A Meta-Regression Analysis on the Association Between Income Inequality and Intergenerational Transmission of Income

A meta-regression analysis on the association between income inequality and intergenerational transmission of income

Ernesto F. L. Amaral Texas A&M University [email protected]

Sharron X. Wang Texas A&M University [email protected]

Shih-Keng Yen Texas A&M University [email protected]

Francisco Perez-Arce University of Southern California [email protected]

Abstract Our overall aim is to understand the association between income inequality and intergenerational transmission of income (degree to which conditions at birth and childhood determine socioeconomic situation later in life). Causality is hard to establish, because both income inequality and inequality in opportunity are results of complex social and economic outcomes. We analyze whether this correlation is observed across countries and time (as well as within countries), in a context of recent increases in income inequality. We investigate Great Gatsby curves and perform meta-regression analyses based on several papers on this topic. Results suggest that countries with high levels of income inequality tend to have higher levels of inequality of opportunity. Intergenerational income elasticity has stronger associations with Gini coefficient, compared to associations with top one percent income share. Once fixed effects are included for each country and study paper, these correlations lose significance. Increases in income inequality not necessarily bring decreases in intergenerational mobility maybe as a result of different drivers of inequality having diverse effects on mobility, as well as a consequence of public policies that might reduce associations between income inequality and inequality of opportunity.

Keywords Income inequality. Intergenerational transmission of income. Intergenerational mobility. Inequality of opportunity. Great Gatsby Curve. Meta-regression analysis.

Citation Amaral EFL, Wang SX, Yen SK, Perez-Arce F. 2018. “A meta-regression analysis on the association between income inequality and intergenerational transmission of income.” Open Science Framework, July 6. (https://doi.org/10.31219/osf.io/8qmhw)

1. Introduction A deeper understanding of the association between inequality and intergenerational mobility across nations is timely. Over the past three decades, income inequality has increased significantly in the United States and most developed countries. Earnings have stagnated except for those at the top end of the income scale, and the distribution of wealth has become more unequal. While stagnant income among low-income individuals is worrisome, an additional concern is that increased inequality may limit mobility and opportunities for their children. The fear is that the bigger the gap between poor and wealthy families, the harder it is for poor children to climb the economic ladder. Some argue that a reduction in intergenerational mobility is a consequence of inequality (OECD, 2011; 2015; Krueger, 2012). The Great Gatsby Curve is used to illustrate the inverse relationship between income inequality and intergenerational mobility: societies with higher level of inequality tend to have lower level of intergenerational mobility (Krueger, 2012; Miles Corak, 2013). However, whether the recent increases in income inequality cause less opportunity for those at the bottom depends on the drivers for greater inequality.

The present study employs meta-regression analysis to understand the correlation between societal inequality and intergenerational mobility and whether increase in inequality and inequality in opportunity move together. Intergenerational mobility is defined as the degree to which conditions at birth and childhood determine outcomes later in life. It measures socioeconomic standings pass from one generation to the next. For example, researchers use father-son income correlation to measure intergenerational mobility. Our study hopes to lead us to a better appraisal of the potential of policies to provide greater opportunities for all. A large range of public policies intend to tackle poverty and inequality. However, we know less about the extent to which each of these policies affect inequality of opportunity and related concepts such as the intergenerational transmission of income (IGTI). In addition, our study hopes to contribute to the literature of social inequality and mobility by examining the association between inequality and opportunity across nations using a novel technique.

The significant increase in income inequality in developed countries has been driven mostly by a combination of increased wages for highly educated workers and higher incomes for top earners

(often managers of large companies and a few other high-paying occupations) (Hout, 2012). Our appraisal of the research literature suggests that the increase in wages for the highly educated is a result of a greater demand for high-skill workers brought about changes in technology that have increased the productivity of skilled workers. The reasons behind the rapid increase in compensation of top earners is not as well understood, but globalization and information technology have played a role by permitting managers and other professionals to control larger operations.

To a lesser extent, there is evidence that income inequality has worsened in the United States due to institutional changes such as the decrease in the minimum wage in real terms, the weaker role of trade unions, and lower barriers to international trade. The first two factors have let wages fall for a sector of the working population. Though international trade cannot explain the raise of inequality in the 1980s and early 1990s, it may have had quantitatively larger impacts since the turn of the century, contributing to more low-paid service jobs and well-paid skill-intensive jobs, as well as to fewer middle-class manufacturing jobs (Kalleberg, 2011).

We analyze the likely associations of these changes with inequality of opportunity. Highly- skilled workers tend to have higher incomes, which may translate into greater investments in their children and thus greater inequality of investment in children’s skills (Gary Becker and Tomes, 1986). However, the quantitatively most important factor in the increase in inequality— higher incomes at the top of the income distribution—does not reduce the investments that most families can make in their children. Thus, from this point of view, increase in inequality is not likely to affect measures of inequality of opportunity that are based on movements throughout the income distribution.

We present empirical evidence regarding the extent to which economic inequality and inequality of opportunity move together across time and geographies, and then attempt to tease out the reasons behind it. We also discuss alternative measures for income inequality, the measures or proxies of inequality of opportunity, and how the use of alternative measures may matter. We describe the results of a meta-regression analysis designed to answer this particular question. Our results indicate that, across countries, there is a correlation between income inequality and the

common measures of inequality. However, across time, increases in inequality are not always accompanied by increases in inequality of opportunity. This suggests that the drivers of cross- country differences in income inequality may be different than those that drive.

2. Literature review 2.1. Main concepts of inequality 2.1.1. Income inequality The human capital theory suggests that there is a positive relation between person’s ability and person’s income level (Mincer, 1958; Gary S. Becker, 1962). Each person has their bargaining power in the labor market. The bargaining power is consisted of the human capital, such as education and working experience (Mincer, 1958; Gary S. Becker, 1962; 1993). In the simple framework below, individuals generate income through the use of their assets in the market: mostly labor and capital. Assets are not only physical resources (capital) but also, and most importantly, individual skills (which allow people to work productively). Individuals have a certain level of skills (assets), they decide whether to work and how much (intensity of use), and they make an income depending on the current wage for those skills (return to assets) (Gary S. Becker, 1993). Similarly, individuals may choose to invest their capital and earn income depending on the return rate of type of investment, such as interest rate.

Market income inequality arises through: (1) Differences in the amount and type of assets owned by individuals. These assets are partly a result of the accumulation of resources, such as savings and investment in education (i.e. achieved status), as well as of the conditions at birth (i.e. ascribed status) (Parsons, 1940). (2) Differences in the intensity of use of those assets. For example, some individuals work full time while others do not, which generates variations in wage. This intensity of use generates a inequality that is a result of the incentive to use assets (Collins, 1971). (3) Differences in income and rising inequality within occupations (Kim and Sakamoto, 2008; A. Sakamoto and Wang, 2017b). Social scientists have been using occupation as a proxy for person’s social status. Recently, however, some researchers have argued that inequality within occupation could be as high or even higher than inequality across occupations. (4) Differences in income across places of residence for the same activities, related to variations in geographical costs of living. For instance, wages for similar work in New York City may be

higher than in an average rural community, which contribute to differences in market earnings. Moreover, inequality rises if returns to capital and assets of families with high income and/or high levels of education increase more than among other families.

Incomes that individuals have available for consumption and investment differs from market income, due to taxes and transfers from the public sector. Disposable income equals market income, added by public transfers, and subtracted by taxes. Market income inequality can differ substantially from disposable income inequality. In fact, much of the cross-country variation in income inequality is due to differences in the role of the public sector (Mendoza et al., 1994). Progressive taxes reduce inequality but raise the classic tradeoff of reducing incentives, which can create inefficiencies.

We now review main concepts related to inequality, as defined for the purposes of this paper. A central concept is the magnitude of the variation in the amounts that people earn (income inequality) or what people have (wealth inequality). 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 compensating wage differentials). Income inequality is the extent to which individuals (or families) income differs from each other. Similarly, wealth inequality refers to the extent that the value of the assets individuals (or families) own differs from each other. Income inequality can be measured in terms of: (1) annual income inequality; (2) lifetime income inequality, which is less commonly measured; (3) wage or labor income inequality; and (4) market or disposable income inequality (the former refers to the income earned directly from labor and capital, while the latter subtracts taxes paid and public transfers received).

