Multidimensional Poverty Index of Alkire and Foster (2011)

Economists, development workers and policy makers all agree that poverty is multi-dimensional in nature. Just improving one dimension, such as income, may not improve the overall well-being of the person. For example, let an individual earn $20,000 a year, and the poverty line is $15,000. This person is not considered poor under any definition. However, if the person has a debilitating illness and medicines cost $7,000 a year, then this person’s effective income now is $13,000 – which is lower than the poverty line. Although the person earns more than the poverty line, their consumption bundle is similar to that of someone in poverty.

Therefore, there is a need to measure different dimensions of well-being, and not just income, to determine the poverty status of a person. Consequently, multi-dimensional poverty indices have been developed, and one of the more popular one is the Alkire and Foster (2011)Multidimensional Poverty Index (MPI). The Oxford Poverty and Human DevelopmentInitiative (OPHI) has been applying this index to measure MPI poverty in different countries, and the UNDP has also adopted this index in its HumanDevelopment Report.

To see how MPI is calculated, lets look at an example. Let there be 5 individuals and 3 dimensions of well-being – income, health and housing. The data is arranged in matrix form:

The rows are for each individual, and first column is income, the second column is health status, and the third column is housing status. If health and housing status is 1, then the person is deprived in that dimension (poor health/poor housing). So the third person has an income of 300, good health (0) and poor housing (1). Let the income poverty line be 350. Then persons 1, 2 and 3 have incomes less than the poverty line. Thus, persons 1, 2 and 3 are deprived (given an indicator of 1) and the rest get a 0, and the above matrix becomes:

The next step in Alkire and Foster (2011) is counting how many people are deprived in k dimensions, where k is less than or equal to 3. From the data above, we see that 1 person is deprived in all three dimensions; 3 are deprived in 2 or more dimensions and 4 are deprived in 1 or more dimensions. 

Thus, the multidimensional headcount poverty measure is:

 1/5 * 100= 20% for k=3. So 20 percent of the population is deprived in all 3 dimensions

3/5 * 100=40% for k>=2. So 60 percent of the population is deprived in 2 or more dimensions

4/5 * 100=80% for k>=1. So 80 percent of the population is deprived in 1 or more dimensions

Notice that even the person who earns 500 can be MPI poor, even though unidimensional poverty measure (just using income to determine the poverty status of a person) may not consider that person to be poor. 

The average deprivation for person 1 is 1, for person 2 is 1/3, person 3 is 2/3, person 4 is 0 and person 5 is 2/3. The M0 equals headcount times the average deprivation of the people who are multidimensionally poor. The M0 measure thus is: 

1/5 * 1/1(3/3) = 1/5 if we consider the cutoff value k=3
3/5 * 1/3(3/3 + 2/3 + 2/3) = 1/3 if we consider the cutoff value k>=2
4/5 * 1/4(3/3 + 1/3 + 2/3 + 2/3) = 8/15 if we consider the cutoff value k>=1

I have also used a version of the MPI to show how it can be used to assess the effectiveness of an anti-poverty program that can have multiple outcomes. The link to the paper is here.