Intermediate Macroeconomics Questions, due on April 29, 3:00pm (UTC+8)

02MeasurementofEconomicInequality.docx

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Measurement of Economic Inequality

1. Economic inequality.

a) Definition

Economic inequality is the unequal distribution of an economic variable such as income, wealth, pay or opportunity between different individuals or groups in society.

b) Types of economic inequality

To determine the type of economic inequality, we need to fix:

· The economic variable of interest, e.g., income.

· The unit of analysis, e.g., province, and the reference group, e.g. Canada.

· Economic variable

The economic variable of interest gives rise to the nature of economic inequality:

Table 1

Economic Variable	Type of economic inequality
Income	Income inequality
Wealth	Wealth inequality
Wage	Wage inequality

· Unit of analysis and reference group

· Within-regional (income) inequality - differences in individual incomes within a region;

· Regional (income) inequality - differences in per capita income across regions.

2. Measuring regional inequality.

a) Creating an index

Income per capita is a measure of average standard of living in a country.

Low (high) levels of income per capita are indicative of low (high) standard of living. GDP per capita is commonly used as a measure of income per capita, where GDP is an abbreviation for Gross Domestic Product.

GDP per capita is measured in dollars (or other currency). To make comparisons across jurisdictions such as provinces, it is convenient to create an index, where for a benchmark country, e.g., Canada, a value of 100 is assigned. The GDP per capita of all each province is viewed as an index relative to Canada. For instance, a province with an index number of 120 has GDP per capita that is 1.2 higher than that of Canada.

Figure 1:

Source: Olfert (2016)

b) Snapshots of regional inequality.

· Comparison between the extremes

It is a comparison between the two countries with the highest and the lowest incomes.

Table 2

Year	1926	1933	2011
Max	120	145	127
Min	48	40	83
Ratio	2.50	3.63	1.53

· Key Insights

Canada’s regional inequality first increased around the 1930s and then declined. This type of pattern is known as the Kuznets Inverted U-shaped curve.

Regional inequality has first increased, then declined.

· Limitations

This approach of comparing only the extremes ignores the dynamics for 80 % of the provinces that lie within the range.

3. Distributional measures.

a) Examination of entire distributions

This approach entails the construction of the cumulative income shares (or the cumulative share of another socioeconomic variable) against the corresponding cumulative population shares.

This approach has more desirable properties (compared to the approach of taking a ratio of the extremes) as it provides a detailed presentation of any development gap. Furthermore, these distributions are comparable to one another if represented by Lorenz curves and Gini coefficients.

b) The Lorenz curve

A Lorenz curve is a graphical representation of income inequality by plotting what income share is being earned a share of the population.

Step 1: Order the population by increasing income.

Step 2: Determine what fraction of total income they earn (e.g., bottom 1% earns .2% of the total, etc.)

The Lorenz curve connects the points with coordinates:

· on the horizontal axis we put the rank in the population (by income, e.g., bottom 10%, bottom 20%, etc.)

· on the vertical axis we put the corresponding percentage of total income this group earns (e.g., bottom 10% earn 2% of total income, the bottom 90% earn 65% of total income, etc.)

Figure 2

Source: Radice (2009)

c) Properties of the Lorenz curve:

i) starts at (0,0), ends at (100,100);

ii) increasing (adding positive numbers);

iii) convex shape (increases at an increasing rate) because we ordered them in increasing income;

iv) two extreme scenarios:

· perfect equality: LC is the 45-degree line;

· perfect inequality: inverted L shape (0 at up to 100% and 1 at 100%).

v) if we have two LCs, line A is always above line B, then A corresponds to lower inequality.

For instance, Figure 3 indicates that income inequality in Canada increased from 1980 to 2011.

Figure 3

Source: Statistics Canada (2020)

· Limitations of the Lorenz curve

A key limitation of the Lorenz curve is that when two Lorenz curves cross, it is ambiguous which income distribution is more unequal.

d) The Gini coefficient.

· Definition

The Gini coefficient (GC) is a single number that aggregates the information from a Lorenz curve.

· Computation

in Figure 2 is the area above the LC and below the 45-degree line;

in Figure 2 is the entire area below the 45-line bounded by the axes.

Figure 4

The domain of GC is , where the extremes are interpreted as follows:

· => perfect equality

· => perfect inequality

Almost all countries have a GC ∈ [0.1, 0.6].

Rule of thumb classification:

=> close to perfect income inequality

=> low levels of income inequality

] => moderate levels of income inequality

=> high levels of income inequality

=> extremely high levels of inequality

e) Properties of the Gini Coefficient:

· anonymity – names of people don't matter, just incomes;

· population size independence – if clone a person into 2, GC remains the same;

· unit independence – change the units in which income is measured does not affect GC);

· the 'transfer principle' – holding all else constant, a transfer of a small amount of income from a richer person to a poorer person, GC declines.

4. Decomposition of income inequality in Canada.

a) Historical evolution of income inequality

· Time trends

A time trend is the ordered set of natural numbers, e.g., , that measures the time span between observations. The slope of a time-trend line represents the growth of a variable, e.g., Gini coefficient.

Figure 5

Source: IRPP (2016)

A time trend allows us:

· to detect the general relationship through the slope (positive vs. negative vs. flat),

· to detect whether the relationship is stable or exhibits variability,

· to detect the type of variability: a break in the time trend vs. cyclical variability.

A break in the time trend indicates an abrupt change in the slope at a certain point in time. However, the slope before and after the break in the time trend is relatively stable.

Cyclical variability in the Gini coefficient could be occurring due to fluctuations in the price of oil for a country dependent on the production of natural resources.

Time trends across countries (or provinces) could be used to compare countries with respect to:

· initial conditions, e.g., Gini coefficient in 1976. The initial conditions are captured by the differences in the vertical intercept at 1976 between two regions.

· relative increase in income inequality over tine. The region with a higher economic growth rate has a time trend with a steeper slope.

· Within-regional income inequality

Figure 6 indicates that the Gini coefficient increased in every province from 1985 to 2011. This implies that within-regional income inequality increased over the period.

Figure 6

Source: IRPP (2016)

· Distribution of income growth gains

Figure 4 indicates that the gains were enjoyed almost exclusively by the top 10 % of the population (the upper middle class and the rich). Those who gain the most are the top 0.01 % and 0.1 % of the population.

Figure 7

Source: IRPP (2016)

This type of unbalanced growth in income shares could have important implications on:

· Reducing the size of the middle class;

· Increasing poverty rates even when average income is growing.

Figure 8 indicates that the unbalanced growth across income groups led to a rapid increase in the income share of the top 1 % during the examined period.

Figure 8

Source: IRPP (2016)

· Functional income inequality

Functional aspects of income inequality refer to the source of income:

· Capital income;

· Labour income.

Who were the gainers?

Figure 9 reveals that the share of labour income declined from 1982 to 2008. This implies that the gains were overwhelmingly captured by capital income earners.

Figure 9

b) Key insights

Income inequality in Canada increased since 1980.

There were three driving forces behind this increase:

· Within-regional inequality increased in every province, while regional inequality decreased.

· The gains in income inequality were captured exclusively by the very top income brackets.

· The share of capital income at the expense of the share of labour income.