**Empirical Project 5** Measuring inequality

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 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. For example, a situation where a small group of elites possesses almost all the money in the economy and everybody else struggles to survive is 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 (progressive tax), and some money collected in taxes is given back to the poor.

- 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*.

## Working in Excel

### Part 5.1 Measuring income inequality

One way to visualize the income distribution in a population is to draw a Lorenz curve. This curve shows the entire population along the horizontal axis from the poorest to the richest. The height of the curve at any point on the vertical axis indicates the fraction of total income received by the fraction of the population, shown on the vertical axis.

We will start by using income decile data from the Global Consumption and Income Project to draw Lorenz curves and compare changes in the income distribution of a country over time. To answer the question below:

- Go to the Globalinc website and download the Excel file containing the data by clicking ‘xlsx’.
- Save it in an easily accessible location, such as a folder on your Desktop or in your personal folder.
- Choose two countries and filter the data so only the values for 1980 and 2014 are visible. You will be using this data as the basis for your Lorenz curves. Copy and paste the filtered data (all columns) into a new tab in your spreadsheet.

- In this new tab, make one table (as shown in Figure 5.1) for each country and year (four tables total). Use the country data you have selected to fill in each table. (Remember that each decile represents 10% of the population.)

Cumulative share of the population (%) | Cumulative share of income (%) |
---|---|

0% | 0 |

10% | |

20% | |

30% | |

40% | |

50% | |

60% | |

70% | |

80% | |

90% | |

100% |

Cumulative share of income owned, for each decile of the population.

Walk-through 5.1Creating a table showing cumulative shares

- We will now use the tables you have made to draw Lorenz curves for each country, in order to visually compare the income distributions over time.

- Draw a line chart with cumulative share of population on the horizontal axis and cumulative share of income on the vertical axis. Plot one chart per country (each chart should have two lines, one for 1980 and one for 2014). Make sure to include a chart legend, and label your axes and chart appropriately.

- Follow the steps in Walk-through 5.2 to add a straight line representing perfect equality to each chart. (Hint: If income was shared equally across the population, the bottom 10% of people would have 10% of the total income, the bottom 20% would have 20% of the total income, and so on.)

Walk-through 5.2Drawing the perfect equality line

- Using your Lorenz curves:

- Compare the distribution of income across time for each country.

- Compare the distribution of income across countries for each year.

- Suggest some explanations for any similarities and differences you observe. (You may want to research your chosen countries to see if there were any changes in government policy, political events, or other factors that may affect the income distribution.)

A rough way to compare income distributions is to use a summary measure such as the Gini coefficient. The Gini coefficient ranges from 0 (complete equality) to 1 (complete inequality). It is calculated by dividing the area between the Lorenz curve and the perfect equality line, by the total area underneath the perfect equality line. Intuitively, the further away the Lorenz curve is from the perfect equality line, the more unequal the income distribution is, and the higher the Gini coefficient will be.

- Using this Gini coefficient calculator, calculate the Gini coefficient for each of your Lorenz curves. You should have four coefficients in total. Label each Lorenz curve with its corresponding Gini coefficient, and check that the coefficients are consistent with what you see in your charts. (Hint: In the Gini calculator, the income values need to be in a single column, but in the spreadsheet the income values are in a single row. You will need to copy and then paste-transpose each row so that your data is in the correct format to enter into the Gini calculator. See Walk-through 2.1 for help on how to paste-transpose.)

Now we will look at other measures of income inequality to see how they can be used with the Gini coefficient to summarize a country’s income distribution. Instead of summarizing the entire income distribution like the Gini coefficient does, we can take the ratio of incomes at two points in the distribution. For example, the 90/10 ratio takes the ratio of the top 10% of incomes (Decile 10) to the lowest 10% of incomes (Decile 1). A 90/10 ratio of five means that the richest 10% of the population earn five times more than the poorest 10%. The higher the ratio, the higher the inequality between these two points in the distribution.

