THE
QUARTERLY JOURNAL OF ECONOMICS
Vol. CXVIII February 2003 Issue 1
INCOME INEQUALITY IN THE UNITED STATES, 1913–1998*
THOMAS PIKETTY AND EMMANUEL SAEZ
This paper presents new homogeneous series on top shares of income and wages from 1913 to 1998 in the United States using individual tax returns data. Top income and wages shares display a U-shaped pattern over the century. Our series suggest that the large shocks that capital owners experienced during the Great Depression and World War II have had a permanent effect on top capital incomes. We argue that steep progressive income and estate taxation may have prevented large fortunes from fully recovering from these shocks. Top wage shares were flat before World War II, dropped precipitously during the war, and did not start to recover before the late 1960s but are now higher than before World War II. As a result, the working rich have replaced the rentiers at the top of the income distribution.
I. INTRODUCTION
According to Kuznets’ influential hypothesis, income inequal- ity should follow an inverse-U shape along the development pro- cess, first rising with industrialization and then declining, as more and more workers join the high-productivity sectors of the economy [Kuznets 1955]. Today, the Kuznets curve is widely held to have doubled back on itself, especially in the United States, with the period of falling inequality observed during the first half
* We thank Anthony Atkinson, Lawrence Katz, and two anonymous referees for their very helpful and detailed comments. We have also benefited from com- ments and discussions with Daron Acemoglu, Philippe Aghion, Alberto Alesina, David Autor, Abhijit Banerjee, Francesco Caselli, Dora Costa, David Cutler, Esther Duflo, Daniel Feenberg, William Gale, Claudia Goldin, Alan Krueger, Howard Rosenthal, and numerous seminar participants. We acknowledge finan- cial support from the MacArthur foundation. All our series are available in machine readable format in an electronic appendix of the working paper version at www.nber.org/papers/W8467.
© 2003 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics, February 2003
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of the twentieth century being succeeded by a very sharp reversal of the trend since the 1970s. This does not, however, imply that Kuznets’ hypothesis is no longer of interest. One could indeed argue that what has been happening since the 1970s is just a remake of the previous inverse-U curve: a new industrial revolu- tion has taken place, thereby leading to increasing inequality, and inequality will decline again at some point, as more and more workers benefit from the innovations.
To cast light on this central issue, we build new homogeneous series on top shares of pretax income and wages in the United States covering the 1913 to 1998 period. These new series are based primarily on tax returns data published annually by the Internal Revenue Service (IRS) since the income tax was insti- tuted in 1913, as well as on the large micro-files of tax returns released by the IRS since 1960.
First, we have constructed annual series of shares of total income accruing to various upper income groups fractiles within the top decile of the income distribution. For each of these frac- tiles we also present the shares of each source of income such as wages, business income, and capital income. Kuznets [1953] did produce a number of top income shares series covering the 1913 to 1948 period, but tended to underestimate top income shares, and the highest group analyzed by Kuznets is the top percentile.1
Most importantly, nobody has attempted to estimate, as we do here, homogeneous series covering the entire century.2 Second, we have constructed annual 1927 to 1998 series of top shares of salaries for the top fractiles of the wage income distribution, based on tax returns tabulations by size of salaries compiled by the IRS since 1927. To our knowledge, this is the first time that a homogeneous annual series of top wage shares starting before the 1950s for the United States has been produced.3 Finally, in order to complete our analysis of top capital income earners, we have also used estate tax returns tabulations to construct quasi-an- nual series (1916 to 1997) of top estates.
1. Analyzing smaller groups within the top percentile is critical because capital income is extremely concentrated.
2. Feenberg and Poterba [1993, 2000] have constructed top income share series covering the 1951–1995 period, but their series are not homogeneous with those of Kuznets. Moreover, they provide income shares series only for the top 0.5 percent, and not for other fractiles.
3. Previous studies on wage inequality before 1945 in the United States rely mostly on occupational pay ratios [Williamson and Lindert 1980; Goldin and Margo 1992; Goldin and Katz 1999].
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Our estimated top shares series display a U-shape over the century and suggest that a pure Kuznets mechanism cannot fully account for the facts. We find that top capital incomes were severely hit by major shocks in the first part of the century. The post-World War I depression and the Great Depression destroyed many businesses and thus significantly reduced top capital in- comes. The wars generated large fiscal shocks, especially in the corporate sector that mechanically reduced distributions to stock- holders. We argue that top capital incomes were never able to fully recover from these shocks, probably because of the dynamic effects of progressive taxation on capital accumulation and wealth inequality. We also show that top wage shares were flat from the 1920s until 1940 and dropped precipitously during the war. Top wage shares have started to recover from the World War II shock in the late 1960s, and they are now higher than before World War II. Thus, the increase in top income shares in the last three decades is the direct consequence of the surge in top wages. As a result, the composition of income in the top income groups has shifted dramatically over the century: the working rich have now replaced the coupon-clipping rentiers. We argue that both the downturn and the upturn of top wage shares seem too sudden to be accounted for by technical change alone. Our series suggest that other factors, such as changes in labor market institutions, fiscal policy, or more generally social norms regarding pay in- equality may have played important roles in the determination of the wage structure. Although our proposed interpretation for the observed trends seems plausible to us, we stress that we cannot prove that progressive taxation and social norms have indeed played the role we attribute to them. In our view, the primary contribution of this paper is to provide new series on income and wage inequality.
One additional motivation for constructing long series is to be able to separate the trends in inequality that are the consequence of real economic change from those that are due to fiscal manipu- lation. The issue of fiscal manipulation has recently received much attention. Studies analyzing the effects of the Tax Reform Act of 1986 (TRA86) have emphasized that a large part of the response observable in tax returns was due to income shifting between the corporate sector and the individual sector [Slemrod 1996; Gordon and Slemrod 2000]. We do not deny that fiscal manipulation can have substantial short-run effects, but we ar- gue that most long-run inequality trends are the consequence of
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real economic change, and that a short-run perspective might lead to attribute improperly some of these trends to fiscal manipulation.
The paper is organized as follows. Section II describes our data sources and outlines our estimation methods. In Section III we present and analyze the trends in top income shares, with particular attention to the issue of top capital incomes. Section IV focuses on trends in top wages shares. Section V offers concluding comments and compares our U. S. findings with comparable series recently constructed for France by Piketty [2001a, 2001b] and for the United Kingdom by Atkinson [2001]. All series and complete technical details about our methodology are gathered in appendices of the working paper version of the paper [Piketty and Saez 2001].
II. DATA AND METHODOLOGY Our estimations rely on tax returns statistics compiled an-
nually by the Internal Revenue Service since the beginning of the modern U. S. income tax in 1913. Before 1944, because of large exemptions levels, only a small fraction of individuals had to file tax returns and therefore, by necessity, we must restrict our analysis to the top decile of the income distribution.4 Because our data are based on tax returns, they do not provide information on the distribution of individual incomes within a tax unit. As a result, all our series are for tax units and not individuals.5 A tax unit is defined as a married couple living together (with depen- dents) or a single adult (with dependents), as in the current tax law. The average number of individuals per tax unit decreased over the century but this decrease was roughly uniform across income groups. Therefore, if income were evenly allocated to individuals within tax units,6 the time series pattern of top shares based on individuals should be very similar to that based on tax units.
4. From 1913 to 1916, because of higher exemption levels, we can provide estimates only within the top percentile.
5. Kuznets [1953] nevertheless decided to estimate series based on individ- uals not tax units. We explain in Piketty and Saez [2001] why his method produced a downward bias in the levels (though not in the pattern) of top shares.
6. Obviously, income is not earned evenly across individuals within tax units, and, because of increasing female labor force participation, the share of income earned by the primary earner has certainly declined over the century. Therefore, inequality series based on income earned at the individual level would be differ- ent. Our tax returns statistics are mute on this issue. We come back to that point when we present our wage estimates.
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Tax units within the top decile form a very heterogeneous group, from the high middle class families deriving most of their income from wages to the super-rich living off large fortunes. More precisely, we will see that the composition of income varies substantially by income level within the top decile. Therefore, it is critical to divide the top decile into smaller fractiles. Following Piketty [2001a, 2001b], in addition to the top decile (denoted by P90 –100), we have constructed series for a number of higher fractiles within the top decile: the top 5 percent (P95–100), the top 1 percent (P99 –100), the top 0.5 percent (P99.5–100), the top 0.1 percent (P99.9 –100), and the top 0.01 percent (P99.99 –100). This also allows us to analyze the five intermediate fractiles within the top decile: P90 –95, P95–99, P99 –99.5, P99.5–99.9, P99.9 –99.99. Each fractile is defined relative to the total number of potential tax units in the entire U. S. population. This number is computed using population and family census statistics [U. S. Department of Commerce, Bureau of Census 1975; Bureau of Census 1999] and should not be confused with the actual number of tax returns filed. In order to get a more concrete sense of size of income by fractiles, Table I displays the thresholds, the average income level in each fractile, along with the number of tax units in each fractile all for 1998.
We use a gross income definition including all income items reported on tax returns and before all deductions: salaries and wages, small business and farm income, partnership and fidu-
TABLE I THRESHOLDS AND AVERAGE INCOMES IN TOP GROUPS WITHIN THE
TOP DECILE IN 1998
Thresholds (1)
Income level (2) Fractiles (3)
Number of tax units (4)
Average income (5)
Full Population 130,945,000 $38,740 P90 $81,700 P90–95 6,550,000 $94,000 P95 $107,400 P95–99 5,240,000 $143,000 P99 $230,200 P99–99.5 655,000 $267,000 P99.5 $316,100 P99.5–99.9 524,000 $494,000 P99.9 $790,400 P99.9–99.99 117,900 $1,490,000 P99.99 $3,620,500 P99.99–100 13,100 $9,970,000
Computations are based on income tax returns statistics (see Piketty and Saez [2001], Appendix A). Income is defined as gross income excluding capital gains and before individual taxes. Amounts are expressed in 1998 dollars.
Source: Table A0 and Table A4, row 1998 in Piketty and Saez [2001].
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ciary income, dividends, interest, rents, royalties, and other small items reported as other income. Realized capital gains are not an annual flow of income (in general, capital gains are realized by individuals in a lumpy way) and form a very volatile component of income with large aggregate variations from year to year de- pending on stock price variations. Therefore, we focus mainly on series that exclude capital gains.7 Income, according to our defi- nition, is computed before individual income taxes and individual payroll taxes but after employers’ payroll taxes and corporate income taxes.8
The sources from which we obtained our data consist of tables displaying the number of tax returns, the amounts re- ported, and the income composition, for a large number of income brackets [U. S. Treasury Department, Internal Revenue Service, 1916 –1998]. As the top tail of the income distribution is very well approximated by a Pareto distribution, we use simple parametric interpolation methods to estimate the thresholds and average income levels for each of our fractiles. We then estimate shares of income by dividing the income amounts accruing to each fractile by total personal income computed from National Income Ac- counts [Kuznets 1941, 1945; U. S. Department of Commerce 2000].9 Using the published information on composition of income by brackets and a simple linear interpolation method, we decom- pose the amount of income for each fractile into five components: salaries and wages, dividends, interest income, rents and royal- ties, and business income.
We use the same methodology to compute top wage shares using published tables classifying tax returns by size of salaries and wages. In this case, fractiles are defined relative to the total number of tax units with positive wages and salaries estimated as the number of part-time and full workers from National Income Accounts [U. S. Department of Commerce 2000] less the number
7. In order to assess the sensitivity of our results to the treatment of capital gains, we present additional series including capital gains (see below). Details on the methodology and complete series are presented in the appendix to Piketty and Saez [2001].
8. Computing series after individual income taxes is beyond the scope of the present paper but is a necessary step to analyze the redistributive power of the income tax over time, as well as behavioral responses to individual income taxation.
9. This methodology using tax returns to compute the level of top incomes, and using national accounts to compute the total income denominator is standard in historical studies of income inequality. Kuznets [1953], for instance, adopted this method.
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of wives who are employees (estimated from U. S. Department of Commerce, Bureau of Census [1975] and Bureau of Census [1999]). The sum of total wages in the economy used to compute shares is also obtained from National Income Accounts [U. S. Department of Commerce 2000].
The published IRS data vary from year to year, and there are numerous changes in tax law between 1913 and 1998.10 To con- struct homogeneous series, we make a number of adjustments and corrections. Individual tax returns micro-files are available since 1960.11 They allow us to do exact computations of all our statistics for that period and to check the validity of our adjustments. Kuznets [1953] was not able to use micro-files to assess possible biases in his estimates due to his methodological assumptions.12
Our method differs from the recent important studies by Feenberg and Poterba [1993, 2000] who derive series of the in- come share of the top 0.5 percent13 for 1951 to 1995. They use total income reported on tax returns as their denominator and the total adult population as their base to obtain the number of tax units corresponding to the top fractiles.14 Their method is simpler than ours but cannot be used for years before 1945 when a small fraction of the population filed tax returns.
III. TOP INCOME SHARES AND COMPOSITION
III. A. Trends in Top Income Shares
The basic series of top income shares are presented in Table II. Figure I shows that the income share of the top decile of tax units from 1917 to 1998 is U-shaped. The share of the top decile fluctuated around 40 to 45 percent during the interwar period. It declined substantially to about 30 percent during World War II and then remained stable at 31 to 32 percent until the 1970s when it increased again. By the mid-1990s the share had crossed the 40 percent level and is now at a level close to the prewar level,
10. The most important example is the treatment of capital gains and the percentage of these gains that are included in the statistics tables.
11. These data are known as the Individual Tax Model files. They contain about 100,000 returns per year and largely oversample high incomes, providing a very precise picture of top reported incomes.
12. In particular, Kuznet’s treatment of capital gains produces a downward bias in the level of his top shares.
13. They also present incomplete series for the top 1 percent. 14. This method is not fully satisfying for a long-run study as the average
number of adults per tax unit has decreased significantly since World War II.
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9INCOME INEQUALITY IN THE UNITED STATES, 1913–1998
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10 QUARTERLY JOURNAL OF ECONOMICS
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although a bit lower. Therefore, the evidence suggests that the twentieth century decline in inequality took place in a very spe- cific and brief time interval. Such an abrupt decline cannot easily be reconciled with a Kuznets-type process. The smooth increase in inequality in the last three decades is more consistent with slow underlying changes in the demand and supply of factors, even though it should be noted that a significant part of the gain is concentrated in 1987 and 1988 just after the Tax Reform Act of 1986 which sharply cut the top marginal income tax rates (we will return to this issue).
Looking at the bottom fractiles within the top decile (P90 –95 and P95–99) in Figure II reveals new evidence. These fractiles account for a relatively small fraction of the total fluctuation of the top decile income share. The drop in the shares of fractiles P90 –95 and P95–99 during World War II is less extreme than that for the top decile as a whole, and they start recovering from the World War II shock directly after the war. These shares do not increase much during the 1980s and 1990s (the P90 –95 share was fairly stable, and the P95–99 share increased by about 2 percentage points while the top decile share increased by about 10 percentage points).
FIGURE I The Top Decile Income Share, 1917–1998
Source: Table II, column P90 –100.
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In contrast to P90 –95 and P95–99, the top percentile (P99 – 100 in Figure II) underwent enormous fluctuations over the twen- tieth century. The share of total income received by the top 1 percent was about 18 percent before World War I, but only about 8 percent from the late 1950s to the 1970s. The top percentile share declined during World War I and the postwar depression (1916 to 1920), recovered during the 1920s boom, and declined again during the Great Depression (1929 to 1932, and 1936 to 1938) and World War II. This highly specific timing for the pattern of top incomes, composed primarily of capital income (see below), strongly suggests that shocks to capital owners between 1914 and 1945 (depression and wars) played a key role. The depressions of the interwar period were far more profound in their effects than the post-World War II recessions. As a result, it is not surprising that the fluctuations in top shares were far wider during the interwar period than in the decades after the war.15
15. The fact that top shares are very smooth after 1945 and bumpy before is therefore not an artifact of an increase in the accuracy of the data (in fact, the data are more detailed before World War II than after), but reflects real changes in the economic conditions.
FIGURE II The Income Shares of P90 –95, P95–99, and P99 –100, 1913–1998
Source: Table II, columns P90 –95, P95–99, and P99 –100.
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Figure II shows that the fluctuation of shares for P90 –95 and P95–99 is exactly opposite to the fluctuation for P99 –100 over the business cycle from 1917 to 1939. As shown below, the P90 –95 and P95–99 incomes are mostly composed of wage income, while the P99 –100 incomes are mostly composed of capital income. During the large downturns of the interwar period, capital in- come sharply fell while wages (especially for those near the top), which are generally rigid nominally, improved in relative terms. On the other hand, during the booms (1923–1929) and the recov- ery (1933–1936), capital income increased quickly, but as prices rose, top wages lost in relative terms.16
The negative effect of the wars on top incomes is due in part to the large tax increases enacted to finance them. During both wars, the corporate income tax (as well as the individual income tax) was drastically increased and this mechanically reduced the distributions to stockholders.17 National Income Accounts show that during World War II, corporate profits surged, but dividend distributions stagnated mostly because of the increase in the corporate tax (that increased from less than 20 percent to over 50 percent) but also because retained earnings increased sharply.18
The decline in top incomes during the first part of the century is even more pronounced for higher fractiles within the top per- centile, groups that could be expected to rely more heavily on capital income. As depicted in Figure III, the income share of the top 0.01 percent underwent huge fluctuations during the century. In 1915 the top 0.01 percent earned 400 times more than the average; in 1970 the average top 0.01 percent income was “only” 50 times the average; in 1998 they earned about 250 times the average income.
Our long-term series place the TRA86 episode in a longer term perspective. Feenberg and Poterba [1993, 2000], looking at the top 0.5 percent income shares series ending in 1992 (respec- tively, 1995), argued that the surge after TRA86 appeared per- manent. However, completing the series up to 1998 shows that the significant increase in the top marginal tax rate, from 31 to
16. Piketty [2001a, 2001b] shows that exactly the same phenomenon is tak- ing place in France during the same period.
17. During World War I, top income tax rates reached “modern” levels above 60 percent in less than two years. As was forcefully argued at that time by Mellon [1924], it is conceivable that large incomes found temporary ways to avoid taxation at a time when the administration of the Internal Revenue Service was still in its infancy.
18. Computing top shares for incomes before corporate taxes by imputing corporate profits corresponding to dividends received is an important task left for future research (see Goldsmith et al. [1954] and Cartter [1954] for such an attempt around the World War II period).
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39.6 percent, enacted in 1993 on did not prevent top shares from increasing sharply.19 From that perspective, looking at Figures II and III, the average increase in top shares from 1985 to 1994 is not significantly higher than the increase from 1994 to 1998 or from 1978 to 1984. As a result, it is possible to argue that TRA86 produced no permanent surge in top income shares, but only a transitory blip. The analysis of top wage shares in Section IV will reinforce this interpretation. In any case, the pattern of top in- come shares cannot be explained fully by the pattern of top income tax rates.
III. B. The Secular Decline of Top Capital Incomes
To demonstrate more conclusively that shocks to capital in- come were responsible for the large decline of top shares in the first part of the century, we look at the composition of income within the top fractiles. Table III reports the composition of income in top groups for various years from 1916 and 1998. Figure IV displays the composition of income for each fractile in
19. Slemrod and Bakija [2000] pointed out that top incomes have surged in recent years. They note that tax payments by taxpayers with AGI above $200,000 increased significantly from 1995 to 1997.
FIGURE III The Top 0.01 Percent Income Share, 1913–1998
Source: Table II, column P99.99 –100.
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1 9 7 4
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2 7 .3
1 6 .0
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5 1 .2
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2 1 .4
7 .0
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2 4 .0
3 5 .2
1 0 .2
2 2 .9
1 8 .3
5 8 .8
1 4 .2
1 9 7 9
8 9 .1
5 .2
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2 .3
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1 0 .1
4 .5
6 4 .4
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FIGURE IV Income Composition of Top Groups within the Top Decile in 1929 and 1998
Capital income does not include capital gains. Source: Table III, rows 1929 and 1998.
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1929 (Panel A) and 1998 (Panel B). As expected, Panel A shows that the share of wage income is a declining function of income and that the share of capital income (dividends, interest, rents, and royalties) is an increasing function of income. The share of entrepreneurial income (self-employment, small businesses, and partnerships) is fairly flat. Thus, individuals in fractiles P90 –95 and P95–99 rely mostly on labor income (capital income is less than 25 percent for these groups), while individuals in the top percentile derive most of their income in the form of capital income. Complete series in Piketty and Saez [2001] show that the sharply increasing pattern of capital income is entirely due to dividends. This evidence confirms that the very large decrease of top incomes observed during the 1914 to 1945 period was to a large extent a capital income phenomenon.
One might also be tempted to interpret the large upturn in top income shares observed since the 1970s as a revival of very high capital incomes, but this is not the case. As shown in Panel B, the income composition pattern has changed drastically be- tween 1929 and 1998. In 1998 the share of wage income has increased significantly for all top groups. Even at the very top, wage income and entrepreneurial income form the vast majority of income. The share of capital income remains small (less than 25 percent) even for the highest incomes. Therefore, the compo- sition of high incomes at the end of the century is very different from those earlier in the century. Before World War II, the richest Americans were overwhelmingly rentiers deriving most of their income from wealth holdings (mainly in the form of dividends). Occupation data by income bracket were published by the IRS in 1916. These data show that, at the very top, the vast majority of taxpayers reported themselves as “Capitalists: Investors and Speculators,” while a small fraction reported themselves as sal- aried workers (see Piketty and Saez [2001], Table 3 for details). In contrast, in 1998 more than half of the very top taxpayers derive the major part of their income in the form of wages and salaries. Thus, today, the “working rich” celebrated by Forbes magazine have overtaken the “coupon-clipping rentiers.”
The dramatic evolution of the composition of top incomes appears robust and independent from the erratic evolution of capital gains excluded in Figures I to IV. The last two columns of Table II display the top 1 percent share including realized capital gains. In column (10), in order to get around the lumpiness of realizations, individuals are ranked by income excluding capital
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gains, but capital gains are added back into income to compute shares. In column (11) individuals are ranked by income includ- ing capital gains, and capital gains are added back into income to compute shares. These additional series show that including capi- tal gains does not modify our main conclusion that very top income shares dropped enormously during the 1914 –1945 period before increasing steadily in the last three decades.20
The decline of the capital income share is a very long-term phenomenon and is not limited to a few years and a few thou- sand tax units. Figure V shows a gradual secular decline of the share of capital income (again excluding capital gains realiza- tions) and dividends in the top 0.5 percent fractile from the 1920s to the 1990s: capital income was about 55 percent of total income in the 1920s, 35 percent in the 1950s–1960s, and 15 percent in the
20. It is interesting, however, to note that during the 1960s, when dividends were strongly tax disadvantaged relative to capital gains, capital gains do seem to represent a larger share in top incomes than during other periods such as the 1920s or late 1990s that also witnessed large increases in stock prices.
FIGURE V The Capital Income Share in the Top 0.5 Percent, 1916 –1998
Series display the share of capital income (excluding capital gains) and divi- dends in total income (excluding capital gains) for the top 0.5 percent income quantile.
Source: Authors’ computations are based on income tax returns statistics (series reported in Piketty and Saez [2001], Table A7, column P99.5–100).
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1990s. Sharp declines occurred during World War I, the Great Depression, and World War II. Capital income recovered only partially from these shocks in the late 1940s and started a steady decline in the mid-1960s. This secular decline is entirely due to dividends: the share of interest, rent, and royalties has been roughly flat while the dividend share has dropped from about 40 percent in the 1920s, to about 25 percent in the 1950s and 1960s, to less than 10 percent in the 1990s.21
Most importantly, the secular decline of top capital incomes is due to a decreased concentration of capital income rather than a decline in the share of capital income in the economy as a whole. As displayed in Figure VI, the National Income Accounts series show that the aggregate capital income share has not declined over the century. As is well-known, factor shares in the corporate sector have been fairly flat in the long run with the labor share around 70 –75 percent, and the capital share around 25–30 per- cent (Panel A). The share of capital income in aggregate personal income is about 20 percent both in the 1920s and in the 1990s (Panel B). Similarly, the share of dividends was around 5 percent in the late 1990s and only slightly higher (about 6 –7 percent) before the Great Depression. This secular decline is very small compared with the enormous fall of top capital incomes.22 Con- trary to a widely held view, dividends as a whole are still alive and well.23
It should be noted, however, that the ratio of total dividends reported on individual tax returns to personal dividends in Na- tional Accounts has declined continuously over the period 1927 to 1995, starting from a level close to 90 percent in 1927, declining slowly to 60 percent in 1988, and dropping precipitously to less than 40 percent in 1995. This decline is due mostly to the growth of funded pension plans and retirement saving accounts through which individuals receive dividends that are never reported as dividends on income tax returns. For the highest income earners,
21. Tax statistics by size of dividends analyzed in Piketty and Saez [2001] confirm a drastic decline of top dividend incomes over the century. In 1998 dollars, top 0.1 percent dividends earners reported on average about $500,000 of dividends in 1927 but less than $240,000 in 1995.
22. The share of dividends in personal income starts declining in 1940 be- cause the corporate income tax increases sharply and permanently, mechanically reducing profits that can be distributed to stockholders.
23. As documented by Fama and French [2000], a growing fraction of firms never pay dividends (especially in the new technology industries, where firms often make no profit at all), but the point is that total dividend payments continue to grow at the same rate as aggregate corporate profits.
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FIGURE VI Capital Income in the Corporate and Personal Sector, 1929 –1998
Source: Authors’ computations are based on National Income and Product Accounts. Panel A from NIPA Table 1.16; consumption of fixed capital and net interest
have been included in the capital share. Panel B from NIPA Table 2.1; capital income includes dividends, interest, and rents.
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this additional source of dividends is likely to be very small relative to dividends directly reported on tax returns.
Estate tax returns statistics (available since the beginning of the estate tax in 1916) are an alternative important source of data to analyze the evolution of large fortunes.24 Lampman [1962] used these data to construct top 1 percent wealth shares for a few years between 1922 and 1956 using the estate multiplier method. We have constructed quasi-annual series of average levels (in 1998 dollars) of gross estates for various fractiles of decedents aged 25 and above (ranked by size of gross estate). Panel A in Figure VII displays the average level of gross estates for the top 0.01 percent of decedents from 1916 to 1997 (these are the largest 225 estates in 1997). Strikingly, the real value of the top estates in 1916 is about the same as in 1997, namely around $80 million, even though the GDP per capita grew by a factor of 3.5 during this period. Therefore, the biggest fortunes have in fact substantially declined in relative terms.25 To emphasize this point, Panel B displays the evolution of average estates in lower fractiles. The average estate in P98 –99 has grown by a factor 3 between 1916 and 1997, and the average estate in P99 –99.5 has been multi- plied by about 2.5. This evidence is consistent with our previous results on the decline in top capital incomes over the century. Popular accounts suggest that estate tax evasion is very impor- tant [Cooper 1979], but academics disagree about the extent of tax evasion [Poterba 2000]. Furthermore, our results would be invalidated only if the level of tax evasion had increased over time much more for the largest estates (top 0.01 percent) than for large estates.
III. C. Proposed Interpretation: The Role of Progressive Taxation
How can we explain the steep secular decline in capital income concentration? It is easy to understand how the macro- economic shocks of the Great Depression and the fiscal shocks of World War I and World War II have had a negative impact on capital concentration. The difficult question to answer is why large fortunes did not recover from these shocks. The most nat-
24. In particular, capital gains not realized before death are never reported on income tax returns, but are included in the value of assessed estates.
25. It is important to keep in mind that estate data reflect the wealth distribution of decedents and thus probably introduce a long lag relative to the current wealth distribution.
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FIGURE VII Evolution of Estates (in real 1998 dollars), 1916 –1997
Source: Authors’ computations are based on estate tax returns statistics [Piketty and Saez 2001, Appendix C, Table C3].
Series report real value of gross estates before deductions (in 1998 dollars) for fractiles P99.99 –100 (Panel A) and P98 –99, P99 –99.5 (Panel B) of decedents aged 25 and above.
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ural and realistic candidate for an explanation seems to be the creation and the development of the progressive income tax (and of the progressive estate tax and corporate income tax). The very large fortunes that generated the top 0.01 percent incomes ob- served at the beginning of the century were accumulated during the nineteenth century, at a time where progressive taxes hardly existed and capitalists could dispose of almost all their income to consume and to accumulate.26 The fiscal situation faced by capi- talists in the twentieth century to recover from the shocks in- curred during the 1914 to 1945 period has been substantially different. Top tax rates were very high from the end of World War I to the early 1920s, and then continuously from 1932 to the mid-1980s. Moreover, the United States has imposed a sharply progressive estate tax since 1916, and a substantial corporate income tax ever since World War II.27 These very high marginal rates applied to only a very small fraction of taxpayers, but created a substantial burden on the very top income groups (such as the top 0.1 percent and 0.01 percent) composed primarily of capital income. In contrast to progressive labor income taxation, which simply produces a level effect on earnings through labor supply responses, progressive taxation of capital income has cu- mulative or dynamic effects because it reduces the net return on wealth which generates tomorrow’s wealth.
It is difficult to prove in a rigorous way that the dynamic effects of progressive taxation on capital accumulation and pretax income inequality have the right quantitative magnitude and account for the observed facts. One would need to know more about the savings rates of capitalists— how their accumulation strategies have changed since 1945. The orders of magnitude do not seem unrealistic, especially if one assumes that the owners of large fortunes, whose pretax incomes were already severely hit by the prewar shocks, were not willing to reduce their consumption to very low levels. Piketty [2001a, 2001b] provides simple numeri- cal simulations showing that for a fixed saving rate, introducing substantial capital income taxation has a tremendous effect on the time needed to reconstitute large wealth holdings after nega- tive shocks. Moreover, reduced savings in response to a reduc- tion in the after-tax rate of return on wealth would accelerate the
26. During the nineteenth century, the only progressive tax was the property tax, but its level was low (see Brownlee [2000] for a detailed description).
27. From 1909 (first year the corporate tax was imposed) to the beginning of World War II, the corporate tax rate was low, except during World War I.
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decrease in wealth inequality. Piketty [2001b] shows that in the classic dynastic model with infinite horizon, any positive capital income tax rate above a given high threshold of wealth will eventually eliminate all large wealth holdings without, however, affecting the total capital stock in the economy.
We are not the first to propose progressive taxation as an explanation for the decrease in top shares of income and wealth. Lampman [1962] did as well, and Kuznets [1955] explicitly men- tioned this mechanism as well as the shocks incurred by capital owners during the 1913 to 1948 period, before presenting his inverted U-shaped curve theory based on technological change. Explanations pointing out that periods of technological revolu- tions such as the last part of the nineteenth century (industrial revolutions) or the end of the twentieth century (computer revo- lution) are more favorable to the making of fortunes than other periods might also be relevant.28 Our results suggest that the decline in income tax progressivity since the 1980s and the pro- jected repeal of the estate tax might again produce in a few decades levels of wealth concentration similar to those at the beginning of the century.
