Measuring Inequality and Arguing About It
How unequal a country is depends on whether you measure income or wealth, before or after tax, and per person or per household. Once the measurement is settled the argument about what is fair can actually begin.
What a learner can do afterwards
- Read cumulative shares used in a Lorenz curve and explain why, for comparable data, a Gini of 0.5 indicates more inequality than 0.3 without fixing the curve's exact shape
- Explain why wealth is usually more unequally held than income
- Present an incentive-based argument for some inequality and an opportunity-based argument against excessive inequality, with a limit to each
1 · Read
Income is money received over a period. Net wealth is assets minus debts at one date. Wealth is often more unequal, though not in every country: differences in saving, investment returns and inheritance can build gaps over time. Choose income or wealth first. For income, match the year, whether it is before or after taxes and transfers, and the person or household unit. Transfers, such as pensions or benefits, are payments received without providing goods or services in return.
Rank households from lowest to highest income. Divide them into five groups with equal numbers of households. Each group is a quintile, or 20% of households. Its income share is its total income divided by income across all households. Equal group size does not mean equal income shares.
A Lorenz curve plots cumulative household share horizontally and cumulative income share vertically, lowest incomes first. Here, the bottom 40% receive 5% + 10% = 15% of income. Equality would give them 40%. Both lines begin at (0%, 0%) and end at (100%, 100%).
For nonnegative incomes with a positive total, Gini is the area between the Lorenz curve and equality line divided by the area below the equality line. Zero means equality; values near 1 mean extreme concentration. Comparable Ginis of 0.5 and 0.3 have different area gaps, not fixed curve shapes. Curves can cross. Negative incomes can give values outside this range.
Extra rewards for training, effort or business risk can encourage useful work and investment. This incentive argument depends on rewards reflecting contributions. Inherited advantages or barriers to competition may create gaps without those benefits.
Unequal access to schooling or influence over rules can waste talent and weaken fair opportunity. This is an argument against excessive inequality, but needs evidence. A Gini alone cannot establish causes, fairness or living standards.
Choose comparable data. Quintiles show group shares; Lorenz curves show cumulative shares. Gini measures an overall gap, not its causes or fairness.
Lesson, questions and flashcards written for this dataset.
Readings and flashcards written for this dataset. Linked video: "Is inequality inevitable?", TED-Ed.
More to read
From group shares to cumulative shares
Suppose household-income quintiles receive 7%, 13%, 18%, 24% and 38% of total income, from lowest to highest. Each group has the same number of households. Their income shares differ and add to 100%.
For a Lorenz curve, add shares from the lowest-income group upward. The bottom 20% receive 7%. The bottom 40% receive 7% + 13% = 20%. The bottom 60% receive 38%, and the bottom 80% receive 62%. All households together receive 100%.
Plot cumulative household share horizontally and cumulative income share vertically. Begin at (0%, 0%) and end at (100%, 100%). Equality would give the bottom 40% of households 40% of income. A chart of separate quintile shares can show the distribution too, but it is not a Lorenz curve.
Compare like with like
A household receives 12,000 coins of income during a year. At the year's end, its assets are worth 40,000 coins and its debts are 15,000. Net wealth is 40,000 - 15,000 = 25,000 coins. Annual income and end-of-year wealth answer different questions.
Country comparisons need consistent definitions. Check the year, treatment of taxes and transfers, and whether observations are people or households. Household size also affects what an income can buy for each member. Identify any method used to adjust for size.
Net wealth can be negative when debts exceed assets. The familiar Gini scale from zero to one assumes nonnegative observations and a positive total. A statistic using negative values needs its method explained; do not apply that scale automatically.
What an inequality number leaves out
Three households receive incomes of 20, 40 and 80 coins. Double each income to 40, 80 and 160. Each household keeps the same share of the total, so the Lorenz curve and Gini stay the same. If prices are unchanged, all three households can buy more despite unchanged measured inequality.
Gini summarizes an overall area gap. It does not identify causes, exact group shares or whether everyone has enough to live on. Two Lorenz curves can cross, so their Ginis do not tell you which curve lies lower at every point.
A policy debate needs other evidence. Extra rewards may encourage training and investment. Barriers to schooling may prevent people from developing their abilities. Find out which mechanisms are present, then consider distribution alongside opportunity and living standards.
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Where it sits
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Where this leads
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.