# income inequality metrics

Income inequality metrics or income distribution metrics are techniques used by economists to measure the distribution of income and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general. These techniques are typically categorized as either absolute measures or relative measures.

Income distribution has 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 relationship between income inequality and economic growth. The article economic inequality discusses the social and policy aspects of income distribution questions.

## Absolute income criteria

Absolute measures define a minimum standard, then calculate the number (or percent) of individuals below this threshold. These methods are most useful when determining the amount of poverty in a society. Examples include:
• Poverty line - This is a measure of the level of income necessary to subsist in a society. It varies from place to place and from time to time, depending on the cost of living and people's expectations. It is usually defined by governments and calculated as that level of income at which a household will devote two thirds (to three quarters) of its income to basic necessities such as food, water, shelter, and clothing.
• Poverty index - This index was developed by Amartya Sen. It takes into account both the number of poor and the extent of their poverty. Sen defined the index as:
I = (P/N)(B − A)/A

where:

P = number of people below the poverty line
N = total number of people in society
B = poverty line income
A = average income of those people below the poverty line

## Relative income criteria

Differences in national income equality around the world as measured by the national Gini coefficient. 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). Countries in red tones have societies with more income inequality than those in green tones.

Relative income compares the income of one individual (or group) with the income of another individual (or group). These measures are most useful when analyzing the scope and distribution of income inequality. Examples include:
• Percentile distributions - One percentile (or quantile) is compared to another. For example, it might be determined that the income of the top ten-percentile is only slightly more than the bottom forty-percentile. Or it might be determined that the top quartile earns 45% of the society's income while the bottom quartile has 10% of society's income. The interquartile range is a standard percentile range from 25% to 75%.
• Lorenz curve - This is a graphic device used to display the relative inequality in a distribution of income values. A society's total income is ordered according to income level and the cumulative total graphed.
• Gini coefficient - This is a popular summary statistic used to quantify the extent of income inequality depicted in a particular Lorenz curve.
• Robin Hood index - Mathematically related to the Gini coefficient, it measures the portion of the total income that would have to be redistributed in order for there to be perfect equality. Of all inequality measures, this measure is the simplest and least interpretative one.
• Theil index - This is also a summary statistic used to measure income inequality. The index is based on information entropy in order not only to indicate plain inequality, but also to indicate the attention, which is given to inequality. Compared to the Gini coefficient, the Theil index is increasingly, but yet less commonly used.
• Standard deviation of income - This measures income dispersion by assessing the square root of variance from the mean. This metric is seldom seen, its use limited to occasional reference in academic journals.
• Relative poverty line - This is a measure of the number or proportion of people or households whose level of income is less than some given fraction of typical incomes. This form of poverty measurement tends to concentrate concern on the bottom half of the income distribution and pay less attention to inequalities in the top half. See poverty line for details.

## Defining income

All of the above measures use income as the basis for evaluating poverty. However, 'income' is here understood different to a common understanding: It means the total amount of goods and services that a person receives, and thus there is not necessarily money or cash involved. If a poor subsistence farmer in Uganda grows her own grain it will count as income. Services like public health and education are also counted in. Often expenditure or consumption (which is the same in an economic sense) is used to measure income. The World Bank uses the so-called living standard measurement surveys (LSMS) to measure income. These consist of questionnaires with 200+ questions. Surveys have been completed in most developing countries.

