Measures of Income Inequality

Why This Matters

Income inequality measures are the tools economists use to evaluate whether markets distribute resources fairly and whether government interventions actually work. You need to understand why different measures exist, what each one captures (and misses), and how policymakers use them to design tax systems, transfer programs, and social safety nets. These measures connect directly to welfare economics, redistribution policy, and the trade-offs between efficiency and equity.

Don't fall into the trap of memorizing formulas without understanding what they reveal. Each measure emphasizes different parts of the income distribution. Some focus on the middle, others on the extremes, and still others let you incorporate value judgments about inequality. Knowing which measure answers which question will prepare you for any prompt that asks you to evaluate policy effectiveness or compare inequality across contexts.

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Comprehensive Distribution Measures

These measures capture the entire income distribution in a single number or visual, making them ideal for broad comparisons across countries or time periods. They consider every point along the distribution, not just specific segments.

Gini Coefficient

The Gini coefficient is the most widely used single-number summary of inequality.

• Ranges from 0 to 1, where 0 means perfect equality (everyone earns the same) and 1 means perfect inequality (one person earns everything)
• Derived from the Lorenz curve as the ratio of the area between the curve and the 45-degree line to the total area under that line: $G = \frac{A}{A + B}$
• A coefficient around 0.25–0.30 indicates low inequality (typical of Scandinavian countries), while 0.50+ signals high inequality (common in parts of Latin America and Sub-Saharan Africa)

One limitation: the Gini is most sensitive to changes around the middle of the distribution. Two very different-looking distributions can produce the same Gini value if their Lorenz curves cross.

Lorenz Curve

The Lorenz curve is the visual foundation behind the Gini coefficient.

• It plots the cumulative share of income (y-axis) against the cumulative share of population (x-axis), ranked from poorest to richest
• The 45-degree line represents perfect equality. The further the actual curve bows below this line, the greater the inequality
• Unlike a single number, the Lorenz curve reveals where in the distribution inequality is concentrated. Two countries with the same Gini can have Lorenz curves that cross, meaning inequality is worse at the bottom in one country and worse at the top in another

Theil Index

The Theil index stands out because of its decomposability.

• Uniquely decomposable into within-group and between-group components, which lets you identify sources of inequality (e.g., how much comes from regional differences vs. demographic factors)
• Ranges from 0 to infinity, with 0 indicating perfect equality. It's rooted in entropy concepts from information theory
• Particularly valuable for multi-level analysis. If a question asks about inequality across states or demographic groups, the Theil index lets you separate those effects cleanly

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Ratio-Based Measures

These measures compare specific points in the distribution rather than summarizing the whole thing. They're intuitive and easy to communicate but sacrifice information about what happens between the comparison points.

Palma Ratio

• Compares the top 10% income share to the bottom 40% income share, focusing on the tails of the distribution where most variation across countries occurs
• Built on the empirical finding (by economist José Gabriel Palma) that the middle 50% of earners consistently capture roughly half of national income across countries, so the real action is in the tails
• More sensitive to extreme inequality than the Gini. A ratio of 1 means the top 10% earns the same total as the bottom 40%; ratios above 2 indicate significant concentration at the top

20:20 Ratio

• Compares the income of the richest 20% to the poorest 20%, giving a straightforward measure of the gap between top and bottom quintiles
• Easy to interpret and communicate to non-economists, making it useful in policy debates about social equity
• Limited scope: it ignores what happens in the middle 60% of the distribution, potentially missing important inequality dynamics

Percentile Ratios (e.g., 90/10 Ratio)

Percentile ratios are flexible tools for diagnosing where in the distribution inequality is changing.

• The 90/10 ratio divides income at the 90th percentile by income at the 10th percentile
• You can construct different ratios to isolate different parts of the distribution. The 90/50 ratio captures upper-half inequality, while the 50/10 ratio captures lower-half inequality
• This flexibility reveals the shape of inequality. If the 90/50 ratio is rising faster than the 50/10, inequality is being driven by gains at the top rather than losses at the bottom

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Population Segment Analysis

These measures divide the population into groups to examine how income is distributed across segments. They're essential for understanding who holds what share of national income and for tracking changes over time.

Income Quintiles and Deciles

• Quintiles divide the population into five equal groups (20% each); deciles divide into ten (10% each), ranked by income from lowest to highest
• They're the foundation for share analysis, enabling statements like "the bottom quintile holds 3% of national income while the top quintile holds 51%"
• Comparing quintile shares across decades reveals whether economic growth is broadly shared or concentrated at the top

Income Share Ratios (Top 1% or 10%)

• Measures concentration at the very top by calculating the share of total national income captured by the highest earners
• Central to debates about wealth concentration. In the U.S., the top 1% income share rose from about 10% in 1980 to over 20% by 2020
• Top shares often rise when capital gains and investment income grow faster than wages, connecting this measure to the broader capital vs. labor income debate

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Welfare-Weighted Measures

These measures incorporate normative judgments about how much inequality matters. They allow analysts to weight inequality differently based on social preferences, making them especially useful for policy evaluation.

Atkinson Index

The Atkinson index is distinctive because it makes value judgments explicit rather than hiding them.

• It incorporates an inequality aversion parameter $\varepsilon$. Higher values of $\varepsilon$ place more weight on inequality at the bottom of the distribution
• Ranges from 0 (perfect equality) to 1, calculated as:

$A = 1 - \left[\frac{1}{n}\sum_{i=1}^{n}\left(\frac{y_i}{\bar{y}}\right)^{1-\varepsilon}\right]^{\frac{1}{1-\varepsilon}}$

where $y_i$ is individual income, $\bar{y}$ is mean income, and $\varepsilon$ reflects society's inequality aversion.

• Directly policy-relevant: the index value tells you the fraction of total income that could theoretically be "wasted" (lost to inefficiency) while still achieving the same level of social welfare, if income were distributed equally. An Atkinson value of 0.20 means society could give up 20% of total income and be equally well off under perfect equality.

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Poverty and Deprivation Measures

These measures focus specifically on the bottom of the distribution, capturing absolute or relative deprivation rather than overall inequality. They answer a different question: not "how unequal is society?" but "how many people lack adequate resources?"

Poverty Rate

• Percentage of the population below a defined poverty line. This can be absolute (a fixed threshold like the World Bank's $2.15/day) or relative (e.g., 50% of median income, common in OECD countries)
• Critical for evaluating social safety nets because it directly measures whether transfer programs reach those in need
• A key limitation: the poverty rate doesn't capture depth or severity. Two countries can have the same poverty rate even if one has people barely below the line and the other has people far below it. Measures like the poverty gap index address this by accounting for how far below the line people fall.

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Quick Reference Table

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Self-Check Questions

1. If a country's Gini coefficient remains constant but its top 1% income share increases significantly, what must be happening in the rest of the distribution? Which measures would capture this shift most effectively?

2. Compare the Palma ratio and the 20:20 ratio. Why might a policymaker prefer one over the other when evaluating the impact of a progressive tax reform?

3. An economist wants to analyze whether income inequality in a country is driven more by regional differences or by educational attainment gaps. Which measure should they use, and why?

4. Explain why two countries could have identical Gini coefficients but very different Atkinson index values. What does this reveal about the limitations of the Gini?

5. A government program successfully reduces the poverty rate from 15% to 10%, but the Gini coefficient increases from 0.35 to 0.38. Is this outcome contradictory? Construct a scenario that explains how both changes could occur simultaneously.