Indicators {GB2}

Monetary Laeken Indicators under the GB2

Description

Functions to calculate four primary social welfare indicators under the GB2, i.e. the at-risk-of-poverty threshold, the at-risk-of-poverty rate, the relative median at-risk-of-poverty gap, and the income quintile share ratio.

Usage

arpt.gb2(prop, shape1, scale, shape2, shape3)
arpr.gb2(prop, shape1, shape2, shape3)
rmpg.gb2(arpr, shape1, shape2, shape3)
qsr.gb2(shape1, shape2, shape3)
main.gb2(prop, shape1, scale, shape2, shape3)
main2.gb2(prop, shape1, scale, shape12, shape13)

Arguments

prop

numeric; proportion (in general is set to 0.6).

arpr

numeric; the value of the at-risk-of-poverty rate.

shape1

numeric; positive parameter.

scale

numeric; positive parameter.

shape2, shape3

numeric; positive parameters of the Beta distribution.

shape12

numeric; the product of the two parameters shape1 and shape2.

shape13

numeric; the product of the two parameters shape1 and shape3.

Details

In June 2006, the Social Protection Committee, which is a group of officials of the European Commisiion, adopts a set of common indicators for the social protection and social inclusion process. It consists of a portfolio of 14 overarching indicators (+11 context indicators) meant to reflect the overarching objectives (a) "social cohesion" and (b) "interaction with the Lisbon strategy for growth and jobs (launched in 2000) objectives"; and of three strand portfolios for social inclusion, pensions, and health and long-term care.

The at-risk-of-poverty threshold (or ARPT) is defined as 60% of the median national equivalized income.

The at-risk-of-poverty rate (or ARPR) is defined as the share of persons with an equivalised disposable income below the ARPT.

The relative median at-risk-of-poverty gap (or RMPG) is defined as the difference between the median equivalised income of persons below the ARPT and the ARPT itself, expressed as a percentage of the ARPT.

The income quintile share ratio (or QSR) is defined as the ratio of total income received by the 20% of the country's population with the highest income (top quintile) to that received by the 20% of the country's population with the lowest income (lowest quintile).

Let x_{0.5} be the median of a GB2 with parameters shape1 = a, scale = b, shape2 = p and shape3 = q. Then,

ARPT(a,b,p,q)=0.6 x_{0.5}

The ARPR being scale-free, b can be chosen arbitrarily and can be fixed to 1.

The QSR is calculated with the help of the incomplete moments of order 1.

main.gb2 and main2.gb2 return a vector containing the following set of GB2 indicators: the median, the mean, the ARPR, the RMPG, the QSR and the Gini coefficient. The only difference is in the input parameters.

Value

arpt.gb2 gives the ARPT, arpr.gb2 the ARPR, rmpg.gb2 the RMPG, and qsr.gb2 calculates the QSR. main.gb2 returns a vector containing the median of the distribution, the mean of the distribution, the ARPR, the RMPG, the QSR and the Gini coefficient. main2.gb2 produces the same output as main.gb2.

Author(s)

Monique Graf

References

https://ec.europa.eu/social/main.jsp?langId=en&catId=750

See Also

qgb2, incompl.gb2

Examples

a <- 3.9
b <- 18873
p <- 0.97
q <- 1.03
ap <- a*p
aq <- a*q

arpt <- arpt.gb2(0.6, a, b, p, q)
arpr <- arpr.gb2(0.6, a, p, q)
rmpg <- rmpg.gb2(arpr, a, p, q)
qsr <- qsr.gb2(a, p, q)

ind1 <- main.gb2(0.6, a, b, p, q)
ind2 <- main2.gb2(0.6, a, b, ap, aq)