However, the measurement of income inequality is not straightforward. One could use simple statistical measures such as standard deviations of income (Atkinson, 1970; 1983). However, 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. Usually, inequality measures need to satisfy two principles. First, inequality measures need to be invariant to the proportionate increase or decrease of income/wealth. Second, inequality

measures need to satisfy the principle of transfers (Allison, 1978), which refers to the increase in inequality when money transfers from low-income persons to high-income persons, no matter how much the transfer is (Dalton, 1920).

The measure most commonly published by statistical agencies is the Gini coefficient (G), which

2 푛 푗 can be interpreted as a function of the mean difference. Gini=1/푛 (∑1 ∑1|푥푖 − 푥푗|)/2푢. Gini is measured in Lorenz curve. Thus, Gini can also be measured using A divided by (A+B). A refers to the area between the Lorenz curve and the line of perfect equality (diagonal). B refers to the area that is under the Lorenz curve. Gini index ranges from 0 to 1. 0 indicates perfect equality and 1 indicates perfect inequality. For example, if we take any two U.S. households at random, the expected difference is 2G percent of the mean (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 distribution, will affect measured inequality. Another advantage of using Gini is that it is insensitive to population’s size. Gini can be used to compare with populations with different sizes. The disadvantage of Gini is that sometimes the same Gini score might be computed from different shape of Loren curve. In addition, Gini does not account for population compositions (age structure, such as baby boom). The OECD countries have Gini ranging from 0.25-0.49. Africa and South America (especially South Africa and Brazil) have the highest Gini score in the world. The U.S. has a Gini score of around 0.46.

Another class of inequality measures are shape measures that are based on specific parts of the distribution, such as top measures, relative poverty, and poverty rates. A key measure includes top one percent share in income, which gauges how much of total income goes to the top one percent of earners. In this measure, changes in the relative income of those at the bottom and those in the middle may not affect inequality. These measures are important because much of the recent increases in inequality have been driven by higher incomes among the top one percent. In some cases, it will be important to distinguish between these classes of measures, as it is possible that the association of income inequality and inequality of opportunity depends on the utilized indicator.

2.1.2. Intergenerational mobility Inequality in opportunity is a less concrete concept. Conceptually, we are interested in the degree to which everyone has the same opportunities. This can be operationalized as the extent to which conditions at birth (including socioeconomic status of the parents) do not affect the probability distributions of income (Roemer et al., 2003). This concept is not possible to be measured in a consistent way across countries and time. However, we can aim to build measures of a related and more concrete concept: intergenerational transmission of income (IGTI) or intergenerational mobility (that we use interchangeably). IGTI refers to how much the income of children (when adults) is determined by the income level of their parents. These terms are intended to be a concrete approximation to inequality of opportunity since they describe the extent to which the income of the children is determined by the income of the parents.

IGTI can be approximated by measures that aim to capture the variation in probability of a child from a certain socioeconomic background reaching a given relative position in the income distribution as an adult. This set of proxy measures is based on how a child’s position in the income distribution is related to that of their parents. We refer to this as relative measures of intergenerational mobility. A common measure is the probability that a child’s adult earnings will be in the top quintile conditional on being born to families whose earnings were in the bottom quintile. In fact, studies usually compute the full transition matrix of children versus parental quintile. A second measure consists of simply estimating the correlation between children and parental earnings. A more complete but less commonly used measure consists of dividing earnings into multiple centiles, and then estimating a regression model where the dependent variable is the centile position of the parent and the independent variable is the position of the child (we refer to this as the rank-rank correlation).

Alternatively, we can use measures that capture the proportional difference in earnings of children born to wealthier parents versus poorer parents. This set of proxy measures looks at how earnings of children are related to earnings of parents. 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 parent’s earnings. A hypothetical example is “in the United States, a child born to a parent whose

earnings were 10% higher than the mean will earn on average 5% more than the mean.” This elasticity, termed intergenerational income elasticity (IGE), is usually estimated through a regression of the logarithm of children’s earnings against the logarithm of parent’s earnings. IGE is a function of the parent-child correlation: the child-parent correlation times the ratio of the standard deviation of the log of child income to the standard deviation of the log of parent income.

Measures based on “rank” might be a good option for our purposes, because they are unrelated to current dispersion in wages. This measure simply aims to capture how much a father’s position in the income ladder matters to the position of the offspring. In contrast, IGE is directly affected by current dispersion of earnings, which can drive the relationship between income inequality and opportunity inequality in a mechanical way. However, IGE is important as well, because it tells us how much being in a given rank matters. IGE can be thought as a ladder, where each rung represents the relative position in a society. When the rungs of the ladder are very close together, then position matters less. In practice, both measures matter, though they have different implications. We investigate both cases in this paper.

2.2. Trends in inequality Inequality has increased significantly in recent decades in the U.S. and most developed countries. This has been driven by a steep increase in income at the top of the distribution, stagnation of incomes throughout most of the distribution, and none to low growth at the bottom. The association between parents’ and adult children’s socioeconomic position is utilized by social scientists to investigate mobility (Torche, 2015). Higher associations mean less mobility. Studies have been conducting descriptive analyzes, which do not intend to measure causal relationships. The purpose is to understand correlations between inequality and mobility, which is a way to understand causal processes of child development and economic mobility, as well as its policy implications. Economists usually use earnings and income measures to investigate intergenerational mobility, while sociologists prefer occupational measures.

The intergenerational elasticity is typically estimated from an ordinary least-squares regression to capture the correlation between parents’ earnings in a previous period (independent variable)

and children’s earnings (dependent variable). This main coefficient measures the percentage difference in child earnings for each percentage point increase in parental earnings. Higher values of intergenerational earnings elasticity means that children’s position in the income distribution is strongly associated with parents’ position, which implies less income mobility across generations (i.e. immobile). Usually, models utilize earnings of fathers and sons to avoid issues related to the increase of female labor force participation across time. This estimation also takes into account terms that capture changes in average earnings (usually 5 years) due to changes in productivity, international trade, technology, labor market institutions, and other influences not correlated with parental earnings.

The intergenerational elasticity is a measure of the degree of economic mobility, but it does not inform the direction of change. For example, in the U.S., researchers documented father-son intergenerational elasticity rose from about 0.15–0.20 in the 1980s (Behrman and Taubman, 1985; Gary Becker and Tomes, 1986) to around 0.40 in the 1990s (Solon, 1999) and to about 0.50 in the 2000s (Mazumder, 2005). These increases were probably due to better measures of earnings across generations and to larger and nationally representative databases (Torche, 2015). In order to capture non-linear correlations between income inequality and intergenerational elasticities, studies have been using spline or locally weighted regressions, kernel density, higher-order polynomial terms of the predictor, transition matrices across percentiles of the earnings distribution, and quantile regression models (Torche, 2015). A recent study using U.S. tax and administrative data indicates that payoff to each additional percent of parental income is substantially larger among better-off families (Mitnik et al., 2015). Moreover, children from parents in the 10th income percentile are expected to have around half of the income of children from parents in the 50th percentile and around one third of the income of children from parents in the 90th income percentile. Transmission of advantage is greater for men’s earnings than for women’s earnings. In addition, intergenerational mobility increases when more people receive a college degree (Hout, 2012). These findings emphasize the need of public policies to increase equality of opportunity in the U.S.

A way to verify whether countries with high levels of income inequality tend to exhibit high levels of intergenerational transmission of economic conditions from parents to their children is

with Great Gatsby curves (Krueger, 2012; Miles Corak, 2013). These figures plot countries in two dimensions: (1) the horizontal axis indicates a measure of income inequality in several countries (Gini coefficient or top one percent income share, for instance); and (2) the vertical axis illustrates a measure of mobility across generations (intergenerational earnings elasticities or rank measures, for instance). Differences between countries in the Great Gatsby curve could be a consequence in the degree of upward mobility for children of low-income parents (Miles Corak, 2013). These differences could also be a result of downward mobility for children of top-income parents. Even with this limitation, intergenerational elasticity has been used to measure equality of opportunity, as Gini coefficient has been utilized to measure income inequality. Higher inequality is associated with lower economic mobility across generations, likely as a result of economic improvement being more unequally allocated among children (Brunori et al., 2013).

