In economics, the Gini coefficient (/ˈdʒiːni/ JEEnee), sometimes called Gini index, or Gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measurement of inequality. It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper Variability and Mutability (Italian: Variabilità e mutabilità).^{[1]}^{[2]}
The Gini coefficient measures the inequality among values of a frequency distribution (for example, levels of income). A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income). A Gini coefficient of 1 (or 100%) expresses maximal inequality among values (e.g., for a large number of people, where only one person has all the income or consumption, and all others have none, the Gini coefficient will be very nearly one).^{[3]}^{[4]} However, a value greater than one may occur if some persons represent negative contribution to the total (for example, having negative income or wealth). For larger groups, values close to or above 1 are very unlikely in practice. Given the normalization of both the cumulative population and the cumulative share of income used to calculate the Gini coefficient, the measure is not overly sensitive to the specifics of the income distribution, but rather only on how incomes vary relative to the other members of a population. The exception to this is in the redistribution of income resulting in a minimum income for all people. When the population is sorted, if their income distribution were to approximate a wellknown function, then some representative values could be calculated.
The Gini coefficient was proposed by Gini as a measure of inequality of income or wealth.^{[5]} For OECD countries, in the late 20th century, considering the effect of taxes and transfer payments, the income Gini coefficient ranged between 0.24 and 0.49, with Slovenia being the lowest and Chile the highest.^{[6]} African countries had the highest pretax Gini coefficients in 2008–2009, with South Africa the world's highest, variously estimated to be 0.63 to 0.7,^{[7]}^{[8]} although this figure drops to 0.52 after social assistance is taken into account, and drops again to 0.47 after taxation.^{[9]} The global income Gini coefficient in 2005 has been estimated to be between 0.61 and 0.68 by various sources.^{[10]}^{[11]}
There are some issues in interpreting a Gini coefficient. The same value may result from many different distribution curves. The demographic structure should be taken into account. Countries with an aging population, or with a baby boom, experience an increasing pretax Gini coefficient even if real income distribution for working adults remains constant. Scholars have devised over a dozen variants of the Gini coefficient.^{[12]}^{[13]}^{[14]}
The Gini coefficient is a single number aimed at measuring the degree of inequality in a distribution. It is most often used in economics to measure how far a country's wealth or income distribution deviates from a totally equal distribution.
The Gini coefficient is usually defined mathematically based on the Lorenz curve, which plots the proportion of the total income of the population (y axis) that is cumulatively earned by the bottom x of the population (see diagram). The line at 45 degrees thus represents perfect equality of incomes. The Gini coefficient can then be thought of as the ratio of the area that lies between the line of equality and the Lorenz curve (marked A in the diagram) over the total area under the line of equality (marked A and B in the diagram); i.e., G = A/(A + B). It is also equal to 2A and to 1 − 2B due to the fact that A + B = 0.5 (since the axes scale from 0 to 1).
If all people have nonnegative income (or wealth, as the case may be), the Gini coefficient can theoretically range from 0 (complete equality) to 1 (complete inequality); it is sometimes expressed as a percentage ranging between 0 and 100. In practice, both extreme values are not quite reached. If negative values are possible (such as the negative wealth of people with debts), then the Gini coefficient could theoretically be more than 1. Normally the mean (or total) is assumed positive, which rules out a Gini coefficient less than zero.
An alternative approach is to define the Gini coefficient as half of the relative mean absolute difference, which is mathematically equivalent to the Lorenz curve definition.^{[15]} 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, to normalize for scale. If x_{i} is the wealth or income of person i, and there are n persons, then the Gini coefficient G is given by:
When the income (or wealth) distribution is given as a continuous probability distribution function p(x), the Gini coefficient is again half of the relative mean absolute difference:
where is the mean of the distribution, and the lower limits of integration may be replaced by zero when all incomes are positive.
The most equal society will be one in which every person receives the same income (G = 0); the most unequal society will be one in which a single person receives 100% of the total income and the remaining N − 1 people receive none (G = 1 − 1/N).
While the income distribution of any particular country need not follow simple functions, these functions give a qualitative understanding of the income distribution in a nation given the Gini coefficient.
An informative simplified case just distinguishes two levels of income, low and high. If the high income group is a proportion u of the population and earns a proportion f of all income, then the Gini coefficient is f − u. An actual more graded distribution with these same values u and f will always have a higher Gini coefficient than f − u.
The proverbial case where the richest 20% have 80% of all income (see Pareto principle) would lead to an income Gini coefficient of at least 60%.
An often cited^{[16]} case that 1% of all the world's population owns 50% of all wealth, means a wealth Gini coefficient of at least 49%.
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 mean the income or wealth of a person or household):
Since the Gini coefficient is half the relative mean absolute difference, it can also be calculated using formulas for the relative mean absolute difference. For a random sample S consisting of values y_{i}, i = 1 to n, that are indexed in nondecreasing order (y_{i} ≤ y_{i+1}), the statistic:
is a consistent estimator of the population Gini coefficient, but is not, in general, unbiased. Like G, G(S) has a simpler form:
There does not exist a sample statistic that is in general an unbiased estimator of the population Gini coefficient, like the relative mean absolute difference.