IV. TOP WAGE SHARES
Table IV displays top wage shares from 1927 to 1998 con- structed using IRS tabulations by size of wages. There are three caveats to note about these long-term wage inequality series. First, self-employment income is not included in wages, and therefore our series focus only on wage income inequality. As self-employment income has been a decreasing share of labor income over the century, it is conceivable that the pool of wage and salary earners has substantially evolved over time, and that total labor income inequality series would differ from our wage inequality series. Second and related, large changes in the wage force due to the business cycle and wars might affect our series through compositional effects because we define the top fractiles relative to the total number of tax units with positive wage income. As can be seen in column (1) of Table II, the number of tax units with wages declined during the Great Depression due to
28. De Long [1998] also points out the potential role of antitrust law. Accord- ing to De Long, antitrust law was enforced more loosely before 1929 and since 1980 than between 1929 and 1980.
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high levels of unemployment, increased sharply during World War II because of the increase in military personnel, and de- creased just after the war. We show in Piketty and Saez [2001, Appendix B3] that these entry effects do not affect top shares when the average wage of the new entrants is equal to about 50 percent of the average wage. This condition is approximately satisfied for military personnel in World War II, and thus top wage shares including or excluding military personnel during World War II are almost identical. Third, our wage income series are based on the tax unit and not the individual. As a result, an increase in the correlation of earnings across spouses, as documented in Karoly [1993], with no change in individual wage inequality, would generate an increase in tax unit wage inequality.29
Figure VIII displays the wage share of the top decile, and Figure IX displays the wage shares of the P90 –95, P95–99, and P99 –100 groups from 1927 to 1998. As for overall income, the pattern of top decile wage share over the century is also U- shaped. There are, however, important differences that we de- scribe below. It is useful to divide the period from 1927 to 1998 into three subperiods: the pre-World War II period (1927 to 1940), the war and postwar period (1941 to 1969), and the last three decades (1970 to 1998). We analyze each of these periods in turn.
IV. A. Wage Inequality Stability before World War II
Top wage shares show a striking stability from 1927 to 1940. This is especially true for the top percentile. In contrast to capital income, the Great Depression did not produce a reduction in top wage shares. On the contrary, the high middle class fractiles benefited in relative terms from the Great Depression. Even though the IRS has not published tables on wage income over the period 1913 to 1926, we can use an indirect source of evidence to document trends in top wage shares. Corporation tax returns require each corporation to report separately the sum of salaries paid to its officers. This statistic, compensation of officers, is reported quasi-annually by the IRS starting in 1917. We report in Figure X the total compensation of officers reported on corporate tax returns divided by the total wage bill in the economy from
29. This point can be analyzed using the Current Population Surveys avail- able since 1962 which allow the estimation of wage inequality series both at the individual and tax unit level.
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TABLE IV TOP WAGE INCOME SHARES, 1927–1998
# tax units with wages (thousands)
Average wage
income (1998 $)
Top wage income shares
P90–100 P90–95 P95–99 P99–100 P99.5–100 P99.9–100
(1) (2) (3) (4) (5) (6) (7) (8)
1927 33,953 12,225 27.89 9.04 10.20 8.65 6.08 2.53 1928 34,197 12,506 29.11 9.33 10.91 8.87 6.20 2.59 1929 35,425 12,769 29.24 9.49 11.09 8.67 6.08 2.56 1930 33,266 12,705 28.63 9.40 10.69 8.54 5.99 2.56 1931 30,386 12,838 29.34 9.65 11.22 8.47 5.81 2.45 1932 27,117 12,395 30.28 10.61 11.39 8.29 5.66 2.37 1933 28,491 11,824 30.08 10.27 11.50 8.31 5.77 2.45 1934 31,565 12,010 29.77 9.83 11.64 8.31 5.76 2.37 1935 32,790 12,274 30.31 10.19 11.72 8.40 5.85 2.40 1936 35,608 12,797 29.70 9.75 11.35 8.60 6.02 2.45 1937 36,654 13,208 30.06 10.01 11.64 8.41 5.89 2.41 1938 35,205 13,003 29.83 10.18 11.53 8.13 5.74 2.36 1939 36,413 13,633 30.65 10.59 11.86 8.20 5.70 2.32 1940 38,087 13,998 30.85 10.78 11.70 8.37 5.84 2.39 1941 41,889 15,024 29.33 10.29 10.94 8.11 5.75 2.39 1942 45,891 16,362 27.08 9.63 10.24 7.21 5.12 2.18 1943 51,108 17,821 25.88 9.62 9.83 6.42 4.51 1.86 1944 51,928 18,924 24.61 9.48 9.56 5.56 3.84 1.56 1945 50,210 19,178 24.05 9.05 9.27 5.73 3.96 1.57 1946 44,370 18,854 25.10 8.92 9.79 6.40 4.33 1.68 1947 44,582 18,006 24.97 8.90 9.80 6.27 4.23 1.60 1948 45,275 17,891 25.03 8.90 9.92 6.21 4.20 1.58 1949 44,088 18,310 25.00 8.95 9.93 6.12 4.11 1.54 1950 45,592 19,033 25.18 9.06 9.89 6.24 4.21 1.57 1951 48,858 19,103 24.71 9.08 9.66 5.97 4.00 1.48 1952 49,963 19,769 24.43 9.01 9.67 5.74 3.78 1.39 1954 49,144 20,850 24.13 8.88 9.65 5.61 3.65 1.32 1956 51,632 22,584 24.53 8.96 10.02 5.56 3.57 1.26 1958 50,153 22,741 24.67 9.07 10.20 5.40 3.43 1.20 1960 52,554 23,970 25.23 9.51 10.46 5.26 3.31 1.14 1961 51,946 24,321 25.21 9.58 10.44 5.20 3.26 1.11 1962 53,338 24,999 25.22 9.60 10.47 5.16 3.24 1.09 1964 55,216 26,411 25.15 9.72 10.31 5.12 3.24 1.07 1966 60,358 27,370 25.34 9.87 10.31 5.16 3.27 1.11 1967 61,571 27,777 25.77 9.97 10.47 5.34 3.38 1.14 1968 62,836 28,511 25.60 9.95 10.42 5.24 3.32 1.12 1969 64,371 28,871 25.71 10.03 10.49 5.19 3.27 1.10 1970 63,778 29,046 25.67 10.03 10.51 5.13 3.21 1.06 1971 63,194 29,558 25.67 10.00 10.49 5.18 3.25 1.08 1972 64,750 30,520 25.81 10.02 10.47 5.32 3.38 1.14 1973 67,614 30,532 26.14 10.09 10.63 5.42 3.43 1.14 1974 68,518 29,497 26.61 10.14 10.81 5.66 3.63 1.26 1975 66,671 29,039 26.46 10.15 10.68 5.64 3.63 1.26 1976 68,459 29,490 26.66 10.16 10.76 5.74 3.70 1.30
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1917 to 1960 along with the shares of the P99.5–100 and P99 – 99.9 wage groups which are close in level to the share of officer compensation. From 1927 to 1960, officer compensation share and these fractiles shares track each other relatively closely. There- fore, the share of officer compensation from 1917 to 1927 should be a good proxy as well for these top wage shares. This indirect evidence suggests that the top share of wages was also roughly constant, or even slightly increasing from 1917 to 1926.
Previous studies have suggested that wage inequality has been gradually decreasing during the first half of the twentieth century (and in particular during the interwar period) using
TABLE IV (CONTINUED) TOP WAGE INCOME SHARES, 1927–1998
# tax units with wages (thousands)
Average wage
income (1998 $)
Top wage income shares
P90–100 P90–95 P95–99 P99–100 P99.5–100 P99.9–100
(1) (2) (3) (4) (5) (6) (7) (8)
1977 70,898 29,574 26.94 10.24 10.84 5.86 3.79 1.35 1978 74,503 29,571 27.43 10.36 11.02 6.06 3.93 1.40 1979 77,038 28,774 27.63 10.39 11.03 6.22 4.06 1.47 1980 76,913 27,712 28.06 10.47 11.17 6.43 4.23 1.57 1981 77,439 27,436 28.14 10.49 11.23 6.43 4.24 1.59 1982 75,771 27,539 28.55 10.53 11.35 6.67 4.42 1.67 1983 76,260 27,988 29.09 10.59 11.54 6.96 4.66 1.80 1984 80,008 28,235 29.61 10.66 11.68 7.27 4.93 1.99 1985 81,936 28,573 29.74 10.70 11.77 7.28 4.92 1.98 1986 83,340 29,183 29.94 10.76 11.86 7.33 4.96 2.02 1987 85,618 29,423 30.59 10.61 11.83 8.15 5.68 2.43 1988 88,121 29,691 31.95 10.58 11.99 9.39 6.79 3.16 1989 90,145 29,293 31.53 10.70 12.13 8.69 6.12 2.69 1990 91,348 29,107 31.79 10.66 12.14 8.99 6.41 2.87 1991 89,813 29,008 31.43 10.66 12.21 8.56 5.97 2.57 1992 89,883 29,463 32.45 10.60 12.22 9.63 6.97 3.33 1993 91,279 29,387 31.85 10.56 12.23 9.05 6.41 2.90 1994 93,270 29,427 31.54 10.59 12.22 8.72 6.07 2.63 1995 95,388 29,558 32.43 10.70 12.48 9.25 6.52 2.91 1996 97,338 29,707 32.98 10.51 12.78 9.73 6.90 3.21 1997 100,161 30,343 33.65 10.46 12.87 10.37 7.45 3.66 1998 103,053 31,422 34.19 10.58 12.80 10.88 7.95 4.13
Number of tax units with positive wages (full-time and part-time employees less married women employees) are estimated from Census data and National Income Accounts.
Total wage income is from National Income Accounts (employment income less employers’ contributions). Top shares are obtained from tax returns tabulations (individual income tax statistics) by size of wages
and Pareto interpolation. Complete details on methodology are in Appendix B of Piketty and Saez [2001], and complete series are reported in Tables B1 and B2.
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series of wage ratios between skilled and unskilled occupations (see, e.g., Keat [1960] and Williamson and Lindert [1980]). How- ever, it is important to recognize that a decrease in the ratio of skilled over unskilled wages does not necessarily imply an overall compression of wage income inequality, let alone a reduction in the top wage shares. Given the continuous rise in the numerical importance of white-collar jobs, it is natural to expect that the ratios of high-skill wages to low-skill wages would decline over time, even if wage inequality measured in terms of shares of top fractiles of the complete wage distribution does not change.30
Goldin and Katz [1999] have recently presented new series of white-collar to blue-collar earnings ratios from the beginning of the twentieth century to 1960, and they find that the decrease in pay ratio is concentrated only in the short periods of the two world wars. Whether or not the compression of wages that oc-
30. For instance, Piketty [2001a] reports a long-run compression (both from 1900 to 1950 and from 1950 to 1998) of the ratio of the average wage of managers over the average wage of production workers in France, even though wage in- equality (measured both in terms of top fractiles wage shares and in terms of P90/P10-type ratios) was constant in the long run.
FIGURE VIII The Top Decile Wage Income Share, 1927–1998
Source: Table IV, column P90 –100.
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curred during World War I was fully reversed during the 1920s in the United States is still an open question.31
IV. B. Sharp Drop in Inequality during World War II with No Recovery
In all of our wage shares series, there is a sharp drop during World War I from 1941 to 1945.32 The higher the fractile, the greater is the decrease. The share of P90 –95 declines by 16 percent between 1940 and 1945, but the share of the top 1 percent declines by more than 30 percent, and the top 0.1 percent by almost 35 percent during the same period (Table IV). This sharp compression of high wages can fairly easily be explained by the wage controls of the war economy. The National War Labor
31. Tax return data available for France make it possible to compute wage inequality series starting in 1913 (as opposed to 1927 in the United States). By using these data, Piketty [2001a, 2001b] found that wage inequality in France (measured both in terms of top wage shares and in terms of P90/P10 ratios) declined during World War I but fully recovered during the 1920s, so that overall wage inequality in 1930 or 1940 was the same as in 1913. Another advantage of the French wage data is that they are always based upon individual wages (as opposed to total tax unit wages in the United States).
32. Note that for fractiles below the top percentile, the drop starts from 1940 to 1941.
FIGURE IX Wage Income Shares for P90 –95, P95–99, and P99 –100, 1927–1998
Source: Table IV, columns P90 –95, P95–99, and P99 –100.
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Board, established in January 1942 and dissolved in 1945, was responsible for approving all wage changes and made any wage increase illegal without its approval. Exceptions to controls were more frequently granted to employees receiving low wages.33
Lewellen [1968] has studied the evolution of executive compen- sation from 1940 to 1963, and his results show strikingly that executive salaries were frozen in nominal terms from 1941 to 1945 consistent with the sharp drop in top wage shares that we find.
The surprising fact, however, is that top wage shares did not recover after the war. A partial and short-lived recovery can be seen for all groups, except the very top. But the shares never recover more than one-third of the loss incurred during World War II. Moreover, after a short period of stability in the late 1940s, a second phase of compression takes place in the top percentile. This compression phase is longer and most pro- nounced the higher the fractile. While the fractiles P90 –95 and P95–99 hardly suffer from a second compression phase and start
33. See Goldin and Margo [1992] for a more detailed description.
FIGURE X Shares of Officers’ Compensation and Wages Shares P99.5–100 and P99 –99.9,
1917–1960 Source: Officers’ compensation from authors’ computations are based on corpo-
rate income tax returns (Table B1, column Officers’ compensation in Piketty and Saez [2001]), and Table IV, columns P99.5–100, and P99 –99.5 � P99.5–99.9.
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recovering just after the war, the top group’s shares experience a substantial loss from 1950 to the mid-1960s. The top 0.1 percent share for example declines from 1.6 percent in 1950 to 1.1 percent in 1964 (Table IV).
The overall drop in top wage shares, although important, is significantly lower than the overall drop in top income shares. The top 1 percent income share dropped from about 18 –19 per- cent before World War I and in the late 1920s to about 8 percent in the late 1950s (Figure II), while the top 1 percent wage share dropped from about 8.5 percent in the 1920s to about 5 percent in the late 1950s (Figure IX). This confirms that capital income played a key role in the decline of top income shares during the first half of the century.
IV. C. The Increase in Top Shares since the 1970s
Many studies have documented the increase in inequality in the United States since the 1970s (see, e.g., Katz and Murphy [1992]). Our evidence on top shares is consistent with this evi- dence. After the World War II compression, the fractiles P90 –95 and P95–99 recovered slowly and continuously from the 1950s to the 1990s, and reached the pre-World War II level in the begin- ning of the 1980s. As described above, the recovery process for groups within the top percentile did not begin until the 1970s and was much faster. In accordance with results obtained from the March Current Population Surveys [Katz and Murphy 1992; Katz and Autor 1999], we find that wage inequality, measured by top fractile wage shares, starts to increase in the early 1970s. This is in contrast to results from the May Current Population Surveys [DiNardo, Fortin, and Lemieux 1996] suggesting that the surge in wage inequality is limited to the 1980s.
From 1970 to 1984 the top 1 percent share increased steadily from 5 percent to 7.5 percent (Figure IX). From 1986 to 1988 the top shares of wage earners increased sharply, especially at the very top (for example, the top 1 percent share jumps from 7.5 percent to 9.5 percent). This sharp increase was documented by Feenberg and Poterba [1993] and is certainly attributable at least in part to fiscal manipulation following the large top marginal tax rate cuts of the Tax Reform Act of 1986 (see the discussion in Section III above). However, from 1988 to 1994, top wage shares
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stay on average constant,34 but increase very sharply from 1994 to 1998 (the top 1 percent wage share increases from 9 percent to 11 percent). While everybody acknowledges that tax reforms can have large short-term effects on reported incomes due to retim- ing, there is a controversial debate on whether changing tax rates can have permanent effects on the level of reported incomes. Looking at long-time series up to 1998 casts doubts on the supply- side interpretation that tax cuts can have lasting effects on re- ported wages.
Part of the recent increase in top wages is due to the devel- opment of stock options that are reported as wages and salaries on tax returns when they are exercised. Stock options are com- pensation for labor services, but the fact that they are exercised in a lumpy way may introduce some upward bias in our annual shares at the very top (top 0.1 percent and above). To cast addi- tional light on this issue and on the timing of the top wage surge, we look at CEO compensation from 1970 to 1999 using the annual surveys published by Forbes magazine since 1971. These data provide the levels and composition of compensation for CEOs in the 800 largest publicly traded U. S. corporations. Figure XI displays the average real compensation level (including stock option exercised) for the top 100 CEOs from the Forbes list, along with the compensation of the CEO ranked 100 in the list, and the salary plus bonus level of the CEO ranked 10 (in terms of the size of salary plus bonus). As a comparison, we also report the average wage of a full-time worker in the economy from National Income Accounts. Consistent with the evolution of top wage shares, av- erage CEO compensation has increased much faster than average wage since the early 1970s. Therefore, the increase in pay gap between top executives and the average worker cannot be attrib- uted solely to the tax episodes of the 1980s.
Thus, by the end of the century, top wage shares are much higher than in the interwar period. These results confirm that the rise in top income shares and the dramatic shift of income com- position at the top documented in Section IV are mainly driven by the surge in top wages during the last three decades.
34. One can note the surge in high wages in 1992 and the dip in 1993 and 1994 due to retiming of labor compensation in order to escape the higher rates enacted in 1993 (see Goolsbee [2000]).
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IV. D. Proposed Interpretation
The pattern of top shares over the century is striking: most of the decline from 1927 to 1960 took place during the four years of World War II. The extent of that decline is large, especially for very high wages. More surprisingly, there is no recovery after the war. We are of course not the first ones to document compression of wages during the 1940s. The Social Security Administration [U. S. Bureau of Old-Age 1952] showed that a Lorenz curve of wages for 1949 displays much more equality than one for 1938. In a widely cited paper Goldin and Margo [1992], using Census micro-data for 1940 and 1950, have also noted that the ratios P90/P10 and P50/P10 declined sharply during that decade. Our annual series allow us to conclude that most of the decline in top wage shares took place during the key years of the war with no previous decline in inequality before and no recovery afterwards.
The compression of wages during the war can be explained by the wage controls of the war economy, but how can we explain the fact that high wage earners did not recover after the wage con- trols were removed? This evidence cannot be immediately recon-
FIGURE XI CEOs’ Pay versus Average Wages, 1970 –1999
Source: Forbes Annual Compensation surveys of CEOs in top 800 companies; Average wages of full-time employees are from National Income Accounts.
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ciled with explanations of the reduction of inequality based solely on technical change as in the famous Kuznets process. We think that this pattern of evolution of inequality is additional indirect evidence that nonmarket mechanisms such as labor market in- stitutions and social norms regarding inequality may play a role in the setting of compensation at the top. The Great Depression and World War II have without doubt had a profound effect on labor market institutions and more generally on social norms regarding inequality. During this period, the income tax acquired its modern form, and its top marginal tax rates were set very high, in excess of 80 percent. It is conceivable that such large income tax rates discouraged corporations from increasing top salaries. During that period, large redistributive programs, such as Social Security and Aid for Families with Dependent Children, were initiated. These strongly redistributive policy reforms show that American society’s views on income inequality and redistri- bution greatly shifted from 1930 to 1945. It is also important to note that unionization increased substantially from 1929 to 1950 and that unions have been traditionally in favor of wage compres- sion. In that context, it is perhaps not surprising that the high wages earners who were the most severely hit by the war wage controls were simply not able, because of social, fiscal, and union pressure, to increase their salaries back to the prewar levels in relative terms.35
Similarly, the huge increase in top wage shares since the 1970s cannot be the sole consequence of technical change. First, the increase is very large and concentrated among the highest income earners. The fractiles P90 –95 and P95–99 experienced a much smaller increase than the very top shares since the 1970s. Second, such a large change in top wage shares has not taken place in most European countries which experienced the same technical change as the United States. For example, Piketty [2001a, 2001b] documents no change in top wage shares in the last decades in France. DiNardo, Fortin, and Lemieux [1996] argue that changes in institutions such as the minimum wage and unionization account for a large part of the increase in U. S.
35. Emphasizing the role of social norms and unionization is of course not new and has been pointed out as important elements explaining the wage com- pression of the 1940s and 1950s by several studies [Brown 1977; Goldin and Margo 1992; Goldin and Katz 1999]. Moreover, as emphasized by Goldin and Margo [1992] and Goldin and Katz [1999], it is possible that the large increase in the supply of college graduates contributed to make the drop in top wage shares persistent.
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wage inequality from 1973 to 1992. As emphasized by Acemoglu, Aghion, and Violante [2001], it is possible that these changes in institutions have been triggered by previous technological changes making it impossible to sustain previous labor market arrangements.36 It seems unlikely, however, that changes in unionization or the minimum wage can explain the surge in very top wages. The marginal product of top executives in large cor- porations is notoriously difficult to estimate, and executive pay is probably determined to a significant extent by herd behavior. Changing social norms regarding inequality and the acceptability of very high wages might partly explain the rise in U. S. top wage shares observed since the 1970s.
V. CONCLUSION
This paper has presented new homogeneous series on top shares of income and wages from 1913 to 1998. Perhaps surpris- ingly, nobody had tried to extend the pioneering work of Kuznets [1953] to more recent years. Moreover, important wage income statistics from tax returns had never been exploited before. The large shocks that capital owners experienced during the Great Depression and World War II seem to have had a permanent effect: top capital incomes are still lower in the late 1990s than before World War I. We have tentatively suggested that steep progressive taxation, by reducing the rate of wealth accumula- tion, has yet prevented the large fortunes to recover fully from these shocks. The evidence for wage series shows that top wage shares were flat before World War II and dropped precipitously during the war. Top wage shares have started recovering from this shock only since the 1970s but are now higher than before World War II.
To what extent is the U. S. experience representative of other developed countries’ long-run inequality dynamics? Existing in- equality series are unfortunately very scarce and incomplete for most countries,37 and it is therefore very difficult to provide a fully satisfactory answer to this question. However, it is interest- ing to compare the U. S. top income share series with comparable series recently constructed for France by Piketty [2001a, 2001b] and for the United Kingdom by Atkinson [2001]. There are im-
36. See also Acemoglu [2002]. 37. See Lindert [2000] and Morrisson [2000] for recent surveys.
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portant similarities between the American, French, and British pattern of the top 0.1 percent income share displayed in Figure XII.38 In all three countries, top income shares fell considerably during the 1914 to 1945 period, and they were never able to come back to the very high levels observed on the eve of World War I. It is plausible to think that in all three countries, top capital incomes have been hit by the depression and wars shocks of the first part of the century and could not recover because of the dynamic effects of progressive taxation on capital. Piketty [2001a] also shows that in France, there was no spontaneous decline of
38. Due to very high exemption thresholds in the United Kingdom prior to World War II, Atkinson was not able to compute top decile or even top percentile series covering the entire century (only the top 0.1 percent, and higher fractiles series are available for the entire century for all three countries).
FIGURE XII Top 0.1 Percent Income Shares in the United States, France, and the United
Kingdom, 1913–1998 Sources: United States: Table II, column P99.9 –100. France: Computations are based on income tax returns by Piketty [2001, Table
A1, column P99.9 –100]. United Kingdom: Computations are based on income tax returns by Atkinson
[2001, column top 0.1 percent in Tables 1 and 4]. Years 1987–1992 and 1994 –1998 are extrapolated from Atkinson top 0.5 percent series. Discontinuity from 1989 to 1990 due to switch from family to individual base is corrected.
In all three countries, income is defined before individual taxes and excludes capital gains. The unit is the family as in the current U. S. tax law.
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top wage shares before World War II. In France, top wage shares declined during World War I, but they quickly recovered during the 1920s and were stable until World War II.
Some important differences, however, need to be empha- sized. First, the shock of World War II was more pronounced in France and in the United Kingdom than in the United States. This is consistent with the fact that capital owners suffered from physical capital losses during the war in Europe, while there was no destruction on U. S. soil.39 Second, the World War II wage compression was very short-lived in France, while it had long- lasting effects in the United States. In France, wage inequality, measured both in terms of top wage shares and in terms of interdecile ratios, appears to have been extremely stable over the course of the twentieth century. The U. S. history of wage in- equality looks very different: the war compression had long-last- ing effects, and then wage inequality increased considerably since the 1970s, which explains the U. S. upturn of top income shares since the 1970s.40 The fact that France and the United States display such diverging trends is consistent with our interpreta- tion that technical change alone cannot account for the U. S. increase in inequality.
These diverging trends in top wages over the past 30 years explain why the income composition patterns of top incomes look so different in France and in the United States at the end of the century. In France, top incomes are still composed primarily of dividend income, although wealth concentration is much lower than what it was one century ago. In the United States, due to the very large rise of top wages since the 1970s, the coupon-clipping rentiers have been overtaken by the working rich. Such a pattern might not last for very long because our proposed interpretation also suggests that the decline of progressive taxation observed since the early 1980s in the United States could very well spur a revival of high wealth concentration and top capital incomes during the next few decades.
EHESS AND CEPREMAP, PARIS HARVARD UNIVERSITY AND NBER
39. Estate tax data also show that the fall in top estates was substantially larger in France (see Piketty [2001a, 2001b]).
40. The United Kingdom also experienced an increase in top shares in the last two decades but much more modest than in the United States.
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Lewellen, Wilbur G., Executive Compensation in Large Industrial Corporations (New York: NBER, 1968).
Lindert, Peter, “Three Centuries of Inequality in Britain and America,” in An- thony Atkinson and François Bourguignon, eds., Handbook of Income Distri- bution (Amsterdam: North-Holland, 2000), pp. 167–216.
Mellon, Andrew, Taxation: The People’s Business (New York: Macmillan, 1924). Morrisson, Christian, “Historical Perspectives on Income Distribution: The Case
of Europe,” in Anthony Atkinson and François Bourguignon, eds., Handbook of Income Distribution (Amsterdam: North-Holland, 2000), pp. 217–260.
Piketty, Thomas, Les hauts revenus en France au 20eme siècle–Inégalités et redis- tributions, 1901–1998 (Paris: Editions Grasset, 2001a).
——, “Income Inequality in France, 1901–1998,” CEPR Discussion Paper No. 2876, 2001b, Journal of Political Economy, forthcoming.
Piketty Thomas, and Emmanuel Saez, “Income Inequality in the United States, 1913–1998,” NBER Working Paper No. 8467, 2001.
Poterba, James, “The Estate Tax and After-Tax Investment Returns,” in Joel Slemrod, ed., Does Atlas Shrug? The Economic Consequences of Taxing the Rich (New York: Russell Sage Foundation; Cambridge, MA: Harvard Univer- sity Press, 2000).
Slemrod, Joel, “High Income Families and the Tax Changes of the 1980s: The Anatomy of Behavioral Response,” in Empirical Foundations of Household Taxation, M. Feldstein and J. Poterba, eds. (Chicago: University of Chicago Press, 1996).
Slemrod, Joel, and Jon Bakija, “Does Growing Inequality Reduce Tax Progressiv- ity? Should it?” NBER Working Paper No. 7576, 2000.
U. S. Bureau of Old-Age, Handbook of Old-Age and Survivors Insurance Statistics, 1949 (Washington, DC: 1952).
U. S. Department of Commerce, Bureau of Census, Historical Statistics of the United States: Colonial Times to 1970 (Washington, DC, 1975).
U. S. Department of Commerce, Bureau of Economic Analysis, National Income and Product Accounts of the United States, 1929 –97 (Washington, DC: 2000) (www.bea.doc.gov/bea/dn/nipaweb/).
U. S. Treasury Department, Internal Revenue Service, Statistics of Income: Indi- vidual Income Tax Returns (Washington, DC: annual 1916 –1998).
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39INCOME INEQUALITY IN THE UNITED STATES, 1913–1998
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Yes, r > g. So what?
By N. Gregory Mankiw
Harvard University
November 24, 2014
This essay was prepared the Annual Meeting of the American Economic Association, January 2014. I am grateful to Laurence Ball, Ben Friedman, David Laibson, Lisa Mogilanski, Lawrence Summers, Gabriel Unger, and Matthew Weinzeirl for comments.
1
Thomas Piketty’s book Capital in the Twenty-First Century captured the public’s
attention in a way that few books by economists have. Though its best-seller status was a
surprise, probably even to its author, it has the ingredients that foster wide appeal. The book
addresses a pressing issue of the day in a manner that is learned, literary, speculative,
provocative, and fascinating from beginning to end. While largely a work of economic history, it
does not stop there. Piketty ultimately leads the reader to a vision of what the future may hold
and advice about what policymakers should do about it. That vision is a dystopia of continually
increasing economic inequality due to the dynastic accumulation of capital, leading to a policy
recommendation of a steeply progressive global tax on wealth.
Although I admire Piketty and his book, I am not persuaded by his main conclusions. A
chain is only as strong as its weakest links, and several links in Piketty’s chain of argument are
especially fragile. Other aspects of Piketty’s book may well pass the test of time, but the bottom
line—his vision of the future and the consequent policy advice—most likely will not.
The book documents that the rate of return on private capital r exceeds the economy’s
growth rate g, and it argues that this will likely continue to be the case, perhaps by a larger
amount in the future. He boldly calls this fact “the central contradiction of capitalism.” He
reasons that if r > g, the wealth of the capitalist class will grow faster than the incomes of
workers, leading to an “endless inegalitarian spiral.” To someone who views relatively unfettered
capitalism as one of the great achievements of human history and the best way to organize a
society, as I do, these conclusions present a significant challenge.
The first thing to say about Piketty’s logic is that it will seem strange to any economist
trained in the neoclassical theory of economic growth. The condition r > g should be familiar. In
2
the textbook Solow growth model, it arrives naturally as a steady-state condition as long as the
economy does not save so much as to push the capital stock beyond the Golden Rule level.
(Phelps 1961) In this model, r > g is not a problem, but r < g could be. If the rate of return is
less than the growth rate, the economy has accumulated an excessive amount of capital. In this
dynamically inefficient situation, all generations can be made better off by reducing the
economy’s saving rate. From this perspective, we should be reassured that we live in a world in
which r > g because it means we have not left any dynamic Pareto improvements unexploited.
There is, moreover, good reason to doubt that r > g leads to the “endless inegalitarian
spiral” that concerns Piketty. Imagine a wealthy person living in an r > g economy who wants to
ensure that he has an endless stream of wealthy descendants. He can pass his wealth on to his
children, but to ensure that his descendants remain wealthy, he faces three obstacles.
First, his heirs will consume some of the wealth they inherit. For this purpose, the
relevant measure of consumption includes not only food, shelter, and riotous living but also
political and philanthropic contributions, which can be sizeable for wealthy families. A plausible
estimate of the marginal propensity to consume out of wealth, based on both theory and
empirical evidence, is about 3 percent. Thus, if wealth earns a rate of return of r, wealth
accumulates at a rate of about r − 3.
Second, as wealth is passed down from generation to generation, it is divided among a
growing number of descendants. (This would not be a problem for the wealthy patron if his
heirs’ mating were perfectly assortative—that is, if they all married someone of equal wealth.