- Look at the following ratios:
- 90/10 ratio = the ratio of Decile 10 income to Decile 1 income
- 90/50 ratio = the ratio of Decile 10 income to Decile 5 income (the median)
- 50/10 ratio = the ratio of Decile 5 income (the median) to Decile 1 income.

- For each of these ratios, explain why policymakers might want to compare the two deciles in the income distribution.

- What kinds of policies or events could affect these ratios?

- Now calculate each ratio in Question 5 and see how they have changed over time for the two countries you have chosen.

- Calculate each ratio over the period 1980–2014, using the income decile data. (You may find it helpful to filter the data first.)

- For each country, plot the three ratios on the same line chart, with the ratio value on the vertical axis and time (in years) on the horizontal axis.

- Using your charts, describe how these ratios have changed over time within each country, and comment on any similarities and differences between countries.

- Suggest some possible explanations for what you observe. (You may want to research specific policies or events that affected the very rich, very poor, and ‘average’ resident of each country.)

We will now compare these summary measures (ratios and the Gini coefficient) for a larger group of countries, using OECD data. The OECD has annual data for different ratio measures of income inequality for 42 countries around the world, and has an interactive chart function that plots this data for you.

Go to the OECD website to access the data. You will see a chart similar to Figure 5.4 which show data for 2015. The countries are ranked from smallest to largest Gini coefficient on the horizontal axis, and the vertical axis gives the Gini coefficient.

- Compare summary measures of inequality:

- Plot the data for the ratio measures by changing the variable selected in the drop-down menu ‘Gini coefficient’. The three ratio measures we looked at previously are called ‘Interdecile P90/P10’, ‘Interdecile P90/P50’, and ‘Interdecile P50/P10’, respectively. (If you click the ‘Compare variables’ option, you can plot more than one variable on the same chart.)

- For each measure, give an intuitive explanation of how it is measured and what it tells is about income inequality. (For example: What do the larger and smaller values of this measure mean? Which parts of the income distribution does this measure use?)

- Do countries that rank highly on the Gini coefficient also rank highly on the ratio measures, or do the rankings change depending on the measure used? Based on your answers, explain why it is important to look at more than one summary measure of a distribution.

The Gini coefficient and the ratios we have used are common measures of inequality, but there are other ways to measure income inequality.

- Go to the Our world in data website, and choose two other measures of income inequality that you find interesting.

- For each measure, give an intuitive explanation of how it is measured and what we can learn about income inequality from it. (For example: What do the larger and smaller values of this measure mean? Which parts of the income distribution does this measure use?)

- If possible, find data or a chart for your chosen measures for the two countries you used in Questions 1 to 6, and explain what these measures tell us about inequality in those countries.

### Part 5.2 Measuring other kinds of inequality

There are many ways to measure income inequality, but income inequality is only one dimension of inequality within a country. To get a more complete picture of inequality within a country, we need to look at other areas in which there may be inequality in outcomes. We will explore two particular areas, focusing on the measures used and their limitations:

- health inequality
- gender inequality in education.

First, we will look at how researchers have measured inequality in health-related outcomes. Besides income, health is an important aspect of wellbeing because it determines how long an individual will be alive to enjoy his or her income. If two people had the same annual income throughout their lives, but the one person had a much shorter life than the other, we might say that the distribution of wellbeing is unequal, despite annual incomes being equal.

As with income, inequality in life expectancy can be measured using a Gini coefficient. In the study ‘Mortality inequality’, researcher Sam Peltzman (2009) estimated Gini coefficients for life expectancy based on the distribution of total years lived (life-years) across people born in a given year (birth cohort). If everybody born in a given year lived the same number of years, then the total years lived would be divided equally among these people (perfect equality). If a few people lived very long lives but everybody else lived very short lives, then there would be a high degree of inequality (Gini coefficient close to 1).

We will now look at lifetime inequality Gini coefficients for ten countries around the world. First, download the data:

- Go to the Our world in data website. In Section 1.1 (Mortality inequality), click the ‘Data’ button at the bottom of the chart shown.
- Click the blue button that appears to download the data in csv format.