For a discrete probability distribution with probability mass function f ( y_{i} ), i = 1 to n, where f ( y_{i} ) is the fraction of the population with income or wealth y_{i} >0, the Gini coefficient is:
where
where
When the population is large, the income distribution may be represented by a continuous probability density function f(x) where f(x) dx is the fraction of the population with wealth or income in the interval dx about x. If F(x) is the cumulative distribution function for f(x), then the Lorenz curve L(F) may then be represented as a function parametric in L(x) and F(x) and the value of B can be found by integration:
The Gini coefficient can also be calculated directly from the cumulative distribution function of the distribution F(y). Defining μ as the mean of the distribution, and specifying that F(y) is zero for all negative values, the Gini coefficient is given by:
The latter result comes from integration by parts. (Note that this formula can be applied when there are negative values if the integration is taken from minus infinity to plus infinity.)
The Gini coefficient may be expressed in terms of the quantile function Q(F) (inverse of the cumulative distribution function: Q(F(x)) = x)
For some functional forms, the Gini index can be calculated explicitly. For example, if y follows a lognormal distribution with the standard deviation of logs equal to , then where is the error function ( since , where is the cumulative standard normal distribution).^{[18]} In the table below, some examples are shown. The Dirac delta distribution represents the case where everyone has the same wealth (or income); it implies that there are no variations at all between incomes.
Income Distribution function  PDF(x)  Gini Coefficient 

Dirac delta function  0  
Uniform distribution  
Exponential distribution  
Lognormal distribution  
Pareto distribution  
Chisquared distribution  
Gamma distribution  
Weibull distribution  
Beta distribution 
Sometimes the entire Lorenz curve is not known, and only values at certain intervals are given. In that case, the Gini coefficient can be approximated by using various techniques for interpolating the missing values of the Lorenz curve. If (X_{k}, Y_{k}) are the known points on the Lorenz curve, with the X_{k} indexed in increasing order (X_{k – 1} < X_{k}), so that:
If the Lorenz curve is approximated on each interval as a line between consecutive points, then the area B can be approximated with trapezoids and:
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 but those proposed have been mathematically complicated and computationally onerous even in an era of fast computers. Ogwang (2000) 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 y_{k};
Ogwang showed that 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. Giles (2004) argued that the standard error of the estimate of A can be used to derive that of the estimate of G directly without using a jackknife at all. This method only requires the use of 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.^{[19]}
However it has since been argued that this is dependent on the model's assumptions about the error distributions (Ogwang 2004) and the independence of error terms (Reza & Gastwirth 2006) and that these assumptions are often not valid for real data sets. It may therefore be better to stick with jackknife methods such as those proposed by Yitzhaki (1991) and Karagiannis and Kovacevic (2000). The debate continues.
Guillermina Jasso^{[20]} and Angus Deaton^{[21]} independently proposed the following formula for the Gini coefficient:
where is mean income of the population, P_{i} 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 JassoDeaton formula rescales the coefficient so that its value is 1 if all the are zero except one. Note however Allison's reply on the need to divide by N² instead.^{[22]}
FAO explains another version of the formula.^{[23]}
The Gini coefficient and other standard inequality indices reduce to a common form. Perfect equality—the absence of inequality—exists when and only when the inequality ratio, , equals 1 for all j units in some population (for example, there is perfect income equality when everyone's income equals the mean income , so that for everyone). Measures of inequality, then, are measures of the average deviations of the from 1; the greater the average deviation, the greater the inequality. Based on these observations the inequality indices have this common form:^{[24]}
where p_{j} weights the units by their population share, and f(r_{j}) is a function of the deviation of each unit's r_{j} from 1, the point of equality. The insight of this generalised inequality index is that inequality indices differ because they employ different functions of the distance of the inequality ratios (the r_{j}) from 1.
Gini coefficients of income are calculated on market income as well as disposable income basis. The Gini coefficient on market income—sometimes referred to as a pretax Gini coefficient—is calculated on income before taxes and transfers, and it measures inequality in income without considering the effect of taxes and social spending already in place in a country. The Gini coefficient on disposable income—sometimes referred to as aftertax Gini coefficient—is calculated on income after taxes and transfers, and it measures inequality in income after considering the effect of taxes and social spending already in place in a country.^{[6]}^{[25]}^{[26]}
The difference in Gini indices between OECD countries, on aftertaxes and transfers basis, is significantly narrower.^{[26]} For OECD countries, over 2008–2009 period, Gini coefficient on pretaxes and transfers basis for total population ranged between 0.34 and 0.53, with South Korea the lowest and Italy the highest. Gini coefficient on aftertaxes and transfers basis for total population ranged between 0.25 and 0.48, with Denmark the lowest and Mexico the highest. For United States, the country with the largest population in OECD countries, the pretax Gini index was 0.49, and aftertax Gini index was 0.38, in 2008–2009. The OECD averages for total population in OECD countries was 0.46 for pretax income Gini index and 0.31 for aftertax income Gini Index.^{[6]}^{[27]} Taxes and social spending that were in place in 2008–2009 period in OECD countries significantly lowered effective income inequality, and in general, "European countries—especially Nordic and Continental welfare states—achieve lower levels of income inequality than other countries."^{[28]}
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 of Gini coefficient section).
