Measures of Poverty

What Is Poverty?

Poverty is a state or condition in which a person or community lacks the financial resources and essentials
for a minimum standard of living. Poverty means that the income level from employment is so low that
basic human needs can't be met.

Poverty line:

The poverty threshold, poverty limit, poverty line or breadline is the minimum level of income deemed
adequate in a particular country. Poverty line is usually calculated by finding the total cost of all the
essential resources that an average human adult consumes in one year.

In practice, like the definition of poverty, the official or common understanding the poverty line is
significantly higher in developed countries than in developing countries.

In October 2015, the World Bank updated the International Poverty Line (IPL), a global absolute minimum,
to $1.90 per day

(Ref: Wikipedia)

1. Headcount Index

By far the most widely-used measure is the headcount index, which simply measures the proportion of
the population that is counted as poor, often denoted by 𝑃0 . Formally,
𝑁𝑝
𝑃0 =
𝑁
Where, 𝑁𝑝 is the number of poor and N is the total population (or sample)

If 60 people are poor in a survey that samples 300 people, then P0 = 60/300 = 0.2 = 20%.

Headcount Index formula can be rewrite as:

Here, 𝐼(. ) is an indicator function that takes on a value of 1 if the bracketed expression is true, and 0
otherwise. So if expenditure (𝑦𝑖 ) is less than the poverty line (z), then 𝐼(. ) equals to 1 and the household
would be counted as poor. 𝑁𝑝 is the total number of the poor.
Clearly there is greater poverty in country A, but the headcount index does not capture this.

2. Poverty gap index

A moderately popular measure of poverty is the poverty gap index, which adds up the extent to which
individuals on average fall below the poverty line, and expresses it as a percentage of the poverty line.
More specifically, define the poverty gap (𝐺𝑖 ) as the poverty line (z) less actual income (𝑦𝑖 ) for poor
individuals; the gap is considered to be zero for everyone else. Using the index function, we have

𝐺𝑖 = (𝑧 − 𝑦𝑖 ). 𝐼(𝑦𝑖 < 𝑧)
Then the poverty gap index (𝑃1 ) may be written as
𝑁
1 𝐺𝑖
𝑃1 = ∑
𝑁 𝑧
𝑖=1

This table shows how the poverty gap is computed, divided by the poverty line, and averaged to give 𝑃1 ,
the poverty gap index.

This measure is the mean proportionate poverty gap in the population (where the non-poor have zero
poverty gap). Some people find it helpful to think of this measure as the cost of eliminating poverty
(relative to the poverty line), because it shows how much would have to be transferred to the poor to
bring their incomes or expenditures up to the poverty line (as a proportion of the poverty line). The
minimum cost of eliminating poverty using targeted transfers is simply the sum of all the poverty gaps in
a population; every gap is filled up to the poverty line.
For both of these countries, the poverty gap rate is 0.10, but most people would argue that country B has
more serious poverty because it has an extremely poor member. Alternatively, one could think of the
distribution in A as being generated from that in B by transferring 20 from the poorest person to the next
poorest person – hardly an improvement in most people’s eyes, yet one that has no effect on the poverty
gap rate!

3. Squared poverty gap (“poverty severity”) index:

To construct a measure of poverty that takes into account inequality among the poor, some researchers
use the squared poverty gap index. This is simply a weighted sum of poverty gaps (as a proportion of the
poverty line), where the weights are the proportionate poverty gaps themselves; a poverty gap of (say)
10% of the poverty line is given a weight of 10% while one of 50% is given a weight of 50%; this is in
contrast with the poverty gap index, where they are weighted equally. Hence, by squaring the poverty
gap index, the measure implicitly puts more weight on observations that fall well below the poverty line.
Formally:
𝑁
1 𝐺𝑖 2
𝑃1 = ∑( )
𝑁 𝑧
𝑖=1

This table shows how the poverty gap is computed, divided by the poverty line, squared, and averaged to
give 𝑃2 , the squared poverty gap index.

The measure lacks intuitive appeal, and because it is not easy to interpret it is not used very widely. It
may be thought of as one of a family of measures proposed by Foster, Greer and Thorbecke (1984), which
may be written, quite generally, as
 𝑁
1 𝐺𝑖 ∝
𝑃∝ = ∑( )
𝑁 𝑧
𝑖=1

4. Sen Index:

Sen (1976) has proposed an index that sought to combine the effects of the number of poor, the depth
of their poverty, and the distribution of poverty within the group. The index is given by

𝑝
𝑃𝑠 = 𝑃0 𝑃1 (1 + 𝐺 𝑃𝑃 )
𝑝
Where, 𝐺 𝑃𝑃 is the Gini coefficient of the poverty gap ratios of only the poor and 𝑃1 is the poverty gap
index calculated over poor individuals only.

Example. In 1996, 12.4% of the population of Quebec province (Canada) was in poverty. The poverty gap
index, applied to the poor only, stood at 0.272. And the Gini coefficient of the poverty gap ratios was
0.924. Calculate the Sen Index.

5. Time taken to exit:

For the 𝑗𝑡ℎ person below the poverty line, the expected time to exit poverty (i.e., to reach the poverty
line), if consumption per capita grows at positive rate g per year is:

𝑗 ln(𝑧) − ln(𝑥𝑗 )
𝑡𝑔 =
𝑔
Economic growth that acts to raise the real consumption levels of the poor can have a powerful effect on
the elimination of poverty.