1.3. El maestro y los valores
1.3.2. Características y rasgos personales del maestro.
Foster, Greer, and Thorbecke Index
Foster, Greer, and Thorbecke (1984) and World Bank (1990) proposed an index that contains the above measures of poverty. This index provides a distributionally sensitive measure through the choice of a poverty aversion parameter . The formulae is given by
P (α) = ∑ (
)
2.3.123
Where α is the FGT parameter, N is the population size, Z is the poverty line, q is the number of persons/households below the poverty line, and Yi the expenditure/income of the household, and α is the FGT parameter which takes the values 0, 1, and 2, depending on the degree of concern about poverty. By increasing the value of α, the
“aversion “to poverty as measured by the index, is increased. Where there is no aversion to poverty, α = 0, which is equal to the poverty headcount ratio, the index measures the incidence of poverty, which is based on the ratio or percentage of the number of individual or household whose income are not equal to the poverty line to the total number of individuals or households (Bardhan, 1973; Ahluwalia 1976;
Ginneken 1980). As mentioned above, poverty headcount ratio expresses poverty in a single index. It measures the proportion of the population that is counted as poor and is denoted by
P( ) ∑ (
) 2.3.2 where N is the total population, q is the total number of the poor, I (Yi ≤Z) is the indicator function that takes on the value of 1 if the bracketed expression is true and 0 otherwise. Yi is the expenditure, and Z is the poverty line. This is the share of the population whose income or consumption is below the poverty line, that is, the share of the population that cannot afford to buy a basic basket of goods. An analyst using several poverty lines, say, one for poverty and one for extreme poverty, can estimate the incidence of both poverty and extreme poverty. Similarly, for nonmonetary indicators the incidence of poverty measures the share of the population that does not
reach the defined threshold (for instance, the percentage of the population with less
than three years of education). The headcount index gives a quick and simple-to-understand first look at the incidence of poverty in a particular area.
If the degree of aversion to poverty is increased such that α = 1, the index becomes
P(1)= ∑ (
)
2.3.324
The above index measures the depth of poverty and is referred to as the income gap measure. It measures the intensity / magnitude of poverty. Here the deviation of the poor‟s incomes from the poverty line is average and divided by the poverty line or expressed as its percentage.
This provides information regarding how far off households are from the poverty line.
This measure captures the mean aggregate income or consumption shortfall relative to the poverty line across the whole population. It is obtained by adding up all the shortfalls of the poor (assuming that the nonpoor have a shortfall of zero) and dividing the total by the population. In other words, it estimates the total resources needed to bring all the poor to the level of the poverty line (divided by the number of individuals in the population). This measure can also be used for nonmonetary indicators, provided that the measure of the distance is meaningful. The poverty gap in education could be the number of years of education needed or required to reach a defined threshold. In some cases, though, the measure does not make sense or is not quantifiable (for example, when indicators are binary, such as literacy, in which case only the concept of the headcount can be used).
The poverty gap can be used as a measure of the minimum amount of resources necessary to eradicate poverty, that is, the amount that one would have to transfer to the poor under perfect targeting (that is, each poor person getting exactly the amount he/she needs to be lifted out of poverty) to bring them all out of poverty. These two measures both have the problem of being very insensitive to the actual level of the poor. Thus a transfer from the poorest to the least poor which raises the income of the latter above poverty would reduce headcount while in the case of poverty gap; it will be less obvious that poverty has fallen.
This is the difference between the poverty line and mean income of the poor, expressed as a ratio of the poverty line (World Bank, 1993). It adds up the extent to which individuals fall below the poverty line (if they do).By definition, poverty gap is the poverty line less actual income, Yi for the poor individuals
( - ) ( )
, therefore, poverty gap is written as25
( ) ∑
2.3.4 If α =2, the index allows for concern about the poorest of the poor through attaching greater weight to the poverty of the poorest than those jus below the poverty line. This is done by squaring the income gap to capture the severity of poverty.P( ) ∑ (
)
2.3.5The severity of poverty index, does not only measure poverty and the depth of poverty, but also includes the distributional effects of the group of people living below the poverty line.
Another advantage of FGT index is that overall poverty can be expressed as the sum of groups poverty weighted by the population share of each of each group thus,
P (α) = ∑
Where j = 1, 2…m groups, is the population share of each group, and
is the poverty measures for each group. The contribution of each group, to the overall poverty can then be calculated.
The above index will be used in the research work to determine the distribution of poverty in Nigeria.