An important measure to indicate income inequality is the share of income owned by the wealthiest groups in a population (Atkinson et al., 2011). In the first half of the twentieth century, several countries experienced significant decreases in top income shares, as a consequence of the world wars and the Great Depression. This fall in top wealth concentration is primarily a capital income phenomenon. At the same time, income groups in the next four percent or in the second quintile are contained primarily by labor income, which fell much less than the top percentile during this period. In the second half of the twentieth century, top percentile shares declined after World War II and increased in recent decades in Europe, North America, Australia, New Zealand, China, and India. The United States experienced the fastest and largest income concentration in the top percentile group. The U.S. has relatively higher inequality than other developed countries. For example, the top 10 percent of the income earners hold more than half of the national income. Americans in the bottom quartile only makes 30% of the medium income.

Both economics and sociologists are interested in studying intergenerational mobility. Economics uses income correlation measure and sociology uses mobility tables to measure intergenerational mobility. The main difference is that economists measure income while sociologists measure occupation. This raises the question about whether occupation or income is a more efficient economic proxy in the analysis of intergenerational reproduction of inequality

(Hauser, 2010). Some researchers argue that occupation is no longer a proxy for long-term well- being. In addition, occupation does not indicate racial and gender wage differentials when holding the same type of occupation. For example, native-born second-generation Nigerian and Ghanaian Americans in the U.S. have higher occupational standings than non-Hispanic whites holding other characteristics constant, but their income level is lower than non-Hispanic whites. Regarding gender differentials, researchers also consistently find that women make less wage than men for the same type of job. Furthermore, it is more common nowadays for people to switch their careers due to rising individualism. Therefore, the popularity of using occupation to measure intergenerational mobility is declining. It is suggested that the income measure is a more proper one for the post-industrial societies (Arthur Sakamoto and Wang, 2017a).

We now explain the methods and data utilized to conduct our research. Our focus is on a meta- regression analysis to investigate the association of income inequality with inequality of opportunity in several countries over time.

3. Data and methods A central concern is that the recent increases in inequality have translated into a society that is less mobile and with opportunities that are less widely shared. However, there is much less evidence about the trends in inequality of opportunity since it is a concept more difficult to measure in a consistent manner. We aim to understand the relationship between income inequality and inequality in opportunity (the degree to which conditions at birth and childhood determine adult chances). In particular, we would like to focus on the question of whether higher inequality necessarily implies greater inequality in opportunity. Causality in this case is hard to establish since both income inequality and inequality in opportunity are results of complex social and economic outcomes. A more tractable question is whether increases in inequality and inequality in opportunity move together.

Previous analyses have shown that in country comparisons, at a given point in time, income inequality is correlated with measures of intergenerational income elasticity (IGE), which is the most widely used measure of intergenerational transmission of income (IGTI). This correlation is often referred to as the Great Gatsby curve (GGC) after being thus dubbed by the chairman of

the Council of Economic Advisers (Krueger, 2012), which has been documented (Miles Corak, 2013; M. Corak et al., 2014). Some argue that greater inequality of opportunity is a consequence of income inequality. For instance, income inequality “can stifle upward social mobility, making it harder for talented and hard-working people to get the rewards they deserve” (OECD, 2011).

We first conducted a comprehensive search of studies dealing with intergenerational income inequality from different countries that used quantitative measures, such as intergenerational elasticity, parental-child correlation, rank-rank regressions, and quintile transition matrices. A database was organized containing the identifying details of the paper, country of study, data source, year of children’s earnings, birth cohort of children, age(s) of children, outcome variable of children, type of income of children (individual or family), gender of children, calendar year of parents’ earnings, birth cohort of parents, age of parents, earnings measure of parents, type of income of parents (individual or family), number of years for which parental income is measured, gender of parents for which income measures are obtained, type of intergenerational of inequality measure, its value and associated standard error, confidence interval, t-test, and number of observations in the model.

Not all papers have information available for all these variables. For the analysis, we selected all articles that satisfied the criteria of following a standard methodology to measure intergenerational transmission of income and that provided enough information about their estimates (Tables 1a, 1b, 1c). >>> Table 1a <<< >>> Table 1b <<< >>> Table 1c <<< Information on income inequality measures was extracted from the Organisation for Economic Co-operation and Development (OECD) (Gini coefficients) and the World Top Income Database (WTID) (measures on top income share). Unfortunately, information on Gini coefficient is not available for some years. When the information of Gini was missing, we instead used the average of closest values (of how many years?) to estimate Gini coefficient for a specific year. Another measure of inequality: estimation of top one percent and top ten percent variables, are extracted from WTID followed these two steps: (1) use values of different top one percent

variables (A1110301–A1110306) and top ten percent variables (A1110101–A1110106) to correct for missing cases; (2) use past/future values to correct for missing cases. These measures of income inequality were matched in three different ways into our database, using: (1) year of children’s earnings; (2) birth cohort of children; and (3) year of parents’ earnings.

In the next section, we illustrate several Great Gatsby curves, which plot the association between inequality measures (Gini coefficient or top one percent income share) and intergenerational mobility (in this study, we focus on intergenerational income elasticity – IGE). We also conducted a meta-regression analysis (MRA), through a series of ordinary least squares estimates for intergenerational income elasticity (dependent variable), using different control variables: (1) Gini coefficient; (2) top one percent income share; (3) country indicators; (4) gender of children; (5) gender of parents; (6) number of years for which parents’ earnings are measured; (7) children’s age; (8) parents’ age; (9) type of children’s income (individual or family); and (10) paper indicators. We present results for the match between measures of inequality and intergenerational immobility by year of children’s earnings. In some cases, we have enough information to perform this match by birth cohort of children, but we do not report these results.

4. Results We study whether there is a correlation between income inequality and measures of intergenerational transmission of income (IGTI) both across countries and within-countries across time. We first update the cross-country correlations that had been reported in earlier studies and test their robustness to using alternative measures of income inequality and IGTI, through a series of Great Gatsby curves. Then, we analyze the evidence for countries for which we have more than one measure, both at an individual and an aggregate level through meta- regression analysis (MRA).

4.1. Great Gatsby curves There is a clear relationship between the Gini coefficient and intergenerational income elasticity (IGE) measures in developed countries. Panel A in Figure 1 shows a scatterplot of these measures, and confirms the result shown earlier (Miles Corak, 2013) that countries with a higher Gini coefficient tend to have a higher IGE coefficient (indicating less intergenerational mobility).

However, IGE estimates are subject to measurement errors and potential biases in their estimation, depending on the econometric methodology employed by a given study. Panel B in Figure 1 illustrates the same relationship as before but using all observations from different studies and different years (and not only one by country). >>> Figure 1 <<< IGE is directly affected by current dispersion of earnings, which can drive the relationship between inequality and inequality of opportunity in a mechanical way (Black and Devereux, 2011). For example, if the cross-country variation in Gini coefficients were entirely driven by recent increases in the dispersion of labor earnings (where recent meaning that they affect children’s cohort but not parents’ cohort), then inequality would be correlated with IGTI even if countries didn’t differ in terms of mobility. To understand why this is the case, consider a society that is perfectly immobile, in the sense that the position of the children in the income distribution is exactly the same as his parents. Now assume that the dispersion of income is increasing in that society, then IGE will go up, as the same difference in the position in the distribution brings a larger difference in terms of wages.

