Applying the Gini Index to Assess Internal Equity in the Organization

Introduction

Internal equity is important for any organization and is one of the overarching priorities of compensation-setting that maintains a basic level of credibility and functionality of the system, which keeps it going. Without it, navigating the pay scene becomes challenging, and justifying pay decisions becomes an everyday struggle.

As individuals, we are susceptible to injustice or the prevalence of inequity in the organizations that we work for. Many paradigms and theories address this extremely important necessity and treat the consequences of too little internal equity as such, as it applies to organizations or the workplace.

Milkovich (2013) defined internal equity as: “pay relationships among different jobs/skills/competencies within a single organization.” It is a relative concept, inherently embedded in the context in which it is discussed. Internal equity, however, can be synonymous with fairness and justice.

In order for compensation systems to be fair and just they must be internally equitable. This means, they must be procedurally, distributionally, and interactionally just as well as fair. Compensation practice pioneered multiple ways by which to measure and monitor internal equity, starting from structure-based compensation setting to advanced metrics and techniques to assess individual equities.?

Internal equity can be measured at the organizational, departmental, or individual levels. In addition, it can be assessed across certain demographics (e.g., age or gender) or job families, or other types of hierarchies. How internal equity is measured is dependent on the context and purpose behind its measurement.

?In this article, I discuss a rather novel technique to measure internal equity in the organization. It is sophisticated and draws from economics . Specifically, it uses the Gini coefficient or the Gini index, which is a statistical technique that measures dispersion in a way to account for inequality of outcomes such as salaries or incomes. The method was devised by Corrado Gini (1884-1965) and is very influential in the economics sphere. Applied at the economy level, measuring the Gini coefficient is an extremely complex task that requires the deployment of highly qualified statisticians and economists. Luckily, however, applying it to just one organization is possible with but a few steps and techniques and this is the purpose of this article.

Understanding the Gini Coefficient

The Gini coefficient measures statistical dispersion in a way that accounts for inequality between frequency (e.g., groups) distribution. For example, it can answer questions such as what percent of all incomes does the lowest 10% of the population in the country has? The coefficient ranges from 0 to 1, with 0 indicating perfect equality, that is all groups have the same income. While 1 indicates maximal inequality that is one group has all the income while all other groups have none. The Gini coefficient varies across nations, some with relatively low Gini index such as Slovenia at 0.24, and some with high Gini index such as South Africa at 0.65. As with any other index, the Gini coefficient is best understood in a specific context or concerning another metric but rarely alone by itself. The index value has no intrinsic worth or meaning but needs to be interpreted to make sense.?

Measuring internal equity with the Gini index (calculations steps)

Step 1: Sorting the groups and finding the fraction of income and population for each

To enable the calculations of the Gini index to measure internal equity in the organization you first need to organize the employees in the organization into frequency distribution or groups. If you are using a structure-based compensation system, this is already done for you through the grades structure, which segment employees specifically into distinct grades, each with ascending salary figure, naturally establishing inequality in distribution. That inequality can be excessive, e.g., your organizational internal equity situation is adverse or optimal, that is, inequality is minimized to the bare necessity. That, the Gini index as calculated here will be able to tell you, but you will first have to adequately interpret it.

So, we will sort all employees in the organization into grade-based groups and generate the headcount for each group (grade). Then, we can take a proxy of each group's salaries by taking the median salary for each group and multiplying it by the headcount to find out the fraction of the income and fraction of the population for each group. So, if you have 10 grades, you will want to find the headcount of employees at each grade, the median salary at each grade, and from that, you will be able to find the fraction of income for each grade group and the fraction of the population based on the headcount.

Step 2: Finding the fraction of the richer population for each group

Next, you will want to compute the fraction of the richer population for each group, which means you will have to sort your groups in descending order and then simply subtract the fraction of the population of that group from the rest. The richest group, which should be the highest grade, should have a fraction of the richer population as 0, while the lowest group or grade should have that value as 100% minus that group’s fraction of the population.

Step 3: Computing the composite score for each group

Once you have the fraction of population, the fraction of income, and the fraction of richer population for each group or frequency at which you are applying the Gini index, which we established as our internal grades you will now be able to generate a composite score for each group, from which we will derive the Gini index at the end. To compute the score, you will simply need to apply the following formula:

Composite Score = Fraction of income * (Fraction of Population +2 * Fraction of Richer Population)
        

Applying the formula for each group should generate a decimal figure for each group accordingly.?

Step 4: Aggregating the scores and finding the Gini index of salaries distribution

Once you have calculated the score for each group, you need to aggregate it by simply adding them all together or using the sum function in Excel. To find the Gini index from that simply subtract the sum figure from 1 or apply the following formula:

Gini index for salaries distribution = 1 – aggregate score
        

You have now just reduced all the complexity of your organizational internal equity into a single number, which can be utilized to understand the state of internal equity in the organization. Quite powerful, however, it is useless without adequate interpretations.?

Interpreting the Gini index of salaries distribution

Indices and statistical values often have no intrinsic worth, they need to be interpreted to make sense, often by combining them with other metrics or embedding them in a context. For the Gini index of salaries distribution, we can first interpret the value which will be (provided you followed the calculations steps properly) between the value of 0 and 1. 0 means all grades group in your organization has the same salary, e.g., there is perfect equality in the organization and 1 means one grade group has all the salaries in the organization, e.g., maximal inequality. Most often that value derived from your organization will vary between the two extremes. A few notes to keep in mind when interpreting it. First, know that a value of 0.25 and below indicates low inequality generally, while a value more than 0.4 indicate mild to high inequality. You can calculate the Gini index separately for each of your departments and then compare the results to see which department is most or least equitable. Furthermore, you can compute the Gini index across the organization at two different time points to measure the gradual shift of internal equity across time. For example, if you measure internal equity at point A to find it at 0.24 and then again at point B to find it at 0.27 this should indicate that inequality slightly increased in the salaries distribution in the organization between the two time points. Only organizations which can be comparable should have their Gini index of salaries distribution values assessed against one another. You also have the option to compare your organization's specific Gini index of salaries distribution against the country's Gini index. Please remember that there are no absolutes here. It is all context-dependent.?

Closing notes

A large part of inequality in salary distribution in the organization is purposeful, that is more senior employees are typically paid more and those employees with complex and demanding jobs are also paid more. Perfect equality is neither practical nor expected in the organization and hence a Gini index of salaries distribution of 0 is as troubling as 1 here. However, given the dynamism of the world of salaries and the influence of market movements and inflation, salary movements could create uncertainty surrounding the ideal internal equity position. The Gini index method discussed in this article helps in adding a tool to monitor and track internal equity in the organization to enable proper decision-making and assessment.

End of Article.