But matters of the heart are rarely so neat.) To get a rough calibration of this effect, suppose
everyone has a typical family of two children, so the number of descendants doubles every
3
generation. Because generations are about 35 years apart, the number of descendants grows at a
rate of 2 percent per year. Thus, if family wealth accumulates at a rate of r − 3, wealth per
descendant grows at a rate of r − 5.
Third, many governments impose taxes on both bequests and capital income. In the
United States today, the estate tax rate is 40 percent (above a threshold). In Massachusetts, where
I live, the state imposes an additional estate tax with a top rate of 16 percent. As a result, at the
margin, about half of a family’s wealth is taxed away by the government once every generation.
If we again assume a generation is 35 years, then estate taxation reduces the accumulation of
dynastic wealth by about 2 percent per year. In addition, capital income taxation during a
person’s life reduces capital accumulation even further. This effect is roughly an additional 1
percent per year, making the total drag of taxes about 3 percent per year. Let’s assume, however,
that our dynasty has especially good tax planning and put the total tax effect at only 2 percent.
Thus, taking taxation into account, wealth per descendant grows at a rate of about r − 7.
We can now recalibrate Piketty’s logic taking these three effects into account. Piketty
reasons that resources of the wealthy would grow relative to the labor income if r > g. We can
now see, however, that this condition is not sufficient once consumption, procreation, and
taxation are accounted for. Instead, to obtain the worrisome “endless inegalitarian spiral,” we
would need the return on capital r to exceed the economy’s growth g by at least 7 percentage
points per year.
This scenario is far from what we have experienced. Piketty estimates the real rate of
return to be about 4 or 5 percent, which seems plausible for a typical balanced portfolio.
Meanwhile, the average growth rate of the U.S. economy has been about 3 percent. So Piketty is
4
right that r has exceeded g, but it has done so by only about 2 percentage points, not the more
than 7 percentage points necessary for the creation of Piketty’s imagined dystopia.
Moreover, while economists are notoriously bad at predicting the future, especially over
long horizons, it seems unlikely that, looking forward, r will start exceeding g by more than 7
percentage points. If the real return remains stable at 5 percentage points, the economy’s growth
rate would need to become a negative 2 percent. Secular stagnation would not be enough; we
would need secular decline. Alternatively, if future growth is 2 percent per year, the real rate of
return to capital would need to rise from its historical 5 percent to more than 9 percent. That
figure is nowhere near the return that pension and endowment managers are now projecting from
a balanced portfolio of stocks and bonds.
Hence, the forces of consumption, procreation, and taxation are, and will probably
continue to be, sufficient to dilute family wealth over time. As a result, I don’t see it as likely that
the future will be dominated by a few families with large quantities of dynastic wealth, passed
from generation to generation, forever enjoying the life of the rentier.
But suppose I am wrong. Suppose the dynastic accumulation of capital describes the
future, as Pikkety suggests. I would nonetheless remain skeptical of Piketty’s proposal to place
an additional tax on wealth. A simple, standard neoclassical growth model illustrates the problem
with this policy.
Consider an economy composed of two kinds of people—workers and capitalists. Many
workers supply labor inelastically and immediately consume their earnings. A few capitalists
own the capital stock and, because they represent an infinitely-living dynasty, set their
consumption according to the standard model of an optimizing infinitely-lived consumer (as in
5
the Ramsey model). Workers and capitalists come together to produce output, using a production
function that experiences labor-augmenting technological progress, and they earn the value of
their marginal product. In addition, following the advice of Piketty, the government imposes a
tax on capital equal to τ per period, the revenue from which is transferred to workers.
To oversimplify a bit, let’s just focus on this economy’s steady state. Using mostly
conventional notation, it is described by the following equations:
(1) cw = w + τk
(2) ck = (r − τ – g)nk
(3) r = f ’(k)
(4) w = f(k) – rk
(5) g = σ(r – τ – ρ)
where cw is consumption of each worker, ck is the consumption of each capitalist, w is the wage,
r is the (before-tax) rate of return on capital, k is the capital stock per worker, n is the number of
workers per capitalist (so nk is the capital stock per capitalist), f(k) is the production function for
output (net of depreciation), g is the rate of labor-augmenting technological change and thus the
steady-state growth rate, σ is the capitalists’ intertemporal elasticity of substitution, and ρ is the
capitalists’ rate of time preference. Equation (1) says that workers consume their wages plus
what is transferred by the government. Equation (2) says that capitalists consume the return on
their capital after paying taxes and saving enough to maintain the steady-state ratio of capital to
effective workers. Equation (3) says that capital earns its marginal product. Equation (4) says
that workers are paid what is left after capital is compensated. Equation (5) is derived from the
6
capitalists’ Euler equation; it relates the growth rate of capitalist’s consumption (which is g in
steady state) to the after-tax rate of return.
Because the steady-state return on capital in this economy is r = g/σ + τ + ρ, the condition
r > g arises naturally. A plausible calibration might be g = 2, τ = 2, ρ = 1, and σ = 1, which leads
to r = 5. In this economy, even though r > g, there is no “endless inegalitarian spiral.” Instead,
there is a steady-state level of inequality. (Optimizing capitalists consume enough to prevent
their wealth from growing faster than labor income.) If we assume the number of workers per
capitalist n is large, then capitalists will enjoy a higher standard of living. In this natural case,
cw/ck , the ratio of workers’ consumption to capitalists’ consumption, can be used as a proxy for
inequality. A more egalitarian outcome is then associated with a higher ratio cw/ck.
Now consider the policy question: What level of capital taxation τ should the government
set? Not surprisingly, the answer depends on the objective function.
If policymakers want to maximize the consumption of workers cw subject to equations (1)
through (5) as constraints, they would choose τ = 0. This result of zero capital taxation is familiar
from the optimal tax literature. (Chamley 1985, Judd 1985, and Atkeson, Chari, and Kehoe 1999,
recently reconsidered by Straub and Werning 2014.) In this economy, because capital taxation
reduces capital accumulation, labor productivity, and wages, it is not desirable even from the
standpoint of workers who hold no capital and who get the subsidies that capital taxation would
finance.
By contrast, suppose the government in this economy were a plutocracy, concerned only
about the welfare of the capitalists. In this case, it would choose τ to maximize ck subject to the
above five equations as constraints. The best plutocratic policy is a capital subsidy financed by
7
taxes on workers. That is, plutocrats would make τ as negative as it can be. If there is some
minimum subsistence level for workers, the labor tax and capital subsidy would be driven so
high as to push workers’ consumption down to subsistence.
Now consider a government concerned about inequality between workers and capitalists.
In particular, suppose that policymakers want to increase the ratio cw/ck. In this case, a positive
value for the capital tax τ is optimal. Indeed, if maximizing cw/ck is the only goal, then the capital
tax should be as large as it can be. Taxing capital and transferring the proceeds to workers
reduces the steady-state consumption of both workers and capitalists, but it impoverishes the
capitalists at a faster rate. For a standard production function (f ’ > 0 and f ” < 0), a higher
capital tax always raises cw/ck.
Thus, in this simple neoclassical growth model, a positive tax on capital has little to
recommend it if we care only about levels of consumption, but it may look attractive if we are
concerned about disparities. To misquote Winston Churchill: the inherent vice of the free-market
equilibrium is the unequal sharing of blessings; the inherent virtue of capital taxation is the more
equal sharing of miseries.
So far, I have included only one policy instrument—the one recommended by Piketty—
but we can consider others. A better way to pursue equality in this model economy, and I believe
the real economy as well, is a progressive tax on consumption. Such a tax could equalize living
standards between workers and capitalists without distorting the intertemporal margin and
thereby discouraging capital accumulation. Under a progressive consumption tax, the capitalists
would be just as wealthy as they are without it, but they would not fully enjoy the fruits of their
wealth.
8
With this model as background, let’s move to the big question: Why should we be
concerned about inequality in wealth? Why should anyone care if some families have
accumulated capital and enjoy the life of the rentier? Piketty writes about such inequality as if we
all innately share his personal distaste for it. But before we embark on policies aimed at reducing
wealth inequality, such as a global tax on capital, it would be useful to explore why this
inequality matters.
One place to look for answers is Occupy Wall Street, the protest movement that drew
attention to growing inequality. This movement was motivated, I believe, by the sense that the
affluence of the financial sector was a threat to other people’s living standards. In the aftermath
of a financial crisis followed by a deep recession, this sentiment was understandable. Yet the
protesters seemed not to object to affluence itself. If they had, Occupy Wall Street would have
been accompanied by Occupy Silicon Valley, Occupy Hollywood, and Occupy Major League
Baseball. From this perspective, the rentier lifestyle of capitalists should not be a concern. As we
have seen, in a standard neoclassical growth model, the owners of capital earn the value of their
marginal contribution to the production process, and their accumulation of capital enhances the
productivity and incomes of workers.
Another possibility is that we object to wealth inequality because it is not fair. Why
should someone be lucky enough to be born into a family of capitalists whereas someone else is
born into a family of workers? The disparity between workers and capitalists is inconsistent with
the ideal of equal opportunity. Yet that ideal conflicts with another—the freedom of parents to
use their resources to help their children. (Fishkin 1984) Moreover, in considering Piketty’s
proposal of a global capital tax, we have to ask: Would you rather be born into a world in which
we are unequal but prosperous or a world in which we are more equal but all less prosperous?
9
Even if equal opportunity is a goal, one might still prefer unequal opportunities to be rich over
equal opportunities to be poor.
A final possibility is that wealth inequality is somehow a threat to democracy. Piketty
alludes to this worry throughout his book. I am less concerned. The wealthy includes supporters
of both the right (the Koch brothers, Sheldon Adelson) and the left (George Soros, Tom Steyer),
and despite high levels of inequality, in 2008 and 2012 the United States managed to elect a left-
leaning president committed to increasing taxes on the rich. The fathers of American democracy,
including George Washington, Thomas Jefferson, John Adams, and James Madison, were very
rich men. With estimated net worth (in today’s dollars) ranging from $20 million to $500
million, they were likely all in the top 0.1 percent of the wealth distribution, demonstrating that
the accumulation of capital is perfectly compatible with democratic values. Yet, to the extent that
wealth inequality undermines political ideals, reform of the electoral system is a better solution
than a growth-depressing tax on capital.
My own view—and I recognize that this is a statement of personal political philosophy
more than economics—is that wealth inequality is not a problem in itself. And I do not see
anything objectionable if the economically successful use their good fortune to benefit their
children rather than spending it on themselves. As a society, we should help those at the bottom
of the economic ladder through such policies as a well-functioning educational system and a
robust social safety net (funded with a progressive consumption tax). And we should help people
overcome impediments to saving, thereby allowing more workers to become capitalists. But if
closing the gap between rich and poor lowers everyone’s standard of living, as I believe Piketty’s
global tax on capital would do, I see little appeal to the proposal.
10
References
Atkeson, Andrew, V.V. Chari and Patrick J. Kehoe, 1999, “Taxing Capital Income: A Bad Idea,”
Federal Reserve Bank of Minneapolis Quarterly Review 23, 3–17.
Chamley, Christophe. 1986. “Optimal Taxation of Capital Income in General Equilibrium with
Infinite Lives,” Econometrica 54 (3), 607–622.
Fishkin, James S., Justice, Equal Opportunity and the Family, New Haven: Yale University
Press, 1984.
Judd, Kenneth L. 1985. “Redistributive Taxation in a Simple Perfect Foresight Model,” Journal
of Public Economics 28 (1), 59–83.
Phelps, Edmund S. 1961. "The Golden Rule of Capital Accumulation". American Economic
Review 51: 638–643.
Straub, Ludwig, and Iván Werning. 2014. “Positive Long-Run Capital Taxation: Chamley-Judd
Revisited,” MIT Working Paper.
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The Economist explains
Thomas Piketty’s “Capital”, summarised in four paragraphs
IT IS the economics book taking the world by storm. "Capital in the TwentyFirst Century", written by the French economist Thomas Piketty, was published in French last year and in English in March of this year. The English version quickly became an unlikely bestseller, and it has prompted a broad and energetic debate on the book’s subject: the outlook for global inequality. Some reckon it heralds or may itself cause a pronounced shift in the focus of economic policy, toward distributional questions. This newspaper has hailed Mr Piketty as "the modern Marx" (Karl, that is). But what’s it all about?
"Capital" is built on more than a decade of research by Mr Piketty and a handful of other economists, detailing historical changes in the concentration of income and wealth. This pile of data allows Mr Piketty to sketch out the evolution of inequality since the beginning of the industrial revolution. In the 18th and 19th centuries western European society was highly unequal. Private wealth dwarfed national income and was concentrated in the hands of the rich families who sat atop a relatively rigid class structure. This system persisted even as industrialisation slowly contributed to rising wages for workers. Only the chaos of the first
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and second world wars and the Depression disrupted this pattern. High taxes, inflation, bankruptcies, and the growth of sprawling welfare states caused wealth to shrink dramatically, and ushered in a period in which both income and wealth were distributed in relatively egalitarian fashion. But the shocks of the early 20th century have faded and wealth is now reasserting itself. On many measures, Mr Piketty reckons, the importance of wealth in modern economies is approaching levels last seen before the first world war.
From this history, Mr Piketty derives a grand theory of capital and inequality. As a general rule wealth grows faster than economic output, he explains, a concept he captures in the expression r > g (where r is the rate of return to wealth and g is the economic growth rate). Other things being equal, faster economic growth will diminish the importance of wealth in a society, whereas slower growth will increase it (and demographic change that slows global growth will make capital more dominant). But there are no natural forces pushing against the steady concentration of wealth. Only a burst of rapid growth (from technological progress or rising population) or government intervention can be counted on to keep economies from returning to the “patrimonial capitalism” that worried Karl Marx. Mr Piketty closes the book by recommending that governments step in now, by adopting a global tax on wealth, to prevent soaring inequality contributing to economic or political instability down the road.
The book has unsurprisingly attracted plenty of criticism. Some wonder whether Mr Piketty is right to think the future will look like the past. Theory argues that it should become ever harder to earn a good return on wealth the more there is of it. And today’s superrich mostly come by their wealth through work, rather than via inheritance. Others argue that Mr Piketty’s policy recommendations are more ideologically than economically driven and could do more harm than good. But many of the sceptics nonetheless have kind words for the book’s contributions, in terms of data and analysis. Whether or not Mr Piketty succeeds in changing policy, he will have influenced the way thousands of readers and plenty of economists think about these issues.
Dig deeper: "Capital" is a great piece of scholarship, but a poor guide to policy (May 2014) Why did the French version of "Capital" not make the same splash? (April 2014) Revisiting an old argument about the impact of capitalism (January 2014)
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NBER WORKING PAPER SERIES
IS THE UNITED STATES STILL A LAND OF OPPORTUNITY? RECENT TRENDS IN INTERGENERATIONAL MOBILITY
Raj Chetty Nathaniel Hendren
Patrick Kline Emmanuel Saez Nicholas Turner
Working Paper 19844 http://www.nber.org/papers/w19844
NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue
Cambridge, MA 02138 January 2014
The views expressed in this paper are those of the authors and do not necessarily represent the views or policies of the US Treasury Department or the Internal Revenue Service or the National Bureau of Economic Research. We thank Sarah Abraham, Alex Bell, Alex Olssen, and Evan Storms for outstanding research assistance. We thank David Autor, Greg Duncan, Lawrence Katz, Alan Krueger, Richard Murnane, Gary Solon, and numerous seminar participants for helpful discussions and comments. Financial support from the Lab for Economic Applications and Policy at Harvard, the Center for Equitable Growth at UC Berkeley, and the National Science Foundation is gratefully acknowledged. The statistics reported in this paper can be downloaded from www.equality-of-opportunity.org
NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
© 2014 by Raj Chetty, Nathaniel Hendren, Patrick Kline, Emmanuel Saez, and Nicholas Turner. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Is the United States Still a Land of Opportunity? Recent Trends in Intergenerational Mobility Raj Chetty, Nathaniel Hendren, Patrick Kline, Emmanuel Saez, and Nicholas Turner NBER Working Paper No. 19844 January 2014 JEL No. H0,J0
ABSTRACT
We present new evidence on trends in intergenerational mobility in the U.S. using administrative earnings records. We find that percentile rank-based measures of intergenerational mobility have remained extremely stable for the 1971-1993 birth cohorts. For children born between 1971 and 1986, we measure intergenerational mobility based on the correlation between parent and child income percentile ranks. For more recent cohorts, we measure mobility as the correlation between a child’s probability of attending college and her parents’ income rank. We also calculate transition probabilities, such as a child’s chances of reaching the top quintile of the income distribution starting from the bottom quintile. Based on all of these measures, we find that children entering the labor market today have the same chances of moving up in the income distribution (relative to their parents) as children born in the 1970s. However, because inequality has risen, the consequences of the “birth lottery” – the parents to whom a child is born – are larger today than in the past.
Raj Chetty Department of Economics Harvard University 1805 Cambridge St. Cambridge, MA 02138 and NBER [email protected]
Nathaniel Hendren Harvard University Department of Economics Littauer Center Room 235 Cambridge, MA 02138 and NBER [email protected]
Patrick Kline Department of Economics UC, Berkeley 508-1 Evans Hall #3880 Berkeley, CA 94720 and NBER [email protected]
Emmanuel Saez Department of Economics University of California, Berkeley 530 Evans Hall #3880 Berkeley, CA 94720 and NBER [email protected]
Nicholas Turner Office of Tax Analysis U.S. Department of the Treasury 1500 Pennsylvania Avenue, NW Washington, D.C. 20220 [email protected]
1
There is a growing public perception that intergenerational income mobility – a child’s chance of
moving up in the income distribution relative to her parents – is declining in the United States (e.g.,
Foroohar 2011, Zakaria 2011). However, empirical evidence on trends in intergenerational mobility
is mixed. Some studies (e.g., Aaronson and Mazumder 2008, Putnam, Frederick, and Snellman
2012) find that income mobility and related indicators have declined in recent decades. But others
find no trend in intergenerational income mobility over a similar time period (e.g., Hertz 2007, Lee
and Solon 2009, Hauser 2010).
We present new evidence on trends in intergenerational mobility using data from de-
identified tax records, building on work by Auten, Gee, and Turner (2013) and Chetty et al. (2014).
These data have less measurement error and much larger sample sizes than prior survey-based
studies and thus yield more precise estimates of intergenerational mobility over time.
We estimate intergenerational mobility for the 1971 to 1993 birth cohorts. For children born
between 1971 and 1986, we measure mobility by estimating (1) the correlation between parent and
child income percentile ranks and (2) the probability that a child reaches the top fifth of the income
distribution conditional on her parents’ income quintile. For children born after 1986, we measure
mobility as the correlation between parent income ranks and children’s college attendance rates,
which are a strong predictor of later earnings.
We find that all of these rank-based measures of intergenerational mobility have not changed
significantly over time. For example, the probability that a child reaches the top fifth of the income
distribution given parents in the bottom fifth of the income distribution is 8.4% for children born in
1971, compared with 9.0% for those born in 1986. Children born to the highest-income families in
1984 were 74.5 percentage points more likely to attend college than those from the lowest-income
families. The corresponding gap for children born in 1993 is 69.2 percentage points, suggesting that
if anything intergenerational mobility may have increased slightly in recent cohorts. Moreover,
intergenerational mobility is fairly stable over time in each of the nine census divisions of the U.S.
even though they have very different levels of mobility.
Although rank-based measures of mobility remained stable, income inequality increased over
time in our sample, consistent with prior work. Hence, the consequences of the “birth lottery” – the
parents to whom a child is born – are larger today than in the past. A useful visual analogy is to
envision the income distribution as a ladder, with each percentile representing a different rung. The
rungs of the ladder have grown further apart (inequality has increased), but children’s chances of
climbing from lower to higher rungs have not changed (rank-based mobility has remained stable).
2
This result may be surprising in light of the well known cross-country relationship between
inequality and mobility, termed the “Great Gatsby Curve” by Krueger (2012). However, as we
discuss in Section IV, much of the increase in inequality has come from the extreme upper tail (e.g.,
the top 1%) in recent decades, and top 1% income shares are not strongly associated with mobility in
the cross-section across countries or metro areas within the U.S. (Chetty et al. 2014).
The paper is organized as follows. The next section presents a simple conceptual framework
for measuring trends in intergenerational mobility and inequality. Section II describes the data and
Section III presents the empirical results. We conclude in Section IV by discussing the findings in the
context of the prior literature.
I. Measuring Intergenerational Mobility: Conceptual Issues
The study of intergenerational mobility amounts to a characterization of the joint distribution of
parent and child income. Prior work (reviewed e.g., in Black and Devereux 2011) has used many
different statistics to summarize this joint distribution: (1) the correlation between parent and child
percentile ranks, (2) quintile transition matrices, and (3) log-log intergenerational elasticities (IGE) of
child income with respect to parent income. Since each of these statistics could exhibit different time
trends, we begin by formalizing how we measure intergenerational mobility.
We decompose the joint distribution of parent and child income into two components: (1) the
joint distribution of parent and child ranks, formally known as the copula of the distribution, and (2)
the marginal distributions of parent and child income. The marginal distributions determine the
degree of inequality within each generation, typically measured by Gini coefficients or top income
shares. The copula is a key determinant of mobility across generations. The first two measures of
mobility described above – rank-rank correlations and quintile transition matrices – depend purely on
the copula. The log-log IGE combines features of the marginal distributions and the copula.
We characterize changes in the copula and marginal distributions of income separately to
distinguish changes in inequality from intergenerational mobility. We find that the copula has not
changed over time: children’s chances of moving up or down in the income distribution have
remained stable. However, as is well known from prior work, the marginal distributions of income
have changed substantially because of growing inequality.
Together, these two facts can be used to construct various measures of mobility. For example, if
one defines mobility based on relative positions in the income distribution – e.g., a child’s prospects
of rising from the bottom to the top quintile – then intergenerational mobility has remained
3
unchanged in recent decades. If instead one defines mobility based on the probability that a child
from a low-income family (e.g., the bottom 20%) reaches a fixed upper income threshold (e.g.,
$100,000), then mobility has increased because of the increase in inequality. However, the increase
in inequality has also magnified the difference in expected incomes between children born to low
(e.g., bottom-quintile) vs. high (top-quintile) income families. In this sense, mobility has fallen
because a child’s income depends more heavily on her parents’ position in the income distribution
today than in the past.
The appropriate definition of intergenerational mobility depends upon one’s normative objective.
By characterizing the copula and marginal distributions separately, we allow readers to focus on the
measure of mobility relevant for their objectives.
II. Data
Our data and methods build closely on our companion paper (Chetty et al. 2014, henceforth CHKS),
which contains complete details on the samples and variables used below. We present a brief
summary of the sample and variable definitions here as a reference.
Sample Construction. For children born during or after 1980, we construct a linked parent-child
sample using population tax records spanning 1996-2012. This population-based sample consists of
all individuals born between 1980-1993 who are U.S. citizens as of 2013 and are claimed as a
dependent on a tax return filed in or after 1996. We link approximately 95% of children in each birth
cohort to parents based on dependent claiming, obtaining a sample with 3.7 million children per
cohort (Appendix Table 1, Column 4).
The population tax records cannot be used to link children to parents for birth cohorts prior to
1980 because they are only available starting in 1996, and our ability to link children to parents
deteriorates after children turn 16 because they begin to leave home. To obtain data on earlier birth
cohorts, we use the Statistics of Income (SOI) annual cross-sections. These cross-sections are
stratified random samples covering approximately 0.1% of tax returns. Starting in 1987, the SOI
cross-sections contain dependent information, allowing us to link children to parents.
Using the SOI cross-sections, we construct a sample of children in the 1971-82 birth cohorts,
which we refer to as the SOI sample, as follows. We first identify all children between the ages of 12
4
and 16 claimed as dependents in the 1987-98 SOI cross-sections. 1 We then pool all the SOI cross-
sections that give us information for a given birth cohort. For example, the 1971 cohort is comprised
of children claimed at age 16 in 1987, while the 1982 cohort is comprised of children claimed at ages
12-16 in 1994-98.
The SOI sample grows from 4,331 children in 1971 to 9,936 children in 1982 (Appendix
Table 1, Column 1) because we have more cross-sections to link parents to children in more recent
cohorts and because the size of the SOI cross-sections has increased over time. Using the sampling
weights, we estimate that the SOI sample represents 88% of children in each birth cohort (based on
vital statistics counts), with slightly lower coverage rates in the early cohorts because children are
less likely to be claimed as dependents as they approach age 18 and because tax credits for claiming
dependents have grown over time (Appendix Table 1, Column 3).
The SOI sample is designed to be representative of the population of children claimed on tax
returns between the ages of 12 and 16 in each birth cohort. 2 Indeed, we confirm in Appendix Table 2
that summary statistics for the SOI sample (using sampling weights) and the population-based
sample are very similar for the overlapping 1980-82 birth cohorts.
Variable Definitions. We define parent family income (in real 2012 dollars) as adjusted gross
income plus tax exempt interest and the non-taxable portion of social security benefits for those who
file tax returns. For non-filers, we define income as the sum of wage earnings (form W-2),
unemployment benefits (form 1099-G), and social security and disability benefits (form SSA-1099).
In years where parents have no tax return and no information returns, family income is coded as zero.
In the population-based sample, we define parent income as mean family income over the
five years when the child is 15-19 years old. 3 In the SOI cross-sections, parent income is observed
only in the year that the child is linked to the parent, and therefore we define parent income as family
income in that year. In both the population and SOI samples, we drop observations with zero or
negative parent income.
1 We do not limit the SOI sample to current citizens because citizenship data are not fully populated for birth cohorts
prior to 1980. The citizenship restriction has a minor impact on the characteristics of the sample (Appendix Table 2)
because most children claimed as dependents between ages 12-16 are U.S. citizens as adults. 2 Children whose parents are sampled in multiple SOI cross-sections appear multiple times in these data. There are
89,345 children in the SOI sample and 189,541 total observations. To ensure that the stratified sampling in the SOI
cross sections does not bias our results, we verify that the results are very similar in the SOI Continuous Wage
History subsample, a pure (unstratified) random panel that contains 10,360 children (not reported). 3 Since the data start in 1996, we use the mean from 1996-2000 (ages 16-20) for the 1980 cohort.
5
We define child family income in the same way as parent income, always using data from the
population files. Results are similar if we use individual rather than family income measures for
children (not reported).
Finally, we define college attendance at age 19 as an indicator for having a 1098-T form in
the calendar year the child turns 19. Because 1098-T forms are filed directly by colleges, we have
records on college attendance for all children. 4
III. Results
Rank-Rank Specification. We begin by measuring intergenerational mobility using a rank-rank
specification, which provides a more robust summary of intergenerational mobility than traditional
log-log specifications (CHKS). We rank each child relative to others in her birth cohort based on her
mean family income at ages 29-30. Similarly, we rank parents relative to other parents of children in
the same birth cohort based on their family incomes. 5
Figure 1 plots the average income rank of children (at ages 29-30) vs. parent income rank for
three sets of birth cohorts in the SOI sample: 1971-74, 1975-78, and 1979-82. To reduce noise, we
divide parent income ranks into 50 (rather than 100) bins and plot the mean child rank vs. the mean
parent rank within each bin. The rank-rank relationship is almost perfectly linear. Its slope can be
interpreted as the difference in the mean percentile rank of children from the richest families vs.
children from the poorest families. The rank-rank slopes for the three sets of cohorts in Figure 1
(estimated using OLS on the binned data) are all approximately 0.30, with standard errors less than
0.01.
When interpreting the intergenerational mobility estimates in Figure 1, one must consider two
potential biases that have been emphasized in prior work: lifecycle bias due to measuring income at
early or late ages and attenuation bias due to noise in annual measures of income (Black and
Devereux 2011). In Section III.B of CHKS, we present a detailed assessment of whether rank-rank
estimates analogous to those in Figure 1 exhibit such biases. We reproduce the key lessons from that
analysis in Appendix Figures 1-3, which establish three results. First, estimates of the rank-rank slope
4 Approximately 6% of 1098-T forms are missing from 1999-2002 because the database contains no 1098-T forms
for some small colleges in those years. This creates a small jump in the college-income gradient of approximately 3
percentage points (relative to a mean of 75 percent) from 2002 to 2003. For simplicity, we use only post-2003
college attendance data here. 5 In the SOI sample, we always define parent and child ranks within each birth cohort and SOI cross-section year.
We use sampling weights when constructing the percentiles so that they correspond to positions in the population.
6
stabilize fully once children reach age 30 and are within 20% of the age 30 estimate at age 26,
indicating that one can obtain considerable information about mobility by age 26 (Appendix Figure
1). Second, estimates of the rank-rank slope are insensitive to the age of parents and children at
which parent income is measured, provided that parents are between 30 and 55 (Appendix Figure 2).
Third, using several years of data to measure parent and child income (as we do in the population-
based sample) instead of one year (as we do in the SOI sample) does not increase the rank-rank slope
appreciably, perhaps because transitory measurement error is less prevalent in tax records than
survey data (Appendix Figure 3). These results indicate that the income definitions used in Figure 1
and in what follows do not suffer from significant lifecycle or attenuation bias.
Trends in Income Mobility. Figure 2 presents our primary estimates of intergenerational mobility by
birth cohort (see Appendix Table 1 for the data plotted in this figure). The series in solid circles plots
estimates of the rank-rank slope for the 1971-1982 birth cohorts using the SOI sample. Each estimate
is based on an OLS regression of child rank on parent rank for the relevant cohort, weighted using
inverse sampling probabilities. Consistent with Figure 1, there is no trend in these rank-rank slopes.
We also find that log-log IGE estimates are stable or, if anything, falling slightly over time
(Appendix Table 1). 6
We cannot measure children’s income at age 30 beyond the 1982 birth cohort because our
data end in 2012. To characterize mobility for younger cohorts, we repeat the preceding analysis
using income measures at age 26. The series in squares in Figure 2 plots the rank-rank slope based on
child income at age 26 for the 1980-86 birth cohorts in the population-based sample. Once again,
there is no trend in this series. Moreover, there is much less fluctuation across cohorts because the
estimates are more precise in the population data.
Importantly, CHKS show that intergenerational mobility estimates based on income at age 26
and age 30 are highly correlated across areas within the U.S. Hence, even though the level of the
rank-rank slopes at age 26 is slightly lower than the estimates at age 30, we expect trends in mobility
based on income at age 26 to provide a reliable prediction of trends in mobility at age 30.
Trends in College Gradients. We cannot use income to assess mobility for children born after 1986
because many of these individuals are still completing their education or just entering the labor
6 The log-log IGE is stable because, as we show below, the marginal distributions of parent and child incomes have
expanded at roughly similar rates. Formally, if parent and child incomes have a Bivariate Lognormal distribution
and the standard deviations of parent and child log income increase by the same percentage over time, stability of
the rank-rank slope implies stability of the log-log IGE.
7
market. We therefore use college attendance to measure intergenerational mobility for these recent
birth cohorts. CHKS demonstrate that the correlation between college attendance rates and parent
income is a strong predictor of differences in intergenerational income mobility across areas within
the U.S. The fact that the college attendance is a good proxy for income mobility is intuitive given
the strong association between higher education and subsequent earnings.
