Foster-Greer-Thorbecke indices

The Foster-Greer-Thorbecke indices (FGT indices) are a family of poverty measures . The family's most widely used index, FGT ₂ , weights the poverty of the poorest individual more heavily, making it a measure of poverty that combines a measure of poverty and a measure of income inequality . It is a popular measure of development economics . The indices were published in 1984 in a scientific paper by economists Erik Thorbecke , Joel Greer and James Foster .

meaning

The individual indices of the family are derived by determining the parameter α in the following equation:

${\displaystyle {\mathit {FGT}}_{\alpha }={\frac {1}{N}}\sum \limits _{i=1}^{H}\left({\frac {z-y_{i}}{z}}\right)^{\alpha }}$,

where z is the poverty line , N is the number of people in an economy , H is the number of poor (whose incomes are less than z ), y _{i is} the income of each individual i .

If α is small, then the FGT indices rate all individuals below the poverty line z approximately equally. The greater the value of α , the more the position of the poorest individual is weighted. The larger the FGT statistic, the poorer an economy is.

FGT ₀ and FGT ₁

If one sets α = 0, then the formula for the poverty rate is reduced , i. H. on the proportion of the population living below the poverty line

${\displaystyle {\mathit {FGT}}_{0}={\frac {H}{N}}}$.

If α = 1, the formula for the poverty gap index is reduced :

${\displaystyle {\mathit {FGT}}_{1}={\frac {1}{N}}\sum \limits _{i=1}^{H}{\frac {z-y_{i}}{z}}}$.

FGT ₂

The two indices presented here are often used. The most commonly used index in development economics, however, is the index that results for α = 2:

${\displaystyle {\mathit {FGT}}_{2}={\frac {1}{N}}\sum \limits _{i=1}^{H}\left({\frac {z-y_{i}}{z}}\right)^{2}}$.

The FGT ₂ can also be written as

${\displaystyle {\mathit {FGT}}_{2}=H\mu ^{2}+\left(1-\mu ^{2}\right)C_{v}^{2}}$,

where C _{v is} the coefficient of variation of the households of the poor and H is the absolute number of poor households. The parameter μ is given by

${\displaystyle \mu ={\frac {1}{H}}\sum \limits _{i=1}^{H}{\frac {z-y_{i}}{z}}}$.

Other breakdowns of the index are also possible.

The only measure that combines FGT ₀ , FGT _1, and the Gini index is the Sen index .

Individual evidence

1. ↑ James Foster, Joel Greer, Erik Thorbecke: A class of decomposable poverty measures . In: Econometrica . 52, No. 3, May 1984, pp. 761-766. doi : 10.2307 / 1913475 .
2. ↑ James Foster, Joel Greer, Erik Thorbecke: The Foster – Greer – Thorbecke (FGT) poverty measures: 25 years later . In: Journal of Economic Inequality . 8, No. 4, December 2010, pp. 491-524. doi : 10.1007 / s10888-010-9136-1 .
3. ^ Mauricio Olavarria-Gambi: Poverty Reduction in Chile: Has economic growth been enough? . (PDF) In: Journal of Human Development . 4, No. 1, March 2003, pp. 103-123. doi : 10.1080 / 1464988032000051504 .