Topic 11: Measuring Inequality and Poverty

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1 Topic 11: Measuring Inequality and Poverty Economic well-being (utility) is distributed unequally across the population because income and wealth are distributed unequally. Inequality is measured by the differences in utility across economic units households or families 1 which varies continuously and can be larger or smaller. Inequality can be measured in numerous ways. Most often, it is measured by the concentration in the distribution of household income. A related concern is the well-being of the population at the very bottom of the income distribution. Households or families at the bottom without sufficient income to afford a basic standard of living are described as living in poverty. Poverty too can be measured in different ways, the most important being the percent of persons living below some poverty line. The poverty line, or Official Poverty Threshold, is a measure of the minimum income necessary for a family to enjoy a basic standard of living. Measuring income inequality The distribution of income across persons or households is called the size distribution of income. The size distribution of income can be presented in a table where the entries are the income shares of households (or families) grouped into different income quintiles. An income quintile is 20% of the population. The economic units (usually households or families) are ordered according to their incomes, from lowest to highest. The 20% of the population with the lowest incomes is the first or lowest quintile, the 20% of the population with the next lowest income is the 2nd quintile, etc. The 20% of the population with the highest incomes is the fifth or top quintile. Income dispersion in the top quintile is high, so the top quintile is often sub-divided into the top 5% or the top 1% The income share of a quintile is the percentage of total income that is received by the households in the quintile. Household income is income received in cash form (excluding in-kind income) before personal taxes. The following table lists the income shares of households by quintiles in the U.S. for the year We see from the table, that households in the top quintile have mean income that 1 Families are related individuals living together whereas households are a single person or several persons living in the same domicile, whether related or not. All families are households but not vice versa. 1

2 is nearly 16 times greater than the households in the bottom quintile. Historical information on the size distribution of income for the US for years earlier than 2012 can be found in the tables here. Quintile Upper Income Limit Mean Income Income share Cumulative income share I $20,599 $11, % 3.8% II $39,764 $29, % 13.0% III $64,582 $51, % 28.1% IV $104,096 $82, % 51.1% V $181, % 100% Top 5% Lower Income limit $191,156 $318, % The Lorenz curve The amount of inequality or concentration in an income distribution can be represented graphically, either with the familiar pie chart or with the less familiar Lorenz curve diagram. The Lorenz curve plots the cumulative shares of quintile income against a hypothetical equality line (45 degree line). Along the hypothetical equality line, each quintile would receive 20% of total income. The farther the Lorenz curve is situated below the equality line, the more concentrated (unequal) the distribution. Using the cumulative share information from the above table, we construct the Lorenz curve for the U.S. in 2012 shown in the diagram below. One can compare different income distributions (say in different countries or different years) by plotting and comparing their respective Lorenz curves. If the Lorenz curve for distribution A lies uniformly farther from the equality line than distribution B, distribution A has greater concentration than does distribution B. (Note, however, in some cases Lorenz curves cross, in which case unambiguous conclusions cannot be drawn.) 2

3 The Gini coefficient It is convenient to summarize the spread or concentration in a distribution with a single statistic. One such statistic is the coefficient of variation, which is the standard deviation of the distribution (a measure of the spread or disparity of a distribution) divided by the mean of the distribution. The most common statistic encountered in the income distribution field is the Gini Coefficient or Gini ratio (also known as the coefficient of concentration), named after the Italian economist Corrado Gini ( ). The Gini coefficient is directly related to the Lorenz curve diagram it is equal to the ratio of the area between the equality line and the Lorenz curve to the total area below the equality line, which is why it is sometimes called the Gini ratio. Thus, the Gini coefficient must lie between zero and one. The farther the Lorenz curve is from the equality line, the greater is the concentration in the distribution and the greater (closer to one) is the Gini coefficient. The Gini coefficient for US household income in 2012 is equal to Over the past 40 years, inequality of the distribution of income in the US has increased steadily. For example, in 1970 the income share of the bottom quintile was 4.1% (about 8% higher than in 2012) while the income share of the top quintile was 43.3% (11.5% lower than in 2012). In 1970, the Gini coefficient was.394, so income concentration increased 21.1% between 1970 and 2012 according to 3

