SA4X6 Michaelmas Term 2014-15

Formative Essay (WAM-A)

STUDENT: PABLO ARAYA

a) The P90/P10 percentile ratio and the Gini coefficient are two summary indices of

income inequality. Explain these measures, and compare their strengths and

weaknesses.

P90/P10 percentile ratio is an ordinal measure of inequality. It may be defined as the

income gap between the upper-limit of the decile 1 and the decile 9, based on the income of

the poorer people, namely upper-limit of the decile 1. This measure gives us a quick glance

of inequality using an easy and transparent way.

Gini coefficient is probably the most common index of inequality. It is derived from the

Lorenz Curve, which summarizes the inequality using cumulative population share against

cumulative income share (Jenkins & Van Kerm, 2009). In other words, it tells what share of

income has a determined proportion of population and so on. For example, 10% of

population get 10% of income or the 50% of population get 50% of income.

If the distribution was completely egalitarian, the Lorenz Curve would be a 45 degree line.

If the Lorenz curve is above this line, the Gini Coefficient would be 0. If one person had all

the income, the inequality would be 1. Thus, the Gini coefficient graphically is the area

below 45 degree line and above the Lorenz curve, divided for all the triangular area below

the 45 degree line. While the Lorenz Curve is far away from 45 degree line, the Gini

coefficient is higher.

P90/P10 and Gini have an easy interpretation, which explain their broad spread. P90/P10

gives a snapshot of the magnitude of earnings inequality. Besides, it is not biased by the

extreme of the distributions. Likewise, Gini is a powerful tool because people easily can

understand how much inequality a country has. Additionally, it is possible to make some

statements of levels of inequality, making comparison among countries whenever there is a

strictly dominance of some curve to another (not cross among curves), which cannot be

done using P90/P10 because is quite simple (ratio) and miss information about other

segments of population.

Nevertheless, Gini does not allow to make stronger statements of inequality either. For

instance, Gini is not consistent in intra-group analysis and it is a measure that gives equals

weight to poorer and richer people. Finally, although the principle of transfer is satisfied,

the transfer is not sensitive because it depends on orderings rather than incomes (Jenkins S.

, 1991).

In conclusion, P90/P10 and Gini indices share some advantages: simple and broadly used.

However their extent is limited when deeper analysis is required, for instance, impact on

inequality in different groups or how much distribution changes when there is a transfer

from one group to another.

b) Australia’s official statistics about income inequality do not report summary

inequality indices such as members of the generalised entropy or Atkinson families.

Discuss the advantages and disadvantages of including estimates of indices such as

these in official statistics (in addition to Gini coefficients and percentile ratios).

Generalized entropy and Atkinson indices families are more complex inequality indices

that measure income distribution highlighting sensitivity of distributions to changes in

share income, its particular components (groups) as well as normative aspects. They

provides additional information about inequality and allow us to make comparison among

different distributions. Besides, they both have some desirable properties for measuring

inequality, namely, scale invariance, population invariance, symmetry and the principle of

transfer.

Firstly, generalized entropy indices measure inequality capturing differences in income in

different parts of the income distribution, thus it can ponder income groups differently. This

“sensibility” is captured by a parameter α, which can takes positive or negatives values.

While more negative is the parameter it is more sensible to low-incomes groups; while

more positive it weight high-income groups (Jenkins & Van Kerm, 2009). Since this index

strength the principle of transfer, this approach focuses on the idea of distance between a

member of the society and a relative measure such as the mean. In this way, the parameter

α could be understood as the “sensitivity” to income transfer (Jenkins S. , 1991).

One of the most important advantages of entropy indices is its property of decomposability.

Basically it means that it is possible to analyse the distribution by groups and subgroups

and the sum of the results do not change the aggregated analysis. This property is relevant

takes into consideration that Gini coefficient, which is the most common inequality index

does not have this property. However, it is not easy to interpret and it is not sensitive to

changes in the distribution depending on if they are in the poorest or richest.

Secondly, the Atkinson indices include some of the characteristics of entropy indices,

although they take into account the concept of social welfare function, namely, they include

a normative idea expressly. The index measures how efficiently society can afford in order

to get a more egalitarian distribution. In order to make that, Atkinson function includes a

parameter 𝜀 which has been called “inequality aversion”. It can be seen as a parameter

which takes values between 0 and 1. If 𝜀 takes the value of 0, it means that society is

indifferent to inequality, while if it takes the value of 1, society has a greater concern on

inequality.