## Proper use of income inequality metrics

1. When using income metrics, it has to be made clear how income should be defined. Should it include capital gains, imputed house rents from home ownership, and gifts? If these income sources or alleged income sources (in the case of "imputed rent") are ignored (as they often are), how might this bias the analysis? How should non-paid work (such as parental childcare or doing ones own cooking instead of hiring a chef for every meal) be handled? Wealth or consumption may be more appropriate measures in some situations. Broader metrics of human well-being might be useful.
2. The comparison of inequality measures requires, that the segmentation of compared groups (societies etc.) into quintiles should be similar.
3. Distiguish properly, whether the basic unit of measurement is households or individuals. The Gini value for households is always lower than for individuals because of income pooling and intra-family transfers. And housholds have a varying amount of members. The metrics will be influenced either upward or downward depending on which unit of measurement is used.
4. Consider life cycle effects. In most Western societies, an individual tends to start life with little or no income, gradually increase income till about age 50, after which incomes will decline, eventually becoming negative. This effects the conclusions which can be drawn from a measured inequality. It has been estimated (by A.S. Blinder in The Decomposition of Inequality, MIT press) that 30% of measured income inequality is due to the inequality an individual experiences as they go through the various stages of life.
5. Clarify, whether real or nominal income distributions should be used. What effect will inflation have on absolute measures? Do some groups (eg., pensioners) feel the effect of inflation more than others?
6. When drawing conclusion from inequality measurements, consider how we should allocate the benefits of government spending? How does the existence of a social security safety net influence the definition of absolute measures of poverty? Do government programs support some income groups more than others?
7. Inequality metrics measure inequality. They do not measure possible causes of income inequality. Some alleged causes include: life cycle effects (age), inherited characteristics (IQ, talent), willingness to take chances (risk aversion), the leisure/industriousness choice, inherited wealth, economic circumstances, education and training, discrimination, and market imperfections.

Keeping these points in mind helps to understand the problems caused by the improper use of inequality measures. However, they do not render inequality coefficients invalid. If inequality measures are computed in a well explained and consistent way, they can provide a good tool for quantitative comparisons of inequalities at least within a research project.

## Inequality, Growth and Progress

The question whether equality is beneficial for economic growth and progress has occupied the minds of the greatest scientific thinkers as well as policy makers. Evidence from a broad panel of recent academic studies shows the relation between income inequality and the rate of growth and investment is indeed robust however not linear.

Robert J. Barro, Harvard University found in his study "Inequality and Growth in a Panel of Countries" that higher inequality tends to retard growth in poor countries and encourage growth in well developed regions.[1] In their study for the World Institute for Development Economics Research, Giovanni Andrea Cornia and Julius Court (2001) reach analogous conclusions.[2] The authors therefor recommend to pursue moderation also as to the distribution of wealth and particularly to avoid the extremes. Both very high egalitarianism and very high inequality cause slow growth.

Extreme egalitarianism leads to incentive traps, free-riding, high operation costs and corruption in the redistribution system, all reducing a country's growth potential. However also extreme inequality diminishes growth potential through the erosion of social cohesion, increasing social unrest and social conflict causing uncertainty of property rights, not to talk about misery and lower life expectancy.

On the other hand, The World Bank World Development Report 2000/2001[3] shows, that inequality and growth are not related. Inequality neither drives growth nor does it impair growth. Other Research (W.Kitterer[4]) also shows, that in perfect markets inequality does not influence growth. In real markets redistribution contributes to growth.

Considering the inequalities in economically well developped countries, public policy should target an ‘efficient inequality range’. The authors claim that such efficiency range roughly lies between the values of the Gini coefficients of 25 (the inequality value of a typical Northern European country) and 40 (that of countries such as China[5] and the USA[6]).

The precise shape of the inequality-growth relationship depicted in the Chart obviously varies across countries depending upon their resource endowment, history, remaining levels of absolute poverty and available stock of social programs, as well as on the distribution of physical and human capital.

## Notes

1. ^ economics.harvard.edu - Inequality and Growth in a Panel of Countries
2. ^ wider.unu.edu - Inequality, Growth and Poverty in the Era of Liberalization and Globalization
3. ^ World Bank World Development Report 2000/2001, chapter 3, box 3.5
4. ^ Wolfgang Kitterer: Mehr Wachstum durch Umverteilung? (More Growth through Redistribution?), 2006
5. ^ Due to the economic dynamics and the increasing income gap between the Chinese east cost and the rest of the country, the Gini index for China may have reached 50. Sources from China report 47 for the year 2005. With regard to the huge population in China and the challenges to data collection, a good understanding of the data is required, based on which the Gini indices are computed.
6. ^ USA: Also countries like France, Germany and UK have a Gini index slightly above 40.

