people and planet

14
BOX 14.1
Different measures can lead to different conclusions on inequality
A hypothetical country example is used to explain how different inequality measures can lead to opposite conclusions. It shows the distribution of the
school attendance rate in two years. In 2000, only 5% of the poorest 20% of children attended school, compared with 40% of the richest 20%. In 2010,
20% of the poorest 20% of children attended school, compared with 82% of the richest 20%.
Four indicative inequality measures are calculated:
• The range, i.e. the absolute difference in the value of the attendance rate between the poorest and richest 20%. By this measure, inequality
increased from 2000 (35 percentage points) to 2010 (62 percentage points) (Figure 14.1a).
• The ratio, i.e. the attendance rate for the poorest over that for the richest, more commonly known as the parity index, in which a higher value
means lower inequality. This measure would have inequality decreasing from 2000 (0.12) to 2010 (0.24) (Figure 14.1b).
• The odds ratio – the odds of attending school (i.e. the chance of attendance instead of non-attendance) among the richest over the odds of
attending school among the poorest. It would indicate that inequality increased from 2000 (14) to 2010 (18) (Figure 14.1c).
• The concentration index, which takes into account the value of the attendance rate not only among the poorest and the richest 20% but for all five
quintiles. It is based on the cumulative distribution of the attendance rate (on the vertical axis) against the cumulative proportion of individuals
ranked from poorest to richest (on the horizontal axis). For example, the poorest 20% were 5% of those attending school in 2000 and 10% in 2010.
If there were perfect equality, the latter share would be 20%. The index measures the distance from the line of perfect equality. It would show
inequality decreasing from 2000 (0.40) to 2010 (0.28) (Figure 14.1d).
Selecting a measure needs to be based on careful weighing of the options’ advantages and disadvantages.
FIGURE 14.1:
For the same population, different measures can yield opposite conclusions on education inequality
Trends in inequality of school attendance rate, by inequality measure, hypothetical example
a. Range
Inequality increased
b. Ratio (parity index)
Inequality decreased
100
40 - 5 = 35 82 - 20 = 62
100
5 / 40 = 0.12 20 / 82 = 0.24
80
82%
Q5 - Richest
80
82%
Q5 - Richest
Attendance rate (%)
60
40
20
0
40%
Q5 - Richest
Q4
Q3
Q2
5% Q1 - Poorest
2000
20%
Q3
Q2
Q1 - Poorest
2010
Q4
Attendance rate (%)
60
40
20
0
40%
2000
Q5 - Richest
Q4
Q3
Q2
5% Q1 - Poorest
20%
Q4
Q3
Q2
Q1 - Poorest
2010
c. Odds ratio
Inequality increased
d. Concentration index
Inequality decreased
Attendance rate (%)
100
80
60
40
20
0
(40/60) / (5/95) = 14 (82/18) / (20/80) = 18
40%
5%
Q4
Q3
Q2
Q1 - Poorest
2000
Q5 - Richest
82%
20%
Q3
Q2
Q1 - Poorest
2010
Q5 - Richest
Q4
Cumulative distribution of attendance
rate (%)
100
80
60
40
20
0
0
2000: Inequality = (B+C)/(A+B+C) = 0.40
2010: Inequality = (C)/(A+B+C) = 0.28
Equity
C
B
A
2010
2000
20
40 60 80 100
Cumulative distribution of population by wealth (%)
Sources: Cowell, 2010; Vallet and Montjourides (2015); O’Donnell et al. (2007).
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CHAPTER 14 | TARGET 4.5 – EQUITY