We have shown that countries with high inequality levels as indicated by “size measures” (such as the Gini coefficient) also have higher levels of inequality of opportunity. Given that the recent increases in inequality have been strongly driven by inequality at the top of the distribution, we analyze whether the relationship holds when using “shape measures,” such as the share of income accrued by the top one percent of earners (Figure 2). The relationship is much weaker, though it remains positive, when we use measures that focus only on the top part of the distribution. The correlation between income inequality and the IGE is stronger when using the Gini Coefficient (0.40 in Panel A of Figure 1) than when using top one percent (0.29 in Panel A of Figure 2), when we consider the most recent observation for each country. The correlation is also stronger when using the Gini coefficient (0.64 in Panel B of Figure 1) than when using top one percent measures (0.38 in Panel B of Figure 2), when considering multiple observations (one observation per country, year, and paper) >>> Figure 2 <<< We now analyze whether changes in income inequality within a country are correlated with changes in IGTI. Few studies have estimated IGE (and other measures of IGTI) for a single

country in different points in time, using the exact same methodology and data sources. This allows us to observe whether the cross-country correlation between income inequality and IGTI can be observed within a country through time. Figure 3 illustrates these patterns using two studies of the US, reflecting different time periods and data sources, but fairly similar methodologies. In Panel A of Figure 3, we calculate a linear trend line for measures of IGTI and income inequality using previous estimates (Chetty et al., 2014). In particular, we find a slightly positive trend in their rank-rank correlation and a slightly negative trend line for IGE. However, for the most part, their measures of IGTI illustrate a stable pattern over this (relatively short) period. This stability contrasts to the increasing income inequality observed in this period in the United States. The orange line shows the top one percent measure of income inequality, which is increasing over the period. In fact, the authors interpret their result as surprising: “the lack of a trend in intergenerational mobility contrasts with the increase in income inequality in recent decades. This contrast may be surprising given the well-known negative correlation between inequality and mobility across countries” (Chetty et al., 2014). However, if what matters is the inequality at early childhood, the results may not be that surprising, since inequality was not growing (or not as fast) in the 1970s when these cohorts were born. This inequality does not exhibit a trend over time (brown line in Panel A of Figure 3). >>> Figure 3 <<< Panel B of Figure 3 illustrates estimates of IGE coefficients from the second half of the 1970s to early 2000s, which exhibit a slight upward trend (Lee and Solon, 2009). As in Panel A of Figure 3, the inequality at time of income and at time of birth exhibited different trends: inequality was increasing since the 1980s, which would suggest income inequality moves in the same direction as inequality of opportunity. However, inequality was falling decades earlier, so if we use that measure we obtain the opposite relationship.

Figure 4 shows the same relationship for selected studies of other countries. Panel A shows the analysis for Australia (Leigh, 2007), Panel B for France (Lefranc and Trannoy, 2005), and Panel C for the United Kingdom (Blanden and Machin, 2008). Overall, from the graphical analysis, there does not seem to be a consistent relationship within country changes in IGTI and income inequality. The importance of inequality at time of birth, compared to inequality at time of birth, in order to predict IGTI is part of a complex discussion. For the Australian case, IGTI seems to

follow the decreasing trend of income inequality at time of birth. In the study about France, IGTI increased over time, while inequality at time of birth decreased over time and inequality at time of income was stable. In the case of United Kingdom, while some IGTI measures increased over time (IGE and rank-rank), inequality at time of birth slightly decreased and inequality at time of income slightly increased. >>> Figure 4 <<< These results emphasize the need to conduct a meta-regression analysis about the association of IGTI measures and income inequality measures (at time of birth and at time of income). The aim is to better understand these correlations in a multivariate approach.

4.2. Meta-regression analysis We formalize the analysis above by conducting a meta-regression analysis (MRA). In the formal regression approach, we combine individual studies of this section and estimate whether income changes have been associated with overall changes in IGTI. More specifically, we estimate ordinary least squares regression models where IGE is the dependent variable and the measure of income inequality is the independent variable of interest. This method allows us to control for methodological differences across studies. Overall, results from graphical analyses are confirmed by regression estimates.

Model 1 in Table 2 is the regression analogue to Panel B in Figure 1: Gini coefficient (independent variable) is statistically significant associated with IGE (dependent variable). The relationship is strengthened once we control for variables related to methodological differences across studies (model 2 in Table 2). More specifically, this association is stronger and remains significant when including controls regarding the methodology used by each study – gender of children, gender of parents for which income measures are obtained, number of years for which parental income is measured, children’s age, parents’ age, type of income of children (individual or family). However, when we control only for country of study (instead of the methodological variables), and thus eliminating the cross-country variation (relying in within country variation), the association of Gini coefficient with IGE drops in size (model 3 in Table 2). >>> Table 2 <<<

In order to consider both the association of methodological strategies and country of study, model 4 in Table 2 illustrates that the association of Gini coefficient with IGE drops but remains statistically significant. The only country that indicates a significant difference from the U.S. is Canada. All other countries that had significant associations with IGE, compared to the U.S. in model 3, do not hold that difference in model 4. As a way to deal with methodological differences and country of studies without the variables used in model 4, we include fixed effects for study paper in model 5. The association of Gini coefficient with IGE raises again to the level of model 1. An interesting aspect of model 5 is the increase in adjusted R2 to 0.676. However, this model doesn’t allow us to see the associations of each country and methodological variable with IGE.

Furthermore, we analyze whether changes in income inequality within a country are correlated with changes in IGE similar to the exercises in Figures 3 and 4, in order to allow only within country/study paper variability. Once we include methodological variables, country indicators, and study paper fixed effects (model 6 in Table 2), the association of Gini coefficient with IGE drops even further, compared to model 4, and is not statistically significant. Given that there remain only few studies that look at trends in IGTI, the association of Gini coefficient with IGE in model 6 is estimated out of only a few observations and are very imprecise. Thus, we do not conclude categorically that within country variation in inequality is in all cases uncorrelated with IGTI, but rather that we do not observe it in existing studies (which are limited in number).

The second set of models in Table 3 explores the association between top one percent income share and IGE. This exercise is similar to the analysis of Panel B in Figure 2, which indicates a significant correlation between top one percent measure and IGE. As we would expect, this measure of income inequality has a positive association with the measure of intergenerational mobility (models 1 and 2 in Table 3). However, this association loses statistical significance when controlling for country indicators (models 3 and 4 in Table 3). When we control for study paper (models 5 and 6 in Table 3), the association becomes significant again. Model 6 also indicates that coefficients for country indicators and methodological variables are not statistically significant. These results might be an indication that differences among countries and

methodological procedures are not important to be included in the model when we want to estimate the association between top one percent income share and IGE. >>> Table 3 <<< Finally, we estimate models to verify the joint association of Gini coefficient and top one percent income share with intergenerational mobility (Table 4). As we observed on Table 2, associations between Gini coefficient and IGE are significant from model 1 to model 5, which emphasizes a consistence of these findings. This association loses statistical significance only when we include country indicators, methodological variables, and fixed effects for study papers (model 6). This last model, as indicated before, reduces the variability in our database, because there are few papers with cross-country comparisons and varying methodology. >>> Table 4 <<< Coefficients for top one percent income share in Table 4 are not consistent with those in Table 3. More specifically, top one percent had significant positive associations with IGE in Table 3 on models 1, 2, 5, and 6, while in Table 4 they have significant negative associations with IGE on models 2, 3, and 4. This is an indication of collinearity between Gini coefficient and top one percent income share in the models of Table 4. The variance inflation factor at the bottom of this table indicates a strong collinearity of these income inequality measures. As expected the issue of collinearity is more pronounced in models with country indicators since Gini coefficient and top one percent income share are available at the country level. Even though these income inequality measures can vary within a country over time, this was not sufficient to overpass the issue of collinearity. We understand the limitations of our models. However, the intention was simply to measure the association between income inequality and intergenerational mobility, controlling for methodological aspects of the papers, unobserved variations at the country level (using country indicators), and other variations at the study paper level (using fixed effects for papers).

Moreover, the fact that Gini coefficient maintained the same results in Table 4 as in Table 2 might be related to the nature of how it is measured. Our measure of intergenerational mobility is based on the entire income distribution (IGE). As a result, our models might be capturing a stronger association of IGE with Gini coefficient (which is also a measure for all values of the income distribution) than with top one percent income share (which is concentrated on the

income of a specific proportion of the population). We also need to be careful with comparisons between the coefficients of these income inequality measures because Gini coefficient and top one percent income share have different units of measurement. In order to compare the magnitude of associations of these measures of income inequality with IGE, it is more appropriate to estimate coefficients in standard deviation units. The standardized coefficients of model 6 clarify that the magnitude of association of Gini coefficient with IGE is much stronger than the association of top one percent income share with IGE.

5. Conclusion There is a strong cross-country association between income inequality and measures of intergenerational mobility. However, it is not true that in all changes in income inequality bring about changes in mobility. This may be a result of: (1) different drivers of inequality trends having different impacts in mobility; and (2) public policies may reduce the impact of changes in inequality on mobility. We argue that recent increases in inequality have been partly driven by changes in the return to human capital and not by increasing disparities in the accumulation of human capital. On the other hand, earlier in the 20th century, a decreasing inequality was benefited by an increasing accumulation of education by large sectors of the population. These two different drivers reduced inequality earlier on, increased inequality recently, and may have had very different impacts on mobility. Public policies may have helped reducing the impact on mobility. Anti-poverty policies have helped holding back poverty in a time of increased inequality, and this may have also prevented mobility from decreasing.