The relationship between college attendance rates and parent income ranks is approximately
linear (Appendix Figure 4). We therefore summarize the association between parent income and
college attendance by regressing an indicator for being enrolled in college at age 19 on parent income
rank. The coefficient in this regression, which we term the college attendance gradient, can be
interpreted as the gap in college attendance rates between children from the lowest- and highest-
income families. The series in triangles in Figure 2 plots the college attendance gradient for the 1984-
93 birth cohorts. The gap in college attendance rates between children from the lowest- and highest-
income families is essentially constant at 74.5% between the 1984-89 birth cohorts. The gap falls
slightly in the most recent cohorts, reaching 69.2% for the 1993 cohort. This suggests that mobility
in the U.S. may be improving, although one must be cautious in extrapolating from the college
gradient to the income gradient as we explain below. We find very similar results when measuring
college attendance at later ages (Appendix Figure 5).
Our estimates of the college attendance gradient for the 1984 cohort are consistent with
Bailey and Dynarski’s (2011) estimates for the 1979-82 cohorts in survey data. Bailey and Dynarski
show that the college attendance gap between children from families in the top vs. bottom quartile of
the income distribution grew between the 1961-64 and 1979-82 birth cohorts. Our data show that the
college attendance gap has stabilized in more recent cohorts. 7
One can obtain a richer prediction of a child’s future income using information not just on
whether a child attends any college, but on which college the child attends. Using data from 1098-T
forms, Chetty, Friedman, and Rockoff (2013) construct an earnings-based index of “college quality”
using the mean individual wage earnings at age 31 of children born in 1979-80 based on the college
they attended at age 20. Children who do not attend college are included in a separate “no college”
category in this index. We assign each child in our population-based sample a value of this college
7 Duncan, Kalil, and Ziol-Guest (2013) show that much of the increase documented by Bailey and Dynarski is
driven by the increased inequality among parents rather than an increase in the association between college
attendance and the level of parent income. The slower growth of income inequality in the 1990s (Card and Dinardo
2002, Autor, Katz, and Kearney 2008) could explain why the relationship between parent income ranks and college
attendance is more stable for recent cohorts.
8
quality index based on the college in which they were enrolled at age 19. We then convert this dollar
index to percentile ranks, assigning the 52.7% of children who do not attend college a rank of 26.6. 8
The relationship between a child’s college quality rank and parent income rank is convex
(Appendix Figure 6), because most children from low-income families do not attend college. To
account for this non-linearity, we define the gradient in college quality as the difference in mean
college quality rank between children with parents around the 75th percentile (percentiles 72 to 78)
and children with parents around the 25th percentile (percentiles 22 to 28). The time series of the
resulting college quality gradient is almost identical to the time series of the college attendance
gradient (Appendix Figure 7). Hence, intergenerational mobility is stable (or improving slightly) not
just based on college attendance rates, but also based on college quality.
Consolidated Series. We construct a consolidated series of intergenerational mobility for the 1971-93
birth cohorts by combining the age 29-30 income gradient (Appendix Table 1, Column 5), the age 26
income gradient (Column 7), and the college attendance gradient (Column 8). To do so, we multiply
the age 26 income gradient by a constant scaling factor of 1.12 to match the level of the age 29-30
income gradient for the 1980-82 cohorts, when both measures are available. Similarly, we multiply
the college gradients by a scaling factor of 0.40 to match the rescaled age 26 income gradients from
1984-1986.
The series in circles in Figure 2 presents the resulting consolidated series from 1971-93. The
solid circles are simply the estimates based on age 29-30 income; the open circles are forecasts based
on age 26 income for the 1983-86 cohorts and college attendance for the 1987-93 cohorts. This
consolidated series provides a forecast of intergenerational income mobility at age 30 for recent
cohorts under the assumption that the college and age 26 income gradients are always a constant
multiple of the age 30 income gradient. 9
The consolidated series is virtually flat. The estimated trend based on an OLS regression
using the 23 observations in this series is -0.0006 per year and the upper bound of the 95%
8 The children in the no-college group all have the same value of the college quality index. Breaking ties at the
mean, we assign these children a rank of 52.7/2+0.3=26.6% because 0.3% of children in the sample attend colleges
whose mean earnings are below the mean earnings of those not in college. 9 The validity of this assumption should be evaluated as data for more cohorts become available. The fact that the
college gradient increased between the 1960 and 1980 birth cohorts (Bailey and Dynarski 2011) while the income
gradient was unchanged (Figure 2 and Lee and Solon 2009) suggests that this assumption did not hold during that
period. The college gradient might provide a better forecast for recent cohorts, as college attendance rates are more
stable over the period we study (Appendix Table 5, Column 10).
9
confidence interval is 0.0008. This implies that intergenerational persistence of income ranks
increased by at most 0.0008/0.3=0.27% per year between the 1971 and 1993 birth cohorts. 10
Transition Matrices. We supplement our analysis of rank-rank slopes by considering an alternative
statistic that directly measures a child’s chances of “success”: the probability that a child reaches the
top quintile of the income distribution (Auten, Gee, and Turner 2013). We define quintiles by
ranking children relative to others in their birth cohort and parents relative to other parents of
children in the same birth cohort.
Figure 3 plots children’s probabilities of reaching the top income quintile of their cohort
conditional on their parents’ income quintile. Children’s incomes are measured at age 26. The series
in circles use the SOI sample, while those in triangles use the population-based sample. All the
series exhibit little or no trend. For instance, the probability of reaching the top quintile conditional
on coming from the bottom quintile of parental income is 8.4% in 1971 and 9% in 1986. Measuring
child income at age 29-30 in the SOI sample yields similar results (Appendix Table 4).
Regional Differences. The trends in mobility are small especially in comparison to the variation
across areas within the U.S. Using data for the 1980-85 cohorts, CHKS show that the probability
that a child rises from the bottom to the top quintile is 4% in some parts of the Southeast but over
12% in other regions, such as the Mountain states. In Figure 4, we assess whether these differences
across areas persist over time. This figure plots the age 26 income rank-rank slopes and college
attendance gradients by birth cohort for selected Census divisions (see Appendix Table 5 for
estimates for all Census divisions). We assign children to Census divisions based on where their
parents lived when they claimed them as dependents and continue to rank both children and parents
in the national income distribution.
The gradients are quite stable: they are consistently highest in the Southeast and lowest in the
Mountain and Pacific states, with New England in the middle. There are, however, some modest
differential trends across areas. For example, the age 26 income rank-rank slope fell from 0.326 to
0.307 from the 1980-1986 birth cohorts in the Southeast, but increased from 0.244 to 0.267 in New
England. Studying such differential trends may be a fruitful path to understanding the causal
determinants of mobility. To facilitate such work, we have publicly posted intergenerational mobility
estimates by commuting zone for the 1980-1993 birth cohorts in Online Data Table 1.
10
Appendix Table 3 replicates this analysis cutting the sample by the child’s gender. We find no trend in mobility
for males or females.
10
Changes in Marginal Distributions. To complement the preceding rank-based characterization of
mobility, we characterize the marginal income distributions for parents and children in our sample.
Appendix Table 6 presents two standard measures of inequality – Gini coefficients and top 1%
income shares – for parents and children by birth cohort. Consistent with prior research, we find that
inequality amongst both parents and children has increased significantly in our sample. The increase
in the Gini coefficient for parents in the bottom 99% of the distribution almost exactly matches the
increase observed in the Current Population Survey (see Appendix A). The increase in the Gini
coefficients for children is smaller, likely because children’s income is measured at an earlier age,
when the income distribution is compressed. Since the trends in the marginal distributions in our
sample closely mirror those in the CPS, existing evidence on changes in marginal income
distributions can be combined with the rank-based estimates of mobility presented here to construct
various mobility statistics of interest.
IV. Discussion
Our analysis of new administrative records on income shows that children entering the labor market
today have the same chances of moving up in the income distribution relative to their parents as
children born in the 1970s. 11
Putting together our results with evidence from Hertz (2007) and Lee
and Solon (2009) that intergenerational elasticities of income did not change significantly between
the 1950 and 1970 birth cohorts, we conclude that rank-based measures of social mobility have
remained remarkably stable over the second half of the twentieth century in the United States. 12
In
light of the findings in our companion paper on the geography of mobility (CHKS), the key issue is
not that prospects for upward mobility are declining but rather that some regions of the U.S.
persistently offer less mobility than most other developed countries.
11
Interestingly, rank-based measures of intragenerational mobility – income mobility over the lifetime for a given
individual – are also stable over this period (Kopczuk, Saez, and Song 2010, Auten, Gee, and Turner 2013). 12
As noted above, the stability of the log-log IGE documented by Hertz and Lee and Solon implies stability of the rank-rank relationship if the marginal distributions of parent and child income are both expanding similarly, which is
approximately true in practice. In contrast to the findings of Hertz and Lee and Solon, Aaronson and Mazumder
(2008) report evidence that mobility fell during the middle of the 20 th
century using Census data. However, Aaronson and Mazumder do not observe parent income in their data and therefore use the child’s state of bir th as a
proxy for parent income, which generates bias if there are significant place effects on income. More recently,
Justman and Krush (2013) also argue that mobility declined over this period, but employ a regression specification
that includes the child’s education as a control. Since education is endogenous to parent income, their regression
coefficients cannot be interpreted as estimates of intergenerational income persistence.
11
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 (Corak 2013). Based on this “Great
Gatsby curve,” Krueger (2012) predicted that recent increases in inequality would increase the
intergenerational persistence of income by 20% in the U.S. 13
One explanation for why this
prediction was not borne out is that much of the increase in inequality has been driven by the extreme
upper tail (Piketty and Saez 2003, U.S. Census Bureau 2013). In CHKS, we show that there is little
or no correlation between mobility and extreme upper tail inequality – as measured e.g. by top 1%
income shares – both across countries and across areas within the U.S. Instead, the correlation
between inequality and mobility is driven primarily by “middle class” inequality, which can be
measured for example by the Gini coefficient among the bottom 99%. Based on CHKS’s estimate of
the correlation between the bottom 99% Gini coefficient and intergenerational mobility across areas,
we would expect the correlation of parent and child income ranks to have increased by only 7.5%
(from 0.30 to 0.323) from the 1971 to 1993 birth cohorts (see Appendix A). From this perspective, it
is less surprising that mobility has not changed significantly despite the rise in inequality.
The stability of intergenerational mobility is perhaps more surprising in light of evidence that
socio-economic gaps in early indicators of success such as test scores (Reardon 2011), parental
inputs (Ramey and Ramey 2010), and social connectedness (Putnam, Frederick, and Snellman 2012)
have grown over time. Indeed, based on such evidence, Putnam, Frederick, and Snellman predicted
that the “adolescents of the 1990s and 2000s are yet to show up in standard studies of
intergenerational mobility, but the fact that working class youth are relatively more disconnected
from social institutions, and increasingly so, suggests that mobility is poised to plunge dramatically.”
An important question for future research is why such a plunge in mobility has not occurred. 14
13
Krueger’s prediction is based on comparing Gini coefficients in 1985 and 2010. Children in the 1971 cohort, the
first cohort in our sample, reached age 10 (roughly the midpoint of childhood) in 1981, while those in the 1993 cohort, the last cohort in our sample, reached age 10 in 2003. The increase in the Gini coefficient between 1981 and
2003 was larger than the increase between 1985 and 2010 (see Appendix A). Hence, based on Krueger’s
extrapolation, we would predict that mobility would fall by more than 20% over the cohorts we study here. 14
There is a strong cross-sectional correlation across areas of the U.S. between intergenerational mobility and
measures of social capital, family structure, and test scores (CHKS), making the lack of a time series relationship
more surprising. One potential explanation is that other countervailing trends – such as improved civil rights for
minorities or greater access to higher education – have offset these forces.
12
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.
14
Appendix A: Changes in Inequality and Predicted Changes in Mobility
In this appendix, we first calculate the change in the Gini coefficient from 1981 to 2003 using data
from the Current Population Survey and tax records. Using this estimate, we then predict the change
in intergenerational mobility based on the cross-sectional relationship between mobility and
inequality reported in CHKS.
Gini Coefficients: Current Population Survey. Based on data from the CPS (Table F-4 at this Census
website), the Gini coefficient for after-tax income of families rose from 0.369 in 1981 (when children
in the 1971 cohort were 10 years old, the mid-point of their childhood) to 0.436 in 2003 (when
children in the 1993 cohort were 10 years old). There is a discontinuity of 2.1 points in the series of
Gini coefficients from 1992 to 1993 due to a change in top-coding methodology. If we eliminate this
jump, the Gini coefficient increases by 0.046=0.436-0.369-0.021 from 1981 to 2003. We interpret
this Gini coefficient as applying to the bottom 99% of the income distribution because income is top-
coded in the CPS. Note that adjusting for the data break in 1993, the increase in the Gini coefficient
from 1985 to 2010, the period studied by Krueger (2012), is 0.030.
Gini Coefficients: Tax Data. Using the SOI public use cross-sections, we calculate Gini coefficients
and top 1% income shares using all tax filers with at least one dependent child. We measure income
as pre-tax adjusted gross income including full realized capital gains for consistency between 1981
and 2003. As in CHKS, we define the Gini coefficient for the bottom 99% as the overall Gini
coefficient minus the top 1% income share. We estimate that the bottom 99% Gini increases from
0.337 in 1981 to 0.382 in 2003. This increase in the bottom 99% Gini coefficient of 0.045 is nearly
identical to the estimate of 0.046 from the CPS.
Predicted Change in Mobility. An unweighted OLS regression of the rank-rank slope (for the 1980-
82 birth cohort) on the bottom 99% Gini coefficient with one observation per commuting zone yields
a coefficient of 0.548 using the data in Online Data Tables V and VIII of CHKS. Therefore, one
would predict that an increase of 0.046 in the bottom 99% Gini coefficient (the estimate based on
CPS data) would increase the rank-rank correlation of parent and child income by approximately
0.548 × 0.046 = 0.025, 7.5% of the mean value of the rank-rank slope (0.334) in the sample analyzed
by CHKS.
Appendix B: Comparison to Clark (2014)
Clark (2014) presents estimates of mobility across generations using surname averages of income,
representations in elite professions, and other related outcomes. He obtains implied IGE estimates
around 0.8, well above the estimates of intergenerational persistence obtained in our analysis and the
prior literature (e.g., Solon 1999). In this appendix, we first replicate Clark's surname-mean approach
in our data and show that estimates from surname means are generally quite similar to those obtained
from conventional micro estimates of the IGE. We then provide a simple hypothesis that may explain
why Clark's focus on rare surnames leads to a much higher estimated IGE.
Surname-Based Estimates. We construct estimates of intergenerational mobility across surnames as
follows. We begin with all the children in our core sample and restrict attention to those whose
surnames are the same as their parents' surnames. As Clark (2014, Appendix 2) notes, surname-based analyses will yield attenuated estimates of the IGE if they include parents and children who do not
actually have the same surname. Consistent with this hypothesis, we find smaller estimates of rank-
15
rank correlations and IGE's when we use the full core sample, without limiting to children who have
the same surname as their parents. We then obtain a de-identified table of surname-level means of
percentile ranks (using the baseline income definition) for both parents and children. Finally, we
regress the surname-level mean ranks for children on surname-level mean ranks for parents (as
suggested by Clark 2014, Appendix 2), weighting by the number of individuals with each surname,
to obtain a surname-level rank-rank slope. We construct surname-level estimates of the log-log IGE
analogously, computing surname level means of log income (excluding zeroes) for children and
parents.
Appendix Table 7 reports the results of this analysis. Each row of the table shows the estimates for different subsets of names. The first row considers all names. Rows 2-4 restrict to rare surnames, i.e.
names held by fewer that 25, 50, or 100 children. Rows 5-8 conversely limit the sample to common
surnames, i.e. names held by more than 100, 1000, 10000, or 20000 people. In each row, we report
the number of children in the sample (Column 1), the number of unique surnames in the sample
(Column 2), surname-mean based estimates of the rank-rank slope (Column 3), individual-level
estimates of the rank-rank slope (Column 4), surname-based estimates of the log-log IGE (Column
5), and individual-level estimates of the log-log IGE (Column 6).
We find that the surname-based estimates are generally slightly larger than the individual-level
estimates. For example, when including all names (row 1), the individual-level rank-rank slope is
0.30, compared with a surname-level rank-rank slope of 0.39. If we restrict to the rarest names
(shared by fewer than 25 people), the individual-level rank-rank slope is 0.27, compared with a
surname-based rank-rank slope of 0.30. The IGE estimates at the individual level are also slightly
smaller than those based on surname averages. The only case in which the surname averages yield
much larger implied IGE's and rank-rank correlations is in the last row of the table, where we restrict
to the 7 most common names in the U.S. population. Here, the surname-based IGE is 0.81, compared
with an individual-level IGE of 0.36. This implies that the rate of convergence in income across
generations across these broad name groups -- which likely capture broad differences in ethnicities or
race -- is much smaller than the rate of convergence within the groups. We return to this point in
greater detail below. However, the general pattern that emerges from this analysis is that surname-
based averages of income generally do not imply much greater intergenerational persistence than
individual-level regressions unless one uses specific subsets of names for the analysis.
Interpretation of Clark (2014) Estimates. Why does Clark obtain much larger estimates of
intergenerational persistence? There are many methodological differences between Clark's analysis
and our approach above. For instance, Clark analyzes multiple generations and uses other proxies for
status (such as professional occupation) rather than income. While a comprehensive analysis of the
source of the difference is outside the scope of this study, we believe that one key difference is
Clark's focus on distinctive surnames. For instance, one comparison Clark (204, page 60, Figure
3.10) gives is of the surname “Katz” vs. “Washington.” As he notes, Katz is a common Jewish
surname, while Washington is a common black surname. The comparison of intergenerational
convergence in income between these two names is thus analogous to using an indicator for race as
an instrument in a traditional individual-level IGE regression.
As is well known from prior work (Solon 1992), such IV estimates tend to yield much larger implied
IGE's, because race may have direct effects on children's income independent of their impacts on
parent income. For example, if one uses an indicator for being black as an instrument, the IGE
estimate is equivalent to the proportional reduction in the black-white income gap across generations.
In 1980, blacks' median earnings were 78.8% that of whites on average (Bureau of Labor Statistics
16
2011, Table 14, page 41). In 2010, blacks's median earnings were 79.9% that of whites. Hence, the
implied between-group IGE is 78.8/79.9=0.986, consistent with Clark's estimates. Importantly, even
though there is very little convergence across racial groups during this time period, there is
considerable social mobility within racial groups. This is why our estimates of the IGE based on
individual-level data (or pooling all surnames) over the same period are much lower.
In sum, we believe that Clark's approach effectively identifies a parameter analogous to the degree of
convergence in income across generations between racial or ethnic groups rather than across
individuals. This is an interesting parameter, but one that differs from standard studies of
intergenerational mobility that seek to measure the extent to which an individual's status is
determined by his parents' idiosyncratic circumstances.This interpretation differs from that put forth
by Clark, who argues that individual-level estimates do not capture latent “status” as well as
surname-based averages. Our analysis of surname means suggests that the differences in the results
are driven by differences in the rate of income convergence within vs. between ethnic groups rather
than a downward bias in measures of integenerational persistence based on individual data. A useful
direction for future research would be to investigate why the rate of income convergence across
certain ethnic groups is small even though intergenerational mobility within these groups is much
higher.
Figure 1. Child Income Rank vs. Parent Income Rank by Birth Cohort
Notes: The figure plots the mean percentile income rank of children at ages 29-30 (y-axis) vs. the
percentile rank of their parents (x-axis) for three groups of cohorts (1971-74, 1975-78, and 1979-
82) in the SOI sample. The figure is constructed by binning parent rank into two-percentile point
bins (so that there are 50 equal-width bins) and plotting the mean child rank in each bin vs. the
mean parent rank in each bin. Note that the number of observations varies across bins because
the SOI sample is a stratified sample. Estimates from OLS regressions on the binned data are
reported for each cohort group, with standard errors in parentheses. Child income is mean family
income at ages 29-30. Parent family income is measured in the year the child is claimed as a
dependent (between the ages of 12 and 16). Children are ranked relative to other children in their
birth cohort and SOI cross-section year. Parents are ranked relative to other parents of children in
the same birth cohort and SOI cross-section year.
Figure 2. Intergenerational Mobility Estimates for the 1971-1993 Birth Cohorts
Notes: The series in solid circles plots estimates from weighted OLS regressions (using sampling
weights) of child income rank at age 29-30 on parent income rank, estimated separately for each
birth cohort in the SOI sample from 1971-82. The series in squares plots estimates from OLS
regressions of child income rank at age 26 on parent income rank using the population-based
sample for the 1980-86 birth cohorts. The series in triangles replicates the series in squares for
the 1984-93 birth cohorts, changing the dependent variable to an indicator for college attendance
at age 19, so that the regression coefficient measures the gradient of college attendance rates with
respect to parent income rank. The series in open circles represents a forecast of
intergenerational mobility based on income at age 26 for the 1983-86 cohorts and college
attendance for the 1987-93 cohorts; see text for details. The slope of the consolidated series is
estimated using an OLS regression, with standard error reported in parentheses. See Appendix
Table 1 for the cohort-level estimates underlying this figure.
Figure 3. Probability of Reaching Top Quintile at Age 26 by Birth Cohort
Notes: The figure plots the percentage of children who reach the top quintile of the income
distribution for children in their birth cohort. We report this percentage separately for children
from each parent income quintile, normalizing the five estimates to sum to one within each birth
cohort. The series in circles show estimates using the SOI sample for the 1971-82 birth cohorts.
The series in triangles show estimates using the population-based sample for the 1980-86 birth
cohorts. Child income is measured at age 26 in both samples. In the SOI sample, parent and
child quintiles are defined (using sampling weights) separately within cohort and SOI cross-
section year. In the population-based sample, child and parent quintiles are defined separately
within each birth cohort. See Appendix Table 4 for estimates using the SOI sample based on
child income at ages 29-30.
Figure 4. Trends in Intergenerational Mobility by Census Division
Notes: The figure presents estimates of income rank-rank slopes when children are 26 (open
symbols) and college attendance gradients when children are 19 (solid symbols) by birth cohort
for four Census divisions. A child’s Census division is defined based on the state from which
parents filed their tax returns in the year they claimed the child as a dependent. Income ranks are
defined nationally, not within each Census division. All estimates use the population-based
sample. See Appendix Table 5 for estimates for all nine Census divisions and mean college
attendance rates by Census division.
Appendix Figure 1. Lifecycle Bias: Rank-Rank Slopes by
Age at which Child’s Income is Measured
Notes: This figure (reproduced from CHKS), evaluates the robustness of the rank-rank slope to
changes in the age at which child income is measured. Child income is defined as mean family
income in 2011-2012. Parent income is defined as mean family income from 1996-2000. Each
point shows the slope coefficient from a separate OLS regression of child income rank on parent
income rank, varying the child's birth cohort and hence the age at which child income is
measured in 2011-12. The blue dots use the population data, while the red triangles use the SOI
sample. The first point corresponds to the children in the 1990 birth cohort, who are 21-22 when
their incomes are measured in 2011-12 (denoted by age 22 on the figure). The last point for
which we have population-wide estimates corresponds to the 1980 cohort, who are 31-32
(denoted by 32) when their incomes are measured. The last point in the SOI sample corresponds
to the 1972 cohort, who are 39-40 (denoted by 40) when their incomes are measured. The dashed
red line is a lowess curve fit through the SOI sample rank-rank slope estimates.
Appendix Figure 2. Mobility Estimates by Age of Parent Income Measurement
A. Rank-Rank Slope by Age at which Parent Income is Measured
B. College Attendance Gradient by Age of Child when Parent Income is Measured
Notes: Panel A (reproduced from CHKS) evaluates the robustness of the rank-rank slope coefficient to
changes in the age at which parent income is measured. Panel A is based on children born in 1980-82 in
the population-based sample. Each point shows the coefficient from an OLS regression of child income
rank on parent income rank, varying the age at which parent income rank is measured. The first point
measures parent income in 1996 only, when the mean age of parents is 41. The second point measures
parent income in 1997, when parents have a mean age of 42. The last point measures income in 2010,
when parents are 55. In Panel B, we evaluate the robustness of the slope of the college-parent income
gradient to the age of the child when parent income is measured. Each point shows the slope coefficient
from an OLS regression of an indicator for the child attending college at age 19 on parent income rank,
varying the year in which parent income rank is measured from 1996 to 2011. In this series, we use data
from the 1993 birth cohort. We list the age of the child on the x axis to evaluate whether the gradient
differs when children are young (although parent age is of course also rising in lockstep).
Appendix Figure 3. Attenuation Bias: Rank-Rank Slopes
by Number of Years used to Compute Parent and Child Income
A. Number of Years Used to Measure Parent Income
B. Number of Years Used to Measure Child Income
Notes: These figures (reproduced from CHKS) evaluate the robustness of the rank-rank slope estimate to
changes in the number of years used compute parent income (Panel A) and child income (Panel B). The
figures are based on the population sample of children in the 1980-82 cohorts. In Panel A, each point
shows the slope coefficient from an OLS regression of child income rank (based on mean income in 2011-
12) on parent income rank as we vary the number of years used to compute mean parent income from 1 to
17. The first point uses parent income data for 1996 only to define parent ranks. The second point uses
mean parent income from 1996-1997. The last point uses mean parent income from 1996-2012, a 17 year
average. In Panel B, each point shows the coefficient from the same rank-rank regression, but here we
always use a five-year (1996-2000) mean to measure parent income and vary the number of years used to
compute mean child income. The point for one year measures child income in 2012 only. The point for two
years uses mean child income in 2011-12. We continue adding data for prior years; the 6th point uses mean
income in years 2007-2012.
Appendix Figure 4. College Attendance Rates vs. Parent Income Rank by Cohort
Notes: The figure plots the percentage of children in college at age 19 (y-axis) vs. the percentile
rank of their parents (x-axis) for three sets of cohorts (1984-87, 1988-90, and 1991-93) in the
population-based sample. The figure is constructed by binning parent rank into two-percentile
point bins (so that there are 50 equal sized bins) and plotting the fraction of children attending
college at 19 within each bin vs. the mean parent rank in each bin. Estimates from OLS
regressions on the binned data are reported for each cohort group, with standard errors in
parentheses.
Appendix Figure 5. Robustness of College Attendance Gradient to
Age at which College Attendance is Measured
Notes: The figure evaluates the robustness of the college attendance gradient to varying the age at
which college attendance is measured. Each series plots the coefficient from a regression of an
indicator for college attendance on parent income rank for children in a given birth cohort,
similar to the series in triangles in Figure 2. In the series in circles, college attendance is defined
as an indicator for the child attending college during or before the year in which he turns 19. The
college attendance indicators in the other series are defined analogously at subsequent ages. The
number of cohorts covered in each series varies based on data availability; for instance, college
attendance by age 25 is only observed up to the 1987 birth cohort, as our last year of data is 2012.
Appendix Figure 6. College Quality vs. Parent Income Rank by Cohort
Notes: The figure plots mean college quality rank (y-axis) vs. the income rank of parents (x-axis)
for three sets of cohorts (1984-87, 1988-90, and 1991-93) in the population-based sample. The
college quality index (taken from Chetty, Friedman, and Rockoff 2013) is defined as the mean
individual wage earnings at age 31 of children born in 1979-80 based on the college they
attended at age 20. Children who do not attend college are included in a separate “no college”
category. We assign each child in our population-based sample a value of this college quality
index based on the college in which they were enrolled at age 19. We then convert this dollar
index to percentile ranks, assigning children who do not attend college a rank of 26.6. The figure
is constructed by binning parent rank into two-percentile point bins (so that there are 50 equal
sized bins) and plotting mean college quality rank in each bin vs. mean parent rank in each bin.
The curves shown are lowess fits. The shaded regions correspond to parent percentiles 22-28 and
72-78. For each cohort group, we estimate the college quality gradient as the difference in mean
college quality rank between these bins.
Appendix Figure 7. Trends in College Attendance vs. College Quality Gradients
Notes: This figure plots the college attendance gradient (right y axis) and college quality gradient (left y
axis) for the 1984-93 birth cohorts in the population-based sample. College attendance and quality are
measured at age 19. In each birth cohort, the college quality gradient is defined as the difference in mean
college quality rank for children with parents around the 75th percentile (percentiles 72 to 78) vs. children
with parents around the 25th percentile (percentiles 22 to 28). See Appendix Figure 6 for further details on
the definition of the college quality gradient. In each birth cohort, the college attendance gradient is defined
as the coefficient from an OLS regression of an indicator for college attendance on parent income rank.
This college attendance gradient reproduces the series in triangles in Figure 2; see notes to that figure for
further details. The data plotted in this figure are reported in Columns 8 and 9 of Appendix Table 1.
Birth College Attend. College Quality Log-Log Log-Log Log-Log
Cohort Income at 29-30 Income at 26 Income at 26 Gradient Gradient (P75-P25) Age 29-30 Age 26 Age 26
SOI Sample Population SOI Sample Population SOI Sample SOI Sample Population Population Population SOI Sample SOI Sample Population
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
1971 4,331 81.5% 0.289 0.212 0.291 0.187 0.289
1972 5,629 83.0% 0.319 0.253 0.346 0.193 0.319
1973 6,179 88.4% 0.274 0.249 0.351 0.281 0.274
1974 7,102 83.7% 0.312 0.261 0.330 0.240 0.312
1975 8,222 85.8% 0.252 0.236 0.254 0.232 0.252
1976 8,257 87.1% 0.282 0.223 0.325 0.202 0.282
1977 8,160 90.4% 0.313 0.233 0.373 0.208 0.313
1978 7,973 88.5% 0.313 0.239 0.338 0.265 0.313
1979 7,593 89.2% 0.330 0.212 0.329 0.240 0.330
1980 7,762 3,092,647 96.1% 85.6% 0.274 0.219 0.273 0.266 0.213 0.274 0.274
1981 8,201 3,323,937 92.7% 91.6% 0.348 0.278 0.279 0.332 0.243 0.271 0.348
1982 9,936 3,448,021 95.8% 93.7% 0.301 0.247 0.274 0.289 0.205 0.257 0.301
1983 3,462,126 95.1% 0.268 0.232 0.300
1984 3,535,065 96.3% 0.261 0.745 0.187 0.219 0.291
1985 3,642,863 96.9% 0.262 0.745 0.190 0.217 0.293
1986 3,650,594 97.2% 0.265 0.739 0.188 0.217 0.296
1987 3,711,400 97.4% 0.751 0.192 0.296
1988 3,815,926 97.6% 0.749 0.192 0.296
1989 3,940,398 97.5% 0.746 0.191 0.294
1990 4,048,638 97.4% 0.732 0.189 0.289
1991 3,994,642 97.2% 0.711 0.182 0.281
1992 3,946,445 97.1% 0.711 0.180 0.281
1993 3,870,924 96.8% 0.692 0.174 0.273
Sample Fraction of Birth Rank-Rank Slope
Notes: Column 1 reports the number of children in the SOI sample by child's birth cohort (which is less than the total number of parent-child observations because of repeated parent sampling across years). Column 2 reports the
number of children in the population-based sample. Columns 3 and 4 report the fraction of the birth cohort represented, which is equal to the total sample size (using SOI sampling weights for the SOI sample) divided by the size of
the birth cohort, based on vital statistics from the Human Mortality Database at UC-Berkeley. Columns 5-8 present estimates from OLS regressions of child outcomes on parent income ranks by cohort. Columns 5-7 regress child
income rank on parent income rank. In the population-based sample, ranks are defined within cohort. In the SOI sample, we define ranks by cohort and SOI cross-section year and use sampling weights in all regressions. Column 5
uses child income averaged across ages 29-30, while 6 and 7 use child income at age 26. Column 8 reports the slope of a regression of college attendance, measured as an indicator for the presence of a 1098-T form in the tax year
where the child turns 19, on parent income rank. Column 9 reports the difference in average college quality percentile rank between children with parents around the 75th percentile (percentiles 72 to 78) and children with parents
around the 25th percentile (percentiles 22 to 28). College quality, taken directly from Chetty, Friedman, and Rockoff (2013), is defined as the mean income at age 31 of children born in 1979-80 based on the college they attended at
age 20; those not enrolled in any college are included in a separate category. Columns 10-12 report regressions similar to Columns 5-7, but regress log child income on log parent income in place of child and parent ranks used in
Columns 5-7. These log-log regressions drop observations in which the child has zero income. Column 13 reports the consolidated series, where estimates for cohorts 1971-1982 are taken from Column 5 and the estimates for 1983-
1993 are constructed based on Columns 7 and 8 as described in the text.
