3. DATA REQUIREMENTS FOR POVERTY
2.1 Monetary approaches to poverty measurement
2.1.4. Choice of poverty measure
Two theoretical “requirements” of poverty measures are worth dis- cussing before specific measures are discussed. One is the requirement of decomposability, the other is the requirement of continuity. A de- composable measure “allows the breakdown of total poverty into com- ponents, and tells us how much of the overall poverty may be attrib- uted to various population subgroups respectively” (Foster and Sen 1997). An intuitive way of understanding this concept is to think of what would happen with measures that are not decomposable: it would be entirely possible for the poverty measure for the whole group (say, for Sri Lanka) to go up while the measure for each subgroup (urban, rural and estate) were to go down.
“Continuity” is also easier to understand in terms of its opposite:
discontinuity or the existence of a “jump” at the poverty line. If we are confident that there really is a “jump” in welfare at the poverty line, and we are confident about the location of the poverty line, then pov-
erty measures that are not continuous are a good thing. On the other hand, if we do not believe the jump occurs at a particular poverty line, then continuity is to be desired. The property of continuity allows a measure of poverty to give highest priority to the “poorest”. This con- cept is illustrated below with regard to the specific poverty measures.
The Headcount Index (H) is one of the best-known and most widely used measures of poverty. It measures the incidence of poverty, that is, the percentage of individuals in a given population whose standard of living lies below the poverty line. The problem with this measure is that it disregards inequality below the poverty line, that is, it contains no information on the degree of poverty (shortfall below the poverty line) of each individual. For example, if a transfer of income from a poorer person to a richer person (both of whom start off below the poverty line) enables that individual to “jump” the poverty line, ac- cording to the headcount index, poverty has decreased; but we disre- gard the effect on the individual who remained below the poverty line, and became poorer.61 Another illustration is that if a poor person were to die, it would reduce the headcount index, not increase it! (Sen 1976).
The advantage of this measure is that it is easy to understand, and it is also decomposable.
The Poverty Gap Index (PG) remedies the lack of information be- low the poverty line by measuring the depth of poverty. It is the aver- age shortfall between an individual's level of consumption and the pov- erty line, where the shortfall for all individuals whose consumption falls above the poverty line is zero. It can be interpreted as a per capita measure of the total shortfall of individual welfare levels below the poverty line.
The income-gap ratio (I), which is the percentage average shortfall of the poor from the poverty line, is more intuitive than the poverty gap ratio, but it gives no information about the numbers in poverty (another way of saying this is that it only indicates the depth of pov-
61 In the language of social welfare and inequality axioms, it violates the principle of transfers.
erty, but not its extent). The poverty gap ratio does both, in that it is the product of the Headcount Index and the income-gap ratio (H x I).
However, in both these measures, if the transfer from a poorer per- son (poor) to a richer person (poor) leaves the richer person below the poverty line, the aggregate (and thus, the per capita) shortfall will not change, because the increase in the poorer person’s shortfall is exactly offset by the decrease in the richer person’s shortfall.
Sen (1976) attempted to remedy this by constructing a measure of poverty (S) that explicitly included inequality below the poverty line.
The original formula for Sen’s index is given by Equation 2:
Equation 2
S = H(GP) - PG(1 - GP)
where GP is the gini coefficient among the poor. The equation above expresses poverty as a combination of the headcount index, and the poverty gap index, specifically as the average of the two, weighted by the gini coefficient. The problem with the gini coefficient is that it is not strictly decomposable, and as a result S is also not decomposable. It is also not a “continuous” measure of poverty.
The Squared Poverty Gap index (PG2) measures the severity of pov- erty. By squaring the shortfall between an individual's level of con- sumption and the poverty line, it places greater weight on poorer indi- viduals. Thus, the squared poverty gap index is sensitive to relative deprivation among the poor. The headcount index, poverty gap index and poverty gap squared index are part of a family of measures of pov- erty known as the Foster-Greer-Thorbecke measures that can be de- fined as
Equation 3
Pα = (1/
n
) Σx<z [(z-xi)/z]αwhere xi is the consumption of the ith individual, z is the poverty line, n is the population size and α is a non-negative parameter. When α is 0, P=H; when α is 1, P=PG; and α is 2, P=PG2 (Foster, Greer and Thorbecke, 1984).62 Table 4 summarises the poverty measures described in this section.
Table 4: Choice of poverty measure
Poverty Measure Description
P0 The percentage of individuals in a given population whose Headcount Index (H) standard of living lies below the poverty line
The incidence of poverty Problem: violates the principle of transfers
I Percentage shortfall of the average income of the poor Income gap ratio Problem: not sensitive to the number of poor people P1 The average shortfall between an individual's level of con- Poverty Gap index (PG) sumption and the poverty line, where the shortfall for all The depth of poverty individuals whose consumption falls above the poverty line
is zero. Sensitive to the number of poor people. Product of H and I. (HI)
Problem: not sensitive to transfers among the poor which leave the richer individual still below the poverty line (the increase in the poorer person’s shortfall is exactly offset by the decrease in the richer person’s shortfall)
PS Expresses poverty as a weighted average of the poverty gap Sen’s measure of poverty and the poverty gap index where the weight is the gini
coefficient. H(Gp) - PG (1-Gp)
Problem: the Gini coefficient is not additively decompos able, therefore neither is Sen’s P.
P2 By squaring the shortfall between an individual's level of Squared Poverty Gap consumption and the poverty line, it places greater weight index (PG2) on poorer individuals.
The severity of poverty
62 Extensions of the FGT measures have been applied in a dynamic framework (Jalan and Ravallion 1998, Christiaensen and Boisvert 2003) as well as in poverty comparisons within a multidimen- sional framework (Duclos, Sahn and Younger 2003).
Shortcomings
While these measures are used extensively in both developing and de- veloped country poverty measurement exercises, they suffer from sev- eral shortcomings. (1) It has already been stated that they would regis- ter a decrease, not an increase if a poor person were to die. Kanbur (2002) has pointed out that in situations where (large numbers of) poor people were to die (such as AIDS victims in Africa, who are mainly the rural poor) because of their poverty (inability to afford expensive treat- ment) the FGT measures (or any measures that focus on the currently living) are inadequate.63 (2) They are also not subgroup sensitive (Subramaniam 2003). The following example from Subramaniam (2003) illustrates this. If for example, one divides the population into two sub- groups, A and B, where A is an historically disadvantaged group (like a depressed caste) and the headcount ratio of poverty for A is 0.7 and for B is 0.3, and the groups comprise half the population each, the total headcount ratio for the country would be 0.5 (0.7*0.5 + 0.3*0.5). If a pure redistribution from B to A were to decrease A’s poverty to 0.6, while increase B’s poverty to 0.4, we may be predisposed (says Subramaniam) to regard this as an improvement, while the headcount index registers none (0.6*0.5 + 0.4*0.5) = 0.5. This idea of incorporat- ing what is sometimes termed horizontal equity into measures of pov- erty is somewhat controversial, although subgroup sensitivity is a stan- dard property of measures of inequality. They are (3) not sensitive to inequality around (above) the poverty line. A new approach by Foster and Szekely (2000) attempts to derive a measure that is more sensitive to the state of income distribution, where the non-poor also receive a weight-which can be made as small as one wishes.