Even though there are several ways to measure inequality, and each has its strengths and weaknesses, there is no question that income inequality is rising, driven by increased market inequality from the labor market. Given that the effects of income on children outcomes are higher in the bottom end of the income, this might be an important reason that precludes the parental determination of children income (a proxy for inequality of opportunity) to rise as rapidly as income inequality. Income inequality and inequality of opportunity are correlated across countries, and this correlation can be driven by a variety of underlying factors. In particular, greater disparities in income translate into greater disparities in families’ capacity to

invest in children’s human capital. In fact, there is evidence that increasing the income of the poor has a causal positive impact on human capital accumulation of their children.

Public policies such as income supplementation can break the links between inequality and inequality in opportunity. A wide range of anti-poverty policies have been implemented in the U.S. over the last five decades, which may have helped stave off poverty and inequality in opportunity, despite the labor market trends towards greater inequality. These policies include conditional income transfers, such as Temporary Assistance for Needy Families (TANF) and Earned Income Tax Credit (EITC); quasi-income, such as Supplemental Nutrition Assistance Program (SNAP), formerly food stamps; and direct services provision, such as Head Start. Not all policies that affect inequality will have the same impact on inequality of opportunity. Some impacts may directly reduce income inequality, but only indirectly benefit their children. Other policies (i.e. policies on children and education) may have a direct impact on inequality of opportunity, but their impacts on contemporaneous inequality may be small or null. However, there are currently no direct measurements that allow us to gauge the current impact of policies on inequality in opportunity.

Given the central importance of this subject, an assessment of policies in terms of their potential impact on equality of opportunity should be made. Studies should investigate whether public policies have impacts on measures of intergenerational transmission of income. Policies can be evaluated in several other manners and intergenerational transmission of income captures all aspects of equality of opportunity, but an analysis linking these aspects would be crucial to deal with this important socioeconomic issue.

6. References Allison, P. D. (1978). Measures of inequality. American Sociological Review, 43(6), 865-880. Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2, 244- 263. Atkinson, A. B. (1983). On the measurement of inequality (with bibliography). In A. B. Atkinson (Ed.), Social Justice and Public Policy (pp. 15-36). Sussex: Wheatsheaf Books Ltd. Atkinson, A. B., & Morelli, S. (2014). Chartbook of economic inequality. Society for the Study of Economic Inequality (ECINEQ) Working Paper Series, ECINEQ WP 2014 - 324, 1- 65. Atkinson, A. B., Piketty, T., & Saez, E. (2011). Top incomes in the long run of history. Journal of Economic Literature, 49(1), 3-71. Becker, G., & Tomes, N. (1986). Human capital and the rise and fall of families. Journal of Labor Economics, 4, S1-S39. Becker, G. S. (1962). Investment in human capital: A theoretical analysis. Journal of Political Economy, 70(5), 9-49. Becker, G. S. (1993). Human capital revisited. In G. S. Becker (Ed.), Human Capital: A Theoretical and Empirical Analysis with Special Reference to Education (pp. 15-28). Chicago: The University of Chicago Press. Behrman, J., & Taubman, P. (1985). Intergenerational earnings mobility in the United States: Some estimates and a test of Becker's intergenerational endowments model. Review of Economics and Statistics, 67, 144-151. Black, S. E., & Devereux, P. J. (2011). Recent developments in intergenerational mobility. In O. Ashenfelter, & D. Card (Eds.), Handbook of Labor Economics (pp. 1487-1541). Amsterdam: Elsevier. Blanden, B., & Machin, S. (2008). Up and down the generational income ladder in Britain: Past changes and future prospects. National Institute Economic Review, 205, 101-116. Brunori, P., Ferreira, F. H. G., & Peragine, V. (2013). Inequality of opportunity, income inequality and economic mobility: Some international comparisons. Policy Research Working Paper, The World Bank, 6304. Chetty, R., Hendren, N., Kline, P., Saez, E., & Turner, N. (2014). Is the United States still a land of opportunity? Recent trends in intergenerational mobility. American Economic Review: Papers & Proceedings, 104(5), 141-147. Collins, R. (1971). Functional and conflict theories of educational stratification. American Sociological Review, 36, 1002-1019. Corak, M. (2013). Income inequality, equality of opportunity, and intergenerational mobility. The Journal of Economic Perspectives, 27(3), 79-102. Corak, M., Lindquist, M. J., & Mazumder, B. (2014). A comparison of upward and downward intergenerational mobility in Canada, Sweden and the United States. Labour Economics, 30, 185-200. Dalton, H. (1920). The measurement of the inequality of incomes. Economic Journal, 30(119), 348-361. Hauser, R. M. (2010). Intergenerational economic mobility in the United States: Measures, differentials and trends. Center for Demography and Ecology (CDE) Working Paper, University of Wisconsin-Madison, 98-12.

Hout, M. (2012). Social and economic returns to college education in the United States. Annual Review of Sociology, 38, 379-400. Kalleberg, A. L. (2011). Good Jobs, Bad Jobs: The Rise of Polarized and Precarious Employment Systems in the United States, 1970s-2000s. New York: Russell Sage Foundation. Kim, C., & Sakamoto, A. (2008). The rise of intra-occupational wage inequality in the United States, 1983 to 2002. American Sociological Review, 73(1), 129-157. Krueger, A. B. (2012) 'The rise and consequences of inequality in the United States' C. o. E. Advisers. January 12. Lee, C. I., & Solon, G. (2009). Trends in intergenerational income mobility. The Review of Economics and Statistics, 91(4), 766-772. Lefranc, A., & Trannoy, A. (2005). Intergenerational earnings mobility in France: Is France more mobile than the US? Annales d'Économie et de Statistique, 78, 57-77. Leigh, A. (2007). Intergenerational mobility in Australia. The B.E. Journal of Economic Analysis & Policy, 7(2), Article 6. Mazumder, B. (2005). Fortunate sons: New estimates of intergenerational mobility in the United States using social security earnings data. The Review of Economics and Statistics, 87(2), 235-255. Mendoza, E. G., Razin, A., & Tesar, L. L. (1994). Effective tax rates in macroeconomics: Cross- country estimates of tax rates on factor incomes and consumption. Journal of Monetary Economics, 34(3), 297-323. Mincer, J. (1958). Investment in human capital and personal income distribution. Journal of Political Economy, 66(4), 281-302. Mitnik, P., Bryant, V., Weber, M., & Grusky, D. B. (2015). New estimates of intergenerational mobility using administrative data. Stanford Center on Poverty and Inequality. OECD. (2011). Divided We Stand: Why Inequality Keeps Rising. Paris: Organization for Economic Cooperation and Development (OECD) Publishing. OECD. (2015). In It Together: Why Less Inequality Benefits All. Paris: Organization for Economic Cooperation and Development (OECD) Publishing. Parsons, T. (1940). An analytical approach to the theory of social stratification. American Journal of Sociology, 45(6), 841-862. Roemer, J. E., Aaberge, R., Colombino, U., Fritzell, J., Jenkins, S. P., Lefranc, A., et al. (2003). To what extent do fiscal regimes equalize opportunities for income acquisition among citizens? Journal of Public Economics, 87(3-4), 539-565. Sakamoto, A., & Wang, S. X. (2017a). A critical appraisal of occupational mobility tables versus economic models in the study of intergenerational mobility. (Paper presented at the Annual Meeting of the Population Association of America (PAA), Chicago) Sakamoto, A., & Wang, S. X. (2017b). Occupational and organizational effects on wages among college-educated workers in 2003 and 2010. Social Currents, 4(2), 175-195. Solon, G. (Ed.) (1999). Intergenerational mobility in the labor market. (Amsterdam: North Holland) Torche, F. (2015). Analyses of intergenerational mobility: An interdisciplinary review. Annals of American Academy of Political and Social Science (AAPSS), 657, 37-62.