The Gini coefficient for the entire world has been estimated by various parties to be between 0.61 and 0.68.^{[10]}^{[11]}^{[29]} The graph shows the values expressed as a percentage in their historical development for a number of countries.
According to UNICEF, Latin America and the Caribbean region had the highest net income Gini index in the world at 48.3, on unweighted average basis in 2008. The remaining regional averages were: subSaharan Africa (44.2), Asia (40.4), Middle East and North Africa (39.2), Eastern Europe and Central Asia (35.4), and Highincome Countries (30.9). Using the same method, the United States is claimed to have a Gini index of 36, while South Africa had the highest income Gini index score of 67.8.^{[30]}
Taking income distribution of all human beings, worldwide income inequality has been constantly increasing since the early 19th century. 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.^{[31]}
The table below presents the estimated world income Gini coefficients over the last 200 years, as calculated by Milanovic.^{[32]}
Year  World Gini coefficients^{[10]}^{[30]}^{[33]} 

1820  0.43 
1850  0.53 
1870  0.56 
1913  0.61 
1929  0.62 
1950  0.64 
1960  0.64 
1980  0.66 
2002  0.71 
2005  0.68 
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 India and China. 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.^{[34]}
Year  World Gini coefficient^{[35]} 

1988  .80 
1993  .76 
1998  .74 
2003  .72 
2008  .70 
2013  .65 
Gini coefficient is widely used in fields as diverse as sociology, economics, health science, ecology, engineering and agriculture.^{[36]} For example, in social sciences and economics, in addition to income Gini coefficients, scholars have published education Gini coefficients and opportunity Gini coefficients.
Education Gini index estimates the inequality in education for a given population.^{[37]} It is used to discern trends in social development through educational attainment over time. From a study of 85 countries by three Economists of World Bank Vinod Thomas, Yan Wang, Xibo Fan, estimate Mali had the highest education Gini index of 0.92 in 1990 (implying very high inequality in education attainment across the population), while the United States had the lowest education inequality Gini index of 0.14. Between 1960 and 1990, China, India and South Korea had the fastest drop in education inequality Gini Index. They also claim education Gini index for the United States slightly increased over the 1980–1990 period.
Similar in concept to income Gini coefficient, opportunity Gini coefficient measures inequality of opportunity.^{[38]}^{[39]}^{[40]} The concept builds on Amartya Sen's suggestion^{[41]} 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 opportunity Gini coefficient explains 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 his 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 2003, Roemer^{[38]}^{[42]} reported Italy and Spain exhibited the largest opportunity inequality Gini index amongst advanced economies.
In 1978, Anthony Shorrocks introduced a measure based on income Gini coefficients to estimate income mobility.^{[43]} This measure, generalized by Maasoumi and Zandvakili,^{[44]} 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, Shorrocks index compares inequality of shortterm earnings such as annual income of households, to inequality of longterm earnings such as 5year or 10year total income for same households.
Shorrocks index is calculated in number of different ways, a common approach being from the ratio of income Gini coefficients between shortterm and longterm for the same region or country.^{[45]}
A 2010 study using social security income data for the United States since 1937 and Ginibased Shorrocks indices concludes that income mobility in the United States has had a complicated history, primarily due to mass influx of women into the American labor force after World War II. Income inequality and income mobility trends have been different for men and women workers between 1937 and the 2000s. When men and women are considered together, the Gini coefficientbased Shorrocks index trends imply longterm income inequality has been substantially reduced among all workers, in recent decades for the United States.^{[45]} Other scholars, using just 1990s data or other short periods have come to different conclusions.^{[46]} For example, Sastre and Ayala, conclude from their study of income Gini coefficient data between 1993 and 1998 for six developed economies, that France had the least income mobility, Italy the highest, and the United States and Germany intermediate levels of income mobility over those 5 years.^{[47]}
The Gini coefficient has features that make it useful as a measure of dispersion in a population, and inequalities in particular.^{[23]} It is a ratio analysis method making it easier to interpret. It also avoids references to a statistical average or position unrepresentative of most of the population, such as per capita income or gross domestic product. For a given time interval, Gini coefficient can therefore be used to compare diverse countries and different regions or groups within a country; for example states, counties, urban versus rural areas, gender and ethnic groups. Gini coefficients can be used to compare income distribution over time, thus it is possible to see if inequality is increasing or decreasing independent of absolute incomes.
