Measuring inequality

An inequality measure compresses a distribution of wages or incomes into one number. The Gini coefficient is the area between the Lorenz curve and the line of perfect equality as a share of the whole area under that line; it runs from 0 (perfect equality) to 1. Percentile ratios such as the 90-10 wage gap compare workers at two points of the distribution. The Gini summarizes the whole distribution but cannot say where inequality lies; percentile ratios can.

Why wages differ

A wage distribution gives the number or share of workers at each wage. The left tail holds the lowest-paid workers and the right tail the highest-paid. Workers are spread along it by three forces:

1. Differences in jobs. Unpleasant or risky jobs pay compensating differentials, and the return to a given skill differs across occupations and labour markets.
2. Differences in human capital. Workers invest different amounts in schooling and on-the-job training. Age matters: young workers are still investing, older workers collect the returns.
3. Differences in ability. Workers differ in talent and in skills formed in childhood. The neighbourhood, school, classmates and community organizations a child grows up with shape the human capital the child acquires; economists call these resources social capital.

The forces compound. Workers with more ability earn a higher return on each year of schooling or training, so they invest more, and they are paid more both for their ability and for their larger stock of human capital. This stretches the top of the distribution and produces positive skewness: a long right tail.

Spread of log earnings (σ)

0.60

Median

$1,200

Mean

$1,437

Mean ÷ median

1.20

Open in Graph Lab

Figure 1. A log-normal distribution of weekly earnings with a median of $1,200. The long right tail pulls the mean ($1,437) above the median, and a wider spread of log earnings raises the mean further while the median stays fixed.

In a right-skewed distribution the mean exceeds the median, because the mean counts every dollar earned in the tail. The median is the wage of the middle worker and is the better guide to typical pay. In 2025 the average hourly wage of Canadian employees was $36.40 and the median $30.77; in Alberta the figures were $37.35 and $32.00.¹

The Lorenz curve

The Lorenz curve ranks households from poorest to richest and plots the cumulative share of households (horizontal axis) against the cumulative share of total income they receive (vertical axis).

• Under perfect equality, the poorest 20 percent receive 20 percent of income, the poorest 40 percent receive 40 percent, and so on: the curve is the 45-degree line.
• Under inequality the poorest households receive less than their population share, so the curve sags below the diagonal. If the poorest 40 percent receive 15 percent of income, the curve passes through (40, 15), 25 points below the line of equality.
• The more unequal the distribution, the further the curve bows from the diagonal. It always runs from (0, 0) to (100, 100).

Curvature of the Lorenz curve (k)

2.0

Gini = A ÷ (A + B)

0.33

Income share of the poorest 20%

4.0%

Income share of the richest 20%

36.0%

Open in Graph Lab

Figure 2. The Lorenz curve plots the cumulative share of income against the cumulative share of households, poorest first. The Gini coefficient is area A divided by A + B; for this curve, on which the poorest fifth receives 4 percent of income, it is 0.33.

The Gini coefficient

The gap between the Lorenz curve and the diagonal differs at every percentile; the Gini adds it up as an area. With $A$ the area between the line of equality and the Lorenz curve and $B$ the area under the Lorenz curve,

$$G = \frac{A}{A + B}.$$

With both axes measured as shares from 0 to 1, the triangle under the diagonal has area $A + B = \tfrac{1}{2}$, so

$$G = 2A = 1 - 2B.$$

$G = 0$ when everyone has the same income ($A = 0$). $G$ approaches 1 when one household has everything and the Lorenz curve runs along the horizontal axis until the last household. With quintile data, the Lorenz curve is five straight segments and $B$ is the sum of five trapezoids:

$$B = \sum_{k=1}^{5} 0.2 \times \frac{L_{k-1} + L_k}{2},$$

where $L_k$ is the cumulative income share of the poorest $k$ fifths, $L_0 = 0$ and $L_5 = 1$. This slightly understates the true Gini because it ignores inequality within each fifth.

Key idea

The Gini coefficient is the area between the line of perfect equality and the Lorenz curve divided by the whole area under the line of equality: $G = A/(A + B)$, from 0 (perfect equality) to 1 (one household has everything).

