Poverty Gap Index
Also known as: Poverty Gap Ratio, Income Gap Measure, Mean Normalized Shortfall, Depth of Poverty
The poverty gap index is the member of the Foster-Greer-Thorbecke family at alpha = 1 and the standard money-metric measure of the depth of poverty. Where the headcount ratio merely counts who is poor, the poverty gap averages how far the poor fall below the poverty line, expressed as a fraction of that line and spread over the whole population. It can be read as the per-capita resource shortfall — the share of the poverty line, per person, that perfect targeting would need to transfer to eliminate poverty — making it the natural complement to the headcount when judging the cost and intensity of poverty.
Key highlights
- Captures the depth of poverty, distinguishing populations with shallowly poor versus deeply poor members that the headcount treats identically.
- Satisfies the monotonicity axiom: it always falls when any poor person's income rises, rewarding gains that do not cross the line.
- Has a direct policy reading as the per-capita (and, when scaled, aggregate) minimum cost of eliminating poverty under perfect targeting.
- Additively decomposable across subgroups and factorable into headcount times income-gap ratio, aiding interpretation and profiling.
Intuition
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How it works
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When to use it
Use the poverty gap index whenever the headcount ratio alone is inadequate because you care about how far the poor fall below the line, not merely how many they are. It is essential for assessing the depth of poverty, for estimating the minimum resources required to eliminate poverty under ideal targeting, and for detecting improvements among the poor that leave the headcount unchanged. Report it alongside the headcount (its prevalence partner) and the squared poverty gap (its severity partner) so that prevalence, depth, and inequality among the poor are all visible. Because it is additively decomposable, it also supports poverty profiling. Be aware that, like all FGT measures, it requires a defensible poverty line and a consistent welfare definition, and that it weights all shortfalls equally, so it is insensitive to inequality among the poor — for that, move to alpha = 2.
Strengths & limitations
- Captures the depth of poverty, distinguishing populations with shallowly poor versus deeply poor members that the headcount treats identically.
- Satisfies the monotonicity axiom: it always falls when any poor person's income rises, rewarding gains that do not cross the line.
- Has a direct policy reading as the per-capita (and, when scaled, aggregate) minimum cost of eliminating poverty under perfect targeting.
- Additively decomposable across subgroups and factorable into headcount times income-gap ratio, aiding interpretation and profiling.
- Insensitive to inequality among the poor: a transfer from a very poor to a less-poor person below the line leaves the index unchanged, so it violates the transfer axiom.
- Depends on an exogenous poverty line and a consistent welfare measure; results shift with the line and with equivalence-scale choices.
- As a money-metric measure it ignores non-income deprivations and the quality of price and income data.
- The minimum-transfer interpretation assumes perfect, costless targeting that no real program achieves, so it understates true elimination budgets.
Common pitfalls
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Applications
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Frequently asked
How is the poverty gap index different from the income-gap ratio?
The income-gap ratio I is the average proportional shortfall computed only among the poor — it answers 'how poor are the poor, on average?' The poverty gap index PG spreads those shortfalls over the entire population, so PG = H × I, where H is the headcount. PG therefore combines how widespread poverty is with how intense it is, and only PG carries the per-capita-shortfall and additive-decomposability interpretations. Reporting I without H can make a population with very few but extremely poor people look the same as one with widespread mild poverty.
Why does the poverty gap not capture inequality among the poor?
Because it sums shortfalls linearly, a one-dollar transfer from a poorer person to a less-poor person (both below the line) reduces one gap and raises the other by the same amount, leaving the total unchanged. The measure is therefore indifferent to the distribution of poverty among the poor and violates the transfer axiom. To make the measure sensitive to such transfers you square the gaps, giving the FGT alpha = 2 squared poverty gap, which penalizes larger shortfalls more heavily.
Can the minimum-transfer cost be taken as the budget needed to end poverty?
Only as an idealized lower bound. The figure z × N × PG is the sum of all income shortfalls and would eliminate poverty only if a planner could transfer exactly each person's deficit at no administrative cost and with no behavioral response. Real programs face imperfect targeting, leakage to the non-poor, administrative overhead, and incentive effects, so the actual budget required is considerably larger. The gap-based figure is best used as a benchmark against which to judge targeting efficiency.
Sources
- 1.Foster, J., Greer, J., & Thorbecke, E. (1984). A class of decomposable poverty measures. Econometrica, 52(3), 761–766.
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Cite this page
ScholarGate. (2026, June 22). Poverty Gap Index. ScholarGate. https://scholargate.app/economics/poverty-gap-index