Income inequality metrics

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Income inequality metrics or income distribution metrics are techniques used by economists to measure the distribution of income among members of a society. In particular these techniques are used to measure the inequality, or equality of income within an economy. These techniques are typically categorized as either absolute measures or relative measures.

Contents

1 Absolute income criteria
2 Relative income criteria
3 Defining income
4 Criticisms of income inequality metrics
5 See also
6 External links

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 and varies from place to place and from time to time depending on the cost of living and peoples' 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

World map of the Gini coefficient

Relative income measures compare 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 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 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.
Theil index - This is also a summary statistic used to measure income inequality, based on information entropy. It is similar to, but less commonly used than the Gini coefficient.
Standard deviation of income - This measures income dispersion by assessing the squared 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 ineqalities in the top half. See poverty line for details.

Defining income

Both 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.

Criticisms of income inequality metrics

It is not clear how income should be defined. Should it include capital gains, imputed house rents from home ownership, and gifts? If these income sources are ignored (as they often are), how might this bias the analysis? How should non-paid work (such as parental childcare) be handled? Wealth or consumption may be more appropriate measures in some situations. Broader metrics of human well-being might be useful.
Should the basic unit of measurement be households or individuals? The Gini value for households is always lower than for individuals because of income pooling and intra-family transfers. The metrics will be biased either upward or downward depending on which unit of measurement is used.
These income inequality metrics ignore 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 will have the effect of significantly overstating 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.
Should real or nominal income distributions be used? What effect will inflation have on absolute measures? Do some groups (eg., pensioners) feel the effect of inflation more than others?
How do we 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?
Income inequality metrics are seldom used to quantify and examine the 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.

These criticisms help 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.

External links

[Inequality data using various metrics, from the US Census Bureau, 1967-2001]
[Survey data from the government of Sri Lanka]
Software
* Users of the [R] data analysis software can install the "ineq" package which allows to compute a variety of inequality metrics including Gini, Atkinson or Theil.