The Foster–Greer–Thorbecke (FGT) poverty measures This section presents the class of poverty measures that has been most widely

The Foster–Greer–Thorbecke (FGT) poverty measures This section presents the class of poverty measures that has been most widely

used in empirical applications, which is the Foster, Greer and Thorbecke (1984) (FGT) class of poverty indices. 24 The headcount ratio is a special case of the FGT indices as we shall see. As well as being robust, this is a very easy class of measures to understand and to compute.

Given an income distribution y = (y 1 ,y 2 ,...,y n ) and a poverty line z, start by calculating the normalized gap for each individual in the distribution. For incomes that are below the poverty line, the normalized gap is the distance between the poverty line and the income value, measured in poverty line units. For incomes that are above the poverty line, their income is replaced by z, the income at the poverty line (recall the focus axiom, we are not interested in incomes of the non-poor), so their normalized gap is simply zero. The normalized gaps are given by:

Now construct a vector g = (g 1 ,g 2 ,...,g n ) where each element is the are just the mean of that vector: (6)

Example: Consider four people whose incomes are y = (7,2,4,8) and the poverty line z = 5.

POVERTY AND INEQUALITY MEASUREMENT

The Headcount Ratio P 0

us a value of 1 if the person is poor and 0 if non-poor, so we can call the g 0 vector the deprivation vector. In this example: g 0 = (0,1,1,0), indicating that the second and third persons in this distribution are poor. The mean of this vector – the P 0 measure – is one half: P 0 0 ) = 2/4, indicating that 50 per cent of the population in this distribution is poor. This measure is known as the headcount ratio (or poverty incidence). Undoubtedly, it provides very useful information. However, as noted by Watts (1969) and Sen (1976), it gives neither information on the depth of poverty nor on its distribution among the poor. For example, if the third person became poorer, experiencing a decrease in her income so that the distribution became y = (7,2,3,8), the measure would still be one half; that is: it violates monotonicity. Also, if there was a progressive transfer between the two poor persons, so that the distribution was

y = (7,3,3,8), the P 0 would not change either, violating the transfer principle. Certainly, the headcount ratio’s insensitiveness to the depth and distribution of poverty is not a minor issue. It has direct policy implications. If this was the official poverty measure in a country (and unfortunately that is very often the case), a government interested in maximizing the impact of resources on poverty reduction would have all the incentives to allocate them among the least poor, those that are closer to the poverty line, leaving the lives of the poorest poor unchanged.

The Poverty Gap P 1 (or FGT-1)

1 (y) vector, which may be called the normalized gap vector, is for the example above, g 1 (y) = (0,3/5,1/5,0). The

aggregate poverty measure P 1 , is the mean of the normalized gap vector. In our example P 1 1 ) = 4/20. As opposed to the headcount ratio P 0 , the P 1 the measure is sensitive to the depth of poverty. It satisfies monotonicity. If the income of the third individual decreased so we had (7,2,3,8) the normalized

gap vector would now be g 1 (y) = (0,3/5,2/5,0) and P 1 would increase to P 1 = an extremely destitute person to a less poor person (who still is poor) would

not change P 1 , since the decrease in one gap would be exactly compensated by the increase in the other. Therefore, by being sensitive to the depth of poverty (i.e. satisfying monotonicity), the P 1 measure does make policy-makers want to decrease the depth of poverty (even if the poor person does not become non- poor). But because of its insensitivity to the distribution among the poor, the

P 1 measure does not provide extra incentives to help the poorest poor.

The Squared Poverty Gap P 2 (or FGT-2)

2 (y) vector, which may be called the squared gap vector, is for the given example g 2 (y) = (0,9/25,1/25,0). The

aggregate poverty measure P 2 is the mean of the normalized gap vector: P 2 (y;z)

2 ) = 10/100. The P 2 measure is sensitive to the depth of poverty: if the

TOPICS

income of the third person decreases in one monetary unit, the squared gap vector becomes g 2 (y) = (0,9/25,4/25,0), increasing the aggregate poverty level to P 2 = 13/100. Moreover, it is also sensitive to the distribution among the poor: if there is a transfer from the third to the second individual of one monetary unit (7,2,4,8) becomes (7,3,3,8), the squared gap vector becomes

g 2 (y) = (0,4/25,4/25,0), decreasing the aggregate poverty level to P 2 = 8/100. By squaring the normalized gaps, the biggest gaps receive a higher weight, which has the effect of emphasizing the poorest poor and providing incentives for

satisfy the transfer property. 25

It is worth repeating that all measures of the FGT family are decomposable in subgroups of population, allowing the identification of each group’s contribution to overall poverty.