Measuring Inequality

Two research institutes publish reports on the same country in the same year.

One reports that inequality has risen substantially over two decades. The other reports that it has been broadly flat since the mid-1990s.

Neither is lying, neither has made an arithmetic error, and both are using official data. They have made different decisions at six points, each of which is defensible, and the decisions between them are worth more than the trend.

This lesson is 7.2.2 applied to the most politically consequential measurement in social science.

Six decisions, and how each one moves the answer.

Decision one: income or wealth?

Income is a flow — what arrives over a period. Wealth is a stock — what you own at a moment, minus what you owe.

Wealth is always far more concentrated than income, everywhere, by a large margin. Income inequality in rich countries typically produces a Gini coefficient somewhere in the range of 0.25 to 0.50. Wealth inequality typically produces 0.6 to 0.9. The reasons are structural: wealth accumulates from saved income, so income inequality compounds into it; returns are earned on it, so it grows by itself; it is inherited, so it crosses generations directly; and a substantial share of households have zero or negative net wealth, which no income distribution can match because you cannot have negative earnings.

A report on wealth and a report on income are not two views of one thing. They are two things, and the wealth one will always look more dramatic.

Decision two: which income?

There are four stages, and each lowers measured inequality.

Market income — earnings, self-employment, private pensions, investment returns. The most unequal figure. Gross income — market income plus cash transfers: pensions, benefits, tax credits. Disposable income — minus direct taxes and social contributions. This is the standard basis for international comparison. Adjusted disposable income — plus the value of in-kind public services, principally health and education. The least unequal figure, and the hardest to compute, because valuing a public service requires deciding what it is worth to the person receiving it.

The gap between the first and the last is enormous — in some countries the redistributive system reduces measured inequality by a third or more. Comparing one country's market income inequality with another's disposable income inequality is a straightforward category error, and it appears in public argument constantly.

Decision three: who is the unit?

Individual, household, family, or tax unit. The household is standard, and it embeds an assumption: that resources are shared within it.

They are not shared equally. Research on intra-household allocation — in rich and poor countries alike — finds systematic differences in control over money, in who goes without when resources are short, and in nutritional and health outcomes within households. A measure that treats the household as a unit makes all intra-household inequality equal to zero by construction, which is a substantive claim disguised as a technical convenience, and it disproportionately conceals inequality between women and men.

And household income must be adjusted for size, because four people need more than one but not four times more. Equivalence scales do this — the common one gives the first adult a weight of 1, each additional adult 0.5, and each child 0.3. The choice of scale is a judgement about economies of scale in households, and different plausible scales change measured poverty rates and inequality rankings.

Decision four: over what period?

Annual income overstates lifetime inequality, because at any moment the distribution contains students who will earn more later and retirees who earned more earlier. Lifetime inequality is lower than annual inequality — and it is still large, because most of what is measured in a year is persistent rather than transitory.

And how much is transitory is itself the finding. A society where the same people are at the bottom every year and one where different people cycle through have identical annual figures and are entirely different places (see 8.3).

Decision five: which measure?

Decision six: which data source?

Both need their own sections, and both do more work than anything above.

Different measures can rank the same two distributions in opposite directions. This is not a defect — it is a fact about what "more unequal" means.

Picture the Lorenz curve: rank everyone from poorest to richest along the bottom, and plot the cumulative share of total income they hold up the side. Perfect equality is a straight diagonal. Any real distribution sags below it, and the more it sags the more unequal the society.

The Gini coefficient is the area between the diagonal and the curve, as a proportion of the whole triangle. One number, from 0 to 1.

Now suppose two countries' Lorenz curves cross. Country A is more equal at the bottom — its poorest 40 per cent hold a larger share. Country B is more equal at the top — its richest 1 per cent hold a smaller share.

Which is more unequal? There is no answer that does not embed a judgement about which part of the distribution matters more. And this is provable rather than rhetorical: when Lorenz curves cross, different inequality measures will rank the two distributions differently, and each is internally consistent.

So choosing a measure is choosing what you care about, which is exactly the argument from 7.6.1 arriving with political consequences.

Six, and you should never see only one.

The Gini coefficient. The standard. Its virtue is comparability — it exists for nearly every country and many decades. Its known property is that it is most sensitive to changes around the middle of the distribution and least sensitive at the extremes, which is precisely where most of the recent action has been. A large transfer from the bottom to the very top can move the Gini remarkably little.

Top income shares. The share going to the top 10, 1 or 0.1 per cent. Transparent, intuitive, and computable from tax records — which is why the modern literature is built on them (below). Blind to everything below the threshold: the top 1 per cent share can be flat while the bottom third collapses.

The Palma ratio. Top 10 per cent share divided by bottom 40 per cent share. Built on the observation that the middle 50 per cent's share is remarkably stable across countries and over time, so the action is at the two ends — which the ratio isolates directly.