Other useful features of the Gini coefficient include:^{[48]}^{[49]}
A Gini index value above 50 is considered high; countries including Brazil, Colombia, South Africa, Botswana, and Honduras can be found in this category. A Gini index value of 30 or above is considered medium; countries including Vietnam, Mexico, Poland, The United States, Argentina, Russia and Uruguay can be found in this category. A Gini index value lower than 30 is considered low; countries including Austria, Germany, Denmark, Slovenia, Sweden and Ukraine can be found in this category.^{[50]}
Household Group 
Country A Annual Income ($) 
Country B Annual Income ($) 

1  20,000  9,000 
2  30,000  40,000 
3  40,000  48,000 
4  50,000  48,000 
5  60,000  55,000 
Total Income  $200,000  $200,000 
Country's Gini  0.2  0.2 
The Gini coefficient is a relative measure. Its proper use and interpretation is controversial.^{[51]} It is possible for the Gini coefficient of a developing country to rise (due to increasing inequality of income) while the number of people in absolute poverty decreases.^{[52]} This is because the Gini coefficient measures relative, not absolute, wealth. Changing income inequality, measured by Gini coefficients, can be due to structural changes in a society such as growing population (baby booms, aging populations, increased divorce rates, extended family households splitting into nuclear families, emigration, immigration) and income mobility.^{[53]} Gini coefficients are simple, and this simplicity can lead to oversights and can confuse the comparison of different populations; for example, while both Bangladesh (per capita income of $1,693) and the Netherlands (per capita income of $42,183) had an income Gini coefficient of 0.31 in 2010,^{[54]} the quality of life, economic opportunity and absolute income in these countries are very different, i.e. countries may have identical Gini coefficients, but differ greatly in wealth. Basic necessities may be available to all in a developed economy, while in an undeveloped economy with the same Gini coefficient, basic necessities may be unavailable to most or unequally available, due to lower absolute wealth.
A Gini index does not contain information about absolute national or personal incomes. Populations can have very low income Gini indices, yet simultaneously very high wealth Gini index. By measuring inequality in income, the Gini ignores the differential efficiency of use of household income. By ignoring wealth (except as it contributes to income) the Gini can create the appearance of inequality when the people compared are at different stages in their life. Wealthy countries such as Sweden can show a low Gini coefficient for disposable income of 0.31 thereby appearing equal, yet have very high Gini coefficient for wealth of 0.79 to 0.86 thereby suggesting an extremely unequal wealth distribution in its society.^{[55]}^{[56]} These factors are not assessed in incomebased Gini.
Household number 
Country A Annual Income ($) 
Household combined number 
Country A combined Annual Income ($) 

1  20,000  1 & 2  50,000 
2  30,000  
3  40,000  3 & 4  90,000 
4  50,000  
5  60,000  5 & 6  130,000 
6  70,000  
7  80,000  7 & 8  170,000 
8  90,000  
9  120,000  9 & 10  270,000 
10  150,000  
Total Income  $710,000  $710,000  
Country's Gini  0.303  0.293 
Gini index has a downwardbias for small populations.^{[57]} Counties or states or countries with small populations and less diverse economies will tend to report small Gini coefficients. For economically diverse large population groups, a much higher coefficient is expected than for each of its regions. Taking world economy as one, and income distribution for all human beings, for example, different scholars estimate global Gini index to range between 0.61 and 0.68.^{[10]}^{[11]} As with other inequality coefficients, the Gini coefficient is influenced by the granularity of the measurements. For example, five 20% quantiles (low granularity) will usually yield a lower Gini coefficient than twenty 5% quantiles (high granularity) for the same distribution. Philippe Monfort has shown that using inconsistent or unspecified granularity limits the usefulness of Gini coefficient measurements.^{[58]}
The Gini coefficient measure gives different results when applied to individuals instead of households, for the same economy and same income distributions. If household data is used, the measured value of income Gini depends on how the household is defined. When different populations are not measured with consistent definitions, comparison is not meaningful.
Deininger and Squire (1996) show that income Gini coefficient based on individual income, rather than household income, are different. For example, for the United States, they find that the individual incomebased Gini index was 0.35, while for France it was 0.43. According to their individual focused method, in the 108 countries they studied, South Africa had the world's highest Gini coefficient at 0.62, Malaysia had Asia's highest Gini coefficient at 0.5, Brazil the highest at 0.57 in Latin America and Caribbean region, and Turkey the highest at 0.5 in OECD countries.^{[59]}
Income bracket (in 2010 adjusted dollars) 
% of Population 1979 
% of Population 2010 

Under $15,000  14.6%  13.7% 
$15,000 – $24,999  11.9%  12.0% 
$25,000 – $34,999  12.1%  10.9% 
$35,000 – $49,999  15.4%  13.9% 
$50,000 – $74,999  22.1%  17.7% 
$75,000 – $99,999  12.4%  11.4% 
$100,000 – $149,999  8.3%  12.1% 
$150,000 – $199,999  2.0%  4.5% 
$200,000 and over  1.2%  3.9% 
Total Households  80,776,000  118,682,000 
United States' Gini on pretax basis 
0.404  0.469 
Expanding on the importance of lifespan measures, the Gini coefficient as a pointestimate of equality at a certain time, ignores lifespan changes in income. Typically, increases in the proportion of young or old members of a society will drive apparent changes in equality, simply because people generally have lower incomes and wealth when they are young than when they are old. Because of this, factors such as age distribution within a population and mobility within income classes can create the appearance of inequality when none exist taking into account demographic effects. Thus a given economy may have a higher Gini coefficient at any one point in time compared to another, while the Gini coefficient calculated over individuals' lifetime income is actually lower than the apparently more equal (at a given point in time) economy's.^{[14]} Essentially, what matters is not just inequality in any particular year, but the composition of the distribution over time.
