The document discusses different measures used to quantify poverty, including the headcount index, poverty gap index, and Sen index. The headcount index measures the proportion of people living below the poverty line. The poverty gap index incorporates the depth of people's poverty by measuring the average distance below the poverty line. However, both indices do not account for inequality among the poor. The Sen index seeks to address this by factoring in the Gini coefficient for inequality within the poor population.

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Poverty Measures
Dr. Santanu Chakraborty
Assistant Professor
Department of Economics
Bhairab Ganguly College
Belghoria,Kolkata-56

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Headcount Index
 measures the proportion of the population that
is in poverty
 the headcount index estimates the percentage
of the population living in households with per
capita consumption below the poverty line
 it thus measures the incidence of poverty

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Poverty Indices: Headcount Index
Formally,
where N = total population
(.) = an indicator function that takes on a
value of 1 (poor); if the bracketed
expression is true, and 0 (nonpoor)
otherwise
yi = expenditure
z = poverty line





N
i
p
i
N
N
z
y
I
N
P
1
0 ,
)
(
1

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Headcount Index
 the great virtue of the headcount index is that it
is simple to construct and easy to understand
 adequate measure of assessing overall
progress in reducing poverty (though preferably
always calculated for at least two poverty lines)

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Headcount Index
Weaknesses:
 The headcount index does not take the intensity
of poverty into account. To see why, suppose
that a poor person suddenly becomes very
much poorer. What will happen to measured
poverty? Nothing. The headcount index is
totally insensitive to differences in the depth of
poverty.

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Example:
There is greater poverty in country A but the
headcount index does not capture this.
Expenditure for each individual in country Headcount Poverty Rate (P0)
Expenditure in Country A 100 100 150 150 50%
Expenditure in Country B 124 124 150 150 50%
Headcount Index

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Headcount Index
 As a welfare function, the headcount index violates the
transfer principle – an idea first formulated by Dalton
(1920) that states that transfers from a richer to a
poorer person should improve the measure of welfare.
Here, if a somewhat poor household were to give to a
very poor household, the headcount index would be
unchanged, even though it is reasonable to suppose
that poverty overall has lessened.
 The headcount index implies that there is a “jump” in
welfare, at about the poverty line, In practice, such a
jump is not found.

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Headcount Index
 The headcount index is very simple to construct
and easy to understand.
 However, it does not indicate how poor the poor
are, and hence does not change if people below
the poverty line become poorer.

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Headcount Index
 The easiest way to reduce the headcount index
is to target benefits to people just below the
poverty line, because these are the ones who
are cheapest to move across the line - but by
most normative standards, people just below
the poverty line are the least deserving of the
poor. Thus, despite its popularity, many
problems result from an undue concentration on
the head-count statistic.

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Headcount Index
 What we calculate using the headcount index is
the percentage of individuals who are poor and
not the percentage of households.
 To be able to do so, we make a critical
assumption that all household members enjoy
the same level of well-being. This assumption
may not hold in many situations.
 For example, some elderly members of a household
may be much poorer that other members of the
same household.
 In reality, not all consumption is evenly shared
across household members.

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Poverty Gap Index
 A moderately popular measure of poverty which
adds up the extent to which individuals fall below
the poverty line (if they do) and expresses it as a
percentage of the poverty line.
 More specifically, define the poverty gap (Gn) as the
poverty line (z) less actual income (yi) for poor
individuals; the gap is considered to be zero for
everyone else.
 This measure reflects the average distances of the
poor below the poverty line so it gives a better idea
of the depth of poverty.

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Poverty Gap Index
 This measure is also thought of as the cost of
eliminating poverty (relative to the poverty line),
since it shows how much would have to be
transferred to the poor to bring their incomes (or
expenditure) up to 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.

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Poverty Gap Index
 However this interpretation is only reasonable if
the transfers could be made perfectly efficiently,
for instance with lump sum transfers. This
assumes that the policy maker has a lot of
information and that a very “pro-poor”
government would need to spend more than the
minimum cost in the name of poverty reduction.

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Poverty Gap Index
 At the other extreme, one can consider the
maximum cost of eliminating poverty, assuming
that the policy maker knows nothing about who
is poor and who is not.
 From the form of the index, it can be seen that
the ratio of the minimum cost of eliminating
poverty with perfect targeting to the maximum
cost with no targeting is simply the poverty gap
index.

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Poverty Gap Index
 Thus, this measure is also an indicator of the
potential saving to the poverty alleviation budget
from budgeting.
 A serious shortcoming of this measure is that it
may not convincingly capture differences in the
severity of poverty amongst the poor.

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Poverty Gap Index
Example:
Consider 2 distributions of consumption for 4
persons. Poverty line = 3.01
– A distribution is (1,2,3,4)
– B distribution is (2,2,2,4)
Thus, headcount index is 0.75 and the poverty
gap index is 0.25 in both cases.

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Poverty Gap Index
However, the poorest person in A has only
half of the consumption of the poorest in B.
One can think of B as being generated from A
by a transfer from the least poor person
(individual with ‘3’ in A) to the poorest. The
poverty gap will be unaffected by such a
transfer.
 Thus, the main drawback of this measure is that
it ignores inequality among the poor.

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Poverty Gap Index
To see this again, consider the following example:
Poverty Gap Rates in A and B, assuming poverty
line of 125
For both countries, the poverty gap rate is 0.10, it could
be argued that country B has more serious poverty
because it has an extremely poor member.
Expenditure for each individual in country Poverty Gap Rate (P1)
Expenditure in Country A 100 100 150 150 0.10
Expenditure in Country B 80 120 150 150 0.10

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Poverty Gap Index
In summary,
The Poverty Gap Index is the average over all people, of
the gaps between poor people’s standard of living and the
poverty line, expressed as a ratio to the poverty line.
The aggregate poverty gap shows the cost of eliminating
poverty by making perfectly targeted transfers to the poor,
i.e. closing all poverty gaps, in the absence of
transactions costs and disincentive effects.

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Poverty Gap Index
– This is unrealistic but it does convey useful
information about the minimum scale of the
financial resources needed to tackle the
poverty problem.
 Moreover, the poverty gap index can show the
value of using survey information to learn about
the characteristics of the poor. A costly way of
eliminating poverty would be to make
completely untargeted poverty line-sized
transfers to everyone in the population.

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Poverty Gap Index
 The poverty gap index gives the ratio of the cost
of eliminating poverty using perfectly targeted
transfers compared with using completely
untargeted transfers.
– Thus, the smaller is the poverty gap index,
the greater the potential economies for a
poverty alleviation budget from identifying the
characteristics of the poor so as to target
benefits and programs.

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Sen Index
 Sen (1976) 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
),
)
1
(
1
(
0
z
G
P
P
P
P
s





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Sen Index
where P0 = headcount index
μP = mean income (or exp) of the poor
GP = Gini coefficient of inequality among
the poor. The Gini coefficient ranges from 0
(perfect equality) to 1 (perfect inequality), and
is discussed further below in the context of
measuring inequality.
The Sen Index can also be written as the
average of the headcount and poverty gap
measures weighted by the Gini coefficient of
the poor, giving:
)
1
(
1
0
P
P
s G
P
G
P
P 



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Sen Index
 The Sen index has the virtue of taking the
income distribution among the poor into
account. However the index is almost never
used outside of the academic literature, perhaps
because it is lacks the intuitive appeal of some
of the simpler measures of poverty, but also
because it “cannot be used to decompose
poverty into contributions from different
subgroups”.