Measurement of Poverty: Some Fundamental Issues

There is by now a vast literature on measurement of poverty. Theoretically, the seminal paper was Sen’s 1976 axiomatization and the associated index that attempted to bring together the headcount ratio the income gap ratio and income inequalities among the poor within a consistent axiomatic framework. Since then, Sen and others following him have moved in the direction of a multidimensional approach to poverty as inadequate capabilities. However, for the purposes of this paper, I will keep within the income poverty concept where a single scalar, money income, is the only relevant variable of interest in measuring poverty and computing the various indexes.

The general intuition behind poverty measurement is that 'poverty' exists when a group of people in a particular society can not attain a 'minimum' level of well-being. The 'minimum' is at least partly dependent upon the prevailing standards of society. However, there are dimensions of well-being such as nutritional requirements that might actually constitute an absolute biological minimum. The idea behind absolute as opposed to relative poverty is that by using generally agreed upon minimum standards of well-being, we can, in fact, define an income poverty line. Such income poverty line gives the cut-off point below which everyone is deemed to be poor. The key questions in applying this idea of poverty for applied policy issues are:

1. How do we assess well-being?
2. How do we decide on a certain poverty line so that when a poor person crosses that threshold s/he is no longer poor?

These are the questions which ask us to identify who the poor are. Therefore, this can be called, using Sen's terminology, the "identification" of poverty. As a second step, the total picture of poverty is arrived at by aggregating. Hence, Sen’s coinage of the term "aggregation problem". Head count ratio is one obvious example in which one simply counts the number of people below the poverty line and then divides this number by the total number of individuals in a particular society.

In terms of identifying the poor through the setting of the poverty line, a number of issues can arise. The following four questions are one way of raising some these issues (Fields 2001):

1. Is the basis income or consumption, and how comprehensively will either one be measured?
2. What is the income-receiving unit: individual, family, per capita, or adult equivalent?
3. Will there be a single poverty line or will there be separate ones for urban and rural areas or different regions of the country?
4. Is the poverty line income determined scientifically, politically, subjectively, or as a matter of convenience?

In terms of both identification and aggregation of poverty, the procedure depends partly on axiomatizing the concept of poverty so that any particular measure has a number of desirable properties. The most common axioms are focus, anonymity, population homogeneity, monotonicity or strong monotonicity, and distributional sensitivity. Among the commonly used indexes, the head count ratio fails both the strong monotonicity and distributional sensitivity axioms.

Since Sen's (1976) axiomatic treatment of poverty comparisons several new indexes of poverty have emerged. Among them is the one developed by Foster, Greer and Thorbecke(FGT).

The FGT index which we will meet later again as the index used most frequently in the macroeconomic models incorporating poverty analysis has many desirable properties. In addition to satisfying the monotonicity and distributional sensitivity axioms, it also has the property of being additively sub-group decomposable. This means that the index is decomposable by subgroups (according to region, income class etc.) among the poor.

Thus this index can take into account the intensity of poverty for different groups of poor people. This is done by looking at the deprivation of calories. The poverty measure is given by:

p = 1/n ∑ (G_j / z)^a

where

n = total population
q = the number of poor
z = the poverty line
G_j = food expenditure shortfall of the jth individual (j = 1,2,…,q )

In the simulation a value of a = 2 is used. At a lower value of 'a' some of the axioms are violated. At a higher value of 'a' the shortfalls of the poorer segments are weighted more heavily; therefore the intensity of deprivation by the poorer segments (in particular the poorest) will be magnified for value of 'a' greater than 2. For this value of 'a' both the monotonicity and transfer axioms of Sen are satisfied. We may recall that both these axioms have to do with the sensitivity of the index to the incomes of the poor as opposed to simply the number of poor. Thus, the monotonicity axiom states that, ceteris paribus, a decrease in the income of a poor person should increase the poverty index. The transfer axiom states that, ceteris paribus, a transfer of income from a lower income poor person to a higher income poor person increases the poverty index. It can be checked easily that this is true for the FGT index when a = 2.

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