Measures of Income Inequality

Why This Matters

Income inequality isn't just a number—it's the lens through which economists evaluate whether markets are distributing resources fairly and whether government interventions are actually working. You're being tested on your ability 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. The measures in this guide connect directly to welfare economics, redistribution policy, and the fundamental 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 allow you to incorporate value judgments about inequality. Know which measure answers which question, and you'll be ready for any FRQ 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 summarize inequality by considering every point along the distribution, not just specific segments.

Gini Coefficient

• Ranges from 0 to 1—where 0 represents perfect equality (everyone earns the same) and 1 represents 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 the line; mathematically expressed as $G = \frac{A}{A + B}$
• Most widely used international comparison tool—a coefficient around 0.25-0.30 indicates low inequality (Scandinavian countries), while 0.50+ signals high inequality (parts of Latin America and Africa)

Lorenz Curve

• Graphical representation plotting 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 in the distribution
• Visual diagnostic tool that reveals where inequality occurs in the distribution, not just how much exists overall

Theil Index

• Decomposable into within-group and between-group components—uniquely useful for identifying sources of inequality (e.g., regional vs. demographic factors)
• Ranges from 0 to infinity, with 0 indicating perfect equality; based on entropy concepts from information theory
• Particularly valuable for multi-level analysis—if an FRQ asks about inequality across states or demographic groups, the Theil index lets you separate those effects

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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 top 10% income share to bottom 40% income share—designed to focus on the tails of the distribution where most variation occurs
• Based on the empirical finding that the middle 50% of earners consistently capture about half of national income across countries
• More sensitive to extreme inequality than the Gini; a ratio of 1 means the top 10% earns the same as the bottom 40%, while ratios above 2 indicate significant concentration

20:20 Ratio

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

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

• Compares income at specific percentile cutoffs—the 90/10 ratio divides 90th percentile income by 10th percentile income
• Flexible diagnostic tool—you can construct 90/50, 50/10, or other ratios to isolate inequality in different parts of the distribution
• Reveals distribution shape—if 90/50 is rising faster than 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 tracking changes over time.

Income Quintiles and Deciles

• Quintiles divide population into five equal groups (20% each); deciles divide into ten (10% each), ranked by income from lowest to highest
• Foundation for share analysis—allows statements like "the bottom quintile holds 3% of national income while the top quintile holds 51%"
• Tracks distributional changes over time—comparing quintile shares across decades reveals whether growth is broadly shared or concentrated

Income Share Ratios (Top 1% or 10%)

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

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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 particularly useful for policy evaluation.

Atkinson Index

• Incorporates an "inequality aversion" parameter (ε)—higher values of ε 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 $\varepsilon$ reflects society's inequality aversion
• Directly policy-relevant—tells policymakers how much income could be "wasted" while still achieving the same social welfare if distributed equally

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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 population below a defined poverty line—can be absolute (fixed threshold like $2.15/day) or relative (e.g., 50% of median income)
• Critical for evaluating social safety nets—directly measures whether transfer programs are reaching those in need
• Doesn't capture depth or severity—two countries can have the same poverty rate even if one has people barely below the line and another has people far below it

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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.