Percentile ratios

A percentile ratio divides the wage at one percentile by the wage at another:

• the 90-10 wage gap, $w_{90}/w_{10}$, measures the spread across most of the distribution;
• the 50-10 wage gap, $w_{50}/w_{10}$, measures how far the middle sits above the bottom;
• the 90-50 wage gap, $w_{90}/w_{50}$, does the same for the top half.

Because $\frac{w_{90}}{w_{10}} = \frac{w_{90}}{w_{50}} \times \frac{w_{50}}{w_{10}}$, the 90-10 gap splits into its two halves.

Percentile ratios are often preferred to the Gini because they locate inequality. Moving 1 percentage point of income share from the poorest fifth to the richest raises a quintile-based Gini by 0.016; so does moving 4 points from the fourth fifth to the richest. The first squeezes the poor and the second the upper middle class, but the Gini cannot tell them apart. Two Lorenz curves can even cross and enclose the same area.

Inequality in both societies (k)

2.0

Gini in both societies

0.33

90-10 ratio in X

9.0

90-10 ratio in Y

3.0

Poorest 20%'s share in X

4.0%

Poorest 20%'s share in Y

10.6%

Richest 20%'s share in X

36.0%

Richest 20%'s share in Y

44.7%

Open in Graph Lab

Figure 3. Societies X and Y have the same Gini coefficient. X is unequal at the bottom, with 4 percent of income going to its poorest fifth; Y is unequal at the top, with 45 percent going to its richest fifth. The 90-10 ratio is 9 in X and 3 in Y.

Percentile ratios have the opposite weakness: they ignore everything outside the two percentiles. Most of Y’s inequality lies above the 90th percentile, so its 90-10 ratio is modest, and a rise in the incomes of the top 1 percent leaves the 90-10 gap unchanged.

Worked example

The poorest to richest fifths of households in a province receive 5, 10, 15, 25 and 45 percent of income.

1. Cumulative shares: $L_1 = 0.05$, $L_2 = 0.15$, $L_3 = 0.30$, $L_4 = 0.55$, $L_5 = 1.00$, with $L_0 = 0$.

2. Trapezoids, each 0.2 wide: $0.2 \times \frac{0 + 0.05}{2} = 0.005$, $0.2 \times \frac{0.05 + 0.15}{2} = 0.020$, $0.2 \times \frac{0.15 + 0.30}{2} = 0.045$, $0.2 \times \frac{0.30 + 0.55}{2} = 0.085$ and $0.2 \times \frac{0.55 + 1.00}{2} = 0.155$.

3. Area under the Lorenz curve: $B = 0.005 + 0.020 + 0.045 + 0.085 + 0.155 = 0.31$.

4. Area between the curve and the diagonal: $A = 0.5 - 0.31 = 0.19$.

5. Gini coefficient: $G = 0.19 / 0.5 = 0.38$, or $1 - 2(0.31) = 0.38$.

6. Percentile ratios. If the 10th percentile hourly wage is $17, the median $29 and the 90th percentile $51, the 90-10 gap is $51/17 = 3.0$, the 50-10 gap $29/17 \approx 1.71$ and the 90-50 gap $51/29 \approx 1.76$; check: $1.76 \times 1.71 \approx 3.0$.

Exercise: a transfer from the fourth fifth to the top

Move 5 points of income from the fourth fifth to the richest: shares 5, 10, 15, 20 and 50 percent, cumulative shares 0.05, 0.15, 0.30, 0.50 and 1.00. The last two trapezoids become $0.2 \times \frac{0.30 + 0.50}{2} = 0.080$ and $0.2 \times \frac{0.50 + 1.00}{2} = 0.150$, so $B = 0.30$ and $G = 1 - 2(0.30) = 0.40$. The poorest fifth’s share is unchanged, yet the Gini rises by 0.02. Moving the 5 points from the poorest fifth to the richest instead (shares 0, 10, 15, 25, 50) raises the Gini to 0.46.

Evidence

Canada over time

Statistics Canada publishes Gini coefficients for three income concepts. Market income is income from work and investments. Total income adds government transfers such as Employment Insurance, the Canada Child Benefit and public pensions. After-tax income subtracts income taxes.

