Intermediatedevelopment
The Gini Coefficient: Inequality in One Number
Overview
The Gini coefficient compresses an entire income distribution into one number between 0 and 1. It appears in every inequality debate, development report, and economics exam — yet few can explain what it actually measures. This lesson builds it from the Lorenz curve, works through a calculation, shows how to read real Ginis (0.27 to 0.63), and explains why professionals never rely on it alone.
Learning objectives
- Construct a Lorenz curve from income data
- Compute the Gini coefficient geometrically and from data
- Interpret real-world Gini values
- Explain the Gini's limitations: shape-blindness, transfers, negatives
- Choose complementary measures for serious analysis
The Lorenz curve
Rank everyone from poorest to richest. The Lorenz curve plots the cumulative share of income against the cumulative share of population. Perfect equality is the 45° line: the bottom 20% earn 20% of income, the bottom 50% earn 50%, and so on. Real distributions bow below the line: the bottom 50% might earn only 20% of income. The more unequal the society, the further the curve sags. The curve is the full picture — every inequality measure, including the Gini, is a summary of it.
Pick a point: 'the poorest 40% earn X% of income.' The gap between the curve and the 45° line at every point is inequality made visible.
From Lorenz to Gini
The Gini is the area between the 45° line and the Lorenz curve, divided by the total area under the 45° line. Geometrically: Gini = A / (A + B), where A is the inequality area and B the area under the Lorenz curve. Perfect equality: the curve is the line, A = 0, Gini = 0. One person has everything: A is the whole triangle, Gini = 1 (or 100 on the 0–100 scale many reports use). Intuition: the Gini equals half the average income difference between all pairs of people, relative to the mean — it measures expected disparity between two randomly chosen individuals.
Gini = (average absolute difference between all pairs) ÷ (2 × mean). A Gini of 0.4 means two random people differ by 80% of mean income on average.
A worked example
Five people earn 10, 20, 30, 40, 100 (mean 40). Cumulative income shares: 5%, 15%, 30%, 50%, 100% at population quintiles 20%–100%. The Lorenz curve sags moderately. Computing via the trapezoid formula: Gini ≈ 0.36 — middling inequality, like the US after taxes and transfers (market-income Gini is higher, ~0.48). Try extremes: incomes 40, 40, 40, 40, 40 → Gini 0. Incomes 0, 0, 0, 0, 200 → Gini 0.8. The exercise builds intuition: Gini rises with the skew, and transfers from rich to poor visibly lift the curve and shrink A.
The standard Gini formula misbehaves with negative incomes (business losses, debts). Adjusted Ginis exist, but comparisons across datasets with different treatments mislead.
Reading real Ginis
Reference points: Nordics and central Europe 0.25–0.30 (most equal); East Asia 0.30–0.40; US ~0.41 (market) / ~0.39 (disposable); Latin America 0.45–0.55; Sub-Saharan Africa 0.43–0.63; South Africa 0.63 (highest). Two cautions: always check whether it's market or disposable income (redistribution cuts 0.1+ in Europe, little in the US), and whether it's income or consumption (consumption Ginis run lower — the poor smooth spending). A falling Gini can even accompany rising absolute poverty if everyone's income drops but compresses — context is everything.
The gap between market-income and disposable-income Gini measures redistribution's bite. Europe's welfare states compress ~0.15; America's ~0.08 — a policy choice made visible.
What the Gini can't see
Three blind spots. Shape-blindness: very different distributions share one Gini — a squeezed middle vs. a pulled-away top look identical. Insensitivity: the Gini is most sensitive to middle transfers, least to extremes — yet politics usually cares most about the top 1% and bottom 10%. And snapshot limits: it ignores mobility (a Gini of 0.4 with high mobility differs profoundly from the same Gini with castes). Professionals therefore pair it with top shares, poverty rates, and mobility data. The Gini is the beginning of inequality analysis, never the end.
Key points
- The Gini = inequality area ÷ total area under the equality line (0 to 1).
- It equals half the average pairwise income gap relative to the mean.
- Nordics ~0.27, US ~0.41, South Africa ~0.63 — always check market vs. disposable.
- The Gini is shape-blind, middle-sensitive, and static — pair it with other measures.
- Redistribution's effect shows in the market-minus-disposable Gini gap.
Common misconceptions
✓ Truth: A falling Gini during a recession (everyone poorer but more equal) isn't progress. Pair the Gini with absolute income and poverty data before celebrating.
✓ Truth: It measures dispersion, not level. A poor equal society and a rich equal society share a low Gini; poverty needs its own headcount and gap measures.
✓ Truth: Income vs. consumption, household vs. individual, market vs. disposable — mixing definitions invalidates comparisons. Harmonized datasets (LIS, SWIID) exist for a reason.
Practice questions
Q1. Geometrically, the Gini coefficient equals:
- The slope of the Lorenz curve
- The area between the equality line and the Lorenz curve, divided by the total area under the equality line
- The top 1% income share
- Mean divided by median
Gini = A/(A+B): the inequality area as a fraction of the maximum possible. Perfect equality gives 0; one person holding everything gives 1.
Q2. Two countries have the same Gini but different Lorenz curves. This shows the Gini is:
- Useless
- Shape-blind — it can hide different distributional patterns
- Always wrong
- Only for wealth
Very different distributions (top-heavy vs. bottom-heavy) can share a Gini. That's why analysts supplement it with top shares, percentile ratios, and poverty data.
Q3. The gap between market-income Gini and disposable-income Gini measures:
- Measurement error
- The equalizing effect of taxes and transfers (redistribution)
- Economic growth
- Inflation
Market Gini is pre-tax/transfer; disposable is post-. The difference — ~0.15 in Scandinavia, ~0.08 in the US — quantifies how much redistribution compresses inequality.
Click a question to reveal the answer and explanation.
Frequently asked questions
How is the Gini actually computed from survey data?
Sort incomes, compute cumulative shares, and apply the trapezoid formula: G = 1 − Σ(X_k − X_{k−1})(Y_k + Y_{k−1}), where X are cumulative population shares and Y cumulative income shares. Statistical software does this routinely.
Why do some sources report Gini as 0–100 instead of 0–1?
Just scaling — 41 means 0.41. The 0–100 form is common in World Bank and policy reports; the 0–1 form in academic work. Always check which you're reading.
Can the Gini exceed 1?
With negative incomes (debts exceeding assets), yes — adjusted measures handle this. Standard presentations cap discussion at 0–1 for non-negative incomes.
What's a 'good' Gini target for policy?
No professional consensus exists on an optimal level. The debate is about trade-offs: Nordics (~0.27) show low inequality coexists with prosperity, but the right level depends on values about incentives vs. equity.