## Literature

• A.B. Atkinson and F. Bourguignon, ed. (2000). Handbook of Income Distribution, v. 1. Elsevier.table of contents
• Yoram Amiel (Author), Frank A. Cowell: Thinking about Inequality: Personal Judgment and Income Distributions, 2000
• Philip B. Coulter: Measuring Inequality, 1989

Income, generally defined, is the money that is received as a result of the normal business activities of an individual or a business.

Internationally, the accounting term income is synonymous to term revenue minus expenses.
Economic inequality refers to disparities in the distribution of economic assets and income. The term typically refers to inequality among individuals and groups within a society, but can also refer to inequality among nations.
Adam Smith FRSE (baptised June 5 (OS) / June 16 (NS) 1723 – July 17, 1790) was a Scottish moral philosopher and a pioneering political economist. He is a major contributor to the modern perception of free market economics.
Thomas Robert Malthus, FRS (13th February, 1766 – 29th December, 1834), was an English demographer and political economist. He is best known for his highly influential views on population growth.
David Ricardo (18 April, 1772–11 September, 1823), a political economist, is often credited with systematizing economics, and was one of the most influential of the classical economists, along with Thomas Malthus and Adam Smith.
Distribution in economics refers to the way total output or income is distributed among individuals or among the factors of production (labor, land, and capital) (Samuelson and Nordhaus, 2001, p. 762).
In economics, factors of production are resources used in the production of goods and services, including land, labor, and capital.

## Land, labor, and capital

Resource in economics distinguish among such factors of production as:

Economic inequality refers to disparities in the distribution of economic assets and income. The term typically refers to inequality among individuals and groups within a society, but can also refer to inequality among nations.
The introduction to this article may be too long. Please help improve the introduction by moving some material from it into the body of the article according to the suggestions at Wikipedia's .
The poverty threshold, or poverty line, is the minimum level of income deemed necessary to achieve an adequate standard of living. In practice, like the definition of poverty, the official or common understanding of the poverty line is significantly higher in developed
Amartya Sen

Born November 3 1933 (age 74)
Santiniketan, India
Residence U.S.
Note: One quartile is equivalent to 25 percentile while 1 decile is equal to 10 percentile.

## Examples

When ISPs bill "Burstable" Internet bandwidth, the 95th or 98th percentile usually cuts off the top 5% or 2% of bandwidth peaks in each month, and then bills at the nearest
Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. Dividing ordered data into q essentially equal-sized data subsets is the motivation for q
In descriptive statistics, the interquartile range (IQR), also called the midspread, middle fifty and middle of the #s, is a measure of statistical dispersion, being equal to the difference between the third and first quartiles.
The Lorenz curve is a graphical representation of the cumulative distribution function of a probability distribution; it is a graph showing the proportion of the distribution assumed by the bottom y% of the values.
Gini coefficient is a measure of statistical dispersion most prominently used as a measure of inequality of income distribution or inequality of wealth distribution. It is defined as a ratio with values between 0 and 1: the numerator is the area between the Lorenz curve of the
The Robin Hood index, also known as the Hoover index, is a measure of income inequality. 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
The Theil index[1], derived by econometrician Henri Theil, is a statistic used to measure economic inequality.

## Mathematics

The formula is

where is the income of the th person, is the mean income, and is the number of people.
Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable.

Shannon entropy quantifies the information contained in a piece of data: it is the minimum average message length, in bits (if using base-2 logarithms), that must
In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma).
The poverty threshold, or poverty line, is the minimum level of income deemed necessary to achieve an adequate standard of living. In practice, like the definition of poverty, the official or common understanding of the poverty line is significantly higher in developed
The World Bank (the Bank) is a part of the World Bank Group (WBG), is a bank that makes loans to developing countries for development programs with the stated goal of reducing poverty.
In finance, a capital gain is profit that results from the sale or exchange of a capital asset over its purchase price. If the price of the capital asset has declined instead of appreciated, this is called a capital loss.
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Quality of Life is a 2004 drama film, telling the fictional story of two graffiti writers in the Mission District of San Francisco.
Robert Joseph Barro (born 1944) is an influential classical liberal macroeconomist and the Paul M. Warburg Professor of Economics at Harvard University.

Barro graduated with a B.S. in physics from the California Institute of Technology in 1965 and earned a Ph.D.