English notes

RAND Corporation

Chapter Title: Framework for Understanding Inequality in Income and Opportunity

Book Title: Inequality and Opportunity Book Subtitle: The Relationship Between Income Inequality and Intergenerational Transmission of Income Book Author(s): Francisco Perez-Arce, Ernesto F. L. Amaral, Haijing Huang and Carter C. Price Published by: RAND Corporation. (2016) Stable URL: https://www.jstor.org/stable/10.7249/j.ctt1d41dcd.10

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3

CHAPTER TWO

Framework for Understanding Inequality in Income and Opportunity

This chapter presents a simple framework of income and opportunity inequality and discusses different measures and proxies of these concepts. We argue that, depending on the sources of the increase in inequality, we may expect different consequences for inequality of opportunity.

Concepts and Measures of Inequality and Inequality in Opportunity

Throughout this report, we focus on two broad concepts of inequality. The first, and most common in the economic literature, is inequality of outcomes, which refers to the extent to which there is variation in outcomes, such as income and wealth in a population. This may refer to variation in the amounts that people earn (income inequality) or what people have (wealth inequality).1 While this may seem notionally straightforward, there are a variety of ways to define both income and wealth, and there are also several ways to measure inequality. While there may be reasons to prefer one measure to another for specific questions, together the various metrics can provide a textured view of the economic landscape and how it has changed over time.

Income can be measured in a variety of ways, including annually or over a lifetime, for individuals or households, and as either market or disposable income. Market income refers to the income earned directly from labor (earned income or earnings) and capital (capital income), while disposable income subtracts taxes paid and adds public transfers received. Thus, market income provides a starting point for looking at income inequality, and the comparison with disposable income can help assess the impact of some government programs and policies. Nei- ther type of income presents a complete picture, but together they can paint a more detailed picture.

Likewise, there are a host of inequality measures that can be used to provide a nuanced understanding of the distribution in question. While simple statistical measures, such as the standard deviation, are frequently used to understand distributions, they are less useful for understanding changes in inequality over time because they can be affected by inflation. Thus, economists have preferred measures that do not depend on the mean of the distribution—i.e., measures that are unchanged if the whole distribution is shifted or multiplied by an integer. The measure most commonly published by statistical agencies is the Gini coefficient, which can be interpreted as a function of the mean difference. (For example, if we take any two U.S.

1 For many purposes, we would like to measure inequality as the variation in earning capacity—in other words, some individuals earn less because they choose occupations that have more desirable characteristics but pay less (called compen- sating wage differentials).

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4 Inequality and Opportunity

households at random, the expected difference is two times the Gini coefficient’s percentage of the mean; see Atkinson and Morelli, 2014.) Since the Gini coefficient is a function of the mean difference, any change in the relative income, either at the bottom or the top of the dis- tribution, will affect measured inequality. The Gini coefficient reduces the level of inequality into a single number, but this simplicity omits much of the texture and context of some other approaches to measuring inequality.

Another class of inequality measures—the “shape measures”—is based on specific parts of the distribution, such as the top, middle, and bottom. Percentile comparisons provide ways of looking at the shape of the distribution. Poverty measures, while not directly metrics of inequality, capture the deprivation at the bottom of the distribution. Likewise, the share of income going to the top is frequently used to assess inequality trends driven by concentration among high earners. It is an important measure because (as we describe in Chapter Five) much of the recent increases in inequality have been driven by higher incomes among the top 1 per- cent. However, this measure is unaffected by changes in the shape of the middle and bottom of the distribution and thus tells only part of the story.

Inequality of opportunity is a less concrete notion, related to the degree to which everyone has the same opportunities to achieve outcomes. Conceptually, inequality of opportunity can be thought of as the extent to which conditions at birth (including socioeconomic status of the parents) affect the likelihood of a specific economic outcome as an adult (Roemer et al., 2003). While it is not possible to assess inequality of opportunity directly, realized opportunity can be measured using intergenerational transmission of income (IGTI), or intergenerational mobility (we use these terms interchangeably). IGTI refers to how much of adults’ income of is deter- mined by the income of their parents while they were raising children; IGTI thereby attempts to capture inequality of opportunity. In practice, IGTI can be approximated by measuring the differences in the probability that children from different socioeconomic backgrounds reach different relative positions in the income distribution when adults. Alternatively, we can use measures that capture the proportional difference in earnings of those born to wealthier versus poorer parents.