Percentile ratios. The 90th percentile divided by the 10th; or 90/50 and 50/10 separately. The most legible measures in existence — anyone can understand "the person near the top has six times the income of the person near the bottom" — and splitting them shows where the change happened, which a single number never can.

The Theil index. Its distinctive property is decomposability: total inequality splits into a between-group component and a within-group component. This is what lets you say how much of a country's inequality is between regions or ethnic groups and how much is within them — which is the vertical/horizontal distinction from 8.1.1, made quantitative, and it is frequently the most interesting result available.

And poverty measures, which answer a different question entirely and are covered in 8.6.

The practical rule: report the Gini for comparability, a top share, a percentile ratio, and — where groups matter — a decomposition. A claim resting on one measure is a claim about that measure.

Where the numbers come from

Three sources, three different sets of blindness.

Household surveys. Representative samples, detailed information on composition, sources and circumstances. Their weakness is at the top and it is severe. Very rich households respond at lower rates; those who do respond under-report capital income systematically; and public datasets are top-coded, capping the highest values to protect anonymity (see 7.2.2). A survey therefore cannot measure the concentration at the top, which is where the change has been.

Tax records. Administrative, covering the whole taxed population, available for a century in some countries, and capable of measuring the top precisely. The modern literature on long-run inequality exists because researchers reconstructed top income shares from tax data — an example of 7.4.4's lesson producing a research revolution.

Their weaknesses are equally specific. They cover only what is declared, missing informal and untaxed income — which matters most at the bottom in poor countries and at the top everywhere. The definition of income changes when tax law changes, so a "trend" can be a legislative history: a reform that shifts income from corporate to personal declaration raises measured top shares with no change in anyone's resources.

National accounts. The totals for the whole economy, consistent over time, with no distribution at all.

And the reconciliation project — distributional national accounts — attempts to allocate the entire national income to individuals, so that the parts sum to the whole and no income goes missing. This is the most ambitious current effort and it forces every previously invisible assumption into the open: how to allocate undistributed corporate profits, imputed rents, public spending and pension accruals.

Which is where the honest part of this lesson lives.

The magnitude is contested, and you should know that rather than be surprised by it.

The direction is not seriously disputed. Top income shares in the United States and several other rich countries rose substantially from around 1980. That is agreed.

How much is disputed, and by serious people using the same tax data. Different research teams reach materially different estimates of the level and rise of the American top 1 per cent's share of income, and the differences come from stateable methodological choices: how to treat income that is never taxed (employer-provided health insurance, retirement accumulations, imputed rent), how to allocate government transfers, how to handle underreported business income, and how to treat the shift of business income between corporate and personal tax forms after tax reforms.

The same is true of wealth. The main modern approach infers wealth from the income it generates — capitalisation, dividing observed capital income by an assumed rate of return. It is powerful and it is sensitive to that assumption: if the very rich earn systematically higher returns than the merely rich, the method understates concentration; if lower, it overstates it. Critics using differentiated return assumptions have produced substantially lower estimates of top wealth shares, and the argument is ongoing.

How to hold this properly, which is 7.9.1 in operation.

Do not conclude that "nobody knows" or that the figures are arbitrary. The direction is robust across methods, and so is the international pattern — countries with similar productivity have very different inequality, which is itself a decisive finding against any account that treats the distribution as technologically determined.

And do not quote a precise figure as settled. "The top 1 per cent's share doubled" is a claim whose magnitude depends on choices that are visible, defensible and disputed. The honest form is: rose substantially, with estimates of the size differing by method, and here is what the difference turns on.

Global inequality: three questions that are constantly confused.

There are three distinct things called global inequality, and they have moved in different directions.

Between countries, counting each country once. Take every country's average income and measure the spread, treating Luxembourg and India as one observation each. Roughly flat or rising over recent decades.

Between countries, weighting by population. The same, but each country counts in proportion to its people. This has fallen sharply since around 1990, driven overwhelmingly by rapid growth in China and, later, India — that is, by the fact that the two largest populations were poor and grew fast.

Between all individuals in the world, ignoring borders. The most comprehensive concept, requiring distributional data from every country. It has fallen since around 2000, again driven largely by Asian growth, and it remains at a level far above any national distribution.

And the composition of the change matters as much as the direction. The best-known summary — a chart showing large gains for the global middle (largely Asian), weak gains for the lower-middle of rich countries, and large gains at the very top — has been contested on technical grounds, particularly over changes in which countries appear in the data across the period. The broad pattern survives; the sharpest version of the popular reading does not.

Two further complications that change conclusions. Converting incomes across countries requires purchasing power parity adjustment rather than market exchange rates, and PPP estimates are revised periodically, sometimes moving global poverty and inequality figures substantially with no change in anyone's circumstances. And within-country inequality has risen in many of the countries whose growth reduced between-country inequality.