Kwok claims income Gini coefficient for Hong Kong has been high (0.434 in 2010^{[54]}), in part because of structural changes in its population. Over recent decades, Hong Kong has witnessed increasing numbers of small households, elderly households and elderly living alone. The combined income is now split into more households. Many old people are living separately from their children in Hong Kong. These social changes have caused substantial changes in household income distribution. Income Gini coefficient, claims Kwok, does not discern these structural changes in its society.^{[53]} Household money income distribution for the United States, summarized in Table C of this section, confirms that this issue is not limited to just Hong Kong. According to the US Census Bureau, between 1979 and 2010, the population of United States experienced structural changes in overall households, the income for all income brackets increased in inflationadjusted terms, household income distributions shifted into higher income brackets over time, while the income Gini coefficient increased.^{[60]}^{[61]}
Another limitation of Gini coefficient is that it is not a proper measure of egalitarianism, as it is only measures income dispersion. For example, if two equally egalitarian countries pursue different immigration policies, the country accepting a higher proportion of lowincome or impoverished migrants will report a higher Gini coefficient and therefore may appear to exhibit more income inequality.
Some countries distribute benefits that are difficult to value. Countries that provide subsidized housing, medical care, education or other such services are difficult to value objectively, as it depends on quality and extent of the benefit. In absence of free markets, valuing these income transfers as household income is subjective. The theoretical model of Gini coefficient is limited to accepting correct or incorrect subjective assumptions.
In subsistencedriven and informal economies, people may have significant income in other forms than money, for example through subsistence farming or bartering. These income tend to accrue to the segment of population that is belowpoverty line or very poor, in emerging and transitional economy countries such as those in subSaharan Africa, Latin America, Asia and Eastern Europe. Informal economy accounts for over half of global employment and as much as 90 per cent of employment in some of the poorer subSaharan countries with high official Gini inequality coefficients. Schneider et al., in their 2010 study of 162 countries,^{[62]} report about 31.2%, or about $20 trillion, of world's GDP is informal. In developing countries, the informal economy predominates for all income brackets except for the richer, urban upper income bracket populations. Even in developed economies, between 8% (United States) to 27% (Italy) of each nation's GDP is informal, and resulting informal income predominates as a livelihood activity for those in the lowest income brackets.^{[63]} The value and distribution of the incomes from informal or underground economy is difficult to quantify, making true income Gini coefficients estimates difficult.^{[64]}^{[65]} Different assumptions and quantifications of these incomes will yield different Gini coefficients.^{[66]}^{[67]}^{[68]}
Gini has some mathematical limitations as well. It is not additive and different sets of people cannot be averaged to obtain the Gini coefficient of all the people in the sets.
Given the limitations of Gini coefficient, other statistical methods are used in combination or as an alternative measure of population dispersity. For example, entropy measures are frequently used (e.g. the Atkinson index or the Theil Index and Mean log deviation as special cases of the generalized entropy index). These measures attempt to compare the distribution of resources by intelligent agents in the market with a maximum entropy random distribution, which would occur if these agents acted like nonintelligent particles in a closed system following the laws of statistical physics.
The Gini coefficient is sometimes alternatively defined as twice the area between the receiver operating characteristic (ROC) curve and its diagonal, in which case the AUC (Area Under the ROC Curve) measure of performance is given by .^{[69]} The Gini coefficient is also closely related to Mann–Whitney U.