Appendix Table 1. Number of Observations and Intergenerational Mobility Statistics by Child's Birth Cohort
Cohort RepresentedSize Consolidated
Series
Sample:
Variable: Mean Median Std. Dev. Mean Median Std. Dev.
(1) (2) (3) (4) (5) (6)
Parents:
Parent Family Income (1996-2000 mean) 86,489 54,272 417,928 87,219 60,129 353,430
Parent Income in Year Matched to Child 76,551 55,562 347,071
Fraction Single Parents 31.4% 46.4% 30.6% 46.1%
Fraction Single Parents Female 65.9% 47.4% 72.0% 44.9%
Father's Age at Child Birth 28.8 28 6.8 28.5 28 6.2
Mother's Age at Child Birth 26.3 26 6.3 26.1 26 5.2
Father's Age When Linked to Child 42.8 42 7.0 43.5 43 6.3
Mother's Age When Linked to Child 40.3 40 6.5 41.1 41 5.2
Children:
Child Family Income (2011-2012 mean) 47,696 34,146 92,397 48,050 34,975 93,182
Child Family Income (Age 29-30 mean) 45,754 32,892 128,877
Fraction with Zero Income (Age 29-30) 6.8% 25.2% 6.1% 23.9%
Fraction Female 49.4% 50.0% 50.0% 50.0%
Parents:
Parent Family Income (1996-2000 mean) 89,130 56,594 493,685
Parent Income in Year Matched to Child 75,858 57,700 379,827
Fraction Single Parents 29.2% 45.5%
Fraction Single Parents Female 64.6% 47.8%
Father's Age at Child Birth 28.4 28 10.4
Mother's Age at Child Birth 25.8 25 6.3
Father's Age When Linked to Child 42.6 42 10.4
Mother's Age When Linked to Child 40.0 40 6.4
Children:
Child Family Income (2011-2012 mean) 58,428 40,742 102,713
Child Family Income (Age 29-30 mean) 49,923 37,553 119,273
Fraction with Zero Income (Age 29-30) 5.4% 22.7%
Fraction Female 49.2% 50.0%
Notes: The table presents summary statistics for the SOI sample (using sampling weights) in columns 1-3 and the population-based
sample used in Chetty et al. (2014) in columns 4-6. Panel A restricts to children in the 1980-82 birth cohorts, while Panel B uses all
cohorts in the SOI sample, 1971-1982. The SOI sample includes all individuals alive at age 30 with a valid SSN or ITIN for whom
we are able to identify parents based on dependent claiming in SOI cross-sections. The population-based sample includes all current
U.S. citizens with a valid SSN or ITIN for whom we are able to identify parents based on dependent claiming (at any point from
1996-2012). Family income is total pre-tax household income as defined in the text. Parents' marital status is measured in the year
the parent is matched to the child. In the population-based sample, the age in which parent is linked to child is measured in 1996, the
most common year in which parents are linked to children. A child is defined as single if he/she does not file with a spouse in both
2011 and 2012. All dollar values are reported in 2012 dollars, deflated using the CPI-U-RS consumer price index. See Chetty et al.
(2014) for additional summary statistics for the population-based sample.
B. 1971-1982 Cohorts
A. 1980-1982 Cohorts
Appendix Table 2. Summary Statistics for SOI and Population-Based Samples
SOI Sample Population
Birth
Cohort
Female Male Female Male Female Male Female Male
(1) (2) (3) (4) (5) (6) (7) (8)
1971 0.298 0.280 0.298 0.280
1972 0.316 0.322 0.316 0.322
1973 0.291 0.262 0.291 0.262
1974 0.304 0.317 0.304 0.317
1975 0.252 0.252 0.252 0.252
1976 0.314 0.251 0.314 0.251
1977 0.282 0.342 0.282 0.342
1978 0.330 0.303 0.330 0.303
1979 0.349 0.311 0.349 0.311
1980 0.276 0.273 0.281 0.266 0.276 0.273
1981 0.335 0.365 0.284 0.274 0.335 0.365
1982 0.336 0.270 0.280 0.270 0.336 0.270
1983 0.272 0.265 0.305 0.297
1984 0.267 0.255 0.739 0.752 0.300 0.286
1985 0.269 0.256 0.736 0.757 0.301 0.286
1986 0.269 0.261 0.730 0.750 0.302 0.292
1987 0.740 0.763 0.303 0.292
1988 0.736 0.763 0.301 0.292
1989 0.732 0.761 0.300 0.291
1990 0.714 0.751 0.292 0.287
1991 0.692 0.731 0.283 0.280
1992 0.692 0.732 0.283 0.280
1993 0.669 0.715 0.274 0.274
Consolidated Series
Notes: This table presents estimates of intergenerational mobility by birth cohort and gender. Ranks are defined in the full
sample (pooling males and females). Columns 1-4 report coefficient estimates from OLS regressions of child income rank on
parent income rank, replicating the specifications in Columns 5 and 7 of Appendix Table 1 conditioning on child gender.
Columns 5-6 report coefficients from regressions of college attendance on parent income rank, replicating the specification
in Column 8 on Appendix Table 1 conditioning on child gender. Columns 7 and 8 report consolidated series, which are
constructed in the same way as column 13 of Appendix Table 1, with separate scaling factors by gender.
Appendix Table 3. Intergenerational Mobility Statistics by Child Gender
Rank-Rank Slope,
Income at 29-30 SOI
Sample
Rank-Rank Slope,
Income at 26 Pop.-
Based Sample
College Attendance
Gradient Pop.-
Based Sample
Q1 Q2 Q3 Q4 Q5 Q1 Q2 Q3 Q4 Q5 Q1 Q2 Q3 Q4 Q5
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
1971 8.4% 17.7% 18.5% 24.5% 31.1% 5.9% 16.7% 15.8% 24.6% 36.9%
1972 10.7% 16.2% 17.4% 25.4% 30.5% 8.5% 13.0% 19.6% 23.7% 35.2%
1973 10.0% 16.0% 21.2% 24.9% 27.9% 9.5% 13.2% 21.1% 25.3% 30.8%
1974 9.0% 15.4% 20.4% 26.5% 29.0% 7.3% 13.2% 20.1% 26.6% 33.1%
1975 10.1% 12.9% 20.4% 26.5% 30.3% 8.6% 16.1% 19.5% 23.3% 32.6%
1976 9.3% 17.4% 22.8% 22.1% 28.7% 9.4% 15.7% 19.3% 21.4% 34.4%
1977 9.5% 18.7% 19.9% 25.9% 26.1% 9.0% 14.2% 16.3% 25.8% 34.8%
1978 10.9% 16.9% 19.6% 22.8% 29.8% 8.7% 15.9% 20.4% 21.7% 33.3%
1979 11.7% 15.4% 21.0% 23.1% 29.1% 8.5% 11.9% 20.8% 26.3% 32.8%
1980 12.2% 14.7% 18.4% 23.8% 31.0% 9.3% 14.6% 20.0% 25.3% 30.7% 8.1% 13.9% 21.4% 22.0% 34.8%
1981 11.1% 13.7% 20.9% 22.9% 31.5% 9.2% 14.3% 20.1% 25.4% 31.1% 6.1% 12.0% 20.8% 26.5% 34.8%
1982 8.4% 14.5% 22.2% 25.8% 29.3% 9.2% 14.3% 20.0% 25.5% 31.0% 8.8% 12.6% 21.7% 24.8% 32.1%
1983 9.0% 14.0% 20.0% 25.7% 31.3%
1984 9.1% 13.9% 20.0% 25.7% 31.3%
1985 9.1% 13.8% 19.9% 25.7% 31.5%
1986 9.0% 13.8% 19.8% 25.7% 31.7%
Notes: Each cell shows the percentage of children in a birth cohort who reached the top fifth of the income distribution given parents in the quintile
specified in the column. Columns 1-5 and 11-15 are computed on the SOI sample using a child's income at age 26 and mean income from age 29-30,
respectively. In the SOI sample, parent and child quintiles are defined (using sampling weights) separately within cohort and SOI cross-section year.
Columns 6-10 use the population-based sample, measuring a child's family income at age 26 as in columns 1-5. In the population-based sample, child
and parent quintiles are defined separately within each birth cohort.
SOI Sample, Income at 26 Population Sample, Income at 26
Appendix Table 4. Probabilities of Child Reaching Top Income Quintile Conditional on Parent Income Quintile
SOI Sample, Income at 29-30
Parent Quintile Parent Quintile Parent Quintile
Birth
Cohort
Birth
Cohort Pacific Mountain
New
England
West
North
Central
West
South
Central
Mid
Atlantic
South
Atlantic
East
North
Central
East
South
Central
All U.S.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
1984 0.659 0.663 0.722 0.734 0.763 0.754 0.747 0.769 0.818 0.745
1985 0.663 0.662 0.723 0.741 0.754 0.756 0.738 0.774 0.816 0.745
1986 0.660 0.655 0.720 0.710 0.752 0.751 0.741 0.766 0.812 0.739
1987 0.666 0.660 0.729 0.747 0.760 0.754 0.750 0.778 0.816 0.751
1988 0.676 0.653 0.718 0.747 0.751 0.749 0.744 0.783 0.813 0.749
1989 0.652 0.671 0.711 0.756 0.740 0.743 0.750 0.775 0.807 0.746
1990 0.639 0.664 0.700 0.736 0.713 0.733 0.740 0.759 0.786 0.732
1991 0.616 0.627 0.699 0.718 0.697 0.717 0.708 0.736 0.777 0.711
1992 0.609 0.618 0.705 0.718 0.705 0.715 0.716 0.732 0.764 0.711
1993 0.597 0.609 0.696 0.696 0.680 0.691 0.713 0.718 0.742 0.692
1984 0.526 0.462 0.590 0.583 0.452 0.571 0.473 0.532 0.400 0.510
1985 0.528 0.467 0.605 0.585 0.454 0.583 0.485 0.553 0.417 0.520
1986 0.523 0.475 0.607 0.581 0.468 0.571 0.482 0.552 0.411 0.518
1987 0.524 0.484 0.611 0.598 0.464 0.593 0.483 0.558 0.413 0.525
1988 0.522 0.478 0.613 0.597 0.466 0.591 0.484 0.552 0.422 0.522
1989 0.527 0.463 0.619 0.597 0.463 0.596 0.480 0.550 0.421 0.521
1990 0.529 0.474 0.625 0.604 0.462 0.602 0.493 0.564 0.429 0.528
1991 0.525 0.490 0.633 0.599 0.480 0.607 0.489 0.562 0.431 0.530
1992 0.516 0.493 0.632 0.611 0.468 0.606 0.501 0.568 0.439 0.532
1993 0.513 0.488 0.623 0.611 0.464 0.602 0.498 0.563 0.445 0.529
1980 0.185 0.219 0.244 0.248 0.278 0.275 0.307 0.303 0.326 0.273
1981 0.192 0.224 0.251 0.262 0.283 0.285 0.312 0.307 0.331 0.279
1982 0.190 0.221 0.256 0.260 0.277 0.282 0.301 0.309 0.326 0.274
1983 0.181 0.223 0.253 0.261 0.274 0.276 0.290 0.306 0.322 0.268
1984 0.181 0.222 0.250 0.257 0.264 0.269 0.274 0.297 0.312 0.261
1985 0.188 0.226 0.261 0.263 0.262 0.274 0.268 0.299 0.307 0.262
1986 0.190 0.222 0.267 0.267 0.251 0.279 0.281 0.301 0.307 0.265
Census Division
Appendix Table 5. Intergenerational Mobility and College Attendance Rates by Census Division
Notes: This table presents estimates of intergenerational mobility by cohort and census division using the population-based sample.
We assign children to Census divisions based on where their parents lived when they claimed them as dependents. Panel A presents
estimates of the college attendance gradient by Census division and cohort. For each Census division and cohort, we report the
coefficient from a regression of an indicator for college attendance at age 19 on parent income rank. Panel B reports the mean
college attendance rates at age 19 by Census division and cohort. Panel C presents the rank-rank slope estimate from a regression of
child income rank on parent income rank, where child income is measured at age 26. In both Panel A and Panel C, income ranks
are defined nationally, not within each Census division.
A. College Attendance Gradients
B. College Attendance Rates
C. Rank-Rank Slopes Using Income at Age 26
SOI Sample SOI Sample Population SOI Sample Population SOI Sample Population
Birth
Cohort 2-year average
income
Annual
income
Annual
income
Annual
income
5-year average
income
Annual
income
5-year average
income
Child Age 29-30 Child Age 26 Child Age 26 Child Age 12-16 Child Age 15-19 Child Age 12-16 Child Age 15-19
(1) (2) (3) (4) (5) (6) (7)
1971 0.396 0.449 0.517 10.1%
1972 0.453 0.478 0.503 11.5%
1973 0.465 0.434 0.500 11.6%
1974 0.465 0.445 0.505 11.2%
1975 0.468 0.453 0.522 11.3%
1976 0.475 0.476 0.515 11.4%
1977 0.473 0.495 0.518 11.4%
1978 0.492 0.498 0.534 11.3%
1979 0.539 0.530 0.524 11.7%
1980 0.557 0.515 0.487 0.524 0.497 11.8% 15.8%
1981 0.546 0.500 0.491 0.510 0.506 12.8% 16.4%
1982 0.535 0.505 0.493 0.498 0.511 13.8% 16.4%
1983 0.501 0.517 16.8%
1984 0.502 0.520 16.8%
1985 0.507 0.529 17.6%
1986 0.507 0.535 17.7%
1987 0.550 19.2%
1988 0.568 21.1%
1989 0.574 21.4%
1990 0.575 21.1%
1991 0.577 20.9%
1992 0.574 20.1%
1993 0.564 18.3%
Notes: This table presents income inequality statistics for parents and children using the income definitions and samples that we used to compute
intergeneratonal mobility statistics in Appendix Table 1. Columns 1-3 report Gini coefficients for child family income. In Column 1, we use the SOI sample
(with sampling weights) and define child income as mean family income over the 2 years when the child is aged 29-30. Column 2 replicates column 1,
measuring child income at age 26 instead of 29-30. Column 3 replicates Column 2 using the population-based sample. Columns 4-5 report Gini coefficients
for parent family income and columns 6-7 report top 1% income shares for parent family income. Columns 4 and 6 use the SOI sample, where parent income
is measured as the family income in the year the parent is linked to the child (when the child is aged 12 to 16; see text for details). Columns 5 and 7 consider
the population-based sample, where parent income is measured as the 5 year average of family income when the child is aged 15 to 19. See Appendix A for a
comparison of these trends to estimates based on the CPS.
Gini Coefficient for Children Gini Coefficient for Parents Top 1% Income Share for Parents
Appendix Table 6. Income Inequality by Cohort
Name Freq. Number of Number
Restriction Children of Names Surname Individual Surname Individual
(1) (2) (3) (4) (5) (6)
1. No restriction 4,843,629 395,439 0.39 0.30 0.42 0.33
2. < 25 1,135,624 375,753 0.30 0.27 0.33 0.30
3. < 50 1,437,280 384,576 0.31 0.27 0.34 0.30
4. < 100 1,784,635 389,611 0.33 0.28 0.36 0.31
5. > 100 3,053,494 5,773 0.46 0.31 0.50 0.33
6. > 1,000 1,650,583 546 0.41 0.31 0.43 0.34
7. > 10,000 390,187 22 0.41 0.33 0.45 0.35
8. > 20,000 202,734 7 0.75 0.34 0.81 0.36
Rank-Rank Slope Log-Log IGE
Appendix Table 7. Estimates of Intergenerational Mobility Using Surname Means vs. Individual Incomes
Notes: This table compares two methods of estimating rank-rank slopes and log-log IGEs. In this table, we restrict the core sample to children who have the same surname (between the ages of 30-32) as their parents. Each row imposes further sample restrictions, shown in the left-most column. We estimate the individual-level rank-rank slopes and log-log IGE's (Columns 4 and 6) as in Table I. In Columns 3 and 5, we estimate the rank-rank slopes and log-log IGE's using OLS regressions on a dataset collapsed to surname-level means, weighted by the number of observations for each name. See Appendix B for further details.
- time_trends_IGE_v36
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THE
QUARTERLY JOURNAL OF ECONOMICS
Vol. 129 November 2014 Issue 4
WHERE IS THE LAND OF OPPORTUNITY? THE GEOGRAPHY OF INTERGENERATIONAL MOBILITY IN
THE UNITED STATES*
Raj Chetty
Nathaniel Hendren
Patrick Kline
Emmanuel Saez
We use administrative records on the incomes of more than 40 million children and their parents to describe three features of intergenerational mo- bility in the United States. First, we characterize the joint distribution of parent and child income at the national level. The conditional expectation of child income given parent income is linear in percentile ranks. On average, a 10 percentile increase in parent income is associated with a 3.4 percentile increase
*The opinions expressed in this article are those of the authors alone and do not necessarily reflect the views of the Internal Revenue Service or the U.S. Treasury Department. This work is a component of a larger project examining the effects of tax expenditures on the budget deficit and economic activity. All results based on tax data in this article are constructed using statistics originally reported in the SOI Working Paper ‘‘The Economic Impacts of Tax Expenditures: Evidence from Spatial Variation across the U.S.,’’ approved under IRS contract TIRNO-12-P-00374 and presented at the National Tax Association meeting on November 22, 2013. We thank David Autor, Gary Becker, David Card, David Dorn, John Friedman, James Heckman, Nathaniel Hilger, Richard Hornbeck, Lawrence Katz, Sara Lalumia, Adam Looney, Pablo Mitnik, Jonathan Parker, Laszlo Sandor, Gary Solon, Danny Yagan, numerous seminar participants, and four anonymous referees for helpful comments. Sarah Abraham, Alex Bell, Shelby Lin, Alex Olssen, Evan Storms, Michael Stepner, and Wentao Xiong provided outstanding research assistance. This research was funded by the National Science Foundation, the Lab for Economic Applications and Policy at Harvard, the Center for Equitable Growth at UC-Berkeley, and Laura and John Arnold Foundation. Publicly available portions of the data and code, including interge- nerational mobility statistics by commuting zone and county, are available at http://www.equality-of-opportunity.org.
! The Author(s) 2014. Published by Oxford University Press, on behalf of President and Fellows of Harvard College. All rights reserved. For Permissions, please email: [email protected] The Quarterly Journal of Economics (2014), 1553–1623. doi:10.1093/qje/qju022. Advance Access publication on September 14, 2014.
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in a child’s income. Second, intergenerational mobility varies substantially across areas within the United States. For example, the probability that a child reaches the top quintile of the national income distribution starting from a family in the bottom quintile is 4.4% in Charlotte but 12.9% in San Jose. Third, we explore the factors correlated with upward mobility. High mo- bility areas have (i) less residential segregation, (ii) less income inequality, (iii) better primary schools, (iv) greater social capital, and (v) greater family stabil- ity. Although our descriptive analysis does not identify the causal mechanisms that determine upward mobility, the publicly available statistics on interge- nerational mobility developed here can facilitate research on such mechanisms. JEL Codes: H0, J0, R0.
I. Introduction
The United States is often hailed as the ‘‘land of opportu- nity,’’ a society in which a person’s chances of success depend little on his or her family background. Is this reputation war- ranted? We show that this question does not have a clear answer because there is substantial variation in intergenera- tional mobility across areas within the United States. The United States is better described as a collection of societies, some of which are ‘‘lands of opportunity’’ with high rates of mo- bility across generations, and others in which few children escape poverty.
We characterize intergenerational mobility using informa- tion from deidentified federal income tax records, which provide data on the incomes of more than 40 million children and their parents between 1996 and 2012. We organize our analysis into three parts.
In the first part, we present new statistics on intergenera- tional mobility in the United States as a whole. In our baseline analysis, we focus on U.S. citizens in the 1980–1982 birth co- horts—the oldest children in our data for whom we can reliably identify parents based on information on dependent claiming. We measure these children’s income as mean total family income in 2011 and 2012, when they are approximately 30 years old. We measure their parents’ income as mean family income be- tween 1996 and 2000, when the children are between the ages of 15 and 20.1
1. We show that our baseline measures do not suffer from significant life cycle or attenuation bias (Solon 1992; Zimmerman 1992; Mazumder 2005) by establish- ing that estimates of mobility stabilize by the time children reach age 30 and are not very sensitive to the number of years used to measure parent income.
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Following the prior literature (e.g., Solon 1999), we begin by estimating the intergenerational elasticity of income (IGE) by regressing log child income on log parent income. Unfortunately, we find that this canonical log-log specification yields very unstable estimates of mobility because the relation- ship between log child income and log parent income is nonlinear and the estimates are sensitive to the treatment of children with zero or very small incomes. When restricting the sample between the 10th and 90th percentiles of the parent income distribution and excluding children with zero income, we obtain an IGE esti- mate of 0.45. However, alternative specifications yield IGEs rang- ing from 0.26 to 0.70, spanning most of the estimates in the prior literature.2
To obtain a more stable summary of intergenerational mobil- ity, we use a rank-rank specification similar to that used by Dahl and DeLeire (2008). We rank children based on their incomes relative to other children in the same birth cohort. We rank par- ents of these children based on their incomes relative to other parents with children in these birth cohorts. We characterize mo- bility based on the slope of this rank-rank relationship, which identifies the correlation between children’s and parents’ posi- tions in the income distribution.3
We find that the relationship between mean child ranks and parent ranks is almost perfectly linear and highly robust to al- ternative specifications. A 10 percentile point increase in parent rank is associated with a 3.41 percentile increase in a child’s income rank on average. Children’s college attendance and teen- age birth rates are also linearly related to parent income ranks. A 10 percentile point increase in parent income is associated with a 6.7 percentage point (pp) increase in college attendance rates and a 3 pp reduction in teenage birth rates for women.
In the second part of the article, we characterize variation in intergenerational mobility across commuting zones (CZs). Com- muting zones are geographical aggregations of counties that are similar to metro areas but cover the entire United States,
2. In an important recent study, Mitnik et al. (2014) propose a new dollar- weighted measure of the IGE and show that it yields more stable estimates. We discuss the differences between the new measure of mobility proposed by Mitnik et al. and the canonical definition of the IGE in Section IV.A.
3. The rank-rank slope and IGE both measure the degree to which differences in children’s incomes are determined by their parents’ incomes. We discuss the conceptual differences between the two measures in Section II.
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including rural areas (Tolbert and Sizer 1996). We assign chil- dren to CZs based on where they lived at age 16—that is, where they grew up—irrespective of whether they left that CZ after- ward. When analyzing CZs, we continue to rank both children and parents based on their positions in the national income dis- tribution, which allows us to measure children’s absolute out- comes as we discuss later.
The relationship between mean child ranks and parent ranks is almost perfectly linear within CZs, allowing us to summarize the conditional expectation of a child’s rank given his parents’ rank with just two parameters: a slope and intercept. The slope measures relative mobility: the difference in outcomes between children from top versus bottom income families within a CZ. The intercept measures the expected rank for children from families at the bottom of the income distribution. Combining the intercept and slope for a CZ, we can calculate the expected rank of children from families at any given percentile p of the national parent income distribution. We call this measure absolute mobility at percentile p. Measuring absolute mobility is valuable because in- creases in relative mobility have ambiguous normative implica- tions, as they may be driven by worse outcomes for the rich rather than better outcomes for the poor.
We find substantial variation in both relative and absolute mobility across CZs. Relative mobility is lowest for children who grew up in the Southeast and highest in the Mountain West and the rural Midwest. Some CZs in the United States have relative mobility comparable to the highest mobility countries in the world, such as Canada and Denmark, while others have lower levels of mobility than any developed country for which data are available.
We find similar geographical variation in absolute mobility. We focus much of our analysis on absolute mobility at p¼25, which we call ‘‘absolute upward mobility.’’ This statistic measures the mean income rank of children with parents in the bottom half of the income distribution given linearity of the rank-rank rela- tionship. Absolute upward mobility ranges from 35.8 in Charlotte to 46.2 in Salt Lake City among the 50 largest CZs. A 1 standard deviation increase in CZ-level upward mobility is associated with a 0.2 standard deviation improvement in a child’s expected rank given parents at p¼25, 60% as large as the effect of a 1 standard deviation increase in his own parents’ income. Other measures of upward mobility exhibit similar spatial variation. For instance,
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the probability that a child reaches the top fifth of the income distribution conditional on having parents in the bottom fifth is 4.4% in Charlotte, compared with 10.8% in Salt Lake City and 12.9% in San Jose. The CZ-level mobility statistics are robust to adjusting for differences in the local cost of living, shocks to local growth, and using alternative measures of income.
Absolute upward mobility is highly correlated with relative mobility: areas with high levels of relative mobility (low rank- rank slopes) tend to have better outcomes for children from low- income families. On average, children from families below percentile p¼85 have better outcomes when relative mobility is greater; those above p¼85 have worse outcomes. Location mat- ters more for children growing up in low-income families: the ex- pected rank of children from low-income families varies more across CZs than the expected rank of children from high income families.
The spatial patterns of the gradients of college attendance and teenage birthrates with respect to parent income across CZs are very similar to the variation in intergenerational income mo- bility. This suggests that the spatial differences in mobility are driven by factors that affect children while they are growing up rather than after they enter labor market.
In the final part of the article, we explore such factors by correlating the spatial variation in mobility with observable char- acteristics. To begin, we show that upward income mobility is significantly lower in areas with larger African American popu- lations. However, white individuals in areas with large African American populations also have lower rates of upward mobility, implying that racial shares matter at the community level.
We then identify five factors that are strongly correlated with the variation in upward mobility across areas. The first is segre- gation: areas that are more residentially segregated by race and income have lower levels of mobility. Second, areas with more inequality as measured by Gini coefficients have less mobility, consistent with the ‘‘Great Gatsby curve’’ documented across countries (Krueger 2012; Corak 2013). Top 1% income shares are not highly correlated with intergenerational mobility both across CZs within the United States and across countries, sug- gesting that the factors that erode the middle class may hamper intergenerational mobility more than the factors that lead to income growth in the upper tail. Third, proxies for the quality of the K-12 school system are positively correlated with mobility.
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Fourth, social capital indexes (Putnam 1995)—which are proxies for the strength of social networks and community involvement in an area—are also positively correlated with mobility. Finally, mobility is significantly lower in areas with weaker family struc- tures, as measured, for example, by the fraction of single parents. As with race, parents’ marital status does not matter purely through its effects at the individual level. Children of married parents also have higher rates of upward mobility in communities with fewer single parents. Interestingly, we find no correlation between racial shares and upward mobility once we control for the fraction of single parents in an area.
We find modest correlations between upward mobility and local tax policies and no systematic correlation between mobility and local labor market conditions, rates of migration, or access to higher education. In a multivariable regression, the five key fac- tors described above generally remain statistically significant predictors of both relative and absolute upward mobility, even in specifications with state fixed effects. However, we emphasize that these factors should not be interpreted as causal determi- nants of mobility because all of these variables are endogenously determined and our analysis does not control for numerous other unobserved differences across areas.
Our results build on an extensive literature on intergenera- tional mobility, reviewed by Solon (1999) and Black and Devereux (2011). Our estimates of the level of mobility in the United States as a whole are broadly consistent with prior results, with the exception of Mazumder’s (2005) and Clark’s (2014) IGE esti- mates, which imply much lower levels of intergenerational mo- bility. We discuss why our findings may differ from their results in Online Appendices D and E. Our focus on within-country com- parisons offers two advantages over the cross-country compari- sons that have been the focus of prior comparative work (e.g., Bjorklund and Jäntti 1997; Jäntti et al. 2006; Corak 2013). First, differences in measurement and methods make it difficult to reach definitive conclusions from cross-country comparisons (Solon 2002). The variables we analyze are measured using the same data sources across all CZs. Second, and more important, we characterize both relative and absolute mobility across CZs. The cross-country literature has focused exclusively on differ- ences in relative mobility; much less is known about how the prospects of children from low-income families vary across coun- tries when measured on a common absolute scale (Ray 2010).
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Our analysis also relates to the literature on neighborhood effects, reviewed by Jencks and Mayer (1990) and Sampson et al. (2002). Unlike recent experimental work on neighborhood effects (e.g., Katz, Kling, and Liebman 2001; Oreopoulos 2003), our de- scriptive analysis does not shed light on whether the differences in outcomes across areas are due to the causal effect of neighbor- hoods or differences in the characteristics of people living in those neighborhoods. However, in a followup paper, Chetty and Hendren (2014) show that a substantial portion of the spatial variation documented here is driven by causal effects of place by studying families that move across areas with children of dif- ferent ages.
The article is organized as follows. We begin in Section II by defining the measures of intergenerational mobility that we study and discussing their conceptual properties. Section III describes the data. Section IV reports estimates of intergenera- tional mobility at the national level. In Section V, we present estimates of absolute and relative mobility by commuting zone. Section VI reports correlations of our mobility measures with observable characteristics of commuting zones. Section VII con- cludes. Statistics on intergenerational mobility and related covar- iates are publicly available by commuting zone, metropolitan statistical area, and county on the project website (www.equali- ty-of-opportunity.org).
II. Measures of Intergenerational Mobility
At the most general level, studies of intergenerational mobil- ity seek to measure the degree to which a child’s social and eco- nomic opportunities depend on his parents’ income or social status. Because opportunities are difficult to measure, virtually all empirical studies of mobility measure the extent to which a child’s income (or occupation) depends on his parents’ income (or occupation).4 Following this approach, we aim to characterize the
4. This simplification is not innocuous, as a child’s realized income may differ from his opportunities. For instance, children of wealthy parents may choose not to work or may choose lower-paying jobs, which would reduce the persistence of income across generations relative to the persistence of underlying opportunities.
