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 &minus; 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


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. In their study for the World Institute for Development Economics Research, Giovanni Andrea Cornia and Julius Court (2001) reach analogous conclusions. 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 shows, that inequality and growth are not related. Inequality neither drives growth nor does it impair growth. Other Research (W.Kitterer ) 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 and the USA ).

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.

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