The Gini index is also related to Pietra index—both of which are a measure of statistical heterogeneity and are derived from Lorenz curve and the diagonal line.^{[70]}^{[71]}
In certain fields such as ecology, inverse Simpson's index is used to quantify diversity, and this should not be confused with the Simpson index . These indicators are related to Gini. The inverse Simpson index increases with diversity, unlike Simpson index and Gini coefficient which decrease with diversity. The Simpson index is in the range [0, 1], where 0 means maximum and 1 means minimum diversity (or heterogeneity). Since diversity indices typically increase with increasing heterogeneity, Simpson index is often transformed into inverse Simpson, or using the complement , known as GiniSimpson Index.^{[72]}
Although the Gini coefficient is most popular in economics, it can in theory be applied in any field of science that studies a distribution. For example, in ecology the Gini coefficient has been used as a measure of biodiversity, where the cumulative proportion of species is plotted against cumulative proportion of individuals.^{[73]} In health, it has been used as a measure of the inequality of health related quality of life in a population.^{[74]} In education, it has been used as a measure of the inequality of universities.^{[75]} In chemistry it has been used to express the selectivity of protein kinase inhibitors against a panel of kinases.^{[76]} In engineering, it has been used to evaluate the fairness achieved by Internet routers in scheduling packet transmissions from different flows of traffic.^{[77]}
The Gini coefficient is sometimes used for the measurement of the discriminatory power of rating systems in credit risk management.^{[78]}
A 2005 study accessed US census data to measure home computer ownership, and used the Gini coefficient to measure inequalities amongst whites and African Americans. Results indicated that although decreasing overall, home computer ownership inequality is substantially smaller among white households.^{[79]}
A 2016 peerreviewed study titled Employing the Gini coefficient to measure participation inequality in treatmentfocused Digital Health Social Networks^{[80]} illustrated that the Gini coefficient was helpful and accurate in measuring shifts in inequality, however as a standalone metric it failed to incorporate overall network size.
The discriminatory power refers to a credit risk model's ability to differentiate between defaulting and nondefaulting clients. The formula , in calculation section above, may be used for the final model and also at individual model factor level, to quantify the discriminatory power of individual factors. It is related to accuracy ratio in population assessment models.
The Gauteng Province's total GDP for 2010 was R811 billion, making the province the single largest contributor to South Africa's GDP with a contribution of 33.8%, despite having only 1.4% of South Africa's land area. Gauteng also generates approximately 10% of the entire African continent's GDP. Gauteng's Gini coefficient of 0.62 makes it more equal than South Africa (the Gini coefficient of which is 0.75) as a whole, although this is still a very high figure by international standards. The cities Johannesburg, Midrand and Pretoria, which are all economic powerhouses, and Vanderbijlpark, which is an industrial powerhouse, are all in Gauteng.
Gauteng is home to the Johannesburg Stock Exchange, the largest stock exchange in Africa, as well as the head offices of over 140 local and international banks. Some of the largest companies in Africa and abroad are based in Gauteng, or have offices and branches there, such as Vodacom, MTN, Neotel, Microsoft South Africa and the largest Porsche Centre in the world.
Hoover indexThe Hoover index, also known as the Robin Hood index or the Schutz index, is a measure of income metrics. It is equal to the portion of the total community income that would have to be redistributed (taken from the richer half of the population and given to the poorer half) for there to be income uniformity.
It can be graphically represented as the longest vertical distance between the Lorenz curve, or the cumulative portion of the total income held below a certain income percentile, and the 45 degree line representing perfect equality.
The Hoover index is typically used in applications related to socioeconomic class (SES) and health. It is conceptually one of the simplest inequality indices used in econometrics. A better known inequality measure is the Gini coefficient which is also based on the Lorenz curve.
Income disparity in MalaysiaAccording to the UNDP 1997 Human Development Report, and the 2004 United Nations Human Development (UNHDP) report, Malaysia has the highest income disparity between the rich and poor in Southeast Asia, greater than that of Philippines, Thailand, Singapore, Vietnam and Indonesia.
The UNHDP Report shows that the richest 10% in Malaysia control 38.4% of the economic income as compared to the poorest 10% who control only 1.7%. However, according to official statistics from the Prime Minister's Department, inequality has been decreasing steadily since 1970, with the Gini coefficient dropping to an alltime low of 0.40 in 2014.
Income distributionIn economics, income distribution is how a nation's total GDP is distributed amongst its population. Income and its distribution have always been a central concern of economic theory and economic policy. Classical economists such as Adam Smith, Thomas Malthus, and David Ricardo were mainly concerned with factor income distribution, that is, the distribution of income between the main factors of production, land, labour and capital. Modern economists have also addressed this issue, but have been more concerned with the distribution of income across individuals and households. Important theoretical and policy concerns include the balance between income inequality and economic growth, and their often inverse relationship.The distribution of income within a society may be represented by the Lorenz curve. The Lorenz curve is closely associated with measures of income inequality, such as the Gini coefficient.
Income in the United KingdomIn terms of global poverty criteria, the United Kingdom is a wealthy country, with virtually no people living on less than £4 a day. In 2012–13, median personal income was approximately £21,000 a year but varies considerably by age, location, data source and occupation. There is both significant income redistribution and income inequality; for instance, in 2013/14 income in the top and bottom fifth of households was £80,800 and £5,500, respectively, before taxes and benefits (15:1). After tax and benefits, household income disparities are significantly reduced to £60,000 and £15,500 (4:1).The UK Gini coefficient for 2013/14 estimated at 0.34. There were 720,000 net worth Sterling millionaires in the United Kingdom in 2015 (1 in 65 adults). In the decade after 2003, incomes generally stagnated, with small increases among nonemployed and higher income groups, and decreases for those in employment but on low incomes.
