# Who is the fairest one of all? Part I

November 25, 2019
David Williams

BCBC recently released its inaugural British Columbia Prosperity Index. One of the twelve indicators that make up the index is income inequality. B.C. ranked as having the 8th most balanced income distribution among 21 jurisdictions in 2017. Let’s explore this a little.

## How to measure the income distribution using the Gini coefficient

The Gini coefficient is a widely-used measure of income dispersion, pioneered by the Italian statistician Corrado Gini in 1912.
It ranges between zero and one (Figure 1). A coefficient of zero indicates a perfectly-balanced income distribution where all households have the same income. A coefficient of one indicates a perfectly-concentrated distribution where one household has all the income. The coefficient can be calculated across households based on their market income (before taxes and transfers) or disposable income (after taxes and transfers).

Note that the Gini coefficient says nothing about absolute income levels. A high-income country can have the same Gini coefficient as a low-income country. The Gini coefficient only measures the dispersion of income across a population.

### Figure 1: Depicting the Gini coefficient

Source: Juhi (2019).

## B.C. has the second most even distribution of market incomes among the Canadian provinces

After Alberta, B.C. has the second most even distribution of market income before taxes and transfers, according to Statistics Canada data (Figure 2). Alberta (0.399) and B.C. (0.411) have considerably lower Gini coefficients than the Canadian average (0.439) and Ontario (0.452), indicating that market incomes are more even in Western Canada.

## B.C. has the sixth most even distribution of disposable incomes among the Canadian provinces

Statistics Canada also calculates the Gini coefficient for disposable income after taxes and transfers, which includes the impact of fiscal equalization across provinces. B.C.’s Gini coefficient with respect to disposable income is 0.302 (Figure 3). This again indicates a more balanced income distribution compared to the Canadian average (0.309) and Ontario (0.322). B.C. has the sixth most even distribution of disposable income after New Brunswick, Prince Edward Island, Quebec, Nova Scotia and Alberta. 

## Conclusion

The evidence suggests that B.C. does a relatively good job in sharing the fruits (i.e. income) flowing from economic prosperity. B.C. has the second most even distribution of market incomes and the sixth most even distribution of disposable incomes among the Canadian provinces. In a future blog, we will explore how income dispersion has changed over time in Canada and B.C.

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 The Gini coefficient is based on the relationship between a country’s cumulative proportion of income and the cumulative proportion of the population earning it. Graphically, the fraction of income is plotted on the vertical axis and the fraction of the population is plotted on the horizontal axis (Figure 1). A 45-degree line plots the “line of equality” for a hypothetical population with perfectly-distributed income. For example, on the line of equality, 30% of the country’s income would be earned by the bottom 30% of the population. Another curve, the Lorenz Curve (shown in red in Figure 1), plots the actual proportion of a country’s total income that is cumulatively earned by the bottom x% of the population.

The Gini coefficient is defined as the area between the Lorenz Curve and the line of equality (shaded yellow), expressed as a proportion of the total area under the line of equality. If the Lorenz curve is equal to the line of equality, the Gini coefficient equals zero (see 1 in Figure 1). If the area between the Lorenz curve and the line of equality takes up all the area under the line of equality, the Gini coefficient equals one (see 4 in Figure 1). The Gini coefficient is therefore a comprehensive statistic about the extent of income inequality.

 The Gini coefficient cited in the British Columbia Prosperity Index is based on disposable income. Statistics Canada data is adjusted slightly to be comparable with OECD data for other jurisdictions.

 Note that income dispersion data does not address the impact of excessive house price inflation in B.C.’s major cities since the mid-2000s on the distribution of wealth and the cost of and access to shelter.

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