There are two sets of proxy measures for IGTI. The first set is measures based on how a person’s position in the income distribution is related to that of his or her parents. We refer to them as relative measures of intergenerational mobility. A common measure is the probability that an adult’s earnings will be in the top quintile, conditional on being born to a family whose earnings were in the bottom quintile. Studies sometimes compute the full “transition matrix” of children’s versus parents’ quintile positions. A second measure within this set consists of simply estimating the parental income correlation: the correlation between child and parental earnings. A more complete but less commonly used measure consists of dividing earnings into multiple centiles and then estimating using a regression model where the dependent (right- hand side) variable is the centile position of the parent and the independent (left-hand side) variable is the position of the child (we refer to this measure as the rank-rank correlation).

The second set of proxy measures looks at how the level of earnings of the children and the parents are related. We refer to these as elasticity measures of intergenerational mobility. One can estimate the elasticity of children’s earnings to that of their parents—that is, the predicted percentage change of a child’s earning based on a percentage change in his or her parent’s earnings. (For example, in the United States, a child born to a parent whose earnings were 10 percent higher than the mean will earn on average 5 percent more than the mean.) This elas- ticity, termed intergenerational elasticity (IGE), is usually estimated through a regression of the

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Framework for Understanding Inequality in Income and Opportunity 5

logarithm of a measure of the child’s earnings against the logarithm of the parent’s earnings. The IGE measure is a function of the parent-child correlation, described above, but also of the variance of income in the parent’s and child’s generations.2

Measures based on the position within the distribution (such as the rank-rank correla- tion) are unrelated to current dispersion in wages; these measures simply aim to capture how much a father’s position on the income ladder matters to the position of the offspring.3 In contrast, IGE is directly affected by dispersion of earnings in the child’s generation, which can drive the relationship between inequality and inequality of opportunity in a mechanical way. The same rank-rank correlation will translate into a higher IGE when the income distribution in the child’s generation is wide and a lower IGE when income is more tightly distributed. Thus, even without changes in the relative measures of income mobility, an increase in income inequality would translate into higher-elasticity measures of intergenerational mobility. The IGE is important as well because it tells us how much the position of parents “matters.”

It should be noted that these mobility measures tend to be applied to income and not wealth. This is partly because of data limitations involving the scarcity of accurate and com- plete wealth data relative to income data, which makes it challenging to empirically produce comparable estimates for wealth mobility.

Income Generation and Sources of Income Disparities

Now that we have established the outcomes of interest, the concepts of opportunity, and some ways of measuring them, we present a framework for investigating their relationship. The simple framework below sets the stage for much of the discussion that follows. Essentially, we are seeking to understand how inequality in one generation will pass on to future generations through an inequality of opportunities.

For this framework, the important actors to consider are individuals and households. Households are composed of a number of individuals who generate income through the use of their capital—either physical or human—in the market. Each individual has a certain level of skills (human capital), decides whether to work and how much (the intensity of use), and earns an income (the return to the asset), depending on the market wage for his or her skills. Similarly, individuals invest their (physical) capital and earn income depending on the rate of return (such as the interest rate).4 The first equation in Figure 2.1 provides a visual representa- tion of this idea.

2 IGE equals the child-parent correlation multiplied by the ratio of the standard deviation of the log of child income to the standard deviation of the log of parent income. 3 Frequently, the father’s income is used for these estimations to avoid complications with fairly measuring women’s income, because of changes in workforce participation related to childbirth. Similarly, some studies focus on father-son income relationships. Given rising labor force participation rates among women, this segregation may not be necessary in the future. 4 Figure 2.1 provides a simple representation, though a more precise representation of this income-generation process would be given by It,g(HC,C,A)=Wt,g(HC,A,h,a) +Rt,g(C,Ic, A,a). Market income is a sum of labor income and capital income. Labor income is expressed as a time- and place-dependent wage function, which largely depends on the skills possessed (HC = human capital) and intensity of use, namely time and effort spent working (h = hours worked). Potentially, other assets (A) used with intensity (such as social connections) may affect how skills and effort are combined to generate labor earnings.

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6 Inequality and Opportunity

From market income, households pay taxes, and some receive cash transfers from the gov- ernment, such as welfare payments, subsidies, or social security, leaving them with disposable income to pay for goods and services (the second equation of Figure 2.1).5

Market income inequality arises through

1. differences in the amount and type of capital owned: These disparities are partly a result of inheritance but also of past behavior (decisions regarding how much to save or how much to invest in human capital—for example, by obtaining more schooling)

2. differences in the intensity of use of capital: Intensity of the use of skill (labor) takes form in the decisions of whether or not to work, how much to work, and how hard

3. the returns that individuals receive: Different types of assets (for example, a stock versus bond or high-school education versus college education) will typically fetch different returns. In a market economy, identical assets would earn the same return, though there could be geographical disparities. For instance, wages for similar work and skill level in a large city may be higher than in a rural community, which contributes to differ- ences in returns and market earnings. Furthermore, over time, inequality may widen if returns to certain assets—typically under the purview of high-income families, such as higher levels of education—increase.