4 the Gini coefficient. The causes of this increasing inequality are widely debated and studied. The alleged causes include the expansion of free international trade, the increasingly capitalintensive and technical nature of modern production, the decline of union power, and increased immigration, among other things. In any case, the causes are beyond the scope of public finance, except for the role of government redistribution programs and policies. Income in the US is more concentrated (unequally distributed) than in most other industrialized countries, although inequality has increased in other countries as well. The OECD table of Gini coefficients for different countries is found here. With countries ranked from lowest Gini coefficient to the highest, the US ranks 31 st out of 34 countries. 2 Differences in the Gini coefficient for different states are found here. The state of New York has the highest Gini coefficient at and Wyoming the lowest at Two historians claim the Gini ratio in the ancient Roman Empire was around.44, less than the US today. Alternative measures of inequality We can also measure inequality in the distribution of wealth (net worth) and consumption across households. Wealth, which is equal to the assets of the household minus its liabilities, is more concentrated than income (see the Appendix to this topic.) On the other hand, the distribution of consumption is less concentrated (more equal) than income. One reason the distribution of consumption is less concentrated is that inequality in household income partly reflects income differences over the life-cycle (that is, income difference by age). People typically have lower incomes when they are young and old, and have higher incomes when they are middle-aged. However, people attempt to smooth consumption over their lives by saving and borrowing. For this reason, we observe less inequality in annual consumption across households than in household annual income. Households can and do move from one income quintile to another over the course of their lives. The income distribution in a particular year should be viewed as a snapshot of households in motion. 2 The US Gini coefficient in the OECD table is much less than that reported by the Census Bureau, probably because a different economic unit or measure of income was used. 4

5 Households do not necessarily remain frozen in the same income quintiles over time. The mobility of households within the income distribution has been studied. This study followed taxpayers over time and found that a taxpayer in the bottom income quintile was just as likely to be in a higher income quintile a decade later as it was to still be in the bottom quintile. However, other studies claim that income mobility has been slowing down along with the increase in inequality. A recent and controversial fact about income inequality is that it is positively correlated with intergenerational income immobility. That is, the greater the degree of income inequality, the less intergenerational mobility across the income distribution. The relationship between income inequality and generational immobility is graphed below in a diagram known as the Great Gatsby curve. The Gini coefficient is measured on the horizontal axis and the intergenerational earnings elasticity 3, a measure of intergenerational earnings immobility, is measured on the vertical axis. 3 The U.S. elasticity coefficient of.47 means that if one s father makes 100% more than another then the son of the high income father will, as an adult, earn 47% more than the son of the relatively lower income father. The United States is among the least inter-generationally mobile countries in the developed world according to this index. 5

6 Measuring Poverty Government redistribution policies may address the entire income distribution, or just part of it. In the US, tax policy is the main policy used to address the whole of the income distribution by the means of a progressive Federal tax system. Government transfer programs motivated by income differences are focused mainly on the lower end of the distribution in particular, families who are in poverty. According to official measures, 9.5million families (11.8% of all families) and 46.5 million persons (15% of total) had incomes below the Federal Official Poverty Threshold (OPT) in In 2012, the OPT for a family of 4 persons (two adults and two related children under age 18) was equal to $23,492. (The OPT varies by family size.) The poverty rate is up sharply from 9.8% (families) and 12.5% (for persons) in 2007 before the recession, and shows no sign of dropping any time soon. You can find historical data on the poverty rate at this Census Bureau site. Absolute and relative measures of poverty How should poverty measured? Poverty measures can be relative or absolute. A relative poverty measure compares a family s income to a measure of the average family s income. For example, one could adopt a poverty measure that adopts the criterion that a family with less than 25% (say) of the mean family income is poor or, alternatively, that every family in (say) the bottom quintile is poor. If poverty is measured relatively, poverty can never be eradicated because it is defined by the lower tail of the income distribution, which will always exist. As all incomes rise, the average income rises, and the lowest incomes along with it. For example, if the average income increases by 100%, and the income of the lowest quintile increases along with it, relative incomes stay the same. If we define poverty relatively, the families in the lowest income quintile remain in poverty even though their income has doubled. The Orshanksy poverty measure The Federal OPT is not a relative measure, it is an absolute measure. Absolute poverty is measured by comparing a family s income to its ability to afford a defined standard of living. An absolute measure of poverty is used in the US, because the current measure of poverty 6

7 was adopted during the Lyndon Johnson administration s war on poverty. The purpose of the war on poverty was to eradicate poverty (it didn t), and poverty can only be eradicated if it is defined absolutely. 4 The method of measuring poverty as an absolute measure was devised by Mollie Orshansky of the Social Security Administration, and is called the Orshansky method. Here is a picture of the late and great Mollie Orshanksy. Mollie Orshansky in Social Security Administration Archives. To attain an absolute poverty measure, it is necessary to determine the cost of a basic standard of living. One needs to determine the cost of food, shelter, utilities, clothing, transportation, etc. for a basic living standard for family of a given size and determine whether the family s income is enough to afford it. The Orshansky method takes a short-cut by determining only the cost of an adequate diet for a family of a given size and the fraction of income spent on food by the average family of the same size. Orshansky instructed the Department of Agriculture to estimate the cost of food at home that provides a nutritious but economical diet for families of different sizes. There are several such estimates, and best one is known as the cost of the Thrifty Food Plan (TFP). Given the cost of the TFP for a family of given size, the OPT is found by dividing the cost by the fraction of income spent on food by a family of the same size with average income. 4 Poverty has not been eradicated anyway. It has been said We fought a war on poverty and poverty won. 7