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joint distribution of a child’s lifetime pretax family income (Yi), and his parents’ lifetime pretax family income (Xi).
5
In large samples, one can characterize the joint distribution of (Yi, Xi) nonparametrically, and we provide such a characteri- zation in the form of a 100�100 centile transition matrix below. However, to provide a parsimonious summary of the degree of mobility and compare rates of mobility across areas, it is useful to characterize the joint distribution using a small set of statis- tics. We divide measures of mobility into two classes that capture different normative concepts: relative mobility and absolute mo- bility. In this section, we define a set of statistics that we use to measure these two concepts empirically and compare their con- ceptual properties.
II.A. Relative Mobility
One way to study intergenerational mobility is to ask, ‘‘What are the outcomes of children from low-income families relative to those of children from high-income families?’’ This question, which focuses on the relative outcomes of children from different parental backgrounds, has been the subject of most prior research on intergenerational mobility (Solon 1999; Black et al. 2011).
The canonical measure of relative mobility is the elasticity of
child income with respect to parent income dE½log YijXi¼x� dlog x
� � , com-
monly called the intergenerational income elasticity (IGE). The most common method of estimating the IGE is to regress log child income (logYi) on log parent income (logXi), which yields a coeffi- cient of
IGE ¼ �XY SDðlogYiÞ
SDðlogXiÞ ; ð1Þ
where �XY¼Corr(logXi, logYi) is the correlation between log child income and parent income and SD() denotes the standard devia- tion. The IGE is a relative mobility measure because it measures the difference in (log) outcomes between children of high versus low income parents.
5. If taxes and transfers do not generate rank reversals (as is typically the case in practice), using post-tax income instead of pretax income would have no effect on our preferred rank-based measures of mobility. See Mitnik et al. (2014) for a com- parison of pretax and post-tax measures of the IGE of income.
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An alternative measure of relative mobility is the correlation between child and parent ranks (Dahl and DeLeire 2008). Let Ri denote child i’s percentile rank in the income distribution of chil- dren and Pi denote parent i’s percentile rank in the income dis- tribution of parents. Regressing the child’s rank Ri on his parents’ rank Pi yields a regression coefficient �PR¼Corr(Pi, Ri), which we call the rank-rank slope.6 The rank-rank slope �PR measures the association between a child’s position in the income distribution and his parents’ position in the distribution.
To understand the connection between the IGE and the rank- rank slope, note that the correlation of log incomes �XY and the correlation of ranks �PR are closely related scale-invariant mea- sures of the degree to which child income depends on parent income.7 Hence, equation (1) implies that the IGE combines the dependence features captured by the rank-rank slope with the ratio of standard deviations of income across generations.8
The IGE differs from the rank-rank slope to the extent that in- equality changes across generations. Intuitively, a given increase in parents’ incomes has a greater effect on the level of children’s incomes when inequality is greater among children than among parents.
We estimate both the IGE and the rank-rank slope to distin- guish differences in mobility from differences in inequality and to provide a comparison to the prior literature. However, we focus primarily on rank-rank slopes because they prove to be much more robust across specifications and are thus more suitable for comparisons across areas from a statistical perspective.
II.B. Absolute Mobility
A different way to measure intergenerational mobility is to ask, ‘‘What are the outcomes of children from families of a given income level in absolute terms?’’ For example, one may be
6. The regression coefficient equals the correlation coefficient because both child and parent ranks follow a uniform distribution by construction.
7. For example, if parent and child income follow a bivariate log normal dis-
tribution, �PR ¼ 6ArcSinð
�XY 2 Þ
p & 3�XY p ¼ 0:95�XY when �XY is small (Trivedi and Zimmer
2007). 8. More generally, the joint distribution of parent and child incomes can be
decomposed into two components: the joint distribution of parent and child percen- tile ranks (the copula) and the marginal distributions of parent and child income. The rank-rank slope depends purely on the copula, whereas the IGE combines both components.
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interested in measuring the mean outcomes of children whose grow up in low-income families. Absolute mobility may be of greater normative interest than relative mobility. Increases in relative mobility (i.e., a lower IGE or rank-rank slope) could be undesirable if they are caused by worse outcomes for the rich. In contrast, increases in absolute mobility at a given income level, holding fixed absolute mobility at other income levels, unambig- uously increase welfare if one respects the Pareto principle (and if welfare depends purely on income).
We consider three statistical measures of absolute mobility. Our primary measure, which we call absolute upward mobility, is the mean rank (in the national child income distribution) of chil- dren whose parents are at the 25th percentile of the national parent income distribution.9 At the national level, this statistic is mechanically related to the rank-rank slope and does not pro- vide any additional information about mobility.10 However, when we study small areas within the United States, a child’s rank in the national income distribution is effectively an absolute out- come because incomes in a given area have little effect on the national distribution.
The second measure we analyze is the probability of rising from the bottom quintile to the top quintile of the income distri- bution (Corak and Heisz 1999; Hertz 2006), which can be inter- preted as a measure of the fraction of children who achieve the ‘‘American Dream.’’ Again, when the quintiles are defined in the national income distribution, these transition probabilities can be interpreted as measures of absolute outcomes in small areas. Our third measure is the probability that a child has family income above the poverty line conditional on having parents at the 25th percentile. Because the poverty line is defined in abso- lute dollar terms in the United States, this statistic measures the
9. This measure is the analog of the rank-rank slope in terms of absolute mo- bility. The corresponding analog of the IGE is the mean log income of children whose parents are at the 25th percentile. We do not study this statistic because it is very sensitive to the treatment of zeros and small incomes.
10. We show below that the rank-rank relationship is approximately linear. Because child and parent ranks each have a mean of 0.5 by construction in the national distribution, the mean rank of children with parents at percentile p is simply 0.5þ�PR(p – 0.5). Conceptually, the slope is the only free parameter in the linear national rank-rank relationship. Intuitively, if one child moves up in the income distribution in terms of ranks, another must come down.
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fraction of children who achieve a given absolute living standard.11
It is useful to analyze multiple measures of mobility because the appropriate measure of intergenerational mobility depends on one’s normative objective (Fields and Ok 1999). Fortunately, we find that the patterns of spatial variation in absolute and rel- ative mobility are very similar using alternative measures. In addition, we provide nonparametric transition matrices and mar- ginal distributions that allow readers to construct measures of mobility beyond those we consider here.
III. Data
We use data from federal income tax records spanning 1996– 2012. The data include both income tax returns (1040 forms) and third-party information returns (such as W-2 forms), which give us information on the earnings of those who do not file tax re- turns. We provide a detailed description of how we construct our analysis sample starting from the raw population data in Online Appendix A. Here, we briefly summarize the key variable and sample definitions. Note that in what follows, the year always refers to the tax year (i.e., the calendar year in which the income is earned).
III.A. Sample Definitions
Our base data set of children consists of all individuals who (i) have a valid Social Security number or individual taxpayer identification number, (ii) were born between 1980 and 1991, and (iii) are U.S. citizens as of 2013. We impose the citizenship requirement to exclude individuals who are likely to have immi- grated to the United States as adults, for whom we cannot mea- sure parent income. We cannot directly restrict the sample to individuals born in the United States because the database only records current citizenship status.
We identify the parents of a child as the first tax filers (be- tween 1996 and 2012) who claim the child as a child dependent and were between the ages of 15 and 40 when the child was born.
11. Another intuitive measure of upward mobility is the fraction of children whose income exceeds that of their parents. This statistic turns out to be problem- atic for our application because we measure parent and child income at different ages and because it is very sensitive to differences in local income distributions.
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If the child is first claimed by a single filer, the child is defined as having a single parent. For simplicity, we assign each child a parent (or parents) permanently using this algorithm, regardless of any subsequent changes in parents’ marital status or depen- dent claiming.12
If parents never file a tax return, we cannot link them to their child. Although some low-income individuals do not file tax re- turns in a given year, almost all parents file a tax return at some point between 1996 and 2012 to obtain a tax refund on their withheld taxes and the Earned Income Tax Credit (Cilke 1998). We are therefore able to identify parents for approximately 95 percent of the children in the 1980–1991 birth cohorts. The fraction of children linked to parents drops sharply prior to the 1980 birth cohort because our data begin in 1996 and many chil- dren begin to the leave the household starting at age 17 (Online Appendix Table I). This is why we limit our analysis to children born during or after 1980.
Our primary analysis sample, which we refer to as the core sample, includes all children in the base data set who (i) are born in the 1980–1982 birth cohorts, (ii) for whom we are able to iden- tify parents, and (iii) whose mean parent income between 1996 and 2000 is strictly positive (which excludes 1.2% of children).13
For some robustness checks, we use the extended sample, which imposes the same restrictions as the core sample, but includes all birth cohorts from 1980 to 1991. There are approximately 10 mil- lion children in the core sample and 44 million children in the extended sample.
1. Statistics of Income Sample. Because we can only reliably link children to parents starting with the 1980 birth cohort in the population tax data, we can only measure earnings of children up to age 32 (in 2012) in the full sample. To evaluate whether
12. Twelve percent of children in our core sample are claimed as dependents by different individuals in subsequent years. To ensure that this potential measure- ment error in linking children to parents does not affect our findings, we show that we obtain similar estimates of mobility for the subset of children who are never claimed by other individuals (row 9 of Online Appendix Table VII).
13. We limit the sample to parents with positive income because parents who file a tax return (as required to link them to a child) yet have zero income are un- likely to be representative of individuals with zero income and those with negative income typically have large capital losses, which are a proxy for having significant wealth.
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estimates of intergenerational mobility would change signifi- cantly if earnings were measured at later ages, we supplement our analysis using annual cross-sections of tax returns main- tained by the Statistics of Income (SOI) division of the Internal Revenue Service (IRS) prior to 1996. The SOI cross-sections pro- vide identifiers for dependents claimed on tax forms starting in 1987, allowing us to link parents to children back to the 1971 birth cohort using an algorithm analogous to that described above (see Online Appendix A for further details). The SOI cross-sections are stratified random samples of tax returns with a sampling probability that rises with income; using sampling weights, we can calculate statistics representative of the national distribution. After linking parents to children in the SOI sample, we use population tax data to obtain data on income for children and parents, using the same definitions as in the core sample. There are approximately 63,000 children in the 1971–1979 birth cohorts in the SOI sample (Online Appendix Table II).
III.B. Variable Definitions and Summary Statistics
In this section, we define the key variables we use to measure intergenerational mobility. We measure all monetary variables in 2012 dollars, adjusting for inflation using the consumer price index (CPI-U).
1. Parent Income. Following Lee and Solon (2009), our primary measure of parent income is total pretax income at the household level, which we label parent family income. More precisely, in years where a parent files a tax return, we de- fine family income as adjusted gross income (as reported on the 1040 tax return) plus tax-exempt interest income and the non- taxable portion of Social Security and Disability (SSDI) benefits. In years where a parent does not file a tax return, we define family income as the sum of wage earnings (reported on form W-2), unemployment benefits (reported on form 1099-G), and gross social security and disability benefits (reported on form SA-1099) for both parents.14 In years where parents have no
14. The database does not record W-2s and other information returns prior to 1999, so nonfiler’s income is coded as 0 prior to 1999. Assigning nonfiling parents 0 income has little effect on our estimates because only 2.9% of parents in our core sample do not file in each year prior to 1999 and most nonfilers have very low W-2 income. For instance, in 2000, median W-2 income among nonfilers was $29.
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tax return and no information returns, family income is coded as zero.15
Our baseline income measure includes labor earnings and capital income as well as unemployment insurance, Social Security, and disability benefits. It excludes nontaxable cash transfers such as Temporary Assistance to Needy Families and Supplemental Security Income, in-kind benefits such as food stamps, all refundable tax credits such as the EITC, nontaxable pension contributions (such as to 401(k)s), and any earned income not reported to the IRS. Income is always measured prior to the deduction of individual income taxes and employee-level payroll taxes.
In our baseline analysis, we average parents’ family income over the five years from 1996 to 2000 to obtain a proxy for parent lifetime income that is less affected by transitory fluctuations (Solon 1992). We use the earliest years in our sample to best re- flect the economic resources of parents while the children in our sample are growing up.16 We evaluate the robustness of our find- ings using data from other years and using a measure of individ- ual parent income instead of family income. We define individual income as the sum of individual W-2 wage earnings, unemploy- ment insurance benefits, SSDI payments, and half of household self-employment income (see Online Appendix A for details).
Furthermore, we show below that defining parent income based on data from 1999 to 2003 (when W-2 data are available) yields virtually identical estimates (Table I, row 5). Note that we never observe self-employment income for nonfilers and there- fore code it as 0; given the strong incentives for individuals with children to file created by the EITC, most nonfilers likely have very low levels of self-employment income as well.
15. Importantly, these observations are true zeros rather than missing data. Because the database covers all tax records, we know that these individuals have 0 taxable income.
16. Formally, we define mean family income as the mother’s family income plus the father’s family income in each year from 1996 to 2000 divided by 10 (by 5 if we only identify a single parent). For parents who do not change marital status, this is simply mean family income over the five-year period. For parents who are married initially and then divorce, this measure tracks the mean family incomes of the two parents over time. For parents who are single initially and then get married, this measure tracks individual income prior to marriage and total family income (in- cluding the new spouse’s income) after marriage. These household measures of income increase with marriage and naturally do not account for cohabitation; to ensure that these features do not generate bias, we assess the robustness of our results to using individual measures of income.
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2. Child Income. We define child family income in the same way as parent family income. In our baseline analysis, we aver- age child family income over the last two years in our data (2011 and 2012), when children are in their early thirties. We report results using alternative years to assess the sensitivity of our findings. For children, we define household income based on cur- rent marital status rather than marital status at a fixed point in time. Because family income varies with marital status, we also report results using individual income measures for children, constructed in the same way as for parents.
3. College Attendance. We define college attendance as an in- dicator for having one or more 1098-T forms filed on one’s behalf when the individual is aged 18–21. Title IV institutions—all col- leges and universities as well as vocational schools and other postsecondary institutions eligible for federal student aid—are required to file 1098-T forms that report tuition payments or scholarships received for every student. Because the forms are filed directly by colleges, independent of whether an individual files a tax return, we have complete records on college attendance for all children. The 1098-T data are available from 1999 to 2012. Comparisons to other data sources indicate that 1098-T forms capture college enrollment quite accurately overall (Chetty, Friedman, and Rockoff 2014, Appendix B).17
4. College Quality. Using data from 1098-T forms, Chetty, Friedman, and Rockoff (2014) construct an earnings-based index of ‘‘college quality’’ using the mean individual wage earn- ings at age 31 of children born in 1979–1980 based on the college they attended at age 20. Children who do not attend college are included in a separate ‘‘no college’’ category in this index. We assign each child in our sample a value of this college quality index based on the college in which they were enrolled at age
17. Colleges are not required to file 1098-T forms for students whose qualified tuition and related expenses are waived or paid entirely with scholarships or grants. However, the forms are frequently available even for such cases, presum- ably because of automated reporting to the IRS by universities. Approximately 6% of 1098-T forms are missing from 2000 to 2003 because the database contains no 1098-T forms for some small colleges in these years. To verify that this does not affect our results, we confirm that our estimates of college attendance by parent income gradients are very similar for later birth cohorts (not reported).
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20. We then convert this dollar index to percentile ranks within each birth cohort. The children in the no-college group, who con- stitute roughly 54 percent of our core sample, all have the same value of the college quality index. Breaking ties at the mean, we assign all of these children a college quality rank of approxi- mately 54
2 ¼ 27.18
5. Teenage Birth. We define a woman as having a teenage birth if she ever claims a dependent who was born while she was between the ages of 13 and 19. This measure is an imperfect proxy for having a teenage birth because it only covers children who are claimed as dependents by their mothers. Nevertheless, the aggregate level and spatial pattern of teenage births in our data are closely aligned with estimates based on the American Community Survey.19
6. Summary Statistics. Online Appendix Table III reports summary statistics for the core sample. Median parent family income is $60,129 (in 2012 dollars). Among the 30.6% of children matched to single parents, 72.0% are matched to a female parent. Children in our core sample have a median family income of $34,975 when they are approximately 30 years old; 6.1% of chil- dren have zero income in both 2011 and 2012; 58.9% are enrolled in a college at some point between the ages of 18 and 21; and 15.8% of women have a teenage birth.
In Online Appendix B and Appendix Table IV, we show that the total cohort size, labor force participation rate, distri- bution of child income, and other demographic characteristics of our core sample line up closely with corresponding estimates in the Current Population Survey and American Community Survey. This confirms that our sample covers roughly the same nationally representative population as previous survey-based research.
18. The exact value varies across cohorts. For example, in the 1980 birth cohort, 55.1% of children do not attend college. We assign these children a rank of 55:1
2 þ0:02 ¼ 27:7% because 0.2% of children in the 1980 birth cohort attend colleges
whose mean earnings are below the mean earnings of those not in college. 19. Of women in our core sample, 15.8% have teenage births; the corresponding
number is 14.6% in the 2003 ACS. The unweighted correlation between state-level teenage birth rates in the tax data and the ACS is 0.80.
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IV. National Statistics
We begin our empirical analysis by characterizing the rela- tionship between parent and child income at the national level. We first present a set of baseline estimates of relative mobility and then evaluate the robustness of our estimates to alternative sample and income definitions.20
IV.A. Baseline Estimates
In our baseline analysis, we use the core sample (1980–1982 birth cohorts) and measure parent income as mean family income from 1996 to 2000 and child income as mean family income in 2011–2012, when children are approximately 30 years old. Figure I Panel A presents a binned scatter plot of the mean family income of children versus the mean family income of their parents. To construct this figure, we divide the horizontal axis into 100 equal-sized (percentile) bins and plot mean child income versus mean parent income in each bin.21 This binned scatter plot provides a nonparametric representation of the con- ditional expectation of child income given parent income, E[YijXi¼x]. The regression coefficients and standard errors re- ported in this and all subsequent binned scatter plots are esti- mated on the underlying microdata using OLS regressions.
The conditional expectation of children’s income given par- ents’ income is strongly concave. Below the 90th percentile of parent income, a $1 increase in parent family income is associ- ated with a 33.5 cent increase in average child family income. In contrast, between the 90th and 99th percentile, a $1 increase in parent income is associated with only a 7.6 cent increase in child income.
20. We do not present estimates of absolute mobility at the national level be- cause absolute mobility in terms of percentile ranks is mechanically related to rel- ative mobility at the national level (see Section II). Although one can compute measures of absolute mobility at the national level based on mean incomes (e.g., the mean income of children whose parents are at the 25th percentile), there is no natural benchmark for such a statistic as it has not been computed in other coun- tries or time periods.
21. For scaling purposes, we exclude the top bin (parents in the top 1%) in this figure only; mean parent income in this bin is $1,408,760 and mean child income is $113,846.
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T A
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in co
m e
0 .4
1 3
0 .4
3 5
0 .3
9 2
0 .3
5 8
0 .3
2 2
0 .3
8 0
0 .4
3 4
(r e co
d in
g z e ro
s to
$ 1 ,0
0 0 )
(0 .0
0 0 4 )
(0 .0
0 0 7 )
(0 .0
0 0 6 )
(0 .0
0 0 6 )
(0 .0
0 0 9 )
(0 .0
0 0 3 )
(0 .0
0 0 9 )
4 .
F a m
il y
in co
m e
ra n
k F
a m
il y
in co
m e
ra n
k 0 .3
4 1
0 .3
3 6
0 .3
4 6
0 .2
8 9
0 .3
1 1
0 .3
2 3
0 .3
5 9
(0 .0
0 0 3 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 7 )
(0 .0
0 0 2 )
(0 .0
0 0 6 )
5 .
F a m
il y
in co
m e
ra n
k F
a m
il y
in co
m e
ra n
k 0 .3
3 9
0 .3
3 3
0 .3
4 4
0 .2
8 7
0 .2
9 4
0 .3
2 3
0 .3
5 7
(1 9 9 9 – 2 0 0 3 )
(0 .0
0 0 3 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 7 )
(0 .0
0 0 2 )
(0 .0
0 0 6 )
6 .
F a m
il y
in co
m e
ra n
k T
o p
p a r.
in co
m e
ra n
k 0 .3
1 2
0 .3
0 7
0 .3
1 7
0 .2
5 6
0 .2
5 3
0 .2
9 6
0 .3
2 7
(0 .0
0 0 3 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 6 )
(0 .0
0 0 2 )
(0 .0
0 0 6 )
7 .
In d
iv id
u a l
in co
m e
ra n
k F
a m
il y
in co
m e
ra n
k 0 .2
8 7
0 .3
1 7
0 .2
5 7
0 .2
6 5
0 .2
7 9
0 .2
8 6
0 .2
9 2
(0 .0
0 0 3 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 7 )
(0 .0
0 0 2 )
(0 .0
0 0 6 )
8 .
In d
iv id
u a l
e a rn
in g s
ra n
k F
a m
il y
in co
m e
ra n
k 0 .2
8 2
0 .3
1 3
0 .2
4 9
0 .2
5 9
0 .2
7 2
0 .2
8 3
0 .2
8 7
(0 .0
0 0 3 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 4 )
(0 .0
0 0 7 )
(0 .0
0 0 2 )
(0 .0
0 0 6 )
9 .
C o ll
e g e
a tt
e n
d a n
ce F
a m
il y
in co
m e
ra n
k 0 .6
7 5
0 .7
0 8
0 .6
4 4
0 .6
4 1
0 .6
6 3
0 .6
7 8
0 .6
6 1
(0 .0
0 0 5 )
(0 .0
0 0 7 )
(0 .0
0 0 7 )
(0 .0
0 0 6 )
(0 .0
0 1 3 )
(0 .0
0 0 3 )
(0 .0
0 1 0 )
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T A
B L
E I
(C O
N T
IN U
E D )
(1 )
(2 )
(3 )
(4 )
(5 )
(6 )
(7 )
S a m
p le
C h
il d
’s o u
tc o m
e P
a re
n t’
s in
co m
e d
e f.
C o re
sa m
p le
M a le
ch il
d re
n F
e m
a le
ch il
d re
n M
a rr
ie d
p a re
n ts
S in
g le
p a re
n ts
1 9 8 0 – 1 9 8 5
co h
o rt
s
F ix
e d
a g e
a t
ch il
d b ir
th
1 0 .
C o ll
e g e
q u
a li
ty ra
n k
F a m
il y
in co
m e
ra n
k 0 .1
9 1
0 .1
8 8
0 .1
9 5
0 .1
7 4
0 .1
7 2
0 .1
9 8
0 .1
8 9
(P 7 5 – P
2 5
g ra
d ie
n t)
(0 .0
0 1 0 )
(0 .0
0 1 4 )
(0 .0
0 1 5 )
(0 .0
0 1 4 )
(0 .0
0 2 0 )
(0 .0
0 0 7 )
(0 .0
0 2 2 )
1 1 .
T e e n
a g e
b ir
th F
a m
il y
in co
m e
ra n
k �
0 .2
9 8
� 0 .2
3 1
� 0 .3
2 2
� 0 .2
8 5
� 0 .2
9 0
(f e m
a le
s o n
ly )
(0 .0
0 0 6 )
(0 .0
0 0 7 )
(0 .0
0 1 6 )
(0 .0
0 0 4 )
(0 .0
0 1 1 )
N u
m b e r
o f
o b se
rv a ti
o n
s 9 ,8
6 7 ,7
3 6
4 ,9
3 5 ,8
0 4
4 ,9
3 1 ,0
6 6
6 ,8
5 4 ,5
8 8
3 ,0
1 3 ,1
4 8
2 0 ,5
2 0 ,5
8 8
2 ,2
5 0 ,3
8 0
N o te
s. E
a ch
ce ll
in th
is ta
b le
re p
o rt
s th
e co
e ffi
ci e n
t fr
o m
a u
n iv
a ri
a te
O L
S re
g re
ss io
n o f
a n
o u
tc o m
e fo
r ch
il d
re n
o n
a m
e a su
re o f
th e ir
p a re
n ts
’ in
co m
e s
w it
h st
a n
d a rd
e rr
o rs
in p
a re
n th
e se
s. A
ll ro
w s
re p
o rt
e st
im a te
s o f
sl o p
e co
e ffi
ci e n
ts fr
o m
li n
e a r
re g re
ss io
n s
o f
th e
ch il
d o u
tc o m
e o n
th e
p a re
n t
in co
m e
m e a su
re e x ce
p t
ro w
1 0 ,
in w
h ic
h w
e re
g re
ss co
ll e g e
q u
a li
ty ra
n k
o n
a q u
a d
ra ti
c in
p a re
n t
in co
m e
ra n
k (a
s in
F ig
u re
IV P
a n
e l
A ).
In th
is ro
w ,
w e
re p
o rt
th e
d if
fe re
n ce
b e tw
e e n
th e
fi tt
e d
v a lu
e s
fo r
ch il
d re
n w
it h
p a re
n ts
a t
th e
7 5 th
p e rc
e n
ti le
a n
d p
a re
n ts
a t
th e
2 5 th
p e rc
e n
ti le
u si
n g
th e
q u
a d
ra ti
c sp
e ci
fi ca
ti o n
. C
o lu
m n
(1 )
u se
s th
e co
re sa
m p
le o f
ch il
d re
n ,
w h
ic h
in cl
u d
e s
a ll
cu rr
e n
t U
.S .
ci ti
z e n
s w
it h
a v a li
d S
S N
o r
IT IN
w h
o a re
(i )
b o rn
in b ir
th co
h o rt
s 1 9 8 0 – 1 9 8 2 ,
(i i)
fo r
w h
o m
w e
a re
a b le
to id
e n
ti fy
p a re
n ts
b a se
d o n
d e p
e n
d e n
t cl
a im
in g ,
a n
d (i
ii )
w h
o se
m e a n
p a re
n t
in co
m e
o v e r
th e
y e a rs
1 9 9 6 – 2 0 0 0
is st
ri ct
ly p
o si
ti v e .
C o lu
m n
s (2
) a n
d (3
) li
m it
th e
sa m
p le
u se
d in
co lu
m n
(1 )
to m
a le
s o r
fe m
a le
s. C
o lu
m n
s (4
) a n
d (5
) li
m it
th e
sa m
p le
to ch
il d
re n
w h
o se
p a re
n ts
w e re
m a rr
ie d
o r
u n
m a rr
ie d
in th
e y e a r
th e
ch il
d w
a s
li n
k e d
to th
e p
a re
n t.
C o lu
m n
(6 )
u se
s a ll
ch il
d re
n in
th e
1 9 8 0 – 1 9 8 5
b ir
th co
h o rt
s. C
o lu
m n
(7 )
re st
ri ct
s th
e co
re sa
m p
le to
ch il
d re
n w
h o se
p a re
n ts
b o th
fa ll
w it
h in
a 5 -y
e a r
w in
d o w
o f
m e d
ia n
p a re
n t
a g e
a t
ti m
e o f
ch il
d b ir
th (a
g e
2 6 – 3 0
fo r
fa th
e rs
; 2 4 – 2 8
fo r
m o th
e rs
); w
e im
p o se
o n
ly o n
e o f
th e se
re st
ri ct
io n
s fo
r si
n g le
p a re
n ts
. C
h il
d fa
m il
y in
co m
e is
th e
m e a n
o f
2 0 1 1 – 2 0 1 2
fa m
il y
in co
m e ,
w h
il e
p a re
n t
fa m
il y
in co
m e
is th
e m
e a n
fr o m
1 9 9 6
to 2 0 0 0 .
P a re
n t
to p
e a rn
e r
in co
m e
is th
e m
e a n
in co
m e
o f
th e
h ig
h e r-
e a rn
in g
sp o u
se b e tw
e e n
1 9 9 9 – 2 0 0 3
(w h
e n
W -2
d a ta
a re
a v a il
a b le
). C
h il
d ’s
in d
iv id
u a l
in co
m e
is th
e su
m o f
W -2
w a g e
e a rn
in g s,
U I
b e n
e fi
ts ,
a n
d S
S D
I b e n
e fi
ts ,
a n
d h
a lf
o f
a n
y re
m a in
in g
in co
m e
re p
o rt
e d
o n
th e
1 0 4 0
fo rm
. In
d iv
id u
a l
e a rn
in g s
in cl
u d
e s
W -2
w a g e
e a rn
in g s,
U I
b e n
e fi
ts ,
S S
D I
in co
m e ,
a n
d se
lf -e
m p
lo y m
e n
t in
co m
e .
C o ll
e g e
a tt
e n
d a n
ce is
d e fi
n e d
a s
e v e r
a tt
e n
d in
g co
ll e g e
fr o m
a g e
1 8
to 2 1 ,
w h
e re
a tt
e n
d in
g co
ll e g e
is d
e fi
n e d
a s
p re
se n
ce o f
a 1 0 9 8 -T
fo rm
. C
o ll
e g e
q u
a li
ty ra
n k
is d
e fi
n e d
a s
th e
p e rc
e n
ti le
ra n
k o f
th e
co ll
e g e
th a t
th e
ch il
d a tt
e n
d s
a t
a g e
2 0
b a se
d o n
th e
m e a n
e a rn
in g s
a t
a g e
3 1
o f
ch il
d re
n w
h o
a tt
e n
d e d
th e
sa m
e co
ll e g e
(c h
il d
re n
w h
o d
o n
o t
a tt
e n
d co
ll e g e
a re
in cl
u d
e d
in a
se p
a ra
te ‘‘n
o co
ll e g e ’’
g ro
u p
); se
e S
e ct
io n
II I.
B fo
r fu
rt h
e r
d e ta
il s.
T e e n
a g e
b ir
th is
d e fi
n e d
a s
h a v in
g a
ch il
d w
h il
e b e tw
e e n
a g e
1 3
a n
d 1 9 .
In co
lu m
n s
(1 )–
(5 )
a n
d (7
), in
co m
e p
e rc
e n
ti le
ra n
k s
a re
co n
st ru
ct e d
b y
ra n
k in
g a ll
ch il
d re
n re
la ti
v e
to o th
e rs
in th
e ir
b ir
th co
h o rt
b a se
d o n
th e
re le
v a n
t in
co m
e d
e fi
n it
io n
a n
d ra
n k
in g
a ll
p a re
n ts
re la
ti v e
to o th
e r
p a re
n ts
in th
e co
re sa
m p
le .
R a n
k s
a re
a lw
a y s
d e fi
n e d
o n
th e
fu ll
sa m
p le
o f
a ll
ch il
d re
n ;
th a t
is ,
th e y
a re
n o t
re d
e fi
n e d
w it
h in
th e
su b sa
m p
le s
in co
lu m
n s
(2 )–
(5 )
o r
(7 ).
In co
lu m
n (6
), p
a re
n ts
a re
ra n
k e d
re la
ti v e
to o th
e r
p a re
n ts
w it
h ch
il d
re n
in th
e 1 9 8 0 – 1 9 8 5
b ir
th co
h o rt
s. T
h e
n u
m b e r
o f
o b se
rv a ti
o n
s co
rr e sp
o n
d s
to th
e sp
e ci
fi ca
ti o n
in ro
w 4 .
