gini2: Gini coefficient

In REAT: Regional Economic Analysis Toolbox

Description

Calculating the Gini coefficient of inequality (or concentration), standardized and non-standardized, and optionally plotting the Lorenz curve

Usage

gini2(x, weighting = NULL, coefnorm = FALSE, na.rm = TRUE) 

Arguments

x	A numeric vector (e.g. dataset of regional incomes)
weighting	A numeric vector containing the weighting data (e.g. regional population)
coefnorm	logical argument that indicates if the function output is the non-standardized or the standardized Gini coefficient (default: coefnorm = FALSE, which means the non-standardized Gini coefficient is returned)
na.rm	logical argument that indicates whether NA values should be excluded before computing results

Details

The Gini coefficient (Gini 1912) is a popular measure of statistical dispersion, especially used for analyzing inequality or concentration. In an economic-geographical context, the Gini coefficient is frequently used to analyse the concentration/inequality of income or wealth within countries (Aoyama et al. 2011). Other areas of application are analyzing regional disparities (Lessmann 2005, Nakamura 2008) and concentration in markets (sales turnover of competing firms).

The Gini coefficient (G) varies between 0 (no inequality/concentration) and 1 (complete inequality/concentration). This function calculates G. As there are several ways to calculate the Gini coefficient, this function uses the formula given in Doersam (2004). Because the maximum of G is not equal to 1, also a standardized coefficient (G*) with a maximum equal to 1 can be calculated alternatively. If a Gini coefficient for aggregated data (e.g. income classes with averaged incomes) or the Gini coefficient has to be weighted, use a weighting vector (e.g. size of the income classes).

Value

A single numeric value of the Gini coefficient (0 < G < 1) or the standardized Gini coefficient (0 < G* < 1) and, optionally, a plot of the Lorenz curve.

Author(s)

Thomas Wieland

References

Aoyama, Y./Murphy, J. T./Hanson, S. (2011): “Key Concepts in Economic Geography”. London : SAGE.

Bahrenberg, G./Giese, E./Mevenkamp, N./Nipper, J. (2010): “Statistische Methoden in der Geographie. Band 1: Univariate und bivariate Statistik”. Stuttgart: Borntraeger.

Cerlani, L./Verme, P. (2012): “The origins of the Gini index: extracts from Variabilita e Mutabilita (1912) by Corrado Gini”. In: The Journal of Economic Inequality, 10, 3, p. 421-443.

Doersam, P. (2004): “Wirtschaftsstatistik anschaulich dargestellt”. Heidenau : PD-Verlag.

Gini, C. (1912): “Variabilita e Mutabilita”. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. Bologna : Cuppini.

Lessmann, C. (2005): “Regionale Disparitaeten in Deutschland und ausgesuchten OECD-Staaten im Vergleich”. ifo Dresden berichtet, 3/2005. https://www.ifo.de/DocDL/ifodb_2005_3_25-33.pdf.

Lorenz, M. O. (1905): “Methods of Measuring the Concentration of Wealth”. In: Publications of the American Statistical Association, 9, 70, p. 209-219.

Nakamura, R. (2008): “Agglomeration Effects on Regional Economic Disparities: A Comparison between the UK and Japan”. In: Urban Studies, 45, 9, p. 1947-1971.

Roberts, T. (2014): “When Bigger Is Better: A Critique of the Herfindahl-Hirschman Index's Use to Evaluate Mergers in Network Industries”. In: Pace Law Review, 34, 2, p. 894-946.

See Also

cv, gini.conc, gini.spec, herf, hoover

Examples

# Market concentration (example from Doersam 2004):
sales <- c(20,50,20,10)
# sales turnover of four car manufacturing companies
gini (sales, lc = TRUE, lcx = "percentage of companies", lcy = "percentrage of sales", 
lctitle = "Lorenz curve of sales", lcg = TRUE, lcgn = TRUE)
# returs the non-standardized Gini coefficient (0.3) and 
# plots the Lorenz curve with user-defined title and labels 
gini (sales, coefnorm = TRUE)
# returns the standardized Gini coefficient (0.4)

# Income classes (example from Doersam 2004):
income <- c(500, 1500, 2500, 4000, 7500, 15000)
# average income of 6 income classes
sizeofclass <- c(1000, 1200, 1600, 400, 200, 600)
# size of income classes
gini (income, weighting = sizeofclass)
# returns the non-standardized Gini coefficient (0.5278)

# Market concentration in automotive industry
data(Automotive)
gini(Automotive$Turnover2008, lsize=1, lc=TRUE, le.col = "black", 
lc.col = "orange", lcx = "Shares of companies", lcy = "Shares of turnover / cars", 
lctitle = "Automotive industry: market concentration", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Turnover 2008:", lcg.lab.x = 0, lcg.lab.y = 1)
# Gini coefficient and Lorenz curve for turnover 2008
gini(Automotive$Turnover2013, lsize=1, lc = TRUE, add.lc = TRUE, lc.col = "red", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Turnover 2013:", lcg.lab.x = 0, lcg.lab.y = 0.85)
# Adding Gini coefficient and Lorenz curve for turnover 2013
gini(Automotive$Quantity2014_car, lsize=1, lc = TRUE, add.lc = TRUE, lc.col = "blue", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Cars 2014:", lcg.lab.x = 0, lcg.lab.y = 0.7)
# Adding Gini coefficient and Lorenz curve for cars 2014

# Regional disparities in Germany:
gdp <- c(460.69, 549.19, 124.16, 65.29, 31.59, 109.27, 263.44, 39.87, 258.53, 
645.59, 131.95, 35.03, 112.66, 56.22, 85.61, 56.81)
# GDP of german regions (Bundeslaender) 2015 (in billion EUR)
gini(gdp)
# returs the non-standardized Gini coefficient (0.5009)

Example output

[1] 0.3
[1] 0.4
[1] 0.5278261
[1] 0.3202108
[1] 0.3736389
[1] 0.4351418
[1] 0.5009348

REAT documentation built on Sept. 5, 2021, 5:18 p.m.