Disposable income inequality—the income that individuals have available for consump- tion and investment—can differ substantially from market income, both in absolute terms and relative to others’, due to taxes and to transfers from the public sector. In fact, as we dis- cuss later, much of the cross-country variation in income inequality arises from the role of the public sector. Progressive taxes reduce inequality but may also reduce incentives to work or invest, which can create inefficiencies and a potential decrease in aggregate income.

The wage function (Wt,g) is time and place dependent, so the return to skills is different across time and space. Similarly, capital (C ) produces a return (R), depending on how much of it is invested and where (Ic). 5 Note, however, that the equations do not assume that assets, the intensity of use, and the return enter the equation mul- tiplicatively, as could be interpreted from the figure.

Figure 2.1 Market and Disposable Income in the Simple Framework

RAND RR1509-2.1

Disposable income

Taxes Public

transfers and goods

Household market income

Return to assets

Intensity of use

Capital Household

market income

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Framework for Understanding Inequality in Income and Opportunity 7

Inequality of Opportunity and the Intergenerational Transmission of Income

As will be discussed in Chapter Four, the earnings of parents and their children are empirically correlated. This fact could be explained with several plausible linkages within the framework above. These linkages will be useful when assessing the potential mechanisms through which income inequality can affect inequality of opportunity. As Figure 2.2 shows, a direct connec- tion may exist between income of parents and their children. More income allows families to invest in their children through better nutrition, enrichment activities, university fees, and so on. In Chapter Five, we present the evidence about the causal link of income and children’s human capital.

An important channel for intergenerational transmission is the transmission of parents’ capital to their children (Figure 2.3). The most obvious transmission is through gifts and

Figure 2.2 Types of Assets and the Human Capital Formation Process

RAND RR1509-2.2

Capital Interest rate,

etc. Savings

Invested (stock market, housing) or “under

the bed”

Skills: Cognitive and noncognitive skills/ education Labor market experience

Wages for different types of employment/skills Returns to schooling

Labor market participation Early childhood education Health Labor market participation

Use of social connections in economic activity

Wage premiums in certain jobs/unions

Other: Social capital, (social connections)

Return Intensity

of use Capital

How is it built?

Figure 2.3 Links Between Income of Parents and Children

NOTE: Arrows denote causal effects. Solid line denotes correlation. Dashed line presents correlation at certain level of locality (i.e., correlation due to tendency of children to live in the same locality or state as their parents). RAND RR1509-2.3

Returns Intensity

of use CapitalIncome

Returns Intensity

of use CapitalIncome

Parent

Child

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8 Inequality and Opportunity

inheritances, but skills also can be transmitted from parents to children (we present a brief overview on the literature on human capital formation in Chapter Five). Parental income and wealth could also be transmitted to their children through high skills if they are used to buy access to better schooling (for example, through housing in high-performing school districts) or other experiences that affect human capital accumulation.

The returns to different types of capital may also correlate to the extent that children live in the same areas as their parents. There are frictions (transaction costs of moving, location- specific social capital, and preferences) that result in children tending to live close to where they grew up. Thus, if geographical differences in returns to assets are persistent, there is a correla- tion between the returns faced by parents and children living in proximity.

These linkages can explain why income inequality may be correlated with inequality of opportunity. Different drivers of income and wealth inequality would affect inequality of opportunity differently. For instance, an increase in the concentration of wealth (changes in the distribution of assets according to the framework above) would likely make society less financially mobile (less equality of opportunity), since wealth can be easily transmitted across generations. On the other hand, increased inequality through higher returns to skill or edu- cation may not have such a large effect (a larger differential of the payoff to education might increase the differences in earnings but might not reduce the probability that a child achieves a given level of education or earnings), except through the increased opportunities for invest- ment in their children’s assets.6

6 However, increased inequality through higher returns to skill or education may have an indirect effect, since those earn- ing a higher return may be able to use that income to invest in their children. We discuss the possible linkages more fully in Chapter Five and the evidence regarding the importance of each of these linkages.

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