MEASURING INCOME INEQUALITY – A HOLISTIC APPROACH | #EBIZRADIO | #INSIGHT| 21st Century

The South African economy has historically been afflicted by income and wealth inequality. This is evidenced by the persistent presence of South Africa ranking in the top 5 most unequal (in terms of income and wealth) countries in the world when comparing each country’s Gini Coefficient. Given, the income inequality and socioeconomic conditions in South Africa, it is not surprising that income inequality within companies has been the topic of much debate. The instrument most commonly used when measuring income inequality within a company is the Wage Gap.

Wage Gap
Although there have been a number of different methodologies used in order to calculate a “Wage Gap”, the methodology used by the United States Securities Exchange Commission is calculated as:

This calculation provides the user with the ratio of how many times higher the CEO’s pay (chosen element of pay) is than the median worker’s pay. The benefit of using this methodology is that it is simple to compute and easily understood. There are weaknesses in the Wage Gap methodology which include:
By simply halving the CEO’s pay, the ratio will halve even if there has been no gain to the worker’s welfare.
The grade of the “median employee” is unknown and therefore an organisation with a high number of lower level employees is more likely to have a higher wage gap.
Limitations in the methodology are not exclusive to the Wage Gap. There are a number of measures of income inequality which can be calculated, all with their own benefits and limitations.
10 -10 Ratio
The 10-10 Ratio is often used as a crude measure of inequality within macroeconomics when all the data needed in order to calculate a Gini Coefficient is not available. It is similar to the Wage Gap in that it measures the ratio of the highest paid employees to the lowest paid employees. It is calculated as

This methodology is more inclusive than the Wage Gap as a number of employees rather than a single employee is used as the numerator.

The benefits of this methodology are:
It is easy to calculate
It is more inclusive than the standard Wage Gap in terms of how the numerator is calculated
The disadvantages are:
It does not provide information regarding the other 80% of the sample
The 10-10 ratio is therefore best used in conjunction with a Wage Gap analysis as it will alert the user to structural issues within the data if they return significantly different results.

Gini Coefficient
This measure is traditionally used in macroeconomics and measures the inequality within a distribution (in this case income). The full methodology of how it is calculated is rather mathematically sophisticated and falls outside of the requirements of this analysis. In layman’s terms it measures the area between the “Line of Equality” (when everyone earns exactly the same) and the Lorenz Curve which is the cumulative distribution of all incomes in the sample, ranked from lowest to highest. The greater the distance (area) between the Line of Equality and the Lorenz Curve, the more unequal the income distribution is.

Figure 1: Graphical Example of a the Gini Coefficient Calculation

The benefits of this methodology are:
• It makes use of the entire population of the sample rather than only a subsection and therefore provides a more inclusive picture of income inequality.
The weaknesses associated with this methodology are:
• A small sample may result in biased results.
• It can be computationally difficult to calculate.
• It does not provide a measure of inequality within sub-sections of the population

The Gini Coefficient’s ability to provide an all-inclusive measure of income inequality is the most advantageous feature of this methodology. A methodology which provides a measure of inequality between sub-sections is the Coefficient of Variation.

Coefficient of Variation
In statistics, the Coefficient of Variation is defined as a normalised measure of dispersion within a sample and is calculated as:

The benefits of this methodology are:
• It can be used to analyse sub-samples within a population. Eg: It can be used to calculate inequality within each grade.
• It can be used to measure macro and micro levels of inequality and therefore on its own it can provide more information than other measures.
• It is easier to calculate than other methodologies which analyse inequality within sub-samples such as the Thiel Index.

The disadvantages to this methodology:
• A large enough sample within each sub-sample is required in order to be able make comparisons between sub-samples and draw significant inference from the analysis.
• If the distribution of the data is far from a normal distribution, it can produce biased results as the standard deviation may be excessively high due to outliers in the data set.

The Coefficient of Variation has the potential to provide the most holistic view of income inequality of all the measures discussed within this analysis. However, given the weaknesses of this methodology it would not be prudent to simply use this method in isolation.
It is clear that each of these methodologies have their own strengths and weaknesses and as a result a “multi-measure” rather than a “single measure” approach is required in order to obtain a holistic view of income inequality.
Conclusion
Income inequality has been at the forefront of many socioeconomic debates within South Africa. This income inequality is often found within organisations and this inequality has typically measured using the Wage Gap. The Wage Gap provides a good starting point for addressing income inequality within an organisation but it does not provide a holistic view. Three alternative measures of income inequality have been discussed within this analysis, each with its own strengths and weaknesses and none of which can provide an accurate holistic view in isolation. This leads one to conclude that in order to obtain a holistic view of income inequality within an organisation, a number of inequality measures should be used in conjunction in order to obtain the true picture of income inequality.

Written by – Bryden Morton, B.Com (Hons) Economics, Data Manager – [email protected] / Chris Blair, B.Sc Engineering, CEO – [email protected]

www.21century.co.za

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