Table 1a. List of countries, years, data sources, and authors of selected studies used for the meta-regression analysis, United States Country Year Data source Authors (year) United 1969-2002 Panel Study of Income Dynamics Vogel (2008) States 1971, 1973, National Longitudinal Study Zimmerman (1992) 1975, 1976, 1978, 1980, 1981 1977-1998, Panel Study of Income Dynamics Lee and Solon (2009) 2000 1979-2000 Cross National Equivalent File Vogel (2008)

1980 N/A Behrman and Taubman (1985) cited in Corak (2006) 1980 1979 National Longitudinal Survey Grawe (2004) cited in Corak (2006) of Youth 1981 National Longitudinal Study Zimmerman (1992) cited in Corak (2006)

1984 Panel Study of Income Dynamics Solon (1992)

1984-1989 Panel Study of Income Dynamics Couch and Dunn (1997)

1984-2006 Panel Study of Income Dynamics Bloome (2015)

1987 N/A Björklund and Jäntti (1997) cited in Corak (2006) 1989-2010 1979 National Longitudinal Survey Bloome (2017) of Youth 1990 Panel Study of Income Dynamics Bjorklund and Jantti (1997)

1990-2009 1979 National Longitudinal Survey Bloome (2015) of Youth 1992 N/A Levine Mazumder (2002) cited in Corak (2006) 1995-1998 Survey of Income and Program Mazumder (2005) Participation 1996-2008 1979 National Longitudinal Survey Bratberg et al. (2017) of Youth 2000-2011 Population tax records Chetty et al. (2014)

1993 Panel Study of Income Dynamics Corak (2006)

1996-2002 1979 National Longitudinal Survey Jäntti et al. (2006) of Youth 1997 N/A Mazumder (2001) cited in Corak (2006)

2000 1979 National Longitudinal Survey Gregg et al. (2017) of Youth 2001 Panel Study of Income Dynamics Leigh (2007) (PSID) 2003-2007 Survey of Income and Program Corak, Lindquist, and Mazumder (2014) Participation 2010 Statistics of Income Mobility Panel Mitnik et al. (2015) Note: The complete list of references used for meta-regression analysis is available on Appendix A.

Table 1b. List of countries, years, data sources, and authors of selected studies used for the meta-regression analysis, Europe Denmark 1998-2000 Administrative data Jäntti et al. (2006)

2000-2011 Danish Tax Agency administrative Boserup, Kopczuk, and Kreiner (2015) data 2002 Administrative Registers at Hussain et al. (2008) Statistics Denmark Finland 1985, 1990, 1970-1995 Quinquennial Censuses Osterbacka (2001) 1995 1993-2000 Administrative data Jäntti et al. (2006)

2000 Finnish Longitudinal Census Pekkarinen, Uusitalo, and Kerr (2009) France 1977, 1985, Formation-Qualification-Profession Lefranc and Trannoy (2005) 1993 surveys 1993 N/A Corak (2006) Germany 1983-2004 German Socio-Economic Panel Vogel (2008)

1983-2004 Cross National Equivalent File Vogel (2008)

1984-1989 German Socio-Economic Panel Couch and Dunn (1997)

1997 German Socio-Economic Panel Corak (2006)

2001-2012 German Socio-economic Panel Bratberg et al. (2017) Italy 2000-2004 Survey of Household Income & Mocetti (2007) Wealth 2000-2004 Bank of Italy Survey on Household Piraino (2007) Income and Wealth Norway 1992-1999 Administrative data Jäntti et al. (2006)

1996-2006 Administrative data Bratberg et al. (2017) Sweden 1971-1980 Swedish income tax records Gustafsson (1994)

1996, 1998, Statistics Sweden's Vosters and Nybom (2017) 2000, 2002, multigenerational register, census, 2004, 2006, and income tax data 2007 1990 Swedish Level of Living Surveys Bjorklund and Jantti (1997) (SLLS) 1990-1992 Swedish Income Panel ÖSterberg (2000)

1990-2007 Statistics Sweden's Corak, Lindquist, and Mazumder (2014) multigenerational register and administrative data 1996-1999 Administrative data Jäntti et al. (2006)

1996-2007 Administrative data Bratberg et al. (2017)

1999 1965-1980 Semidecennial Censuses Bjorklund and Chadwick (2003)

1999 Swedish tax register Bjorklund, Lindahl, and Plug (2006)

1999 Statistics Sweden Hirvonen (2008)

2006 Swedish registry data Gregg et al. (2017) United 1975-1978 Rowntree survey and follow-up Atkinson (1981) Kingdom 1981, 1991, National Child Development Study Gregg, Macmillan, and Vittori (2017) 2000 2004, 2008 1991 N/A Corak (2006)

1991 National Child Development Dearden, Machin, and Reed (1997) Survey 1991 National Child Development Study Blanden, Gregg, and Macmillan (2013)

1991-1999 National Child Development Study Jäntti et al (2006)

1991-2003 British Household Panel Survey Nicoletti and Ermisch (2007)

1991, 2004 National Child Development Study Blanden and Machin (2008) & British Cohort Study 1996, 2000, British Cohort Study Gregg, Macmillan, and Vittori (2017) 2004, 2008, 2012 2000 British Cohort Study Blanden, Gregg, and Macmillan (2013)

2012 British 1970 Cohort Study Gregg et al. (2017) Note: The complete list of references used for meta-regression analysis is available on Appendix A.

Table 1c. List of countries, years, data sources, and authors of selected studies used for the meta-regression analysis, other countries Australia 1965-2004 Negotiating the Life Course Survey Leigh (2007) & Household Income and Labour Dynamics in Australia Survey 2014-2015 Household Income and Labour Murray et al. (2017) Dynamics Australia Brazil 1996 Pesquisa Nacional por Amostra de Dunn (2007) Domicílios 1996, 1998, National Household Sample Survey Ribeiro (2017) 2000, 2002, & Social Dimensions of Inequalities 2004, 2006, Survey 2008 Canada 1993-1996, Intergenerational Income Data Chen, Ostrovsky, and Piraino (2017) 2003-2006, 2001-2008 1995 Administrative data & Canadian Corak and Heisz (1999) income tax 1996 Canadian Intergenerational Income Corak (2006) Data 1997-1999 Statistics Canada/administrative Corak, Lindquist, and Mazumder (2014) data China 1989, 1991, China Health and Nutrition Survey Yuan (2017) 1993, 1997, 2000, 2004, 2006, 2009 South 2008-2015 National Income Dynamics Study Finn, Leibbrandt, and Ranchhod (2016) Africa Vietnam 2004, 2008, Viet Nam Household Living Lam and Cuong (2017) 2010, 2014 Standard Surveys Note: The complete list of references used for meta-regression analysis is available on Appendix A.

Figure 1. Intergenerational transmission of income, IGTI (intergenerational income elasticity, IGE) by income inequality (Gini coefficient), matched by year of children’s earnings Panel A. Most recent observation for each country

Correlation of Gini and IGE: 0.395 (p=0.230; p=0.197, when clustering standard errors by study). Panel B. One observation per country, year, and paper

Correlation of Gini and IGE: 0.640 (p=0.000; p=0.001, when clustering standard errors by study). Source: Gini coefficient is from the Organisation for Economic Co-operation and Development (OECD) and intergenerational transmission of income (IGTI) measure is from a series of studies listed in reference section. Income inequality measure used is for the year contemporaneous to the year of IGTI measure.

Figure 2. Intergenerational transmission of income, IGTI (intergenerational income elasticity, IGE) by income inequality (top 1% income share), matched by year of children’s earnings Panel A. Most recent observation for each country

Correlation of top 1% and IGE: 0.292 (p=0.384; p=0.276, when clustering standard errors by study). Panel B. One observation per country, year, and paper

Correlation of top 1% and IGE: 0.384 (p=0.000; p=0.085, when clustering standard errors by study). Source: Top income share is from the World Top Incomes Database and intergenerational transmission of income (IGTI) measure is from a series of studies listed in reference section. Income inequality measure used is for the year contemporaneous to the year of IGTI measure.

Figure 3. Trends of intergenerational transmission of income and income inequality by year, United States Panel A. Chetty et al. (2014)

Panel B. Lee and Solon (2009)

Note: Top 1% income share is in the 0–1 scale. “Top 1% at time of birth” was merged to intergenerational transmission of income (IGTI) by birth cohort of children, but it is shown in graph using year of children’s earnings. Source: Gini coefficient is from the Organisation for Economic Co-operation and Development (OECD), top income share is from the World Top Incomes Database, and IGTI measure is from a series of studies listed in reference section. Income inequality measure used is for the year contemporaneous to the year of IGTI measure.

