The Foster, Greer and Thorbecke (1984) Family of Poverty Measure

Once a poverty line has been set, the poverty status of a person is determined by comparing their income with the poverty line. If the person earns less than the poverty line, then that person is considered to be poor. This type of poverty measure is called a unidimensional poverty measure, because they use one dimension of well being (income in most cases) to assess the poverty level of a person. A mathematical function is used to aggregate poverty. One of the most popular mathematical function used to measure poverty is the Foster, Greer and Thorbecke (1984) family of poverty measures (a modified version is presented below): 

Each individual is denoted by i, and there is a total of n individuals. z is the poverty line, and xi is the income of person i. The function I(xi <=z) is an indicator function, which is equal to 1 if income of person i is less than the poverty line, and zero otherwise. α is a number equaling 0, 1, 2.... 

As an example, consider this. Lets say there are 5 individuals (so n=5), and each person has the following income: 


Person 1: 100
Person 2: 200
Person 3: 300
Person 4: 400
Person 5: 500

Let the poverty line, z, equals to 250. 

When α=0, then the first part of the equation, which is:

becomes equal to 1, because anything raised to the power of 0 equals to 1. So, the indicator function remains, and it equals to 1 for persons 1 and 2, and 0 for persons 3, 4 and 5. So, the poverty measure when α=0 is 2/5 or 40 percent. This measure is also called the 'headcount' measure, and it measures the proportion of individuals who earn below the poverty line. 

However, the headcount measure does not measure the depth of poverty. Person 1 is clearly worse off than person 2, but the headcount measure does not differentiate that. This issue can be circumvented when α=1. The equation that's after the summation sign: 

thus becomes

 Since I(300<=250), I(400<=250) and I(500<=250) all equal to zero, the equation simplifies to:

Thus, when α=1, the poverty measure is (0.6+0.2)/5 = 0.16. This is called the poverty gap measure. It measures the average shortfall of income of the poor from the poverty line. 


When α=2, the measure is called a squared poverty gap, and this measure puts more weight on the poorer individuals when compared to those who are poor, but closer to the poverty line. When α=3, it puts more weight on the poor individuals, and so forth. 

This FGT (1984) measure is widely used to assess the poverty rate of nations across the world.