Foster Greer Thorbecke
The Foster-Greer-Thorbecke (sometimes referred to as FGT) metric is a generalized measure of poverty within an economy. It measures the weighted shortfall from the poverty line. It is also incorporates the inequality among the poor.
The formula for the FGT is given by:
where is an agreed upon poverty line (1.25$ or 2$ per day adjusted for purchasing power parity are the two most common poverty lines used by the World Bank. Developed countries usually have much higher poverty lines), is the number of people in an economy, is the number of poor (those with incomes at or below ), are individual incomes and is a "sensitivity" parameter. If is low then the FGT metric weights all the individuals with incomes below z roughly the same. If is high, those with the lowest incomes (farthest below ) are given more weight in the measure. The higher the FGT statistic, the more poverty there is in an economy.
The FGT measure corresponds to other measures of poverty for particular values of . For , the formula reduces to
which is the Headcount ratio, or the fraction of the population which lives below the poverty line. If then the formula is
which is the average poverty gap, or the amount of income necessary to bring everyone in poverty right up to the poverty line, divided by total population. This can be thought of as the amount that an average person in the economy would have to contribute in order for poverty to be just barely eliminated.
While the two above versions are widely reported, a good deal of technical literature on poverty uses the version of the metric:
as in this form, the index combines information on both poverty and income inequality among the poor. Specifically in this instance the FGT can be rewritten as:
where is the coefficient of variation among those with incomes less than , is the total number of the poor as above, and is given by
The version of the index was part of the Mexican Constitution and was used to allocate inter-regionally funds from the Federal Government in Mexico for educational, health and nutritional programs benefiting the poor. In 2010 the Government of Mexico adopted a multidimensional poverty measure based on a variant of the FGT measure that is to be used in targeting the allocation of social funds to poor households at the municipality level.
- Foster, James; Joel Greer and Erik Thorbecke (1984). "A class of decomposablepoverty measures". Econometrica. 3 52: 761–766. doi:10.2307/1913475.
- Mauricio Olavarria-Gambi: "Poverty Reduction in Chile: has economic growth been enough?", Journal of Human Development, Vol. 4, No. 1, 2003
- http://www.economics.cornell.edu/et17/ET-Short%20bio%202013.doc. Missing or empty