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# Income inequality metrics

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

## 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

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. See Lorenz curve for details.
• Gini coefficient - This is a summary statistic used to quantify the extent of income inequality depicted in a particular Lorenz curve. See Gini coefficient for details.
• 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.

## Criticisms of income inequality metrics

1. 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.
2. 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.
3. These income inequality metrics ignore life cycle effects. 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 stages of life.
4. Absolute measures often give very different results than relative measures. For example, in measuring inequality changes due to the development of less developed countries, absolute measures typically show improvements as the general income level rises, but it is also common for relative measures to deteriorate as the new wealth becomes concentrated in the hands of the upper percentiles. The diverging results can be a problem if they are used inappropriately or interpreted incorrectly.
5. 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?
6. 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?
7. Income inequality metrics are seldom used to quantify and examine the causes of income inequality. The main causes are: 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.
8. This criticism helps to understand the problems caused by the improper use of inequality measures. However, it does not render inequality coefficients invalid. If inequality measures are computed in a well explained and consistent way, they provide a good tool for quantitative comparisons of inequalities at least within a research project.