- Using the mortality inequality data:

- Plot all the countries on the same line chart, with Gini coefficient on the vertical axis and year (1952–2002) on the horizontal axis. Make sure to include a legend showing country names and label the axes appropriately.

- Describe any general patterns in lifetime inequality over time, as well as any similarities and differences between countries.

- Now compare the Gini coefficients in the first year of your line chart (1952) with the last year (2002).

- For the year 1952, sort the countries according to their lifetime inequality Gini coefficient from smallest to largest. Plot a column chart showing these Gini coefficients on the vertical axis, and country on the horizontal axis. Add data labels to display the Gini coefficient for each country.

- Repeat Question 2
*(a)*for the year 2002.

- Compared to your chart for 1952 and 2002. Have the rankings between countries changed? Suggest some explanations for any observed changes. (You may want to do some additional research, for example, look at the healthcare systems of these countries.)

Walk-through 5.3Drawing a column chart with sorted values

Other measures of health inequality, such as those used by the World Health Organization (WHO), are based on access to healthcare, affordability of healthcare, and quality of living conditions. Choose one of the following measures of health inequality to answer Question 3:

- access to essential medicines
- basic hospital access
- composite coverage index.

To download the data for your chosen measure:

- If you choose to look at either the access to essential medicines or the basic hospital access measure, go to the WHO’s Universal Health Coverage Data Portal and select your chosen measure.
- A drop-down menu with three buttons will appear: ‘Map’ shows a visual description of the data, ‘Data’ contains the data files, and ‘Metadata’ contains information about your chosen measure.
- Click on the ‘Data’ button, then select ‘CSV table’ from the ‘Download complete data set as’ list.
- If you choose to look at the composite coverage index measure, go to WHO’s Global Health Observatory data repository, and select one category to compare (economic status, education, or place of residence). To download the data for that category, click ‘CSV table’ from the ‘Download complete data set as’ list. You can read further information about this index in the WHO’s technical notes.

- For your chosen measure:

- Explain how it is constructed and what outcomes it assesses.

- Create an appropriate chart to summarize the data. (You can replicate a chart shown on the website or draw a similar chart.)

- Explain what your chart shows about health inequality within and between countries, and discuss the limitations of using this measure (for example, measurement issues or other aspects of inequality that this measure ignores).

Since an individual’s income and available options in later life partly depends on their level of education, inequality in educational access or attainment can lead to inequality in income and other outcomes. We will focus on the aspect of gender inequality in educational attainment, using data from the Our world in data website, to make our own comparisons between countries and over time. Choose one of the following measures to answer Question 4:

- gender gap in primary education (share of enrolled female primary education students)
- share of women, between 15 and 19 years old, with no education
- share of women, 15 years and older, with no education.

To download the data for your chosen measure:

- Go to the Our world in data website and find the chart for your chosen measure.
- Click the ‘Data’ button at the bottom of the chart, then click the blue button that appears to download the data in csv format.

- For your chosen measure:

- Choose ten countries that have data from 1980 to 2010. Plot your chosen countries on the same line chart, with year on the horizontal axis and share on the vertical axis. Make sure to include a legend showing country names and label the axes appropriately.

- Describe any general patterns in gender inequality in education over time, as well as any similarities and differences between countries.

- Calculate the change in the value of this measure between 1980 and 2010 for each of country chosen. Sort these countries according to this value, from the smallest change to largest change. Now plot a column chart showing the change (1980 to 2010) on the vertical axis, and country on the horizontal axis. Add data labels to display the value for each country.

- Which country had the largest change? Which country had the smallest change?

- Suggest some explanations for your observations in Question 4
*(b)*and 4*(d)*(You may want to do some background research on your chosen countries.)

- Discuss the limitations of using this measure to assess the degree of gender inequality in educational attainment and propose some alternative measures.

## Working in R

This section is under development and will be in the next release of *Doing Economics: Empirical Projects*