Unlike entropy indices, Atkinson ones have an easier interpretation. The inequality index is

expressed as follow: I = 1 – (y Ɛ - µ). If 𝐴 = .4, means that society just should redistribute

60% at the same proportion to get the same level of welfare (Jenkins S. , 1991)

Nevertheless, there is an important trade-off when this index is implemented since

inequality depends on social welfare function definition. In other words, it is lesser

“objective” than other measures.

In summary, these type of indices provides information about sensitivity of the distribution

and adds normative assumptions on inequality. Derived from this, it is possible to assess

the impact of some changes in the distribution of income, thus impact on social welfare. As

Jenkins states: “(…) is better to use measures that at the outset measure (sets of) social

values in a consistent way. This suggest increased utilization of indices from Atkinson or

Generalized Entropy indices family and relatively less emphasis on commonly used indices

such as the Gini Coefficient” (Jenkins S. , 1991). Therefore, it would be recommendable to

add these indices as they provide more information and assess normatively the inequality

impact, despite its interpretation is not as easy as Gini or P/90-10 are.

c) With reference to Table 1 below, comment on how income inequality in Australia

changed between 2002–03, 2003–04, and 2009–10. Discuss whether your conclusions

are robust to the choice of summary index

Australia has presented an upward trend of inequality during the period 2002/03-2009/10.

Nevertheless, before to make a definitive statement about the topic, figures should be

analysed carefully since assumptions about the data are made, final conclusions may be

restricted. In this way, it should be taken into account which factors may explain changes in

the inequality during the period, mainly because during the period 2003/04 it was observed

a sharp decline in inequality.

One of these restrictions may be data collection. For instance, data could be collected by

different survey methodologies during the period 2003/04, what could explain why there

was a sharp increase of the income share by the 1st quintile group from 2002/03 to

2003/2004. Causes may be inclusion of state transfers or changes in the definition of

income among others. Secondly, an improvement of data collection (sample size, design)

could suggest why figures changed from one year to another.

Regardless of the restrictions in the analysis, the figures show that the gap between the 1st

and the 5th quintiles increased. For instance, the poorest group (1st quintile) shared a 7.6%

of the total income during the period 2002-2003, reaching a significant 8% the following

year, but it decreased by 7.4% at the end of the decade. Figures from P80/P20 confirms this

tendency. This ratio was 2.63 during the period 2002/03, dropping to 2.55 in 2003/04.

However, during 2009/10 it increased to 2.7, namely, overcame the levels of the beginnings

of the first middle of the decade.

The proportion of income of middle quintiles held unchanged from 2002/03 to 2003/04 in

the 2nd and 3rd quintiles, but it went down for both 2nd, 3rd and 4th quintiles groups at the

end of the decade. People that belong to the 5th quintile increased their share of the national

income during the period.

The ratios and Gini decreased in the period 2003/04, which is consistent with the

distribution of income among the quintiles, although it is not clear the reason as it has been

stated above. However, they show a higher inequality at the end of the decade in Australia.

Taking into consideration that there was an increase of the mean income during the period,

the distribution among quintiles and the indices demonstrate that this additional income

were not equally distributed and, the 5th quintile gained the higher share. One probable

reason is the effect of crisis at the end of the decade, where vulnerable groups are more

affected than the richest households.

In conclusion, inequality in Australia increased according to Gini and P90/P10 ratio from

2002/03 to 2009/10, which is robust with changes in share of income among quintile

groups, although partial results of 2003/04 period are difficult to interpret.

d) Briefly explain why and how the information about mean income might be useful

for comparing the three income distributions.

Mean income is a relative measure of well-being typically used to assess economic and

social progress among societies. It is defined as the total income divided by all member of

the society. Making a histogram of the income distribution is very likely that mean income

was higher than median income (50th percentile), which shows a relative idea of inequality

in the society (fewer people concentrate more income). In fact, while larger was the gap

between the mean and median, higher levels of inequality should be observed.

In the case of Australia, mean income increased in the 3 period. Figures are updated

according to 2011/12 prices, thus are comparable (real income, not nominal). This set data

is key to demonstrate that mean income should be located in the 4th or 5th quintile given that

share of income of the 5th quintile increased during the period, meanwhile the rest got a less

proportion. Therefore, mean income provides a relative measure to understand how higher

incomes (more is better) are really redistributed among the member of the society.

References

Jenkins, S. (1991). Measurement of Income Inequality. En L. Osberg, Economic inequality

and poverty international perspectives (Pages 3-38). London.

Jenkins, S. P., & Van Kerm, P. (2009). The Measurement of Economic Inequality. En W.

Salverda, B. Nolan, & T. M. Smeeding, The Oxford Handbook of Economic

Inequality (Pages 40-67). Oxford University Press.