Figure 4. Trends of intergenerational transmission of income and income inequality by year Panel A. Australia by Leigh (2007)

Panel B. France by Lefranc and Trannoy (2005)

Panel C. United Kingdom by Blanden and Machin (2008)

Table 2. Ordinary least squares estimates for intergenerational income elasticity (dependent variable) using Gini coefficient Variables Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Constant -0.111*** 0.009 0.027 0.054 -0.217** -0.221 (0.030) (0.067) (0.164) (0.185) (0.098) (0.307) Gini coefficient 1.424*** 1.681*** 1.115** 1.057* 1.439*** 0.857 (0.099) (0.123) (0.458) (0.542) (0.178) (0.736) Male children ref. ref. ref.

Both children -0.077*** -0.091*** -0.010 (0.018) (0.018) (0.032) Female children -0.023* -0.016 -0.029*** (0.013) (0.012) (0.011) Fathers ref. ref. ref.

Both parents -0.013 -0.014 0.092** (0.016) (0.016) (0.045) Mothers -0.158*** -0.164*** -0.057 (0.040) (0.038) (0.038) 1 year of parents’ earnings ref. ref. ref.

Missing -0.023 0.021 0.179 (0.030) (0.030) (0.113) 2 years 0.014 0.039 0.021 (0.020) (0.025) (0.041) 3+ years 0.014 0.069*** 0.167*** (0.017) (0.024) (0.049) Children’s age -0.003*** 0.002 4.35e-05 (0.001) (0.001) (0.002) Parents’ age -0.003*** -0.002** 0.003 (0.001) (0.001) (0.004) Children’s individual income ref. ref. ref.

Missing -0.110*** -0.072** dropped (0.033) (0.036) Children’s family income 0.028* 0.020 0.015 (0.015) (0.015) (0.020) United States ref. ref. ref.

Canada -0.117*** -0.168*** -0.202* (0.031) (0.039) (0.112) Denmark -0.115* -0.109 -0.122 (0.061) (0.075) (0.111) Finland -0.147** -0.070 -0.095 (0.072) (0.083) (0.122) France 0.020 0.031 -0.034 (0.045) (0.053) (0.124) Germany -0.072 -0.076 -0.021 (0.058) (0.065) (0.084) Italy 0.094*** 0.039 0.126* (0.032) (0.034) (0.066) Norway -0.132* -0.111 -0.103 (0.079) (0.087) (0.109) Sweden -0.044 -0.092 -0.022 (0.060) (0.077) (0.109) United Kingdom -0.091*** -0.042 0.014 (0.017) (0.028) (0.046) Fixed effects Paper Paper R2 0.373 0.535 0.526 0.622 0.717 0.760 Adjusted R2 0.371 0.519 0.512 0.598 0.676 0.708 Observations 349 347 349 347 349 347 Note: Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Source: Selected papers, Organisation for Economic Co-operation and Development (OECD), and World Top Incomes Database.

Table 3. Ordinary least squares estimates for intergenerational income elasticity (dependent variable) using top one percent income share Variables Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Constant 0.167*** 0.375*** 0.345*** 0.514*** 0.235 0.200 (0.029) (0.083) (0.045) (0.123) (0.177) (0.398) Top 1% income share 0.016*** 0.017*** 0.004 0.004 0.020*** 0.025*** (0.003) (0.003) (0.004) (0.006) (0.005) (0.009) Male children ref. ref. ref.

Both children -0.095*** -0.090** -0.018 (0.033) (0.035) (0.078) Female children -0.054** -0.034 -0.044* (0.023) (0.023) (0.026) Fathers ref. ref. ref.

Both parents -0.026 -0.004 0.069 (0.025) (0.031) (0.108) Mothers -0.213*** -0.152* -0.062 (0.076) (0.078) (0.093) 1 year of parents’ earnings ref. ref. ref.

Missing -0.085* -0.026 -0.050 (0.050) (0.053) (0.184) 2 years -0.083*** -0.047 -0.011 (0.030) (0.036) (0.056) 3+ years -0.050** -0.002 0.046 (0.023) (0.032) (0.060) Children’s age -0.005** 3.47e-04 -0.003 (0.002) (0.003) (0.004) Parents’ age -1.69e-04 -0.004** -0.001 (0.001) (0.002) (0.009) Children’s individual income ref. ref. ref.

Missing -0.041 -0.024 dropped (0.059) (0.068) Children’s family income 0.028 0.0038 0.021 (0.027) (0.030) (0.049) United States ref. ref. ref.

Canada -0.149*** -0.196*** -0.170 (0.032) (0.048) (0.233) Denmark -0.194*** -0.198*** 0.061 (0.049) (0.072) (0.150) Finland -0.246*** -0.166** 0.036 (0.059) (0.080) (0.177) France -0.027 -0.092 0.154 (0.046) (0.065) (0.276) Germany -0.147** -0.162** 3.34e-05 (0.065) (0.082) (0.105) Italy 0.098* 0.031 0.087 (0.052) (0.067) (0.235) Norway -0.217** -0.236** 0.032 (0.106) (0.116) (0.156) Sweden -0.114*** -0.160*** 0.089 (0.025) (0.059) (0.130) United Kingdom -0.078*** -0.108** 0.137 (0.026) (0.050) (0.117) Fixed effects Paper Paper R2 0.063 0.146 0.165 0.197 0.262 0.277 Adjusted R2 0.062 0.127 0.150 0.165 0.189 0.175 Observations 558 554 558 554 558 554 Note: Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Source: Selected papers, Organisation for Economic Co-operation and Development (OECD), and World Top Incomes Database.

Table 4. Ordinary least squares estimates for intergenerational income elasticity (dependent variable) using Gini coefficient and top one percent income share Model 6 Variables Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 (standardized coefficients) Constant -0.101*** -0.154** -0.252 -0.358 -0.195* -0.224 (0.032) (0.076) (0.217) (0.218) (0.108) (0.320) Gini coefficient 1.302*** 2.569*** 2.344*** 3.002*** 1.271*** 0.871 0.373 (0.171) (0.243) (0.777) (0.776) (0.377) (0.880) Top 1% income share 0.002 -0.014*** -0.010* -0.018*** 0.002 -2.01e-04 -0.006 (0.003) (0.003) (0.005) (0.005) (0.005) (0.007) Male children ref. ref. ref. ref.

Both children -0.064*** -0.086*** -0.010 -0.026 (0.017) (0.018) (0.032) Female children -0.022* -0.018 -0.029*** -0.095 (0.012) (0.012) (0.011) Fathers ref. ref. ref. ref.

Both parents -0.015 -0.004 0.092** 0.310 (0.016) (0.016) (0.045) Mothers -0.159*** -0.164*** -0.057 -0.061 (0.039) (0.037) (0.038) 1 year of parents’ earnings ref. ref. ref. ref.

Missing -0.001 0.026 0.180 0.432 (0.030) (0.030) (0.114) 2 years 0.049** 0.040 0.021 0.068 (0.022) (0.025) (0.041) 3+ years 0.039** 0.061** 0.167*** 0.628 (0.017) (0.024) (0.049) Children’s age -0.002* 0.002 5.01e-05 0.002 (0.001) (0.001) (0.002) Parents’ age -0.003*** -0.003*** 0.003 0.171 (0.001) (0.001) (0.004) Children’s individual income ref. ref. ref. ref.

Missing -0.153*** -0.095*** dropped dropped (0.034) (0.036) Children’s family income 0.043*** 0.019 0.015 0.053 (0.015) (0.015) (0.020) United States ref. ref. ref.

Canada -0.083** -0.118*** -0.202* -0.458 (0.035) (0.041) (0.112) Denmark -0.065 -0.056 -0.123 -0.205 (0.066) (0.075) (0.112) Finland -0.081 0.010 -0.095 -0.130 (0.079) (0.085) (0.122) France 0.035 0.035 -0.035 -0.054 (0.045) (0.052) (0.126) Germany -0.008 0.014 -0.021 -0.020 (0.067) (0.069) (0.085) Italy 0.070** -0.008 0.125* 0.178 (0.034) (0.036) (0.073) Norway -0.074 -0.044 -0.103 -0.072 (0.084) (0.088) (0.109) Sweden 0.043 0.025 -0.022 -0.072 (0.074) (0.083) (0.109) United Kingdom -0.123*** -0.098*** 0.013 0.037 (0.023) (0.032) (0.055) Fixed effects Paper Paper Paper R2 0.374 0.559 0.531 0.635 0.717 0.760 0.760 Adjusted R2 0.371 0.541 0.516 0.611 0.675 0.707 0.707 Variance Inflation Factor (VIF) Gini coefficient 2.98 8.15 79.84 98.13 28.04 167.67 167.67 Top 1% income share 2.98 6.31 15.18 19.22 18.96 38.68 38.68 Mean VIF 2.98 3.16 15.91 12.63 9.54 22.29 22.29

Observations 349 347 349 347 349 347 347 Note: Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Variance inflation factor is shown only for Gini coefficient and top one percent income share, but it was also estimated for all other covariates. Source: Selected papers, Organisation for Economic Co-operation and Development (OECD), and World Top Incomes Database.