8 The logic behind the Orshansky method is that the fundamental definition of absolute poverty is the inability to afford adequate nutrition. A family with income below the OPT cannot afford a nutritious diet even if it spends the same fraction of its income on food as does the average household. (In other words, to afford adequate nutrition a family below the OPT would have to spend a larger fraction of its income on food than the average family.) For example, if the cost of the TFP for a family of 4 is $500 a month ($6000 a year), and the average family spends 25% (fraction ¼) of its income on groceries, the OPT is equal to $24,000 per year for a family of 4 using the Orshansky method. This means a family with income equal to the OPT can just afford the TFP if it spends 25% of its income on food at home. A family below the OPT cannot. Using the Orshansky method, the poverty rate is determined as follows: for each family, counted income is compared to the OPT for that family. (This would be done for all families in a census year, and by sample in non-census years.) Counted income is equal to beforetax cash income all forms of in kind income are excluded. A family with cash income less than the OPT is officially poor. A family with cash income $1 less than the OPT is counted in the same way as a family with no income at all, so depth of poverty is ignored. The poverty rate of families is equal to the number of families who have cash incomes below the OPT as a percentage of all families. The poverty rate of persons is equal to the number of persons in families who are poor as a percentage of all persons. The OPT defines a fine and bright line between families who are poor and those who are not. A family with counted income $1 more than the OPT is not counted as poor. Families with cash incomes between the OPT and two times the OPT are counted unofficially as near poor. Although the Orshansky method was originally used to determine the OPT in the 1960s, since then the OPT each year has been determined simply by increasing the previous year s OPT by the change in the Consumer Price Index (CPI-U). No adjustments are made for changes in the fraction of income spent on food by the average family (it has fallen). In dollars of constant purchasing power, the OPT has remained constant for half a century. 8

9 Alternative poverty measures Alternative measures of poverty seek to overcome the problems of the OPT. Some measures try to expand the Orshansky method to include other necessities in addition to food, such as shelter. Other measures change the definition of counted income, either to include in-kind income and transfers, like food stamps and Medicaid, or to subtract personal taxes, or both. These changes may increase or decrease the measured poverty rate. However, the different poverty rates tend to show the same pattern of changes over time. Another poverty measure, called the income deficit, is designed to measure the depth of poverty as well as the number of families in poverty. The income deficit is equal to the dollar transfer needed to raise all families currently below the OPT up to the OPT. In 2011, the income deficit was equal to $91 billion. Despite the shortcomings of the official poverty measure, changing or even modifying it is a politically-charged issue because the OPT determines eligibility for many government welfare programs. However, the Census publishes a supplementary poverty measure that adjusts for the problems with the official measure. The Heritage Foundation, a politically conservative research organization, challenges the view that families living below the poverty line are seriously deprived by documenting how many of them have computer games, air-conditioning, etc. in this study. Steven Colbert satirizes the Heritage study in this funny episode of Comedy Central (must see tv). The effects of government redistribution programs on inequality and poverty The impacts of government transfer and tax policies on the distribution of income for the year 2005 are shown in the table below. The column headed Market Income is reports the before-tax income that households receive from private market activity. This is their income from their own resources. The column headed Market Income + Social Insurance reports before-tax incomes including government cash transfers that are not means tested, such as Social Security and Unemployment benefits. The column headed Disposable Income reports after-tax household incomes plus meanstested and social insurance government transfers. The means-tested transfers include some in-kind transfers, such as food stamps, but not 9

10 the value of Medicaid. The social insurance transfers do not include the value of Medicare. More information can be found here in the Census document The Effect of Taxes and Transfers on Income and Poverty in the United States: The quintile income shares for each income measure as well as the corresponding Gini coefficients are shown in the table below. Quintile Market Income Market Income + Social Insurance Disposable Income I 1.5% % II 7.3% % III 14.0% % IV 23.4% % V 53.8% % Gini As the table shows, the Social Insurance and Means-tested transfers plus taxes have about equal effects at reducing income inequality in the nation. Social insurance transfers reduce the Gini coefficient from.49 to.45 and means-tested transfers and taxes reduce it further from.45 to.42. In all, as measured by the Gini coefficient, government tax and transfer polices reduce inequality by about 14%. It should be noted, however, that neither the social insurance transfers nor the means tested transfers include all in-kind transfers. In particular, they do not include two very large transfer programs Medicare for the aged and Medicaid for the poor. Including these transfers would further reduce inequality. The Census document from which this table is taken also computes the hypothetical poverty rate of persons if households had to rely on market income alone. The 2005 poverty rate would have been 18.9% of persons as compared to the 10.3% official rate. Thus, government tax and transfer programs reduced the 2005 poverty rate by 46%. Neil Bruce

11 Appendix on the Distribution of Wealth, 2007 Source: E.N. Wolff, Recent Trends in Household Wealth in the United States March