Robin Hood index
Encyclopedia
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 perfect equality.
It can be graphically represented as the longest vertical distance between the Lorenz curve
, or the cumulative portion of the total income held below a certain income percentile, and the 45 degree line representing perfect equality.
The Hoover index is typically used in applications related to socio-economic class (SES) and health. It is conceptually the simplest inequality index used in econometrics. A better known inequality measure is the Gini coefficient
which is also based on the Lorenz curve.
of quantile
s only appears as upper border of summations
. Thus, inequities can be computed for quantiles with different widths
. For example, 
could be the income in the quantile #i and 
could be the amount (absolute or relative) of earners in the quantile #i. 
then would be the sum of incomes of all 
quantiles and 
would be the sum of the income earners in all 
quantiles.
Computation of the Robin Hood index
:
Income inequality metrics
The concept of inequality is distinct from that of poverty and fairness. Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of income, and economic inequality among the participants in a particular economy, such as that of a specific...
. 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 perfect equality.
It can be graphically represented as the longest vertical distance between the Lorenz curve
Lorenz curve
In economics, the Lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth; it is a graph showing the proportion of the distribution assumed by the bottom y% of the values...
, or the cumulative portion of the total income held below a certain income percentile, and the 45 degree line representing perfect equality.
The Hoover index is typically used in applications related to socio-economic class (SES) and health. It is conceptually the simplest inequality index used in econometrics. A better known inequality measure is the Gini coefficient
Gini coefficient
The Gini coefficient is a measure of statistical dispersion developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper "Variability and Mutability" ....
which is also based on the Lorenz curve.
Computation
For the formula, a notation is used, where the amount of quantileQuantile
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-quantiles; the quantiles are the data values marking the boundaries between consecutive subsets...
s only appears as upper border of summations
Summation
Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed may be integers, rational numbers,...
. Thus, inequities can be computed for quantiles with different widths
. For example, could be the income in the quantile #i and could be the amount (absolute or relative) of earners in the quantile #i. then would be the sum of incomes of all quantiles and would be the sum of the income earners in all quantiles.Computation of the Robin Hood index
:-
For comparison, here also the computation of the symmetrized Theil indexTheil indexThe Theil index is a statistic used to measure economic inequality. It has also been used to measure the lack of racial diversity. The basic Theil index TT is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy. It is a special...
is given:
-
Both formulas can be used in spreadsheet computations.
Literature
- Edgar Malone HOOVER jr.: The Measurement of Industrial Localization, Review of Economics and Statistics, 1936, Vol. 18, No. 162-171
- Edgar Malone HOOVER jr.: An Introduction to Regional Economics, 1984, ISBN 0075544407
- Philip B. COULTER: Measuring Inequality, 1989, ISBN 0-8133-7726-9 (This book describes about 50 different inequality measures - it's a good guide, but it contains some mistakes, so watch out.)
- Robert SAPOLSKYRobert SapolskyRobert Maurice Sapolsky is an American scientist and author. He is currently Professor of Biological Sciences, and Professor of Neurology and Neurological Sciences and, by courtesy, Neurosurgery, at Stanford University. In addition, he is a Research Associate at the National Museums of...
: Sick of Poverty, Scientific AmericanScientific AmericanScientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
, December 2005
External links
- Free Inequality Calculator: Online and downloadable scripts (PythonPython (programming language)Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
and LuaLua programming languageLua is a lightweight multi-paradigm programming language designed as a scripting language with extensible semantics as a primary goal. Lua has a relatively simple C API compared to other scripting languages.- History :...
) for Atkinson, Gini, and Hoover inequalities
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