Squared poverty gap index
Also called: Poverty severity index · Topic: Poverty and Inequality: Measurement and Policy · NCERT: Beyond NCERT
Meaning
The squared poverty gap index (SPG) measures the severity of poverty. It squares each poor person's gap from the line before averaging. Squaring makes large gaps count far more than small ones, so the index gives more weight to the poorest. It also captures inequality among the poor.
SPG = (1/n) Σ [(z − yᵢ)/z]², summed over the poor. Here z is the poverty line, yᵢ is a poor person's income and n is the total population.
It is the Foster-Greer-Thorbecke (FGT, 1984) measure with α = 2.
Example
Take a poverty line of 100 and incomes 60, 90, 120 and 150. The squared gaps are 0.16 and 0.01, so SPG = (0.16 + 0.01)/4 = 0.0425. If the poorest person fell from 60 to 40, SPG would rise to 0.0925. The head-count ratio would not change.
Don't confuse with
- Poverty gap index: it measures average depth (α = 1). A ₹1 shortfall counts the same whoever has it. SPG gives extra weight to the poorest.