Robin Hood index


Robin Hood index

The Robin Hood index, also known as 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 by force 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.

Mathematically, the Robin Hood index for Lorenz curve scriptstyle L(x) is scriptstyle max (x - L(x)).

The Robin Hood 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 based on the Lorenz curve.

Computation

For the formula, a notation [The notation using E and A follows the notation of a small calculus published by Lionnel Maugis: "Inequality Measures in Mathematical Programming for the Air Traffic Flow Management Problem with En-Route Capacities" (für IFORS 96), 1996] is used, where the amount N of quantiles only appears as upper border of summations. Thus, inequities can be computed for quantiles with different widths A. For example, E_i could be the income in the quantile #i and A_i could be the amount (absolute or relative) of earners in the quantile #i. E_ ext{total} then would be the sum of incomes of all N quantiles and A_ ext{total} would be the sum of the income earners in all N quantiles.

Computation of the Robin Hood index H:

: H = {frac{1}{2 sum_{i=1}^N color{Blue} left| color{Black} {fracE}_i}E}_ ext{total} - {fracA}_i}A}_ ext{total} color{Blue} ight| color{Black}.

For comparison [For an explanation of the comparison with Henri Theil's index see: Theil index] , here also the computation of the symmetrized Theil index T_s is given:

: T_s = {frac{1}{2 sum_{i=1}^N color{Blue} ln{fracE}_i}A}_i left( color{Black} {fracE}_i}E}_ ext{total} - {fracA}_i}A}_ ext{total} color{Blue} ight) color{Black}.

References

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 SAPOLSKY: "Sick of Poverty", Scientific American, December 2005

External links

* Free Inequality Calculator: [http://www.poorcity.richcity.org/calculator Online] and [http://luaforge.net/project/showfiles.php?group_id=49 downloadable scripts] (Python and Lua) for Atkinson, Gini, and Hoover inequalities


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Robin-Hood-Index — Der Robin Hood Index (Robin Hood nachempfunden) – auch Ricci Schutz Index (nach dem italienischen Ökonom Umberto Ricci [1879–1946] und dem US amerikanischen Ökonom Robert R. Schutz [* 1915]), maximaler Nivellierungssatz (nach Lindahl) (gemäß …   Deutsch Wikipedia

  • Robin Hood — is an archetypal figure in English folklore, whose story originates from medieval times but who remains significant in popular culture where he is painted as a man known for robbing the rich to give to the poor and fighting against injustice and… …   Wikipedia

  • Robin Hood (2006 TV series) characters — Robin Hood is a British television drama series, produced by Tiger Aspect Productions for BBC One, which debuted in October 2006. The programme uses the majority of the familiar characters from the traditional Robin Hood legends, notably omitting …   Wikipedia

  • Robin Hood Engineering — Ltd was a British kit car manufacturer based in Mansfield Woodhouse, Nottinghamshire. The factory covered convert|30000|sqft|m2 and was on a one and a half acre site.The company was founded in 1984 in Sherwood, Nottinghamshire and started by… …   Wikipedia

  • Robin Hood Foundation — The Robin Hood Foundation is a charitable organization which attempts to alleviate problems caused by poverty in New York City, New York. The Robin Hood Foundation was featured in Fortune s 18 September 2006 issue where the article states that… …   Wikipedia

  • Robin Hood, West Yorkshire — infobox UK place country = England official name= Robin Hood latitude= 53.73 longitude= 1.50 population = metropolitan borough= City of Leeds metropolitan county= West Yorkshire region= Yorkshire and the Humber constituency westminster= post town …   Wikipedia

  • Young Robin Hood — (1991 1992) is an animated series produced by Cinar and Hanna Barbera. The series takes place when Robin is a teenager, Richard the Lion Heart is on his first crusade and Robin Hood s father, the Earl of Huntington, joins him. ynopsisRobin Hood… …   Wikipedia

  • Index of business ethics, political economy, and philosophy of business articles — Articles related to business ethics, political economy and philosophy of business include: Accounting reform Bait and switch Black market Collectivism Conservation movement Consumerism Corporate accountability Corporate crime Creative accounting… …   Wikipedia

  • Robin (comics) — Infobox comics set index code name=Robin caption=Batman and Robin reinterpreted by painter Alex Ross. Based on the cover to Batman #9 by Bob Kane. publisher=DC Comics debut= Detective Comics #38 (April 1940) creators=Bob Kane Jerry Robinson Bill… …   Wikipedia

  • Robin Hoods Vergeltung — Filmdaten Deutscher Titel Robin Hoods Vergeltung Originaltitel Rogues of Sherwood Forest …   Deutsch Wikipedia