T h
e n
u m
b e r
o f
o b se
rv a ti
o n
s is
a p
p ro
x im
a te
ly 7 %
lo w
e r
in ro
w 1
b e ca
u se
w e
e x cl
u d
e ch
il d
re n
w it
h z e ro
in co
m e .
T h
e n
u m
b e r
o f
o b se
rv a ti
o n
s is
a p
p ro
x im
a te
ly 5 0 %
lo w
e r
in ro
w 1 1
b e ca
u se
w e
re st
ri ct
to th
e sa
m p
le o f
fe m
a le
ch il
d re
n .
T h
e re
a re
8 6 6
ch il
d re
n in
th e
co re
sa m
p le
w it
h u
n k
n o w
n se
x ,
w h
ic h
is w
h y
th e
n u
m b e r
o f
o b se
rv a ti
o n
s in
th e
co re
sa m
p le
is n
o t
e q u
a l
to th
e su
m o f
th e
o b se
rv a ti
o n
s in
th e
m a le
a n
d fe
m a le
sa m
p le
s.
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1. Log-Log Intergenerational Elasticity Estimates. Partly mo- tivated by the nonlinearity of the relationship in Figure I Panel A, the canonical approach to characterizing the joint distribution of child and parent income is to regress the log of child income on the log of parent income (as discussed in Section II), excluding chil- dren with zero income. This regression yields an estimated IGE of 0.344, as shown in the first column of row 1 of Table I.
Unfortunately, this estimate turns out to be quite sensitive to changes in the regression specifications for two reasons, illus- trated in Figure I Panel B. First, the relationship between log child income and log parent income is highly nonlinear, consis- tent with the findings of Corak and Heisz (1999) in Canadian tax data. This is illustrated in the series in circles in Figure I Panel B, which plots mean log child income versus mean log family income by percentile bin, constructed using the same method as Figure I Panel A. Because of this nonlinearity, the IGE is sensitive to the point of measurement in the income distribution. For example, restricting the sample to observations between the 10th and 90th percentile of parent income (denoted by the vertical dashed lines in the graph) yields a considerably higher IGE estimate of 0.452.
Second, the log-log specification discards observations with zero income. The series in triangles in Figure I Panel B plots the fraction of children with zero income by parental income bin. This fraction varies from 17% among the poorest families to 3% among the richest families. Dropping children with zero income there- fore overstates the degree of intergenerational mobility. The way these zeros are treated can change the IGE dramatically. For instance, including the zeros by assigning those with zero income an income of $1 (so that the log of their income is zero) raises the estimated IGE to 0.618, as shown in row 2 of Table I. If instead we treat those with 0 income as having an income of $1,000, the estimated IGE becomes 0.413. These exercises show that small differences in the way children’s income is measured at the bottom of the distribution can produce substantial variation in IGE estimates.
Columns (2)–(7) in Table I replicate the baseline specification in column (1) for alternative subsamples analyzed in the prior literature. Columns (2)–(5) split the sample by the child’s gender and the parents’ marital status in the year they first claim the child. Column (6) replicates column (1) for the extended sample of 1980–1985 birth cohorts. Column (7) restricts the
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sample to children whose mothers are between the ages of 24 and 28 and fathers are between 26 and 30 (a 5-year window around the median age of birth). This column eliminates variation in parent income correlated with differences in parent age at child birth and restricts the sample to parents who are younger than 50 years when we measure their incomes (for children born in 1980). Across these subsamples, the IGE estimates range from 0.264 (for children of single parents, excluding children with zero income) to 0.697 (for male children, recoding zeroes to $1).
The IGE is unstable because the income distribution is not well approximated by a bivariate log-normal distribution, a result that was not apparent in smaller samples used in prior work. This makes it difficult to obtain reliable comparisons of mobility across samples or geographical areas using the IGE. For example, income measures in survey data are typically top-coded and sometimes include transfers and other sources of income that increase incomes at the bottom of the distribution, which may lead to larger IGE estimates than those ob- tained in administrative data sets such as the one used here.
In a recent paper, Mitnik et al. (2014) propose a new measure of the IGE, the elasticity of expected child income with respect to
parent income dlog E½YijXi¼x� dlog x
� � , which they show is more robust to
the treatment of small incomes. In large samples, one can estimate this parameter by regressing the log of mean child income in each percentile bin (plotted in Figure I Panel A) on the log of mean parent income in each bin. In Online Appendix C, we show that Mitnik et al.’s statistic can be interpreted as a dollar-weighted average of elasticities (placing greater weight on high-income chil- dren), whereas the traditional IGE weights all individuals with positive income equally. These two parameters need not coincide in general and the ‘‘correct’’ parameter depends on the policy ques- tion one seeks to answer. However, it turns out that in our data, the Mitnik et al. dollar-weighted IGE estimate is 0.335, very sim- ilar to our baseline IGE estimate of 0.344 when excluding children with zero income (Online Appendix Figure I Panel A).22
22. Mitnik et al. (2014) find larger estimates of the dollar-weighted IGE in their sample of tax returns. A useful direction for further work would be to understand why the two samples yield different IGE estimates.
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In another recent study, Clark (2014) argues that traditional estimates of the IGE understate the persistence of status across generations because they are attenuated by fluctuations in real- ized individual incomes across generations. To resolve this prob- lem, Clark estimates the IGE based on surname-level means of income in each generation and obtains a central IGE estimate of 0.8, much larger than that in prior studies. In our data, estimates of mobility based on surname means are similar to our baseline estimates based on individual income data (Online Appendix Table V). One reason that Clark (2014) may obtain larger esti- mates of intergenerational persistence is that his focus on distinc- tive surnames partly identifies the degree of convergence in income between racial or ethnic groups (Borjas 1992) rather than across individuals (see Online Appendix D for further details).23
2. Rank-Rank Estimates. Next we present estimates of the rank-rank slope, the second measure of relative mobility dis- cussed in Section II. We measure the percentile rank of parents Pi based on their positions in the distribution of parent incomes in the core sample. Similarly, we define children’s percentile ranks Ri based on their positions in the distribution of child incomes within their birth cohorts. Importantly, this definition allows us to include zeros in child income.24 Unless otherwise noted, we hold the definition of these ranks fixed based on positions in the aggregate distribution, even when analyzing subgroups.
Figure II Panel A presents a binned scatter plot of the mean percentile rank of children E[RijPi¼p] versus their parents’ per- centile rank p. The conditional expectation of a child’s rank given his parents’ rank is almost perfectly linear. Using an OLS regres- sion, we estimate that a 1 percentage point (pp) increase in parent rank is associated with a 0.341 pp increase in the child’s mean
23. For example, Clark (2014, p. 60, Figure 3.10) compares the outcomes of individuals with the surname Katz (a predominantly Jewish name) versus Washington (a predominantly black name). This comparison generates an implied IGE close to 1, which partly reflects the fact that the black-white income gap has changed very little over the past few decades. Estimates of the IGE based on indi- vidual-level data (or pooling all surnames) are much lower because there is much more social mobility within racial groups.
24. In the case of ties, we define the rank as the mean rank for the individuals in that group. For example, if 10% of a birth cohort has zero income, all children with zero income would receive a percentile rank of 5.
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203040506070
Mean Child Income Rank
0 1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
1 0 0
R a n k-
R a n k
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p e =
0 .3
4 1
(0 .0
0 0 3 )
P a re
n t In
co m
e R
a n k
203040506070
0 1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
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1 0
0
Mean Child Income Rank
C a n a d a
D e n m
a rk
R a n k-
R a n k
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C a n a d a )
= 0
.1 7 4
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R a n k-
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D e n m
a rk
) =
0 .1
8 0
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U n ite
d S
ta te
s P
a re
n t In
co m
e R
a n k
A M
e a n
C h
il d
I n
c o
m e R
a n
k v
s . P
a re
n t
In c o
m e R
a n
k i n
t h
e U
.S .
C ro
s s -C
o u
n tr
y C
o m
p a ri
s o
n s
B
F IG
U R
E II
A ss
o ci
a ti
o n
b e tw
e e n
C h
il d
re n
’s a n
d P
a re
n ts
’ P
e rc
e n
ti le
R a n
k s
T h
e se
fi g u
re s
p re
se n
t n
o n
p a ra
m e tr
ic b in
n e d
sc a tt
e r
p lo
ts o f
th e
re la
ti o n
sh ip
b e tw
e e n
ch il
d re
n ’s
a n
d p
a re
n t’
s p
e rc
e n
ti le
in co
m e
ra n
k s.
B o th
fi g u
re s
a re
b a se
d o n
th e
co re
sa m
p le
(1 9 8 0 – 1 9 8 2
b ir
th co
h o rt
s) a n
d b a se
li n
e fa
m il
y in
co m
e d
e fi
n it
io n
s fo
r p
a re
n ts
a n
d ch
il d
re n
. C
h il
d in
co m
e is
th e
m e a n
o f
2 0 1 1 – 2 0 1 2
fa m
il y
in co
m e
(w h
e n
th e
ch il
d is
a p
p ro
x im
a te
ly 3 0
y e a rs
o ld
), a n
d p
a re
n t
in co
m e
is m
e a n
fa m
il y
in co
m e
fr o m
1 9 9 6
to 2 0 0 0 .
C h
il d
re n
a re
ra n
k e d
re la
ti v e
to o th
e r
ch il
d re
n in
th e ir
b ir
th co
h o rt
, a n
d p
a re
n ts
a re
ra n
k e d
re la
ti v e
to a ll
o th
e r
p a re
n ts
in th
e co
re sa
m p
le .
P a n
e l
A p
lo ts
th e
m e a n
ch il
d p
e rc
e n
ti le
ra n
k w
it h
in e a ch
p a re
n t
p e rc
e n
ti le
ra n
k b in
. T
h e
se ri
e s
in tr
ia n
g le
s in
P a n
e l
B p
lo ts
th e
a n
a lo
g o u
s se
ri e s
fo r
D e n
m a rk
, co
m p
u te
d b y
B o se
ru p
, K
o p
cz u
k ,
a n
d K
re in
e r
(2 0 1 3 )
u si
n g
a si
m il
a r
sa m
p le
a n
d in
co m
e d
e fi
n it
io n
s. T
h e
se ri
e s
in sq
u a re
s p
lo ts
e st
im a te
s o f
th e
ra n
k -r
a n
k se
ri e s
u si
n g
th e
d e ci
le -d
e ci
le tr
a n
si ti
o n
m a tr
ix fr
o m
C o ra
k a n
d H
e is
z (1
9 9 9 ).
T h
e se
ri e s
in ci
rc le
s in
P a n
e l
B re
p ro
d u
ce s
th e
ra n
k -r
a n
k re
la ti
o n
sh ip
in th
e U
n it
e d
S ta
te s
fr o m
P a n
e l
A a s
a re
fe re
n ce
. T
h e
sl o p
e s
a n
d b e st
-fi t
li n
e s
a re
e st
im a te
d u
si n
g a n
O L
S re
g re
ss io
n o n
th e
m ic
ro d
a ta
fo r
th e
U n
it e d
S ta
te s
a n
d o n
th e
b in
n e d
se ri
e s
(a s
w e
d o
n o t
h a v e
a cc
e ss
to th
e m
ic ro
d a ta
) fo
r D
e n
m a rk
a n
d C
a n
a d
a .
S ta
n d
a rd
e rr
o rs
a re
re p
o rt
e d
in p
a re
n th
e se
s.
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rank, as reported in row 4 of Table I. The rank-rank slope esti- mates are generally quite similar across subsamples, as shown in columns (2)–(7) of Table I.
Figure II Panel B compares the rank-rank relationship in the United States with analogous estimates for Denmark constructed using data from Boserup, Kopczuk, and Kreiner (2013) and esti- mates for Canada constructed from the decile transition matrix reported by Corak and Heisz (1999).25 The relationship between child and parent ranks is nearly linear in Denmark and Canada as well, suggesting that the rank-rank specification provides a good summary of mobility across diverse environments. The rank-rank slope is 0.180 in Denmark and 0.174 in Canada, nearly half that in the United States.
Importantly, the smaller rank-rank slopes in Denmark and Canada do not necessarily mean that children from low-income families in these countries do better than those in the United States in absolute terms. It could be that children of high- income parents in Denmark and Canada have worse outcomes than children of high-income parents in the United States. One
TABLE II
NATIONAL QUINTILE TRANSITION MATRIX
Parent quintile Child quintile 1 2 3 4 5
1 33.7% 24.2% 17.8% 13.4% 10.9% 2 28.0% 24.2% 19.8% 16.0% 11.9% 3 18.4% 21.7% 22.1% 20.9% 17.0% 4 12.3% 17.6% 22.0% 24.4% 23.6% 5 7.5% 12.3% 18.3% 25.4% 36.5%
Notes. Each cell reports the percentage of children with family income in the quintile given by the row conditional on having parents with family income in the quintile given by the column for the 9,867,736 children in the core sample (1980–1982 birth cohorts). See notes to Table I for income and sample definitions. See Online Appendix Table VI for an analogous transition matrix constructed using the 1980–1985 cohorts.
25. Both the Danish and Canadian studies use administrative earnings infor- mation for large samples as we do here. The Danish sample, which was constructed to match the analysis sample in this article as closely as possible, consists of chil- dren in the 1980–1981 birth cohorts and measures child income based on mean income between 2009 and 2011. Child income in the Danish sample is measured at the individual level, and parents’ income is the mean of the two biological parents’ income from 1997 to 1999, irrespective of their marital status. The Canadian sample is less comparable to our sample, as it consists of male children in the 1963–1966 birth cohorts and studies the link between their mean earnings from 1993 to 1995 and their fathers’ mean earnings from 1978 to 1982.
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cannot distinguish between these possibilities because the ranks are defined within each country. One advantage of the within– United States CZ-level analysis implemented below is that it nat- urally allows us to study both relative and absolute outcomes by analyzing children’s performance on a fixed national scale.
3. Transition Matrixes. Table II presents a quintile transition matrix: the probability that a child is in quintile m of the child income distribution conditional on his parent being in quintile n of the parent income distribution. One statistic of particular in- terest in this matrix is the probability of moving from the bottom quintile to the top quintile, a simple measure of success that we return to later. This probability is 7.5% in the United States, compared with 11.7% in Denmark (Boserup, Kopczuk, and Kreiner 2013) and 13.4% in Canada (Corak and Heisz 1999). In this sense, the chances of achieving the American dream are con- siderably higher for children in Denmark and Canada than those in the United States.
In Online Data Table I, we report a 100�100 percentile-level transition matrix for the United States. Using this matrix and the marginal distributions for child and parent income in Online Data Table II, one can construct any mobility statistic of interest for the U.S. population.26
IV.B. Robustness of Baseline Estimates
We now evaluate the robustness of our estimates of interge- nerational mobility to alternative specifications. We begin by evaluating two potential sources of bias emphasized in prior work: life cycle bias and attenuation bias.
1. Life Cycle Bias. Prior research has shown that measuring children’s income at early ages can understate intergenerational persistence in lifetime income because children with high lifetime incomes have steeper earnings profiles when they are young (Solon 1999; Grawe 2006; Haider and Solon 2006). To evaluate whether our baseline estimates suffer from such life cycle bias, Figure III Panel A plots estimates of the rank-rank slope by the age at which the child’s income is measured. We construct the
26. All of the online data tables are available at http://www.equality-of-oppor tunity.org/index.php/data.
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A L
if e
c y
c le
B ia
s :
R a
n k
-R a
n k
S lo
p e
s b
y A
g e
o f
C h
il d
A tt
e n
u a
ti o
n B
ia s
: R
a n
k -R
a n
k S
lo p
e s
b y
N u
m b
e r
o f
Y e
a rs
U s
e d
t o
M e
a s
u re
P a
re n
t In
c o
m e
B
F IG
U R
E II
I
R o b u
st n
e ss
o f
In te
rg e n
e ra
ti o n
a l
M o b il
it y
E st
im a te
s
T h
is fi
g u
re e v a lu
a te
s th
e ro
b u
st n
e ss
o f
th e
ra n
k -r
a n
k sl
o p
e e st
im a te
d in
F ig
u re
II P
a n
e l
A to
ch a n
g e s
in th
e a g e
a t
w h
ic h
ch il
d in
co m
e is
m e a su
re d
(P a n
e l
A )
a n
d th
e n
u m
b e r
o f
y e a rs
u se
d to
m e a su
re p
a re
n ts
’ in
co m
e (P
a n
e l
B ).
In b o th
p a n
e ls
, ch
il d
in co
m e
is d
e fi
n e d
a s
m e a n
fa m
il y
in co
m e
in 2 0 1 1
to 2 0 1 2 .
In P
a n
e l
A ,
p a re
n t
in co
m e
is d
e fi
n e d
a s
m e a n
fa m
il y
in co
m e
fr o m
1 9 9 6
to 2 0 0 0 .
E a ch
p o in
t in
P a n
e l
A sh
o w
s th
e sl
o p
e co
e ffi
ci e n
t fr
o m
a se
p a ra
te O
L S
re g re
ss io
n o f
ch il
d in
co m
e ra
n k
o n
p a re
n t
in co
m e
ra n
k ,
v a ry
in g
th e
ch il
d ’s
b ir
th co
h o rt
a n
d h
e n
ce th
e ch
il d
’s a g e
in 2 0 1 1 – 2 0 1 2
w h
e n
th e
ch il
d ’s
in co
m e
is m
e a su
re d
. T
h e
ci rc
le s
u se
th e
e x te
n d
e d
sa m
p le
in th
e p
o p
u la
ti o n
d a ta
, a n
d th
e tr
ia n
g le
s u
se th
e 0 .1
% S
ta ti
st ic
s o f
In co
m e
(S O
I) st
ra ti
fi e d
ra n
d o m
sa m
p le
. T
h e
fi rs
t p
o in
t in
P a n
e l
A co
rr e sp
o n
d s
to th
e ch
il d
re n
in th
e 1 9 9 0
b ir
th co
h o rt
, w
h o
a re
2 1 – 2 2
w h
e n
th e ir
in co
m e s
a re
m e a su
re d
in 2 0 1 1 – 2 0 1 2
(d e n
o te
d b y
a g e
2 2
o n
th e
fi g u
re ).
T h
e la
st p
o in
t fo
r w
h ic
h w
e h
a v e
p o p
u la
ti o n
-w id
e e st
im a te
s co
rr e sp
o n
d s
to th
e 1 9 8 0
co h
o rt
, w
h o
a re
3 1 – 3 2
(d e n
o te
d b y
3 2 )
w h
e n
th e ir
in co
m e s
a re
m e a su
re d
. T
h e
la st
p o in
t in
th e
S O
I sa
m p
le co
rr e sp
o n
d s
to th
e 1 9 7 1
co h
o rt
, w
h o
a re
4 0 – 4 1
(d e n
o te
d b y
4 1 )
w h
e n
th e ir
in co
m e s
a re
m e a su
re d
. T
h e
d a sh
e d
li n
e is
a lo
w e ss
cu rv
e fi
t th
ro u
g h
th e
S O
I 0 .1
% sa
m p
le ra
n k
-r a n
k sl
o p
e e st
im a te
s. In
P a n
e l
B ,
w e
fo cu
s o n
ch il
d re
n in
th e
co re
sa m
p le
(1 9 8 0 – 1 9 8 2
b ir
th co
h o rt
s) in
th e
p o p
u la
ti o n
d a ta
. E
a ch
p o in
t in
th is
fi g u
re sh
o w
s th
e co
e ffi
ci e n
t fr
o m
th e
sa m
e ra
n k
-r a n
k re
g re
ss io
n a s
in F
ig u
re II
P a n
e l
A ,
v a ry
in g
th e
n u
m b e r
o f
y e a rs
u se
d to
co m
p u
te m
e a n
p a re
n t
in co
m e .
T h
e fi
rs t
p o in
t u
se s
p a re
n t
in co
m e
d a ta
fo r
1 9 9 6
o n
ly to
d e fi
n e
p a re
n t
ra n
k s.
T h
e se
co n
d p
o in
t u
se s
m e a n
p a re
n t
in co
m e
fr o m
1 9 9 6
to 1 9 9 7 .
T h
e la
st p
o in
t u
se s
m e a n
p a re
n t
in co
m e
fr o m
1 9 9 6
to 2 0 1 2 ,
a 1 7 -y
e a r
a v e ra
g e .
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series in circles by measuring children’s income as mean family income in 2011–2012 and parent income as mean family income between 1996 and 2000, as in our baseline analysis. We then replicate the OLS regression of child income rank on parent income rank for each birth cohort between 1980 and 1990. For children in the 1980 birth cohort, we measure earnings in 2011– 2012 at age 31–32 (denoted by 32 in the figure); for the 1990 cohort, we measure earnings at age 21–22.27 The rank-rank slope rises very steeply in the early twenties as children enter the labor force, but stabilizes around age 30. It increases by 2.1% from age 30 to 31 and 0.2% from age 31 to 32.
To obtain estimates beyond age 32, we use the SOI 0.1% random sample described in Section III.A, which contains data back to the 1971 birth cohort. The series in triangles in Figure III Panel A replicates the analysis above within the SOI sample, using sampling weights to recover estimates representative of the population. The estimates in the SOI sample are very similar to those in the full population prior to age 32. After age 32, the estimates remain roughly constant. These findings indicate that rank-rank correlations exhibit little life cycle bias provided that child income is measured after age 30, as in our baseline definition.
We also find that estimates of the IGE using the traditional log-log specification (limiting the sample between the 10th and 90th percentiles of the parent income distribution) stabilize around age 30, as shown in Online Appendix Figure II Panel A. In the population data, the IGE estimate is a strictly concave function of age and rises by only 1.7% from age 31 to 32. The SOI 0.1% sample exhibits a similar (albeit noisier) pattern.
An analogous life cycle bias can arise if parent income is measured at very old or young ages. In Online Appendix Figure II Panel B we plot the rank-rank slope using the core sample, varying the five-year window used to measure parent income from a starting year of 1996 (when mothers are 41 years old on average) to 2010 (when mothers are 55 years old). The rank-rank estimates exhibit virtually no variation with the age of parent income measurement within this range.
27. We obtain very similar results if we instead track a single cohort and vary age by measuring earnings in different calendar years.
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A closely related concern is that parent income at earlier ages might matter more for children’s outcomes, for example, if re- sources in early childhood are relevant for child development (e.g., Heckman 2006; Duncan, Ziol-Guest, and Kalil 2010). Although we cannot measure parent income before age 14 for children in our core sample, we can measure parent income at earlier ages for later birth cohorts. In Chetty et al. (2014), we use data from the 1993 birth cohort and regress an indicator for col- lege attendance at age 19 on parent income rank in each year from 1996 to 2012. We reproduce the coefficients from those regressions in Online Appendix Figure II Panel C. The relation- ship between college attendance rates and parent income rank is virtually constant when children are between ages 3 and 19. Once again, this result indicates that the point at which parent income is measured (provided parents are between ages 30–55) does not significantly affect intergenerational associations, at least in ad- ministrative earnings records.28
2. Attenuation Bias. Income in a single year is a noisy measure of lifetime income, which attenuates estimates of inter- generational persistence (Solon (1992)). To evaluate whether our baseline estimates suffer from such attenuation bias, Figure III Panel B plots estimates of the rank-rank slope, varying the number of years used to calculate mean parent family income. In this figure, we plot the slope from an OLS regression of child rank on parent rank (as in row 4, column (1) of Table I), varying the number of years used to calculate mean parent income from one (1996 only) to 17 (1996–2012). The rank-rank slope based on five years of data (0.341) is 6.6% larger than the slope based on one year of parent income (0.320). Solon (1992) finds a 33% in- crease in the IGE (from 0.3 to 0.4) when using a five-year average instead of one year of data in the PSID. We find less attenuation bias for three reasons: (i) income is measured with less error in the tax data than in the PSID; (ii) we use family income measures
28. Although we cannot measure income before the year in which children turn 3, the fact that the college-income gradient is not declining from ages 3 to 19 makes it unlikely that the gradient is significantly larger prior to age 2. Parent in- come ranks in year t have a correlation of 0.91 with parent income ranks in year tþ1, 0.77 in year tþ5, and 0.65 in year tþ15. The decay in this autocorrelation would generate a decreasing slope in the gradient in Online Appendix Figure II Panel C if there were a discontinuous jump in the gradient prior to age 2.
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rather than individual income, which fluctuates more across years; and (iii) we use a rank-rank specification rather than a log-log specification, which is more sensitive to income fluctua- tions at the bottom of the distribution.
Mazumder (2005) reports that even five-year averages of parent income yield attenuated estimates of intergenerational persistence relative to longer time averages. Contrary to this result, we find that the rank-rank slope is virtually unchanged by adding more years of data beyond 5 years: the estimated slope using 15 years of data to measure parent income (0.350) is only 2.8% larger than the baseline slope of 0.341 using 5 years of data. We believe our results differ because we directly measure parent income, whereas Mazumder imputes parent income based on race and education for up to 60% of the observations in his sample, with a higher imputation rate when measuring parent income using more years (see Online Appendix E for further details). Such imputations are analogous to instrumenting for income with race and education, which is known to yield upward- biased estimates of intergenerational persistence (Solon 1992).
We analyze the effect of varying the number of years used to measure the child’s income in Online Appendix Figure II Panel D. The rank-rank slope increases very little when increasing the number of years used to compute child family income, with no detectable change once one averages over at least two years, as in our baseline measure. An ancillary implication of this result is that our estimates of intergenerational mobility are not sensitive to the calendar year in which we measure children’s incomes. This finding is consistent with the results of Chetty et al. (2014), who show that estimates of intergenerational mobility do not vary significantly across birth cohorts when income is mea- sured at a fixed age.
3. Alternative Income Definitions. In rows 5–8 of Table I, we explore the robustness of the baseline rank-rank estimate to al- ternative definitions of child and parent income. In row 5, we verify that the missing W-2 data from 1996 to 1998 does not create significant bias by defining parent income as mean income from 1999 to 2003. The rank-rank estimates are virtually unchanged with this redefinition.
In row 6, we define the parent’s rank based on the individual income of the parent with higher mean income from 1999
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to 2003.29 This specification eliminates the mechanical variation in family income driven by the number of parents in the house- hold, which could overstate the persistence of income across gen- erations if parent marital status has a direct effect of children’s outcomes. The rank-rank correlation falls by approximately 10 percent, from 0.341 to 0.312 when we use top parent income. The impact of using individual parent income instead of family income is modest because (i) most of the variation in parent income across households is not due to differences in marital status and (ii) the mean ranks of children with married parents are only 4.6 percentile points higher than those with single parents.
Next, we consider alternative income definitions for the chil- dren. Here, one concern is that children of higher income parents may be more likely to marry, again exaggerating the observed persistence in family income relative to individual income. Using individual income to measure the child’s rank has differ- ential impacts by the child’s gender, consistent with Chadwick and Solon (2002). For male children, using individual income in- stead of family income reduces the rank-rank correlation from 0.336 in the baseline specification to 0.317, a 6 percent reduction. For female children, using individual income reduces the rank- rank correlation from 0.346 to 0.257, a 26 percent reduction. The change may be larger for women because women from high income families tend to marry high-income men and may choose not to work.
Finally, in row 8 of Table I, we define a measure of child income that excludes capital and other nonlabor income using the sum of individual wage earnings, UI benefits, SSDI benefits, and Schedule C self-employment income. We divide self-employment income by two for married individuals. This individual earnings measure also yields virtually identical esti- mates of the rank-rank slope.
29. We use 1999–2003 income here because we cannot allocate earnings across spouses before 1999, as W-2 forms are available starting only in 1999. Note that top income rank differs from family income rank even for single parents because some individuals get married in subsequent years and because these individuals are ranked relative to the population, not relative to other single individuals.
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C o ll.
Q u a lit
y G
ra d ie
n t (P
7 5 -P
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= 0
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20406080100
20406080100
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
0 1
0 0
C o
ll. A
tt e
n d
a n
ce S
lo p
e =
0 .6
7 5
(0 .0
0 0
5 )
Percent Attending College at Ages 18-21
College Quality Rank at Age 20
C o lle
g e A
tt e n d a n ce
R a te
C o lle
g e Q
u a lit
y R
a n k
(0 .0
0 1
0 )
P a re
n t In
co m
e R
a n k
A C
h il d
re n
’s C
o ll e g
e A
tt e n
d a n
c e R
a te
a n
d Q
u a li ty
v s . P
a re
n t
In c o
m e R
a n
k F
e m
a le
C h
il d
re n
’s T
e e n
a g
e B
ir th
R a te
v s . P
a re
n t
In c o
m e R
a n
k B
F IG
U R
E IV
G ra
d ie
n ts
o f
C o ll
e g e
A tt
e n
d a n
ce a n
d T
e e n
a g e
B ir
th b y
P a re
n t
R a n
k
T h
e se
fi g u
re s
p re
se n
t n
o n
p a ra
m e tr
ic b in
n e d
sc a tt
e r
p lo
ts o f
th e
re la
ti o n
sh ip
b e tw
e e n
ch il
d re
n ’s
co ll
e g e
a tt
e n
d a n
ce ra
te s
(P a n
e l
A ,
ci rc
le s)
, co
ll e g e
q u
a li
ty ra
n k
(P a n
e l
A ,
tr ia
n g le
s) ,
a n
d te
e n
a g e
b ir
th ra
te s
(P a n
e l
B )
v e rs
u s
p a re
n ts
’ p
e rc
e n
ti le
ra n
k .
B o th
fi g u
re s
a re
b a se
d o n
th e
co re
sa m
p le
(1 9 8 0 – 1 9 8 2
b ir
th co
h o rt
s) .
P a re
n t
ra n
k is
d e fi
n e d
b a se
d o n
m e a n
fa m
il y
in co
m e
fr o m
1 9 9 6
to 2 0 0 0 .
In P
a n
e l
A ,
th e
ci rc
le s
p lo
t th
e fr
a ct
io n
o f
ch il
d re
n e v e r
a tt
e n
d in
g co
ll e g e
b e tw
e e n
a g e
1 8 – 2 1
w it
h in
e a ch
p a re
n t-
in co
m e
p e rc
e n
ti le
b in
; th
e tr
ia n
g le
s p
lo t
th e
a v e ra
g e
co ll
e g e
q u
a li
ty ra
n k
a t
a g e
2 0
w it
h in
e a ch
p a re
n t-
in co
m e
p e rc
e n
ti le
b in
. C
o ll
e g e
a tt
e n
d a n
ce is
d e fi
n e d
a s
th e
p re
se n
ce o f
a 1 0 9 8 -T
fo rm
fi le
d b y
a co
ll e g e
o n
b e h
a lf
o f
th e
st u
d e n
t. C
o ll
e g e
q u
a li
ty ra
n k
is d
e fi
n e d
a s
th e
p e rc
e n
ti le
ra n
k o f
th e
co ll
e g e
th a t
th e
ch il
d a tt
e n
d s
a t
a g e
2 0
b a se
d o n
th e
m e a n
e a rn
in g s
a t
a g e
3 1
o f
ch il
d re
n w
h o
a tt
e n
d e d
th e
sa m
e co
ll e g e
(c h
il d
re n
w h
o d
o n
o t
a tt
e n
d co
ll e g e
a re
in cl
u d
e d
in a
se p
a ra
te ‘‘n
o co
ll e g e ’’
g ro
u p
); se
e S
e ct
io n
II I.
