The Foster–Greer–Thorbecke indices are a family of
poverty metrics. The most commonly used index from the family, ''FGT
2'', puts higher weight on the poverty of the poorest individuals, making it a combined measure of poverty and
income inequality
There are wide varieties of economic inequality, most notably income inequality measured using the distribution of income (the amount of money people are paid) and wealth inequality measured using the distribution of wealth (the amount of we ...
and a popular choice within
development economics
Development economics is a branch of economics which deals with economic aspects of the development process in low- and middle- income countries. Its focus is not only on methods of promoting economic development, economic growth and structural ...
. The indices were introduced in a 1984 paper by economists
Erik Thorbecke
Erik Thorbecke (born February 17, 1929) is a development economist. He is a co-originator of the widely used Foster-Greer-Thorbecke poverty measure and played a significant role in the development and popularization of Social Accounting Matrix ...
,
Joel Greer, and
James Foster.
The individual indices within the family are derived by substituting different values of the
parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
''α'' into the following equation:
where ''z'' is the
poverty threshold
The poverty threshold, poverty limit, poverty line or breadline is the minimum level of income deemed adequate in a particular country. The poverty line is usually calculated by estimating the total cost of one year's worth of necessities for t ...
,'' N'' is the number of people in the economy, ''H'' is the number of poor (those with incomes at or below ''z''), ''y
i'' is the income of each individual ''i. ''If
is low then the FGT metric weights all the individuals with incomes below z roughly the same. The higher the value of ''α, ''the greater the weight place on the poorest individuals. The higher the FGT statistic, the more poverty there is in an economy.
FGT0 and FGT1
With ''α ''= 0, the formula reduces to the
headcount ratio: the fraction of the population that lives below the poverty line.
With ''α ''= 1, the formula reduces to the
poverty gap index
The poverty gap index is a measure of the intensity of poverty. It is defined as the average poverty gap in the population as a proportion of the poverty line.
The poverty gap index is an improvement over the poverty measure head count ratio whic ...
.
The ''FGT
1'' can be rewritten as:
,
where
is the average income of the poor. Thus, the ''FGT
1'' can be expressed as the product of the ''FGT
0'' and the average income gap of the poor.
FGT2
While the two reduced indexes are widely used, the most common FGT-specific index in development economics is the ''α'' = 2 version, which is the lowest (whole) parameter to weigh income inequality along with poverty.
The ''FGT
2'' can be rewritten as: