# MEASURING INEQUALITY: LORENZ CURVES AND GINI COEFFICIENTS - CORE Econ

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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 There are many criteria that policymakers can use to assess outcomes or CORE PROJECTS allocations of economic interactions, in order for them to evaluate which This empirical project is related to outcome is ‘better’ than the others. One important criterion for assessing material in: an allocation is efficiency, and another is fairness. Outcomes that eco- • Unit 5 (https://tinyco.re/ nomists would define as ‘efficient’—those that cannot make one person 5600166) of Economy, Society, better off without making someone else worse off—may be undesirable and Public Policy because they are unfair. To read more about how economists use the • Unit 5 (https://tinyco.re/ word ‘efficiency’, see Section 3.3 (https://tinyco.re/2876321) in Economy, 5986623) and Unit 19 Society, and Public Policy. (https://tinyco.re/1408798) of The Economy. 259

EMPIRICAL PROJECT 5 MEASURING INEQUALITY: LORENZ CURVES AND GINI COEFFICIENTS For example, a situation where a small fraction of the population lives in Lorenz curve A graphical luxury and everybody else struggles to survive may be efficient, but few representation of inequality of people would say it is desirable due to the vast inequality between the rich some quantity such as wealth or and poor. In this case, policymakers might intervene by implementing a tax income. Individuals are arranged in system where richer people pay a greater proportion of their income than ascending order by how much of poorer people (a progressive tax), and some revenue collected in taxes is this quantity they have, and the transferred to the poor. Empirical evidence on people’s views about the cumulative share of the total is fairness of the income distribution and further discussion of the concept of then plotted against the fairness can be found in Sections 3.4 (https://tinyco.re/7883386) and 3.5 cumulative share of the population. (https://tinyco.re/7126396) of Economy, Society, and Public Policy. For complete equality of income, To assess inequality economists often use a measure called the Gini for example, it would be a straight coefficient, which is based on the differences in incomes, wealth, or some line with a slope of one. The extent other measure between people. We will first look at how the Gini coeffi- to which the curve falls below this cient is calculated and compare it with other measures of inequality perfect equality line is a measure between the rich and poor, such as the 90/10 ratio. We will also use Lorenz of inequality. See also: Gini coeffi- curves to show the entire distribution of income in a country. Then, we cient. 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). Gini coefficient A measure of To learn more about how the Gini coefficient is calculated from differ- inequality of any quantity such as ences in people’s endowments, see Section 5.8 (https://tinyco.re/5748024) income or wealth, varying from a of Economy, Society, and Public Policy. value of zero (if there is no inequal- ity) to one (if a single individual receives all of it). 260

EMPIRICAL PROJECT 5 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 horizontal 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. Note that income here refers to market income, which does not take into account taxes or government transfers (see Section 5.9 (https://tinyco.re/1276323) of Economy, Society, and Public Policy for further details). To answer the question below: • Go to the Globalinc website (http://tinyco.re/9553483) 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. 1 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 popula- tion.) 261

EMPIRICAL PROJECT 5 WORKING IN EXCEL Cumulative share of the population (%) Cumulative share of income (%) 0 0 10 20 30 40 50 60 70 80 90 100 Figure 5.1 Cumulative share of income owned, for each decile of the population. EXCEL WALK-THROUGH 5.1 Creating a table showing cumulative shares Figure 5.2 How to create a table showing cumulative shares. 1. The data We will be using data from Afghanistan and Albania for this example. The data has been copied and pasted into a new tab on the spreadsheet. We will make a cumulative table for Afghanistan in 1980. (The other three tables are made in the same way.) 262

PART 5.1 MEASURING INCOME INEQUALITY 2. Calculate the cumulative share of income using the SUM function. To calculate the cumulative share of income, we need to add up all the incomes corresponding to that decile and all smaller deciles, and then divide by the sum of all incomes. 3. Calculate the cumulative share of income using the SUM function. Decile 2 and the remaining deciles are calculated slightly differently from Decile 1, because we have to also include the incomes of lower deciles in the calculation. 263

EMPIRICAL PROJECT 5 WORKING IN EXCEL 4. Calculate the cumulative share of income using the SUM function You can use this table to plot a Lorenz curve with the first column as the hori- zontal axis values, and the second column as the vertical axis values. 2 Use the tables you have made to draw Lorenz curves for each country in order to visually compare the income distributions over time. (a) Draw a line chart with cumulative share of population on the hori- zontal 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. (b) Follow the steps in Excel 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.) 264

PART 5.1 MEASURING INCOME INEQUALITY EXCEL WALK-THROUGH 5.2 Drawing the perfect equality line Figure 5.3 How to draw the perfect equality line. 1. The data We will use the Lorenz curve for Afghanistan in 1980 as an example. The values we need to plot the perfect equality line are given in cells C9 to C19 (labelled ‘perfect equality line’). You will notice that these values are the same as those in cells A9 to A19, because the perfect equality line is where the horizontal and vertical axis values are equal to each other. 265

EMPIRICAL PROJECT 5 WORKING IN EXCEL 2. Add the required cells to the line chart For the perfect equality line to show up on the chart, we need to add it as a separate data series. 3. Add the required cells to the line chart Since the values in cells A9 to A19 and C9 to C19 are the same, it doesn’t matter which range of cells you add to the chart. After step 6, the perfect equality line will appear on your chart. 3 Using your Lorenz curves: (a) Compare the distribution of income across time for each country. 266

PART 5.1 MEASURING INCOME INEQUALITY (b) Compare the distribution of income across countries for each year. (c) 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. 4 Using a Gini coefficient calculator (http://tinyco.re/8392848), 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 Excel walk-through 2.1 (page 79) 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 dis- tribution. 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. 5 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. (a) For each of these ratios, explain why policymakers might want to compare the two deciles in the income distribution. (b) What kinds of policies or events could affect these ratios? We will now compare these summary measures (ratios and the Gini coeffi- cient) for a larger group of countries, using OECD data. The OECD has annual data for different ratio measures of income inequality for 42 coun- tries around the world, and has an interactive chart function that plots this data for you. 267

EMPIRICAL PROJECT 5 WORKING IN EXCEL Go to the OECD website (http://tinyco.re/5057087) 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 hori- zontal axis, and the vertical axis gives the Gini coefficient. 6 Compare summary measures of inequality: (a) 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.) (b) For each measure, give an intuitive explanation of how it is measured and what it tells us 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?) (c) 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. 7 Go to the ‘income inequality’ section (http://tinyco.re/4140440) of the Our world in data website, and choose two other measures of income inequality that you find interesting. Figure 5.4 OECD countries ranked according to their Gini coefficient. 268

PART 5.2 MEASURING OTHER KINDS OF INEQUALITY (a) 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?) (b) 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’ (http://tinyco.re/ 8593466), 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 mortality inequality Gini coefficients for ten coun- tries around the world. First, download the data: • Go to the ‘health inequality’ section (http://tinyco.re/2668264) of 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. 1 Using the mortality inequality data: (a) 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. (b) Describe any general patterns in mortality inequality over time, as well as any similarities and differences between countries. 269

EMPIRICAL PROJECT 5 WORKING IN EXCEL 2 Now compare the Gini coefficients in the first year of your line chart (1952) with the last year (2002). (a) For the year 1952, sort the countries according to their mortality 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. (b) Repeat Question 2(a) for the year 2002. (c) Comparing 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.) EXCEL WALK-THROUGH 5.3 Drawing a column chart with sorted values Figure 5.5 How to draw a column chart with sorted values. 1. Sort the data from smallest to largest Gini coefficient We will use the Gini coefficients for 1952 as an example. The data has been filtered to show values for the year 1952 only. 270

PART 5.2 MEASURING OTHER KINDS OF INEQUALITY 2. Sort the data from smallest to largest Gini coefficient After step 2, the countries will now be sorted according to their Gini coefficient (from smallest to largest). 3. Draw a column chart Now we will make a column chart with the sorted Gini coefficients. After step 5, the column chart will look like the one shown above. 271

EMPIRICAL PROJECT 5 WORKING IN EXCEL 4. Change the horizontal axis labels to country names Now we will change the horizontal axis labels to country names. 5. Change the horizontal axis labels to country names After step 8, the horizontal axis labels are now country names. 272

PART 5.2 MEASURING OTHER KINDS OF INEQUALITY 6. Add data labels to the columns Data labels will make the vertical values easier to see, especially for values that are very close to each other. After step 9, the Gini coefficients will appear in boxes above the columns. 7. Round the Gini coefficients to two decimal places The chart may be too crowded at first because the data labels are not rounded to two decimal places. If we round the Gini coefficient values, the data labels will change accordingly. 273

EMPIRICAL PROJECT 5 WORKING IN EXCEL 8. Add axis titles and a chart title After step 16, your chart will look similar in style to that of Figure 5.4 (page 268). 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 (http://tinyco.re/9304620), click on the tab ‘Explore UHC Indicators’, and select your chosen measure. • A drop-down menu with three buttons will appear: ‘Map’ (or ‘Graph’) 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 (http://tinyco.re/ 3968368), 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 (http://tinyco.re/5693881). 274

PART 5.2 MEASURING OTHER KINDS OF INEQUALITY 3 For your chosen measure: (a) Explain how it is constructed and what outcomes it assesses. (b) Create an appropriate chart to summarize the data. (You can replicate a chart shown on the website or draw a similar chart.) (c) 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 depend 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 ‘educational mobility and inequality’ section (http://tinyco.re/ 8784776) of 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. 4 For your chosen measure: (a) 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. (b) Describe any general patterns in gender inequality in education over time, as well as any similarities and differences between countries. (c) Calculate the change in the value of this measure between 1980 and 2010 for each 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. (d) Which country had the largest change? Which country had the smallest change? 275

EMPIRICAL PROJECT 5 WORKING IN EXCEL (e) Suggest some explanations for your observations in Questions 4(b) and (d). (You may want to do some background research on your chosen countries.) (f) Discuss the limitations of using this measure to assess the degree of gender inequality in educational attainment and propose some alternative measures. 276

EMPIRICAL PROJECT 5 SOLUTIONS These are not model answers. They are provided to help students, including those doing the project outside a formal class, to check their progress while working through the questions using the Excel or R walk-throughs. There are also brief notes for the more interpretive questions. Students taking courses using Doing Economics should follow the guidance of their instructors. PART 5.1 MEASURING INCOME INEQUALITY 1 China and the US are used as examples. China, 1980 Cumulative share of the population (%) Cumulative share of income (%) 0 0.00 10 3.14 20 7.63 30 13.43 40 20.47 50 28.82 60 38.55 70 49.92 80 63.28 90 79.33 100 100.00 Solution figure 5.1 Table showing cumulative income shares for China (1980). 311

EMPIRICAL PROJECT 5 SOLUTIONS China, 2014 Cumulative share of the population (%) Cumulative share of income (%) 0 0.00 10 0.92 20 2.84 30 5.81 40 9.95 50 15.44 60 22.55 70 31.75 80 43.95 90 61.43 100 100.00 Solution figure 5.2 Table showing cumulative income shares for China (2014). United States, 1980 Cumulative share of the population (%) Cumulative share of income (%) 0 0.00 10 2.29 20 6.22 30 11.52 40 18.08 50 25.89 60 35.04 70 45.73 80 58.44 90 74.39 100 100.00 Solution figure 5.3 Table showing cumulative income shares for the US (1980). 312

PART 5.1 MEASURING INCOME INEQUALITY United States, 2014 Cumulative share of the population (%) Cumulative share of income (%) 0 0.00 10 1.88 20 5.14 30 9.66 40 15.41 50 22.45 60 30.92 70 41.09 80 53.58 90 69.90 100 100.00 Solution figure 5.4 Table showing cumulative income shares for the US (2014). 2 (a) Solution figures 5.5 and 5.6 show the Lorenz curves for China and the US, the perfect equality line applies to the next question’s solution. (b) Solution figures 5.5 and 5.6 show the Lorenz curves for China and the US, with the perfect equality line. Solution figure 5.5 Lorenz curves for China. 313

EMPIRICAL PROJECT 5 SOLUTIONS Solution figure 5.6 Lorenz curves for the US. 3 (a) The area between the perfect equality line and the Lorenz curve reflects inequality. Inequality in both countries widened between 1980 and 2014. The change in China is far larger than that in the US. (b) Although income distribution is more equal in China than in the US in 1980, it is less equal in China than in the US in 2014. (c) China had a mostly planned economy in 1980, which prioritized equality. Since 1978, China has undertaken waves of reforms to marketize the economy and improve efficiency. The rapid growth has come at the cost of equality. By introducing market reforms, opportunities emerged for private gain through entrepreneurial activities. Although rapid growth and high inequality are negatively correlated both in high income countries and in a group of ‘catching up’ countries, as discussed in Section 19.11 (https://tinyco.re/ 1686411) of The Economy, rapid growth in China has come at the cost of rising inequality. Inequality in the US is higher than in most developed countries. Many people attribute the higher inequality to policies favouring the rich. Worsening inequality in the US can be explained by a range of factors, including tax policies that favour the rich, education policies that dampen the opportunities for intergenerational mobility (see Section 19.2 (https://tinyco.re/3301931) of The Economy), the skill- biased technological change that raises the incomes of workers with skills complementary to ICT and reduces that of workers with skills substitutable by ICT, and the decline of labour unions (http://tinyco.re/434258). 4 Solution figures 5.7 and 5.8 show the Lorenz curves for China and the US with Gini coefficients labelled. 314

PART 5.1 MEASURING INCOME INEQUALITY Solution figure 5.7 Lorenz curves for China, with labelled Gini coefficients. Solution figure 5.8 Lorenz curves for the US, with labelled Gini coefficients. 5 (a) These ratios all help give policymakers an idea of the distribution of income in the economy and where income is concentrated. Policy- makers may use the information to decide on policies favouring certain income deciles of the population. • The 90/10 ratio compares the two extremes of the income distribution and tells policymakers about the difference between the richest and the poorest. Policymakers can use 315

EMPIRICAL PROJECT 5 SOLUTIONS the information to decide how much income to redistribute to the poorest. • The 90/50 ratio tells policymakers about how the middle class is doing relative to the richest. The ratio can also be used to determine the distribution of tax burden among the relatively rich population. • The 50/10 ratio reveals the distribution of income among the relatively poor population. Policymakers can use the information to determine the amount of income to be redistributed to each group, and to determine who is in relative poverty (many governments define the poverty line relative to the median income). (b) See Section 19.8 (https://tinyco.re/2299150) of The Economy to see how governments can affect income inequality. 6 (a) Students will plot the data for the ratio measures by changing the variable selected for the Gini coefficient. (b) The inter-decile ratios are calculated as the ratios between incomes of various deciles of income distribution. The 90/10 ratio, for example, is the ratio of the income of the 9th decile to the income of the 1st decile. Larger values mean the income from one decile of the distribution is higher relative to the income from another decile. (c) Countries that rank highly on the Gini coefficient also generally rank highly on ratio measures. There are, however, some exceptions. Slovenia, for example, while being the most equal country in terms of the Gini coefficient in 2015, was only the 5th most equal country in terms of the 90/10 ratio. The potential differences in rankings of dif- ferent measures mean it is important to look at more than one measure. The Gini coefficient is an overall measure of a distribution that may mask extreme inequalities between certain groups of the population. 7 Measures chosen here are the share of income going to the top 1%, and the share of children living in relative poverty. • Share of income going to the top 1%: This measure looks at the high end of the income distribution (the right tail). Larger values indicate that the very rich have a larger share of the income, and that there is therefore more inequality between the very rich and the rest of society. However, this is a narrower measure of inequality than the Gini coefficient because it only tells us about how the very rich are doing. • Share of children living in relative poverty: This measure is defined as the share of children living in a household with half of the disposable income of the median household. A larger value indicates that a larger proportion of children are living in relative poverty. 316

PART 5.2 MEASURING OTHER KINDS OF INEQUALITY PART 5.2 MEASURING OTHER KINDS OF INEQUALITY 1 (a) Solution figure 5.9 shows the mortality inequality Gini coefficients for the ten countries. (b) Mortality inequality has been falling over time in all countries except Russia. Developing countries tend to have greater mortality inequality than developed countries. Industrialized, richer countries seem to have materialized most of the available improvement (somewhere at a mor- tality Gini of 0.1) since the 1960s. Exceptions to this are India and Brazil, which are both still on a significant downward trend and still not close to a mortality Gini value of 0.1. The only country in this set of countries where some of the gains are being reversed is Russia, although the latest upward movement is fairly modest, and one may interpret this as Russia having settled on a higher mortality Gini of about 0.15. 2 (a) Solution figure 5.10 shows Gini coefficients by country for 1952. (b) Solution figure 5.11 shows Gini coefficients by country for 2002. (c) The rankings are different in 1952 and 2002. Japan, for example, moved up five places in the ranking to become the second most equal country in 2002. The rapid economic development in Japan has led to rising life expectancy. Living to old age is now the norm in Japan rather than a privilege enjoyed only by the rich. The rising proportion of elderly voters has contributed to policies aimed at improving elderly care, which have reduced the variation in life expectancy. The United States, on the other hand, dropped four places to become a relatively less equal nation in the group. The high costs of healthcare may prevent poor people from accessing treatment, especially if uninsured. It is more likely for disadvantaged groups in society such as minorities or part-time workers to lack insurance coverage. 3 This example looks at access to essential medicines. Solution figure 5.9 Mortality inequality Gini coefficients (1952–2002). 317

EMPIRICAL PROJECT 5 SOLUTIONS Solution figure 5.10 Countries ranked according to mortality inequality Gini coefficients in 1952. Solution figure 5.11 Countries ranked according to mortality inequality Gini coefficients in 2002. (a) The median availability of selected generic medicines (in percentage terms) is a measure of the access to treatment. Data on availability, defined as the percentage of medicine outlets where a medicine was found on a given day, are collected through surveys in multiple regions for each country. (b) Solution figures 5.12 and 5.13 provide two charts summarizing the data. (c) There are large disparities in health inequality across countries. For example, availability in the Russian Federation is 100%, whereas in China it is about 15%. The availability of medicines within a country can differ depending on whether an outlet belongs to the public or 318

PART 5.2 MEASURING OTHER KINDS OF INEQUALITY Solution figure 5.12 Median availability of selected generic medicines in the private sector. Solution figure 5.13 Median availability of selected generic medicines in the public sector. the private sector. In some countries, such as Brazil, private sector availability of medicines is far higher than that in the public sector. The reverse is true for other countries such as Sao Tome and Principe. Note that a higher availability of medicines in the private sector does not necessarily mean greater access for the entire popula- tion, since the private sector is only open to individuals with the ability to pay. This disparity means that richer individuals can access a wider range of medical treatments. 319

EMPIRICAL PROJECT 5 SOLUTIONS The data has some limitations. The basket of medicines differs across countries. The data reflects availability on the day of data collection, which may not be a representative day. Outlets could stockpile medicines in expectation of the arrival of the data collection team. Availability does not account for the dosage and strengths of the products. 4 Solution figure 5.14 looks at the gender gap in primary education. (a) Note: It is difficult to find ten countries without any missing data point between 1980 and 2010. Countries with full data may not be as interesting as others. The lines below connect all available data points. (b) For most countries in the selected group, the share of female pupils in primary education fluctuated around levels just below 50% throughout the period. China and India were the most unequal coun- tries in 1980. India had the greatest improvement in equality over the period, and by 2010 the female share reached nearly 48%. Note the inverse U-shape for China, which could be due to the increasing gender imbalance in the school-age population (around 112 males per 100 females in 2010 (http://tinyco.re/7113498)). (c) Solution figure 5.15 shows the percentage change in the measure between 1980 and 2010. (d) India had the largest change, whereas France had the smallest change. (e) India had the lowest share of enrolled female primary education students in the group in 1980. Rapid development and changing beliefs have contributed to the efforts to reduce gender education Solution figure 5.14 Female pupils as a percentage of total enrolment in primary education. 320

PART 5.2 MEASURING OTHER KINDS OF INEQUALITY inequalities. Universal primary education and promotion of gender equality are among the 8 goals in the Millennium Development Goals (MDGs) to which India committed to achieve by 2015 since 2000. France, as a developed country, had relatively high equality from the beginning of the period and hence had experienced relatively little change over the period (due to less scope for improvement). From Question 4(c), it is apparent that countries which already had very a high percentage of female enrolment (PFE) saw no change. Those countries with initially low female participation have significantly improved. The data demonstrates that the past few decades have seen a significant improvement in access to education for girls. If you repeated the above analysis for all countries, you would see similar results. (f) The measure depends on the gender composition of the population. If there are more male than female children of primary schooling age in a country, then the share of female enrolled must be less than 50%. The ratio of female to male in enrolment rate, which provides a pop- ulation-adjusted measure of gender parity, can be used instead. Remember that all we can see here is enrolment in primary education. It is possible that males could receive more education overall (secondary and higher levels). In fact, if you go back to the ‘educational mobility and inequality’ section (http://tinyco.re/ 8784776) of the Our world in data website, you will see that in many regions females still receive a significantly smaller amount of education overall. Solution figure 5.15 Change (%) in female pupils’ share of total enrolment in primary education. 321

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