**Empirical Project 5** Measuring inequality: Lorenz curves and Gini coefficients

## Learning objectives

In this project you will:

- draw Lorenz curves and interpret the Gini coefficient
- calculate and interpret alternative measures of income inequality
- research other dimensions of inequality and how they are measured.

## Key concepts

Concepts needed for this project: ratio and decile.Concepts introduced in this project: Gini coefficient and Lorenz curve.

## Introduction

## CORE projects

This empirical project is related to material in:

There are many criteria that policymakers can use to assess outcomes or allocations of economic interactions, in order for them to evaluate which outcome is ‘better’ than the others. One important criterion for assessing an allocation is efficiency, and another is fairness. Outcomes that economists would define as ‘efficient’—those that cannot make one person better off without making someone else worse off—may be undesirable because they are unfair. To read more about how economists use the word ‘efficiency’, see Section 3.3 in *Economy, Society, and Public Policy*.

For example, a situation where a small fraction of the population lives in luxury and everybody else struggles to survive may be efficient, but few people would say it is desirable due to the vast inequality between the rich and poor. In this case, policymakers might intervene by implementing a tax system where richer people pay a greater proportion of their income than poorer people (a progressive tax), and some revenue collected in taxes is transferred to the poor. Empirical evidence on people’s views about the fairness of the income distribution and further discussion of the concept of fairness can be found in Sections 3.4 and 3.5 of *Economy, Society, and Public Policy*.

- Gini coefficient
- A measure of inequality of any quantity such as income or wealth, varying from a value of zero (if there is no inequality) to one (if a single individual receives all of it).

- Lorenz curve
- A graphical representation of inequality of some quantity such as wealth or income. Individuals are arranged in ascending order by how much of this quantity they have, and the cumulative share of the total is then plotted against the cumulative share of the population. For complete equality of income, for example, it would be a straight line with a slope of one. The extent to which the curve falls below this perfect equality line is a measure of inequality.
*See also: Gini coefficient.*

To assess inequality economists often use a measure called the **Gini coefficient**, which is based on the differences in incomes, wealth, or some other measure between people. We will first look at how the Gini coefficient is calculated and compare it with other measures of inequality between the rich and poor, such as the 90/10 ratio. We will also use **Lorenz curves** to show the entire distribution of income in a country. Then, we will look gender inequality to see how this dimension can be measured. Finally, we will look at how inequality can be accounted for in indices of wellbeing, such as the Human Development Index (HDI).

To learn more about how the Gini coefficient is calculated from differences in people’s endowments, see Section 5.8 of *Economy, Society, and Public Policy*.