Appendix A. References for studies on Tables 1a, 1b, and 1c Atkinson, A. B. (1981). On intergenerational income mobility in Britain. Journal of Post Keynesian Economics, 3(2), 194-218. Björklund, A., Lindahl, M., & Plug, E. (2006). The origins of intergenerational associations: Lessons from Swedish adoption data. The Quarterly Journal of Economics, 121(3), 999- 1028. Bjorklund, A., & Chadwick, L. (2003). Intergenerational income mobility in permanent and separated families. Economics Letters, 80(2), 239-246. Bjorklund, A., & Jantti, M. (1997). Intergenerational income mobility in Sweden compared to the United States. The American Economic Review, 87(5), 1009-1018. Blanden, J., Gregg, P., & Macmillan, L. (2013). Intergenerational persistence in income and social class: the effect of within-group inequality. Journal of the Royal Statistical Society: Series A (Statistics in Society), 176(2), 541-563. Blanden, J., & Machin, S. (2008). Up and down the generational income ladder in Britain: Past changes and future prospects. National Institute Economic Review, 205, 101-116. Bloome, D. (2015). Income inequality and intergenerational income mobility in the United States. Social Forces, 93(3), 1047–1080. Bloome, D. (2017). Childhood family structure and intergenerational income mobility in the United States. Demography, 54, 541-569. Boserup, S. H., Kopczuk, W., & Kreiner, C. T. (2015). Born with a silver spoon: Danish evidence on intergenerational wealth formation from cradle to adulthood. Working Paper, Department of Economics, University of Copenhagen. Bratberg, E., Davis, J., Mazumder, B., Nybom, M., Schnitzlein, D. D., & Vaage, K. (2017). A comparison of intergenerational mobility curves in Germany, Norway, Sweden, and the US. The Scandinavian Journal of Economics, 119(1), 72-101. Chen, W.-H., Ostrovsky, Y., & Piraino, P. (2017). Lifecycle variation, errors-in-variables bias and nonlinearities in intergenerational income transmission: new evidence from Canada. Labour Economics, 44, 1-12. Chetty, R., Hendren, N., Kline, P., Saez, E., & Turner, N. (2014). Is the United States still a land of opportunity? Recent trends in intergenerational mobility. American Economic Review: Papers & Proceedings, 104(5), 141-147. Corak, M. (2006). Do poor children become poor adults? Lessons from a cross country comparison of generational earnings mobility. IZA Discussion Paper Series No. 1993. Corak, M., & Heisz, A. (1999). The intergenerational earnings and income mobility of Canadian men: Evidence from longitudinal income tax data. The Journal of Human Resources, 34(3), 504-533. Corak, M., Lindquist, M. J., & Mazumder, B. (2014). A comparison of upward and downward intergenerational mobility in Canada, Sweden and the United States. Labour Economics, 30, 185-200. Couch, K. A., & Dunn, T. A. (1997). Intergenerational correlations in labor market status: A comparison of the United States and Germany. The Journal of Human Resources, 32(1), 210-232. Dearden, L., Machin, S., & Reed, H. (1997). Intergenerational mobility in Britain. The Economic Journal, 107(440), 47-66. Dunn, C. E. (2007). The intergenerational transmission of lifetime earnings: Evidence from Brazil. The B.E. Journal of Economic Analysis & Policy, 7(2), Article 2.

Finn, A., Leibbrandt, M., & Ranchhod, V. (2016). Patterns of persistence: Intergenerational mobility and education in South Africa. SALDRU Working Paper No. 175. Gregg, P., Jonsson, J. O., Macmillan, L., & Mood, C. (2017). The role of education for intergenerational income mobility: A comparison of the United States, Great Britain, and Sweden. Social Forces, 96(1), 121-152. Gregg, P., Macmillan, L., & Vittori, C. (2017). Moving towards estimating sons' lifetime intergenerational economic mobility in the UK. Oxford Bulletin of Economics and Statistics, 79(1), 79-100. Gustafsson, B. (1994). The degree and pattern of income immobility in Sweden. Review of Income and Wealth, 40(1), 67-86. Hirvonen, L. H. (2008). Intergenerational earnings mobility among daughters and sons: Evidence from sweden and a comparison with the United States. American Journal of Economics and Sociology, 67(5), 777-826. Hussain, M. A., Munk, M. D., & Bonke, J. (2008). How sensitive is intergenerational earnings mobility to different measures? The Danish National Centre for Social Research Working Paper No. 7. Jäntti, M., Bratsberg, B., & Røed, K. et al. (2006). American exceptionalism in a new light: A comparison of intergenerational earnings mobility in the Nordic countries, the United Kingdom and the United States. IZA Discussion Paper Series No. 1938. Lam, N. T., & Cuong, N. V. (2017). Intragenerational and intergenerational mobility in Viet Nam. ADBI Working Paper No. 722. Lee, C.-I., & Solon, G. (2009). Trends in intergenerational income mobility. The Review of Economics and Statistics, 91(4), 766-772. Lefranc, A., & Trannoy, A. (2005). Intergenerational earnings mobility in France: Is France more mobile than the US? Annales d'Économie et de Statistique, 78, 57-77. Leigh, A. (2007). Intergenerational mobility in Australia. The B.E. Journal of Economic Analysis & Policy, 7(2), Article 6. Mazumder, B. (2005). Fortunate sons: New estimates of intergenerational mobility in the United States using social security earnings data. The Review of Economics and Statistics, 87(2), 235-255. Mitnik, P., Bryant, V., Weber, M., & Grusky, D. B. (2015). New estimates of intergenerational mobility using administrative data. Stanford Center on Poverty and Inequality. Mocetti, S. (2007). Intergenerational earnings mobility in Italy. The B.E. Journal of Economic Analysis & Policy, 7(2), Article 5. Murray, C., Clark, R., Mendolia, S., & Siminski, P. (2017). Direct measures of intergenerational income mobility for Australia. IZA Discussion Paper No. 11020. Nicoletti, C., & Ermisch, J. F. (2007). Intergenerational earnings mobility: Changes across cohorts in Britain. The B.E. Journal of Economic Analysis & Policy, 7(2), Article 9. Osterbacka, E. (2001). Family background and economic status in Finland. Scandinavian Journal of Economics, 103(3), 467-484. ÖSterberg, T. (2000). Intergenerational income mobility in Sweden: What do tax-data show? Review of Income and Wealth, 46(4), 421-436. Pekkarinen, T., Uusitalo, R., & Kerr, S. (2009). School tracking and intergenerational income mobility: Evidence from the Finish comprehensive school reform. Journal of Public Economics, 93, 965-973.

Piraino, P. (2007). Comparable estimates of intergenerational income mobility in Italy. The B.E. Journal of Economic Analysis & Policy, 7(2), Article 1. Ribeiro, C. A. C. (2017). Occupational and income intergenerational mobility in Brazil between the 1990s and 2000s. Sociologia & Antropologia, 7(1), 157-285. Vogel, T. (2008). Reassessing intergenerational mobility in Germany and the United States: The impact of differences in lifecycle earnings patterns. SFB Discussion Paper No. 2006-055, Humboldt University, Berlin. Vosters, K., & Nybom, M. (2017). Intergenerational persistence in latent socioeconomic status: Evidence from Sweden and the United States. Journal of Labor Economics, 35(3), 869- 901. Yuan, W. (2017). The sins of the fathers: Intergenerational income mobility in China. Review of Income and Wealth, 63(2), 219-233. Zimmerman, D. J. (1992). Regression toward mediocrity in economic stature. The American Economic Review, 82(3), 409-429.