Income inequality in BrazilBrazil has been tackling problems of income inequality despite high rates of growth. Its GDP (gross domestic product) growth in 2010 was 7.5%. In recent decades, there has been a decline in inequality for the country as a whole. Brazil’s GINI coefficient, a measure of income inequality, has slowly decreased from in 0.596 in 2001 to 0.543 in 2009. However, the numbers still point to a rather significant problem of income disparity.
The country's high income concentration is depicted by the richest one per cent of the population (less than 2 million people) having 13 percent of all household income. This percentage is similar to that of the poorest 50 per cent  about 80 million Brazilians. This inequality results in poverty levels that are inconsistent with an economy the size of that of Brazil.
Income inequality in ChinaChina’s current mainly market economy features a high degree of income inequality. According to the Asian Development Bank Institute, “before China implemented reform and opendoor policies in 1978, its income distribution pattern was characterized as egalitarianism in all aspects.” At this time, the Gini coefficient for rural – urban inequality was only 0.16. As of 2012, the official Gini coefficient in China was 0.474, although that number has been disputed by scholars who “suggest China’s inequality is actually far greater.” A study published in the PNAS estimated that China’s Gini coefficient increased from 0.30 to 0.55 between 1980 and 2002.
Income inequality in IndiaAs of November 2016, India is the second most unequal country in the world after Russia. The richest 1% of Indians own 58.4% of wealth. The richest 10 % of Indians own 80.7 % of the wealth. This trend is going in the upward direction every year, which means the rich are getting richer at a much faster rate than the poor. Inequality worsened since the establishment of income tax in 1922, overtaking the British Raj's record of the share of the top 1% in national income, which was 20.7% in 1939–40.
Income inequality in the PhilippinesIncome Inequality is the extent at which household income is unevenly distributed amongst a population. In other words, it also refers to the gap in income between who can be considered the rich of the population as opposed to the income of those who can be considered the poor of a population.
Income inequality in the Philippines is the extent to which income, most commonly measured by household or individual, is distributed in an uneven manner in the Philippines. The difference of income between the rich and the poor could cause tension in society and political instability.
Inequality in GermanyAccording to data from the World Bank, Germany has the 14th lowest Gini coefficient in the world. However, since the mid1990s, income, gender and social inequality in Germany has been rising.
Kakwani indexThe Kakwani index is a measure of the progressivity of a social intervention, and is used by social scientists, statisticians, and economists. It is named after the economist who first proposed and used it, Nanak Chand Kakwani.
The Kakwani index uses the Gini framework to measure how progressive a social intervention is. It is equal to the difference between the Gini index for the social intervention, and the Gini index for incomes before imposition of the policy intervention. Theoretically, the Kakwani index can vary between −1 to 1; the larger the index is, the more progressive is the social intervention.
The index is calculated using the following formula:
where denotes individual , is the total number of individuals in society, is the share of total taxes paid by individual , and is the beforetax Gini coefficient. Using the formula for the Gini coefficient, the equation for the Kakwani index can be reduced to:
where denotes the share of income received by individual .
The Kakwani index was originally devised to measure the progressivity of tax systems, in which case, it would be equal to the Gini concentration index^{[clarification needed]} for the taxes collected minus the Gini index for pretax incomes. This can be shown to be equal to the absolute decline in the Gini index for incomes, caused by the imposition of taxation, divided by the average net rate of taxes.
The Kakwani index is also commonly used to examine the equity of government health care provision. In that situation, the Kakwani index would be equal to the difference between the Gini coefficient for incomes and the Gini concentration index for out‐of‐pocket health care payments.
List of U.S. states by Gini coefficientThe Gini coefficient is a measure of inequality of incomes (or sometimes wealth) across individuals.
A score of "0" on the Gini coefficient represents complete equality, i.e., every person has the same income. A score of 1 would represent complete inequality, i.e., where one person has all the income and others have none. Therefore, a lower Gini score is roughly associated with a more equal distribution of income, and vice versa.
The information was tabulated in 2010 from data from the American Community Survey conducted by the US Census Bureau. Utah, Alaska, New Hampshire, and Wyoming show the smallest income disparities while the District of Columbia, New York State, Louisiana, and Connecticut have the largest disparities in income between wage earners in all income categories.U.S. income inequality was at its highest level since the United States Census Bureau began tracking household income in 1967. The U.S. also has the greatest disparity among western industrialized nations.
List of countries by income equalityThis is a list of countries or dependencies by income inequality metrics, including Gini coefficients. The Gini coefficient is a number between 0 and 1, where 0 corresponds with perfect equality (where everyone has the same income) and 1 corresponds with perfect inequality (where one person has all the income—and everyone else has zero income). Income distribution can vary greatly from wealth distribution in a country (see List of countries by distribution of wealth). Income from black market economic activity is not included and is the subject of current economic research.