So the honest sentence is: global inequality between people has fallen, driven by Asian growth; inequality within many countries has risen; and which of these you mention determines what your audience concludes.

Because the definitional choices are where the argument is actually taking place, and they are almost never stated.

Six questions for any inequality claim, and they take a minute.

Income or wealth? Which income — market, gross, disposable, or adjusted for services? What unit — individual or household, and equivalised how? What measure — Gini, top share, ratio, decomposition? What source — survey (blind at the top), tax records (blind to the undeclared), or a reconciliation? And between whom — individuals, households, groups, countries, or all people on earth?

Change any one and the answer can change. Change three and you can produce nearly any story you like from the same underlying reality, honestly, without a single false statement.

Which is not a reason for cynicism. It is a reason to ask the six questions, and to notice that a report which answers them in its first two pages is telling you it expects to be checked — and one that does not is telling you something else (see 7.9.1).

And the finding that survives every definitional choice is the one to hold on to. Countries at similar levels of productivity and technology have markedly different distributions, and the differences track institutions, bargaining arrangements, tax and transfer systems and public services. Whatever measure you use, the distribution is not a fact of nature. That is the central empirical result of this whole field, and it is why the rest of Part 8 is worth reading.

Two honest reports on the same country can disagree, because six decisions each move the answer.

Income is a flow, wealth a stock, and wealth is always far more concentrated — typical income Ginis of 0.25–0.50 against wealth Ginis of 0.6–0.9, because wealth compounds, earns returns, is inherited, and can be negative.

Four income stages, each less unequal: market, gross (plus cash transfers), disposable (minus direct taxes) — the international standard — and adjusted (plus in-kind services). Comparing across stages is a category error and it happens constantly.

The household is the standard unit and it assumes pooling, which the evidence on intra-household allocation contradicts — making all inequality within households zero by construction, disproportionately concealing inequality between women and men. Equivalence scales are a judgement. And annual inequality exceeds lifetime inequality, though most of it is persistent rather than transitory.

When Lorenz curves cross, different measures rank the same two distributions differently — so choosing a measure is choosing what you care about. The Gini is comparable and least sensitive at the extremes; top shares are transparent and blind below the threshold; the Palma isolates the two ends; percentile ratios are the most legible and can be split to locate the change; and the Theil decomposes into between-group and within-group — which quantifies the horizontal/vertical distinction.

Surveys are blind at the top; tax records are blind to the undeclared and change when tax law changes; national accounts have no distribution; and distributional national accounts try to reconcile all three.

The direction of the rise is not disputed; the magnitude is, by serious researchers using the same data, over the treatment of untaxed income, transfers, underreported business income, and shifts between corporate and personal declaration — and, for wealth, over the rate-of-return assumption in the capitalisation method. The honest form of the claim states the direction and attributes the magnitude.

Three global concepts move differently: between countries unweighted (flat or rising), population-weighted (falling sharply, driven by China and India), and between all individuals (falling since about 2000). PPP revisions move the figures without anyone's circumstances changing.

And the finding that survives all of it: countries with similar technology have very different distributions. The distribution is not a fact of nature.

Flow / stock — income over a period; wealth at a moment.

Market / gross / disposable / adjusted disposable income — before transfers; plus cash transfers; minus direct taxes; plus in-kind services.

Equivalisation — adjusting household income for size and composition.

Intra-household inequality — unequal allocation within a household, set to zero by household-level measurement.

Lorenz curve — cumulative income share against cumulative population share; the diagonal is equality.

Gini coefficient — the area between the diagonal and the Lorenz curve; least sensitive at the extremes.

Lorenz crossing — when two curves intersect, measures can rank the distributions oppositely.

Top share / Palma ratio / percentile ratio / Theil index — the concentration at the top; the two ends against each other; legible spread that can be split; and the decomposable measure.

Top-coding — capping recorded values, which makes surveys blind at the top.

Distributional national accounts — allocating all national income to individuals so the parts sum to the whole.

Capitalisation method — inferring wealth from the capital income it generates; sensitive to assumed returns.

Purchasing power parity — cross-country price adjustment; revisions move global figures.

Concepts 1, 2 and 3 of global inequality — between countries unweighted, population-weighted, and between all individuals.

One — find the definition. Take any inequality figure quoted in your country's press and answer the six questions. Most reports answer two of them.

Two — compare the stages. Look up your country's Gini for market income and for disposable income. The gap is the measured effect of the tax and transfer system, and it is usually much larger than people expect.

Three — do the ratio by hand. Find the 90th and 10th percentile of household income where you live. Then ask which of the two moved over the last decade — the single number would not have told you.

Four — check a wealth claim. Take any statement about wealth concentration and find out whether it came from a survey, from tax records, or from capitalisation. Then find one criticism of that method.

Five — state the global sentence properly. In two sentences, describe what has happened to inequality between countries and within them. Then notice how differently the same facts read depending on which you put first.