Theil index
Topic: Poverty and Inequality: Measurement and Policy · NCERT: Beyond NCERT
Meaning
The Theil index is an entropy-based measure of inequality. Entropy is a concept borrowed from information theory. The formula is:
T = (1/N) Σ (yᵢ/μ) ln(yᵢ/μ)
Here yᵢ is a person's income, μ is the average income and N is the population. The index is 0 when everyone has the same income. Its key strength is that it is decomposable: total inequality splits exactly into inequality within groups plus inequality between groups.
Example
Divide India's population into rural and urban groups. The Theil index shows how much of total inequality comes from the gap between rural and urban average incomes. It also shows how much comes from inequality inside villages and inside cities. The same split works for states or castes, which helps direct policy to the right gap.
Don't confuse with
- Gini coefficient: it is easier to read on a 0–1 scale, but it does not break down neatly into within-group and between-group parts.