Lorenz asymmetry coefficientThe Lorenz asymmetry coefficient (LAC) is a summary statistic of the Lorenz curve that measures the degree of asymmetry of the curve. The Lorenz curve is used to describe the inequality in the distribution of a quantity (usually income or wealth in economics, or size or reproductive output in ecology). The most common summary statistic for the Lorenz curve is the Gini coefficient, which is an overall measure of inequality within the population. The Lorenz asymmetry coefficient can be a useful supplement to the Gini coefficient. The Lorenz asymmetry coefficient is defined as
where the functions F and L are defined as for the Lorenz curve, and μ is the mean. If S > 1, then the point where the Lorenz curve is parallel with the line of equality is above the axis of symmetry. Correspondingly, if S < 1, then the point where the Lorenz curve is parallel to the line of equality is below the axis of symmetry.
If data arise from the lognormal distribution, then S = 1, i.e., the Lorenz curve is symmetric.
The sample statistic S can be calculated from n ordered size data, , using the following equations:
where m is the number of individuals with a size or wealth less than μ and . However, if one or more of the data size is equal to μ, then S has to defined as an interval instead of a number (see #LAC interval when some data is equal to μ).
The Lorenz asymmetry coefficient characterizes an important aspect of the shape of a Lorenz curve. It tells which size or wealth classes contribute most to the population’s total inequality, as measured by the Gini coefficient. If the LAC is less than 1, the inequality is primarily due to the relatively many small or poor individuals. If the LAC is greater than 1, the inequality is primarily due to the few largest or wealthiest individuals.
For incomes distributed according to a lognormal distribution, the LAC is identically 1.
Pareto principleThe Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes. Management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who noted the 80/20 connection while at the University of Lausanne in 1896, as published in his first work, Cours d'économie politique. Essentially, Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population.
It is an axiom of business management that "80% of sales come from 20% of clients".Mathematically, the 80/20 rule is roughly followed by a power law distribution (also known as a Pareto distribution) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution.The Pareto principle is only tangentially related to Pareto efficiency. Pareto developed both concepts in the context of the distribution of income and wealth among the population.
Poverty in CanadaPoverty in Canada remains prevalent within some segments of society and according to a 2008 report by the Organisation for Economic Cooperation and Development, the rate of poverty in Canada, is among the highest of the OECD member nations, the world's wealthiest industrialized nations. There is no official government definition and therefore, measure, for poverty in Canada. However, Dennis Raphael, author of Poverty in Canada: Implications for Health and Quality of Life reported that the United Nations Development Program, the United Nations Children's Fund (UNICEF), the Organisation for Economic Cooperation and Development and Canadian poverty researchers find that relative poverty is the "most useful measure for ascertaining poverty rates in wealthy developed nations such as Canada." In its report released the Conference Board.
Currently, an income inequality measure known as low income cutoff (LICO) published by Statistics Canada is frequently used as a poverty rate and is 10.8% as of 2005. The Central Intelligence Agency uses the LICO as the relative measure results in a higher poverty figure than an absolute one. Statistics Canada has refused to endorse any metric as a measure of poverty, including the lowincome cut off it publishes, without a mandate to do so from the federal government. Statistics Canada is looking into creating an initiative on how to better calculate the poverty line. The Government of Canada has announced that Market Basket Measure (MBM) will become the official poverty measure in Canada.Some elements that work towards reducing poverty in Canada include Canada's strong economic growth, government transfers to persons of $164 billion per annum as of 2008, universal medical and public education systems, and minimum wage laws in each of the provinces and territories of Canada.
In recent times, after a spike in poverty and lowincome rates around the 1996 recession, relative poverty has continued to decline. Certain groups experience higher lowincome rates, including children, families with singleparent mothers, aboriginals, the mentally ill, the physically handicapped, recent immigrants, and students.
Social issues in BrazilBrazil ranks 49.3 in the Gini coefficient index, with the richest 10% of Brazilians earning 42.7% of the nation's income, the poorest 34% earn less than 1.2%.The Human Development Index of Municipalities dramatically improved in Brazil during the last two decades. According to PNUD, in 1991, 99.2% of the municipalities had a low/very low HDI; but this number has fallen to 25.2% in 2010. On the other hand, the number of municipalities with high/very high HDI jumped from 0% in 1991 to 34,7% in 2010. In 2012, the Brazilian HDI was 0.730, ranking in 83rd and considered high.
Suits indexThe Suits index of a public policy is a measure of tax progressiveness, named for economist Daniel B. Suits. Similar to the Gini coefficient, the Suits index is calculated by comparing the area under the Lorenz curve to the area under a proportional line. For a progressive tax (for example, where higher income tax units pay a greater fraction of their income as tax), the Suits index is positive. A proportional tax (for example, where each unit pays an equal fraction of income) has a Suits index of zero, and a regressive tax (for example, where lower income tax units pay a greater fraction of income in tax) has a negative Suits index. A theoretical tax where the richest person pays all the tax has a Suits index of 1, and a tax where the poorest person pays everything has a Suits index of −1. Tax preferences (credits and deductions) also have a Suits index.
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