Hoover index

An economic measure of income inequality

Overview

The Hoover index, also known as the Robin Hood index, is a measure of income inequality. It is used to quantify the distribution of income or wealth within a population. The index is named after the economist Herbert Hoover, although it is not directly related to him, and it is sometimes referred to as the Robin Hood index because it represents the proportion of total income that would need to be redistributed to achieve perfect equality.

Illustration of the Robin Hood index

Calculation

The Hoover index is calculated as the proportion of total community income that would have to be redistributed (taken from the richer half of the population and given to the poorer half) for there to be perfect equality. Mathematically, it is defined as:

\[ H = \frac{1}{2} \sum_{i=1}^{n} \left| \frac{x_i}{\mu} - \frac{1}{n} \right| \]

where:

• \( x_i \) is the income of individual \( i \),
• \( \mu \) is the mean income of the population,
• \( n \) is the total number of individuals in the population.

The index ranges from 0 to 1, where 0 indicates perfect equality (everyone has the same income) and 1 indicates maximal inequality (one person has all the income).

Interpretation

The Hoover index provides a straightforward interpretation: it is the percentage of total income that would need to be redistributed to achieve equality. For example, a Hoover index of 0.3 means that 30% of the total income would need to be redistributed from the richer half to the poorer half to achieve perfect equality.

Comparison with Other Indices

The Hoover index is one of several measures of income inequality. Other commonly used indices include the Gini coefficient, the Theil index, and the Atkinson index. Each of these indices has its own method of calculation and interpretation, and they may emphasize different aspects of inequality.

Applications

The Hoover index is used in various fields such as economics, sociology, and public policy to assess the level of inequality within a society. It can be applied to different types of data, including income, wealth, and consumption.

Related pages

• Gini coefficient
• Theil index
• Atkinson index
• Income inequality
• Wealth distribution