Income inequality in Canada: Gini coefficients

Adjusted market, total and after-tax household income

• Market income
• Total income
• After-tax income

Gini coefficients of Canadian household income, adjusted for household size. Market-income inequality rose from 0.365 in 1979 to about 0.44 by the late 1990s and has stayed near that level; transfers and taxes lower it by about 0.13. Survey methods changed several times (see the notes under the chart).Source: Statistics Canada, Table 11-10-0134-01, Gini coefficients of adjusted market, total and after-tax income. Retrieved 2026-10-23.

Show the data and notes

Household income divided by the square root of household size; 0 = everyone has the same income, 1 = one person has it all. Market income is before government transfers and taxes, total income adds transfers, after-tax income subtracts income taxes. Survey sources change over time: Survey of Consumer Finances (1976–1992), SCF and Survey of Labour and Income Dynamics (1993–1997), SLID (1998–2011), Canadian Income Survey (2012 on); CIS methods changed from 2021 and 2018–2023 were revised with the 2021 Census. Household income counts the income of members aged 15 and over, except 16 and over in SLID years and CIS years before 2022. Canada excludes the territories before 2018.

Period	Market income	Total income	After-tax income
1976	0.384	0.330	0.300
1977	0.368	0.315	0.286
1978	0.375	0.320	0.291
1979	0.365	0.315	0.286
1980	0.370	0.313	0.286
1981	0.369	0.313	0.285
1982	0.388	0.320	0.288
1983	0.403	0.329	0.296
1984	0.401	0.326	0.293
1985	0.395	0.322	0.290
1986	0.395	0.322	0.290
1987	0.392	0.321	0.287
1988	0.391	0.318	0.282
1989	0.388	0.318	0.281
1990	0.403	0.326	0.286
1991	0.422	0.334	0.292
1992	0.429	0.334	0.291
1993	0.429	0.329	0.289
1994	0.432	0.333	0.290
1995	0.430	0.336	0.293
1996	0.439	0.346	0.301
1997	0.438	0.348	0.304
1998	0.446	0.356	0.311
1999	0.437	0.356	0.310
2000	0.439	0.362	0.317
2001	0.440	0.360	0.318
2002	0.439	0.360	0.318
2003	0.437	0.358	0.316
2004	0.442	0.365	0.322
2005	0.435	0.358	0.317
2006	0.433	0.356	0.316
2007	0.434	0.358	0.316
2008	0.430	0.355	0.314
2009	0.438	0.355	0.315
2010	0.441	0.356	0.315
2011	0.433	0.352	0.311
2012	0.432	0.354	0.315
2013	0.435	0.357	0.317
2014	0.426	0.351	0.310
2015	0.435	0.354	0.314
2016	0.431	0.347	0.306
2017	0.438	0.352	0.309
2018	0.429	0.345	0.304
2019	0.421	0.338	0.299
2020	0.440	0.322	0.281
2021	0.433	0.333	0.289
2022	0.433	0.348	0.302
2023	0.430	0.346	0.301
2024	0.436	0.351	0.305

• Market-income inequality rose in two steps, around the recessions of the early 1980s and early 1990s, from 0.365 in 1979 to 0.446 in 1998. It has stayed between about 0.42 and 0.44 since and was 0.436 in 2024.
• Transfers and taxes reduce inequality sharply. In 2024 they lowered the Gini from 0.436 to 0.305; transfers did most of it, since the total-income Gini was 0.351.
• After-tax inequality rose much less, from 0.289 in 1993 to 0.318 in 2001, about 10 percent. On an axis starting near 0.28 that rise looks dramatic; on an axis starting at zero it is modest. In 2020, market-income inequality jumped as the pandemic cut earnings, while after-tax inequality fell to 0.281, matching its 1989 low, because transfers rose so sharply.

