Foster-Greer-Thorbecke Index
Also known as: FGT Index, FGT Poverty Measures, P-alpha Poverty Index, Foster-Greer-Thorbecke Poverty Measure
The Foster-Greer-Thorbecke (FGT) index is a parametric class of poverty measures introduced by James Foster, Joel Greer, and Erik Thorbecke in 1984 that became the workhorse of applied poverty analysis. A single parameter alpha tunes how much weight the measure places on the depth and distribution of poverty: alpha = 0 gives the headcount ratio (the share of people below the poverty line), alpha = 1 gives the poverty gap (the average normalized shortfall), and alpha = 2 gives poverty severity (which weights larger shortfalls more heavily). Its defining virtue is additive decomposability — total poverty is the population-weighted sum of subgroup poverty — which makes it ideal for profiling poverty across regions, sectors, and demographic groups.
Key highlights
- Provides a single coherent family in which a tunable parameter alpha moves smoothly from prevalence (headcount) to depth (gap) to severity, so one framework answers several questions.
- Additively decomposable: national poverty is the exact population-weighted sum of subgroup poverty, enabling poverty profiles and targeting.
- For alpha greater than or equal to 1 the measure satisfies the monotonicity axiom, and for alpha greater than 1 it satisfies the transfer axiom, giving it sound axiomatic foundations.
- Simple to compute from survey microdata and universally implemented in poverty-analysis software, making results comparable across studies.
Intuition
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How it works
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When to use it
Use the FGT index when you have a credible welfare indicator (income or, preferably in developing-country settings, consumption) for individuals or households and a defensible poverty line, and you want a coherent family of measures that can describe not just how many people are poor but how poor they are. Report P_0, P_1, and P_2 together: the headcount communicates prevalence, the gap communicates depth and the cost of elimination, and the severity measure captures inequality among the poor and responds to transfers. The additive decomposability makes FGT the natural choice for poverty profiling — apportioning national poverty across regions, urban/rural sectors, or household types. Choose higher alpha when distributional concern among the poor matters; rely on the headcount alone only for the simplest communication, since it is insensitive to how far below the line people fall.
Strengths & limitations
- Provides a single coherent family in which a tunable parameter alpha moves smoothly from prevalence (headcount) to depth (gap) to severity, so one framework answers several questions.
- Additively decomposable: national poverty is the exact population-weighted sum of subgroup poverty, enabling poverty profiles and targeting.
- For alpha greater than or equal to 1 the measure satisfies the monotonicity axiom, and for alpha greater than 1 it satisfies the transfer axiom, giving it sound axiomatic foundations.
- Simple to compute from survey microdata and universally implemented in poverty-analysis software, making results comparable across studies.
- Requires an exogenously chosen poverty line z, and rankings — especially of the headcount — can be sensitive to where that line is drawn.
- The headcount member (alpha = 0) violates monotonicity and the transfer axiom: it ignores how far below the line the poor are and can fall when a poor person becomes destitute (if another crosses the line).
- The choice of alpha is not data-driven; different alphas can rank distributions differently, so conclusions may hinge on a normative parameter.
- Like all unidimensional money-metric measures it ignores non-income dimensions of deprivation and the quality of the underlying welfare and price data.
Common pitfalls
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Applications
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Frequently asked
What does the alpha parameter actually control?
Alpha is a poverty-aversion parameter that governs how sensitive the measure is to the depth and distribution of poverty. At alpha = 0 only the count of the poor matters. At alpha = 1 the average size of shortfalls matters, so the measure captures depth. At alpha greater than 1 larger shortfalls are weighted disproportionately, so the measure becomes sensitive to inequality among the poor and responds (in the right direction) to transfers from poorer to less-poor individuals. Raising alpha thus shifts attention from the prevalence of poverty toward its intensity and concentration.
Why divide by total population N instead of by the number of poor q?
Dividing by the full population N is what makes the FGT class additively decomposable: total poverty becomes the population-weighted sum of subgroup poverty, so each subgroup's contribution to the national figure can be read off directly. If you instead divided by q you would obtain a conditional mean among the poor (such as the average normalized gap among the poor), which is interpretable but no longer aggregates across subgroups with simple population weights.
How does FGT relate to the separate poverty-gap and Watts indices?
The poverty-gap index is exactly the FGT member at alpha = 1, so it is a special case rather than a different method. The Watts index, by contrast, sits outside the FGT class: it uses the logarithm of the ratio of the line to income rather than a power of the normalized gap, which makes it a distinct distribution-sensitive measure. All three belong to the broader literature on decomposable, subgroup-consistent poverty measurement.
Sources
- 1.Foster, J., Greer, J., & Thorbecke, E. (1984). A class of decomposable poverty measures. Econometrica, 52(3), 761–766.
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ScholarGate. (2026, June 22). Foster-Greer-Thorbecke Index. ScholarGate. https://scholargate.app/economics/foster-greer-thorbecke-index