a positive mean or total, precluding a Gini coefficient below zero. [25]

An alternative approach is to define the Gini coefficient as half of the relative mean absolute difference, which is equivalent to the definition based on the Lorenz curve.[26] The mean absolute difference is the average absolute difference of all pairs of items of the population, and the relative mean absolute difference is the mean absolute difference divided by the average, x \displaystyle \bar x , to normalize for scale. If xi is the wealth or income of person i, and there are n persons, then the Gini coefficient G is given by:

While the income distribution of any particular country will not correspond perfectly to the theoretical models, these models can provide a qualitative explanation of the income distribution in a nation given the Gini coefficient.

In some cases, this equation can be applied to calculate the Gini coefficient without direct reference to the Lorenz curve. For example, (taking y to indicate the income or wealth of a person or household):

is the resulting approximation for G. More accurate results can be obtained using other methods to approximate the area B, such as approximating the Lorenz curve with a quadratic function across pairs of intervals or building an appropriately smooth approximation to the underlying distribution function that matches the known data. If the population mean and boundary values for each interval are also known, these can also often be used to improve the accuracy of the approximation.

The Gini coefficient calculated from a sample is a statistic, and its standard error, or confidence intervals for the population Gini coefficient, should be reported. These can be calculated using bootstrap techniques, mathematically complicated and computationally demanding even in an era of fast computers.[42] Economist Tomson Ogwang made the process more efficient by setting up a "trick regression model" in which respective income variables in the sample are ranked, with the lowest income being allocated rank 1. The model then expresses the rank (dependent variable) as the sum of a constant A and a normal error term whose variance is inversely proportional to yk:

Thus, G can be expressed as a function of the weighted least squares estimate of the constant A and that this can be used to speed up the calculation of the jackknife estimate for the standard error. Economist David Giles argued that the standard error of the estimate of A can be used to derive the estimate of G directly without using a jackknife. This method only requires using ordinary least squares regression after ordering the sample data. The results compare favorably with the estimates from the jackknife with agreement improving with increasing sample size.[43]

However, it has been argued that this depends on the model's assumptions about the error distributions and the independence of error terms. These assumptions are often not valid for real data sets. There is still ongoing debate surrounding this topic.

where μ \displaystyle \mu is mean income of the population, Pi is the income rank P of person i, with income X, such that the richest person receives a rank of 1 and the poorest a rank of N. This effectively gives higher weight to poorer people in the income distribution, which allows the Gini to meet the Transfer Principle. Note that the Jasso-Deaton formula rescales the coefficient so that its value is one if all the X i \displaystyle X_i are zero except one. Note however Allison's reply on the need to divide by N instead.[46]

Using the Gini can help quantify differences in welfare and compensation policies and philosophies. However, it should be borne in mind that the Gini coefficient can be misleading when used to make political comparisons between large and small countries or those with different immigration policies (see limitations section).

The Gini coefficient for the entire world has been estimated by various parties to be between 0.61 and 0.68.[12][13][53] The graph shows the values expressed as a percentage in their historical development for a number of countries.

Taking income distribution of all human beings, worldwide income inequality has been constantly increasing since the early 19th century (and will keep on increasing over the years) . There was a steady increase in the global income inequality Gini score from 1820 to 2002, with a significant increase between 1980 and 2002. This trend appears to have peaked and begun a reversal with rapid economic growth in emerging economies, particularly in the large populations of BRIC countries.[55]

More detailed data from similar sources plots a continuous decline since 1988. This is attributed to globalization increasing incomes for billions of poor people, mostly in countries like China and India. Developing countries like Brazil have also improved basic services like health care, education, and sanitation; others like Chile and Mexico have enacted more progressive tax policies.[58]

The Gini coefficient is widely used in fields as diverse as sociology, economics, health science, ecology, engineering, and agriculture.[60] For example, in social sciences and economics, in addition to income Gini coefficients, scholars have published education Gini coefficients and opportunity Gini coefficients.

Though India's education Gini Index has been falling from 1960 through 1990, most of the population still has not received any education, while 10 percent of the population received more than 40% of the total educational hours in the nation. This means that a large portion of capable children in the country are not receiving the support necessary to allow them to become positive contributors to society. This will lead to a deadweight loss to the national society because there are many people who are underdeveloped and underutilized.[62]

Similar in concept to the Gini income coefficient, the Gini opportunity coefficient measures inequality in opportunities.[63][64][65] The concept builds on Amartya Sen's suggestion[66] that inequality coefficients of social development should be premised on the process of enlarging people's choices and enhancing their capabilities, rather than on the process of reducing income inequality. Kovacevic, in a review of the Gini opportunity coefficient, explained that the coefficient estimates how well a society enables its citizens to achieve success in life where the success is based on a person's choices, efforts and talents, not their background defined by a set of predetermined circumstances at birth, such as gender, race, place of birth, parent's income and circumstances beyond the control of that individual.

In 1978, Anthony Shorrocks introduced a measure based on income Gini coefficients to estimate income mobility.[68] This measure, generalized by Maasoumi and Zandvakili,[69] is now generally referred to as Shorrocks index, sometimes as Shorrocks mobility index or Shorrocks rigidity index. It attempts to estimate whether the income inequality Gini coefficient is permanent or temporary and to what extent a country or region enables economic mobility to its people so that they can move from one (e.g., bottom 20%) income quantile to another (e.g., middle 20%) over time. In other words, the Shorrocks index compares inequality of short-term earnings, such as the annual income of households, to inequality of long-term earnings, such as 5-year or 10-year total income for the same households.

3a8082e126