Percentile ratios show where wage inequality moved. Among Canadian full-time employees, the 50-10 ratio of gross earnings fell from 2.00 in 1997 to 1.75 in 2024 while the 90-50 ratio rose from 1.76 to 1.89.² The bottom half compressed as the top half spread out, two movements a single Gini would average away. Fortin and Lemieux attribute the faster wage growth at the bottom after 2005 mainly to minimum wage increases, and find that the resource boom compressed wages in Alberta, Saskatchewan and Newfoundland and Labrador by raising the pay of less-educated and younger workers most.³

Across countries

Country	Gini, disposable income	Gini, market income	90-10 ratio, full-time earnings, 2024
Norway	0.26 (2023)	0.43	2.30
Denmark	0.28 (2022)	0.44	2.61
Finland	0.28 (2024)	0.52	2.44
France	0.30 (2023)	0.52	2.82
Canada	0.31 (2023)	0.43	3.31
Germany	0.31 (2023)	0.50	2.89
United Kingdom	0.37 (2023)	0.52	2.95
United States	0.39 (2023)	0.51	4.79

Market-income Ginis are for the same year as the disposable-income Gini. Sources: OECD Income Distribution Database and OECD earnings data.⁴²

Canada sits in the middle of rich countries on disposable income: more equal than the United States and the United Kingdom, less equal than the Nordic countries. Before taxes and transfers the ranking changes: Canada and Norway have the lowest market-income Ginis in the table, and the United States is close to France, Germany and the United Kingdom. Much of the gap between countries in disposable-income inequality therefore comes from taxes and transfers. Market-income Ginis are hard to compare across countries, though, because public pensions count as transfers, which raises measured market inequality where pensions are generous and retirees numerous. Wage inequality among full-time workers is highest in the United States, where the 90th percentile earns 4.8 times the 10th, against 3.3 times in Canada.

Common mistakes

Traps on exams

• Reading the Lorenz curve backwards. The further the curve bows below the diagonal, the more unequal the distribution; a curve on the diagonal is perfect equality.
• Treating the Gini as a full description. Identical Ginis can come from very different distributions. Use percentile ratios to say which part of the distribution changed.
• Calling the mean the typical wage. In a right-skewed distribution the mean exceeds the median; the median describes the typical worker.
• Mixing income concepts. Market-income and after-tax Ginis measure different things; compare like with like across years and countries.

On the exam

For “list two measures of inequality”, give the Gini coefficient with its Lorenz-curve definition, $A/(A+B)$, and a percentile ratio such as the 90-10 or 50-10 wage gap, then add why the ratios can be preferred: they show which part of the distribution moved.

Check yourself

1.

Country A's Lorenz curve lies below Country B's at every point. Which statement is correct?

1Income is more unequal in A, and A has the higher Gini coefficient2Income is more unequal in B, because B's Lorenz curve is higher3The two countries have the same Gini coefficient, because both curves start at (0, 0) and end at (100, 100)4A has more households, so its curve sags further

Check answer

2.

Why might a researcher prefer percentile ratios such as the 90-10 and 50-10 wage gaps to the Gini coefficient?

1They show which part of the distribution changed, whereas very different shifts of income can move the Gini by the same amount2They include every worker's wage, whereas the Gini ignores the tails3They are always larger than the Gini, so changes are easier to see4They are the only measures that adjust for household size

Check answer

3.

Societies X and Y have the same Gini coefficient, but their Lorenz curves cross. What can you conclude?

1Inequality is located in different parts of the two distributions, so percentile ratios such as the 90-10 can differ sharply2The two societies have identical income distributions3One of the Lorenz curves must have been drawn incorrectly, because curves with the same Gini cannot cross4The society whose curve is lower at the bottom must have the higher 90-10 ratio and the higher Gini

Check answer

Practise more questions on this topic

Sources

1. Statistics Canada, Table 14-10-0064-01, Employee wages by industry, annual. All employees aged 15 and over, full- and part-time, all industries, 2025. ↩

2. OECD, Decile ratios of gross earnings, gross earnings of full-time dependent employees, retrieved 23 October 2026. ↩ ↩²

3. Fortin, N. M. and Lemieux, T. (2015). Changes in wage inequality in Canada: An interprovincial perspective. Canadian Journal of Economics, 48(2), 682 to 713. ↩

4. OECD, Income Distribution Database, Gini coefficients of disposable and market household income, total population, current income definition, retrieved 23 October 2026. ↩