Income inequality metrics

One form of income is the total amount of goods and services that a person receives, and thus there is not necessarily money or cash involved.

The Gini index is a summary statistic that measures how equitably a resource is distributed in a population; income is a primary example.

In addition to a self-contained presentation of the Gini index, we give two equivalent ways to interpret this summary statistic: first in terms of the percentile level of the person who earns the average dollar, and second in terms of how the lower of two randomly chosen incomes compare, on average, to mean income.

The reason for its popularity is that it is easy to understand how to compute the Gini index as a ratio of two areas in Lorenz curve diagrams.

This measure tries to capture the overall dispersion of income; however, it tends to place different levels of importance on the bottom, middle and top end of the distribution.

Palma has suggested that distributional politics pertains mainly to the struggle between the rich and poor, and who the middle classes side with.

The carbon Palma ratios in developed countries are comparatively lower; however, their greater historical obligations to warming indicate that they significantly reduce emissions of all people, in order to increase national mitigation contributions systematically.

On a global scale, the current carbon Palma ratio is noticeably higher than within any country, indicating an exceedingly severe inequality when individual emissions are considered outside territorial boundaries.

[15] The Hoover index is the simplest of all inequality measures to calculate: It is the proportion of all income which would have to be redistributed to achieve a state of perfect equality.

Coefficient of variation will be therefore lower in countries with smaller standard deviations implying more equal income distribution.

The first one could be attributed to CV not having and upper limit, unlike the Gini coefficient, therefore causing difficulties with interpretation and comparison.

Secondly, as the mean and standard deviation may be heavily affected by anomalous borderline values, the coefficient would not be an appropriate choice of income inequality measure for a case of abnormal data distribution.

[16] Compared to the Gini coefficient in practice, CV puts higher weight on the right tail of the scale, making it sensitive to the rich.

Coefficient of variation may be a suitable choice of measure if the goal of a study is to analyze the wealth concentration at the top of the distribution.

[19] This scale invariant measure of relative inequality is sensitive to the left tail, making it ideal to use when studying the levels of poverty of the lower income half (the poor).

[20] This measure has been developed by Nobel Prize winner Amartya Sen but has not yet been used in the field of income inequality hypothesis.

Although it has been greeted with enthusiasm, the Sen poverty index does not fulfill number of ideal conditions, e.g. it fails to satisfy the transfer axiom, it is not decomposable or subgroup consistent.

[21] As described in a section below, Theil-L is an income-distribution's dis-entropy per person, measured with respect to maximum entropy (which is achieved with complete equality).

In comparison, the Hoover index indicates the minimum size of the income share of a society, which would have to be redistributed in order to reach maximum entropy.

Applying the Theil index to allocation processes in the real world does not imply that these processes are stochastic: the Theil yields the distance between an ordered resource distribution in an observed system to the final stage of stochastic resource distribution in a closed system.

Greater weight can be placed on changes in a given portion of the income distribution by choosing ε, the level of "inequality aversion", appropriately.

Conversely, as the level of inequality aversion falls (that is, as ε approaches 0) the Atkinson becomes less sensitive to changes in the lower end of the distribution.

Another common class of metrics is to take the ratio of the income of two different groups, generally "higher over lower".

From these data inequality measures as well as the related welfare functions are computed and displayed in fields with green background.

Evidence from a broad panel of recent academic studies shows that there is a nonlinear relation between income inequality and the rate of growth and investment.

[35] According to Pak Hung Mo, income inequality has significant negative effect on the rate of GDP growth.

However, the direct impact of income inequality on the rate of productivity growth accounts for more than 55 percent of its overall total effect.

[36] In their study for the World Institute for Development Economics Research, Giovanni Andrea Cornia and Julius Court (2001) reach slightly different conclusions.

The findings imply that excluding intergenerational mobility leads to misspecification, which explains why the empirical literature on income inequality and growth has been so inconclusive.

[40] The precise shape of the inequality-growth curve 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.

US federal minimum wage if it had kept pace with productivity. Also, the real minimum wage.
GDP per capita PPP vs Gini index in countries
GDP per capita PPP vs 20:20 ratio in countries
GDP per capita PPP vs Palma ratio in countries
Illustration of the relation between Theil index and the Hoover index for societies divides into two quantiles ("a-fractiles"). Here the Hoover index and the Theil are equal at a value of around 0.46. The red curve shows the difference between the Theil index and the Hoover index as a function of the Hoover index. The green curve shows the Theil index divided by the Hoover index as a function of the Hoover index.
Income of a given percentage as a ratio to median, for 10th (red), 20th, 50th, 80th, 90th, and 95th (grey) percentile, for 1967–2003 in the United States (50th percentile is 1:1 by definition)
Income of the given percentiles from 1947 to 2010 in 2010 dollars. The two columns of numbers in the right margin are the cumulative growth 1970–2010 and the annual growth rate over that period. The vertical scale is logarithmic, which makes constant percentage growth appear as a straight line. From 1947 to 1970, all percentiles grew at essentially the same rate; the light, straight lines for the different percentiles for those years all have the same slope. Since then, there has been substantial divergence, with different percentiles of the income distribution growing at different rates. For the median American family, this gap is $39,000 per year (just over $100 per day): if the economic growth during this period had been broadly shared as it was from 1947 to 1970, the median household income would have been $39,000 per year higher than it was in 2010. This plot was created by combining data from the US Census Bureau [ 26 ] and the US Internal Revenue Service. [ 27 ] There are systematic differences between these two sources, but the differences are small relative to the scale of this plot. [ Note 4 ]
Share of pre-tax household income received by the top 1%, top 0.1% and top 0.01% in the US, between 1917 and 2005 [ 28 ] [ 29 ]