B fo
r fu
rt h
e r
d e ta
il s.
P a n
e l
B p
lo ts
th e
fr a ct
io n
o f
fe m
a le
ch il
d re
n w
h o
g iv
e b ir
th w
h il
e te
e n
a g e rs
w it
h in
e a ch
p a re
n ta
l p
e rc
e n
ti le
b in
. H
a v in
g a
te e n
a g e
b ir
th is
d e fi
n e d
a s
e v e r
cl a im
in g
a d
e p
e n
d e n
t ch
il d
w h
o w
a s
b o rn
w h
il e
th e
m o th
e r
w a s
a g e d
1 3 – 1 9 .
T h
e sl
o p
e s
a n
d b e st
-fi t
li n
e s
fo r
co ll
e g e
a tt
e n
d a n
ce a n
d te
e n
a g e
b ir
th a re
e st
im a te
d u
si n
g li
n e a r
re g re
ss io
n s
o f
th e
o u
tc o m
e o f
in te
re st
o n
p a re
n t
in co
m e
ra n
k in
th e
m ic
ro d
a ta
. W
e re
g re
ss co
ll e g e
q u
a li
ty ra
n k
o n
a q u
a d
ra ti
c in
p a re
n t
ra n
k to
m a tc
h th
e n
o n
li n
e a ri
ty o f
th e
re la
ti o n
sh ip
. T
h e
co ll
e g e
q u
a li
ty g ra
d ie
n t
is d
e fi
n e d
a s
th e
d if
fe re
n ce
b e tw
e e n
th e
fi tt
e d
v a lu
e s
fo r
ch il
d re
n w
it h
p a re
n ts
a t
th e
7 5 th
p e rc
e n
ti le
a n
d p
a re
n ts
a t
th e
2 5 th
p e rc
e n
ti le
u si
n g
th is
q u
a d
ra ti
c sp
e ci
fi ca
ti o n
.
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IV.C. Intermediate Outcomes: College Attendance and Teenage Birth
We supplement our analysis of intergenerational income mo- bility by studying the relationship between parent income and two intermediate outcomes for children: college attendance and teenage birth.
The series in circles in Figure IV Panel A presents a binned scatter plot of the college attendance rate of children versus the percentile rank of parent family income using the core sample. College attendance is defined as attending college in one or more years between the ages 18 and 21. The relationship between col- lege attendance rates and parental income rank is again virtually linear, with a slope of 0.675. That is, moving from the lowest- income to highest-income parents increases the college atten- dance rate by 67.5 percentage points, similar to the estimates reported by Bailey and Dynarski (2011) using survey data.
The series in triangles in Figure IV Panel A plots college quality ranks versus parent ranks. We define a child’s college quality rank based on the mean earnings at age 30 of students who attended each college at age 20. The 54 percent of children who do not attend college at age 20 are included in this analysis and are assigned the mean rank for the noncollege group, which is approximately 54
2 ¼ 27 (see Section III.B for details). The rela-
tionship between college quality rank and parent income rank is convex because most children from low-income families do not attend college, and hence increases in parent income have little impact on college quality rank at the bottom. To account for this non-linearity, we regress college quality ranks on a quadratic function of parent income rank and define the gradient in college quality as the difference in the predicted college quality rank for children with parents at the 75th percentile and children with parents at the 25th percentile. The P25–75 gap in college quality ranks is 19.1 percentiles in our core sample.
Figure IV Panel B plots teenage birth rates for female chil- dren versus parent income ranks. Teenage birth is defined (for females only) as having a child when the mother is aged 13–19. There is a 29.8 percentage point gap in teenage birth rates be- tween children from the highest- and lowest-income families.
These correlations between intermediate outcomes and parent income ranks do not vary significantly across subsam- ples or birth cohorts, as shown in rows 9–11 of Table I. The
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strength of these correlations indicates that much of the diver- gence between children from low- versus high-income families emerges well before they enter the labor market, consistent with the findings of prior work (such as Neal and Johnson 1996; Cameron and Heckman 2001; Bhattacharya and Mazumder 2011).
V. Spatial Variation in Mobility
We now turn to our central goal of characterizing the varia- tion in intergenerational mobility across areas within the United States. We begin by defining measures of geographic location. We then present estimates of relative and absolute mobility by area and assess the robustness of these estimates to alternative specifications.
V.A. Geographical Units
To characterize the variation in children’s outcomes across areas, one must first partition the United States into a set of geographical areas in which children grow up. One way to con- ceptualize the choice of a geographical partition is using a hier- archical model in which children’s outcomes depend on conditions in their immediate neighborhood (such as peers or resources in their city block), local community (such as the quality of schools in their county), and broader metro area (such as local labor market conditions). To fully characterize the geography of intergenera- tional mobility, one would ideally estimate all of the components of such a hierarchical model.
As a first step toward this goal, we characterize intergenera- tional mobility at the level of commuting zones. CZs are aggrega- tions of counties based on commuting patterns in the 1990 census constructed by Tolbert and Sizer (1996) and introduced to the economics literature by Dorn (2009). Since CZs are designed to span the area in which people live and work, they provide a nat- ural starting point as the coarsest partition of areas. CZs are similar to metropolitan statistical areas (MSAs), but unlike MSAs, they cover the entire United States, including rural areas. There are 741 CZs in the United States; on average, each CZ contains four counties and has a population of 380,000. See Online Appendix Figure III for an illustration of the Boston CZ.
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We focus on CZ-level variation because mobility statistics in very small neighborhoods are likely to be heavily affected by sort- ing. Because property prices are typically homogeneous within narrow areas and home values are highly correlated with parent income, comparisons within a small neighborhood effec- tively condition on a proxy for parent income. As a result, the variation in parent income across individuals in a small area (such as a city block) must be correlated with other latent factors that could affect children’s outcomes directly, making it difficult to interpret the resulting mobility estimates.30 Nevertheless, to obtain some insight into within-CZ variation, we also report sta- tistics on intergenerational mobility by county in Online Data Table III. There is almost as much variance in intergenerational mobility across counties within a CZ as there is across CZs, sug- gesting that the total amount of geographical variation may be even greater than that documented below.31
We permanently assign each child to a single CZ based on the ZIP code from which his or his parent filed their tax return in the first year the child was claimed as a dependent. We interpret this CZ as the area where a child grew up. Because our data begin in 1996, location is measured in 1996 for 95.9% of children in our core sample.32 For children in our core sample of 1980–1982 birth cohorts, we therefore typically measure location when children were approximately 15 years old. For the children in the more recent birth cohorts in our extended sample, location is measured at earlier ages. Using these more recent cohorts, we find that 83.5 percent of children live in the same CZ at age 16 as they did at age 5. Furthermore, we verify that the spatial patterns for the outcomes we can measure at earlier ages (college
30. For example, it would be difficult to estimate the degree of intergenerational mobility on Park Avenue in Manhattan because any families with low observed income in such a high-property-value area would have to be latently wealthy to be able to afford to live there.
31. We also report statistics by MSA in Online Data Table IV. For CZs that intersect MSAs, correlations between CZ-level and MSA-level mobility statistics exceed 0.9.
32. Location is measured after 1996 for approximately 3% of children because they were linked to parents based on tax returns filed after 1996. We have no in- formation on location for the remaining 1% of children in the national sample be- cause the ZIP code listed on the parent’s tax returns is invalid or missing (see Online Appendix Table I); these children are excluded from the analysis in the remainder of the article.
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A B
S a lt
L a k e C
it y v
s . C
h a rl
o tt
e S
a n
F ra
n c is
c o
v s . C
h ic
a g
o
F IG
U R
E V
In te
rg e n
e ra
ti o n
a l
M o b il
it y
in S
e le
ct e d
C o m
m u
ti n
g Z
o n
e s
T h
e se
fi g u
re s
p re
se n
t n
o n
p a ra
m e tr
ic b in
n e d
sc a tt
e r
p lo
ts o f
th e
re la
ti o n
sh ip
b e tw
e e n
ch il
d a n
d p
a re
n t
in co
m e
ra n
k s
in se
le ct
e d
C Z
s. B
o th
p a n
e ls
a re
b a se
d o n
th e
co re
sa m
p le
(1 9 8 0 – 1 9 8 2
b ir
th co
h o rt
s) a n
d b a se
li n
e fa
m il
y in
co m
e d
e fi
n it
io n
s fo
r p
a re
n ts
a n
d ch
il d
re n
. C
h il
d re
n a re
a ss
ig n
e d
to C
Z s
b a se
d o n
th e
lo ca
ti o n
o f
th e ir
p a re
n ts
(w h
e n
th e
ch il
d w
a s
cl a im
e d
a s
a d
e p
e n
d e n
t) ,
ir re
sp e ct
iv e
o f
w h
e re
th e y
li v e
a s
a d
u lt
s. P
a re
n t
a n
d ch
il d
p e rc
e n
ti le
ra n
k s
a re
a lw
a y s
d e fi
n e d
a t
th e
n a ti
o n
a l
le v e l,
n o t
th e
C Z
le v e l.
T o
co n
st ru
ct e a ch
se ri
e s,
w e
g ro
u p
p a re
n ts
in to
5 0
e q u
a ll
y si
z e d
(2 p
e rc
e n
ti le
p o in
t) b in
s a n
d p
lo t
th e
m e a n
ch il
d p
e rc
e n
ti le
ra n
k v e rs
u s
th e
m e a n
p a re
n t
p e rc
e n
ti le
ra n
k w
it h
in e a ch
b in
. W
e re
p o rt
tw o
m e a su
re s
o f
m o b il
it y
b a se
d o n
th e
ra n
k -r
a n
k re
la ti
o n
sh ip
s in
e a ch
C Z
. T
h e
fi rs
t is
re la
ti v e
m o b il
it y
(r 1 0 0 �
r 0 ),
w h
ic h
is 1 0 0
ti m
e s
th e
ra n
k -r
a n
k sl
o p
e e st
im a te
. T
h e
se co
n d
is a b so
lu te
u p
w a rd
m o b il
it y
(r 2 5 ),
th e
p re
d ic
te d
ch il
d in
co m
e ra
n k
a t
th e
2 5 th
p e rc
e n
ti le
o f
p a re
n t
in co
m e
d is
tr ib
u ti
o n
, d
e p
ic te
d b y
th e
d a sh
e d
v e rt
ic a l
li n
e in
th e
fi g u
re s.
A ll
m o b il
it y
st a ti
st ic
s a n
d b e st
-fi t
li n
e s
a re
e st
im a te
d o n
th e
u n
d e rl
y in
g m
ic ro
d a ta
(n o t
th e
b in
n e d
m e a n
s) .
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attendance and teenage birth) are similar if we define CZs based on location at age 5 instead of age 16.
The CZ where a child grew up does not necessarily corre- spond to the CZ he lives in as an adult when we measure his income (at age 30) in 2011–2012. In our core sample, 38% of chil- dren live in a different CZ in 2012 relative to where they grew up.
V.B. Measures of Relative and Absolute Mobility
In our baseline analysis, we measure mobility at the CZ level using the core sample (1980–1982 birth cohorts) and the defini- tions of parent and child family income described in Section III.B. Importantly, we continue to rank both children and parents based on their positions in the national income distribution (rather than the distribution within their CZ).
We begin by examining the rank-rank relationship in se- lected CZs. Figure V Panel A presents a binned scatter plot of the mean child rank versus parent rank for children who grew up in the Salt Lake City, UT (circles), or Charlotte, NC (trian- gles), CZs. The rank-rank relationship is virtually linear in these CZs. The linearity of the rank-rank relationship is a remarkably robust property across CZs, as illustrated for the 20 largest CZs in Online Appendix Figure IV.
Exploiting this approximate linearity, we summarize the conditional expectation of a child’s rank given his parents’ rank in each CZ using two parameters: a slope and an intercept. Let Ric denote the national income rank (among children in his birth cohort) of child i who grew up in CZ c. Similarly, let Pic denote his parent’s rank in the income distribution of parents in the core sample. We estimate the slope and intercept of the rank-rank relationship in CZ c by regressing child rank on parent rank:
Ric ¼ �c þ�cPic þ"ic: ð2Þ
The slope of the rank-rank relationship (�c) in equation (2) mea- sures degree of relative mobility in CZ c, as defined in Section II. In Salt Lake City, �c¼0.264.
33 The difference between the ex- pected ranks of children born to parents at the top and bottom of the income distribution is r100;c � r0;c ¼ 100� �c ¼ 26:4 in Salt Lake City. There is much less relative mobility (i.e., much greater
33. We always measure percentile ranks on a 0–100 scale and slopes on a 0–1 scale, so �c ranges from 0 to 100 and �c ranges from 0 to 1 in equation (3).
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persistence of income across generations) in Charlotte, where r100 � r0 ¼ 39:7.
Following the discussion in Section II, we define absolute mobility at percentile p in CZ c as the expected rank of a child who grew up in CZ c with parents who have a national income rank of p:
rpc ¼ �c þ�cp: ð3Þ
We focus much of our analysis on average absolute mobility for children from families with below-median parent income in the national distribution (E[RicjPic < 50]), which we call absolute up- ward mobility.34 Because the rank-rank relationship is linear, the average rank of children with below-median parent income equals the average rank of children with parents at the 25th percentile in the national distribution (r25;c ¼ �c þ25�c), illustrated by the dashed vertical line in Figure V Panel A. Absolute upward mobility is r25 ¼ 46:2 in Salt Lake City, compared with r25 ¼ 35:8 in Charlotte. That is, among families earning $28,800—the 25th per- centile of the national parent family income distribution—children who grew up in Salt Lake City are on average 10 percentile points higher in their birth cohort’s income distribution at age 30 than are children who grew up in Charlotte.
Absolute mobility is higher in Salt Lake City not just for below- median families, but at all percentiles p of the parent income dis- tribution. The gap in absolute outcomes is largest at the bottom of the income distribution and nearly zero at the top. Hence, the greater relative mobility in this particular comparison comes purely from better absolute outcomes at the bottom of the distri- bution rather than worse outcomes at the top. Of course, this is not always the case. Figure V Panel B shows that San Francisco has substantially higher relative mobility than Chicago: r100 � r0 ¼ 25:0 in San Francisco versus r100 � r0 ¼ 39:3 in Chicago. But part of the greater relative mobility in San
34. We integrate over the national parent income distribution rather than the local distribution when defining E[RicjPic < 50] to ensure that our cross-CZ com- parisons are not affected by differences in local income distributions. We focus on the absolute outcomes of children from low-income families both because the out- comes of disadvantaged youth are a central focus of policy interest and because there is more variation across areas in the outcomes of children from low-income families than those from high-income families, as we show in Figure VII. However, the CZ-level statistics in Online Data Tables V and VI can be used to analyze spatial variation in the outcomes of children from high-income families.
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FIGURE VI
The Geography of Intergenerational Mobility
These figures present heat maps of our two baseline measures of interge- nerational mobility by CZ. Both figures are based on the core sample (1980– 1982 birth cohorts) and baseline family income definitions for parents and children. Children are assigned to CZs based on the location of their parents (when the child was claimed as a dependent), irrespective of where they live as adults. In each CZ, we regress child income rank on a constant and parent income rank. Using the regression estimates, we define absolute upward mo- bility (r25) as the interceptþ25�(rank-rank slope), which corresponds to the predicted child rank given parent income at the 25th percentile (see Figure V). We define relative mobility as the rank-rank slope; the difference between the outcomes of the child from the richest and poorest family is 100 times this coefficient (r100 � r0). The maps are constructed by grouping CZs into 10 deciles and shading the areas so that lighter colors correspond to higher absolute mo- bility (Panel A) and lower rank-rank slopes (Panel B). Areas with fewer than 250 children in the core sample, for which we have inadequate data to estimate mobility, are shaded with the cross-hatch pattern. In Panel B, we report the unweighted and population-weighted correlation coefficients between relative mobility and absolute mobility across CZs. The CZ-level statistics underlying these figures are reported in Online Data Table V.
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Francisco comes from worse outcomes for children from high- income families. Below the 60th percentile, children in San Francisco have better outcomes than those in Chicago; above the 60th percentile, the reverse is true.
The comparisons in Figure V illustrate the importance of measuring both relative and absolute mobility. Any social welfare function based on mean income ranks that respects the Pareto principle would rate Salt Lake City above Charlotte. But norma- tive comparisons of San Francisco and Chicago depend on the weight one puts on relative versus absolute mobility (or, equiva- lently, on the weights one places on absolute mobility at each percentile p).
V.C. Baseline Estimates by CZ
We estimate equation (2) using OLS to calculate absolute upward mobility (r25;c ¼ �c þ25�c) and relative mobility (�c) by CZ. The estimates for each CZ are reported in Online Data Table V.
1. Absolute Upward Mobility. Figure VI Panel A presents a heat map of absolute upward mobility. We construct this map by dividing CZs into deciles based on their estimated value of r25;c. Lighter colors represent deciles with higher levels of r25;c.
35
Upward mobility varies significantly across areas. CZs in the top decile have r25;c > 52.0, whereas those in the bottom decile have r25;c < 37:4. Note that the 37th percentile of the family income dis- tribution for children at age 30 is $22,900, whereas the 52nd per- centile is $35,500; hence, the difference in upward mobility across areas translates to substantial differences in children’s incomes.
Pooling all CZs, the unweighted standard deviation of r25;c is 5.68; the population-weighted standard deviation is 3.34. The un- conditional standard deviation of children’s income ranks (which have a uniform distribution) is 100ffiffiffiffi
12 p ¼ 28:9. Hence, a 1 standard
35. We cannot estimate mobility for 32 CZs in which we have fewer than 250 children in the core sample, shown by the cross-hatched areas in the maps in Figure VI. These CZs account for less than 0.05% of the U.S. population in the 2000 census. In Online Appendix Figure V, we present a version of this map in which we use data from the 1980–1985 cohorts to estimate mobility for the CZs that have fewer than 250 observations in the core (1980–1982) sample. The esti- mates of mobility in the CZs with missing data are quite similar to those in neigh- boring CZs, consistent with the spatial autocorrelation evident in the rest of the map.
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deviation improvement in CZ ‘‘quality’’—as measured by its level
of absolute upward mobility r25;c—is associated with a 5:68 2:89 ¼ 0:20
standard deviation increase in the expected income rank of chil- dren whose parents are at the 25th percentile.36 For comparison, a 1 standard deviation increase in parent income rank is associ- ated with a 0.34 standard deviation increase in a child’s income rank (Figure II Panel A). Hence, a 1 standard deviation improve- ment in CZ quality is associated with 60 percent as large an in- crease in a child’s income as a 1 standard deviation increase in his own parent’s income.
There are three broad spatial patterns in upward mobility evident in Figure VI Panel A. First, upward mobility varies sub- stantially at the regional level. Upward mobility is lowest in the Southeast and highest in the Great Plains. The West Coast and Northeast also have high rates of upward mobility, though not as high as the Great Plains.
Second, there is substantial within-region variation as well. Using unweighted CZ-level regressions of the upward mobility estimates on census division and state fixed effects, we estimate that 53 percent of the cross-CZ variance in absolute upward mo- bility is within the nine census divisions and 36 percent is within states. For example, many parts of Texas exhibit relatively high rates of upward mobility, unlike much of the rest of the South. Ohio exhibits much lower rates of upward mobility than nearby Pennsylvania. The statistics also pick up much more granular variation in upward mobility. For example, South Dakota gener- ally exhibits very high levels of upward mobility, with the excep- tion of a few areas in the southwest corner of the state. These areas are some of the largest Native American reservations in the United States and are well known to suffer from very high rates of persistent poverty.
The third generic pattern is that urban areas tend to exhibit lower levels of intergenerational mobility than rural areas on
36. An analogous calculation using the estimates of college attendance gradi- ents by CZ in Section IV.C implies that a 1 standard deviation increase in CZ quality is associated with a 0.19 standard deviation (9.3 percentage point) increase in col- lege attendance rates for children with parents at the 25th percentile. Using data from the PSID, Solon, Page, and Duncan (2002, p. 390) estimate that a 1 standard deviation increase in neighborhood quality is associated with a 0.32 standard de- viation increase in years of education. We find less variation in outcomes across neighborhoods presumably because commuting zones are much larger than the PSID sampling clusters analyzed by Solon, Page, and Duncan.
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TABLE III
INTERGENERATIONAL MOBILITY IN THE 50 LARGEST COMMUTING ZONES
(1) (2) (3) (4) (5) (6) (7)
Upward mobility rank CZ name Population
Absolute upward mobility
P(child in Q5 j parent in Q1)
Pct. above
poverty line
Relative mobility
rank-rank slope
1 Salt Lake City, UT 1,426,729 46.2 10.8 77.3 0.264 2 Pittsburgh, PA 2,561,364 45.2 9.5 74.9 0.359 3 San Jose, CA 2,393,183 44.7 12.9 73.5 0.235 4 Boston, MA 4,974,945 44.6 10.5 73.7 0.322 5 San Francisco, CA 4,642,561 44.4 12.2 72.5 0.250 6 San Diego, CA 2,813,833 44.3 10.4 74.3 0.237 7 Manchester, NH 1,193,391 44.2 10.0 75.0 0.296 8 Minneapolis, MN 2,904,389 44.2 8.5 75.2 0.338 9 Newark, NJ 5,822,286 44.1 10.2 73.7 0.350 10 New York, NY 11,781,395 43.8 10.5 72.2 0.330 11 Los Angeles, CA 16,393,360 43.4 9.6 73.8 0.231 12 Providence, RI 1,582,997 43.4 8.2 73.6 0.333 13 Washington DC 4,632,415 43.2 11.0 72.2 0.330 14 Seattle, WA 3,775,744 43.2 10.9 72.0 0.273 15 Houston, TX 4,504,013 42.8 9.3 74.7 0.325 16 Sacramento, CA 2,570,609 42.7 9.7 71.3 0.257 17 Bridgeport, CT 3,405,565 42.4 7.9 72.4 0.359 18 Fort Worth, TX 1,804,370 42.3 9.1 73.6 0.320 19 Denver, CO 2,449,044 42.2 8.7 73.3 0.294 20 Buffalo, NY 2,369,699 42.0 6.7 73.1 0.368 21 Miami, FL 3,955,969 41.5 7.3 76.3 0.267 22 Fresno, CA 1,419,998 41.3 7.5 71.3 0.295 23 Portland, OR 1,842,889 41.3 9.3 70.5 0.277 24 San Antonio, TX 1,724,863 41.1 6.4 74.3 0.320 25 Philadelphia, PA 5,602,247 40.8 7.4 69.6 0.393 26 Austin, TX 1,298,076 40.4 6.9 71.9 0.323 27 Dallas, TX 3,405,666 40.4 7.1 72.6 0.347 28 Phoenix, AZ 3,303,211 40.3 7.5 70.6 0.294 29 Grand Rapids, Michigan 1,286,045 40.1 6.4 71.3 0.378 30 Kansas City, MI 1,762,873 40.1 7.0 70.4 0.365 31 Las Vegas, NV 1,568,418 40.0 8.0 71.1 0.259 32 Chicago, IL 8,183,799 39.4 6.5 70.8 0.393 33 Milwaukee, WI 1,660,659 39.3 4.5 70.3 0.424 34 Tampa, FL 2,395,997 39.1 6.0 71.3 0.335 35 Orlando, FL 1,697,906 39.1 5.8 71.5 0.326 36 Port St. Lucie, FL 1,533,306 39.0 6.2 71.2 0.303 37 Baltimore, MD 2,512,431 38.8 6.4 67.7 0.412 38 St. Louis, MO 2,325,609 38.4 5.1 69.0 0.413 39 Dayton, OH 1,179,009 38.3 4.9 68.2 0.397 40 Cleveland, OH 2,661,167 38.2 5.1 68.7 0.405 41 Nashville, TN 1,246,338 38.2 5.7 67.9 0.357 42 New Orleans, LA 1,381,652 38.2 5.1 69.5 0.397 43 Cincinnati, OH 1,954,800 37.9 5.1 66.4 0.429 44 Columbus, OH 1,663,807 37.7 4.9 67.1 0.406
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average. For instance, children from low-income families who grow up in the Chicago area have significantly lower incomes at age 30 than those who grow up in rural areas in Illinois. On av- erage, urban areas—which we define as CZs that intersect MSAs—have upward mobility of r25;c ¼ 41:7, wheras rural areas have r25;c ¼ 45:8. In interpreting this comparison, it is im- portant to recall that our definition of geography is based on where children grew up, not where they live as adults. Of children who grow up in rural areas, 44.6% live in urban areas at age 30. Among those who rose from the bottom quintile of the national income distribution to the top quintile, 55.2 percent of children who grew up in rural areas live in urban areas at age 30.
Table III shows statistics on intergenerational mobility for the 50 largest CZs by population. Among these cities, absolute upward mobility ranges from 46.2 in the Salt Lake City area to 35.8 in Charlotte (column (4)). There is considerable variation even between nearby cities: Pittsburgh is ranked second in terms of upward mobility among large metro areas, while Cleveland—approximately 100 miles away—is ranked in the bottom 10. Upward mobility is especially low in certain cities in
TABLE III
(CONTINUED)
(1) (2) (3) (4) (5) (6) (7)
Upward mobility rank CZ name Population
Absolute upward mobility
P(child in Q5 j parent in Q1)
Pct. above
poverty line
Relative mobility
rank-rank slope
45 Jacksonville, FL 1,176,696 37.5 4.9 68.9 0.361 46 Detroit, MI 5,327,827 37.3 5.5 68.5 0.358 47 Indianapolis, IN 1,507,346 37.2 4.9 67.5 0.398 48 Raleigh, NC 1,412,127 36.9 5.0 67.3 0.389 49 Atlanta, GA 3,798,017 36.0 4.5 69.4 0.366 50 Charlotte, NC 1,423,942 35.8 4.4 67.0 0.397
Notes. This table reports estimates of intergenerational mobility for the 50 largest CZs according to their populations in the 2000 census. The CZs are sorted in descending order by absolute upward mobility (column (4)). The mobility measures are calculated using the core sample (1980–1982 birth cohorts) and the baseline family income definitions described in Table I (except for column (5), which uses the 1980– 1985 birth cohorts). The measures in columns (4) and (7) are both derived from within-CZ OLS regressions of child income rank against parent income rank. Column (7) reports the slope coefficient from this regression, which is equal to the difference in mean child income rank between children with parents in the 100th percentile and children with parents in the 0th percentile (divided by 100). Column (4) reports the predicted value at parent income rank equal to 25. Column (5) reports the percentage of children whose family income is in the top quintile of the national distribution of child family income conditional on having parent family income in the bottom quintile of the parental national income distri- bution. These probabilities are taken directly from Online Data Table VII. Column (6) reports the fitted values at parent rank 25 from a regression of an indicator for child family income being above the poverty line on parent income rank (see Online Appendix F for details). See Online Data Table V for estimates for all CZs as well as estimates using alternative samples and income definitions.
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the Rust Belt, such as Indianapolis and Columbus and cities in the Southeast such as Atlanta and Raleigh. The fact that children who grow up in low-income families in Atlanta and Raleigh fare poorly is especially noteworthy because these are generally con- sidered to be booming cities in the South with relatively high rates of job growth.
In column (5) of Table III, we consider an alternative measure of upward mobility: the probability that a child born to a family in the bottom quintile of the national income distribution reaches the top quintile of the national income distribution.37 To improve pre- cision in smaller CZs, we estimate this probability pooling the 1980–1985 birth cohorts.38 The ranking of areas based on this sta- tistic is similar to that based on the mean rank measure of upward mobility. The probability that a child from the lowest quintile of parental income rises to the top quintile is 10.8% in Salt Lake City, compared with 4.4% in Charlotte. The city with the highest prob- ability of moving from the bottom fifth to the top fifth is San Jose, where the probability (12.9%) is nearly three times that in Charlotte. The chances of rising from the bottom fifth to the top fifth for children growing up in San Jose are comparable to those in Denmark and Canada (see Section IV.A). Note that if parent income played no role in determining children’s outcomes, all the quintile transition probabilities would be 20%. Hence, the varia- tion in rates of upward mobility across areas is large relative to the maximum plausible range of 0 to 20%.
In column (6) of Table III, we consider another measure of absolute upward mobility: the probability that a child has family income above the poverty line conditional on having parents at
37. In principle, differences in local income distributions within the bottom quintile could generate differences in this probability. In an earlier version of this analysis (v1.0 available on the project website, www.equality-of-opportunity. org), we accounted for these differences by calculating the chance of reaching the top quintile separately for each percentile and computed the unweighted mean across the percentiles, effectively integrating over the national parent income dis- tribution. The adjusted CZ-level transition probabilities obtained using this ap- proach were virtually identical to the raw transition probabilities we report in this article.
38. We verify that including more recent cohorts does not generate significant bias by showing that the national transition matrix based on the 1980–1985 cohorts (Online Appendix Table VI) is virtually identical to the matrix based on the 1980– 1982 cohorts in Table II. We report the quintile transition matrix for each CZ in Online Data Table VI and provide statistics on the marginal distributions of parent and child income by CZ in Online Data Table VII.
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the 25th percentile (see Online Appendix F for details on the con- struction of this measure). This statistic also generates very sim- ilar rankings across CZs, confirming that our results are not sensitive to the way we measure upward mobility.
2. Relative Mobility. Figure VI Panel B presents a heat map of relative mobility. This map is constructed in the same way as Panel A, dividing CZs into deciles based on the rank-rank slope �c. In this map, lighter areas denote areas with greater relative mobility (lower �c). Relative mobility also varies substantially across areas. The expected rank of children from the richest versus poorest families differs by more than 40.2 percentiles in CZs in the bottom decile of relative mobility. The corresponding gap is less than 23.5 percentiles for CZs in the top decile.
The geographical patterns in relative mobility in Panel B are similar to those for absolute upward mobility in Panel A. The unweighted correlation across CZs between the two measures is �0.68; the population-weighted correlation is �0.61. This indi- cates that areas with greater relative mobility tend to have better absolute outcomes for children from low-income families.
To investigate the connection between absolute and relative mobility more systematically, let �pc¼E[RicjPic¼p] denote a child’s expected rank given a parent rank of p in CZ c. We esti- mate �pc in each CZ nonparametrically as the mean value of Ric for children in each percentile bin of the parent income distribu- tion p¼0, . . . , 99.39 For each of the 100 values of p, we estimate an unweighted OLS regression of �pc on relative mobility �c with one observation per CZ:
�pc ¼ aþ�p�c þ�pc:
In this equation, �p measures the association across CZs between a 1 unit increase in �c (i.e., greater intergenerational
39. The expected value �pc differs from rpc defined above because �pc is esti- mated nonparametrically using only data in percentile bin p, whereas rpc is cal- culated based on the linear approximation to the rank-rank relationship in equation (3). In practice, the two estimates are extremely similar. For instance, in the 100 largest CZs, where �pc is estimated with very little error, the correlation between �pc and rpc exceeds 0.99. We use the linear approximation rpc in most of our analysis to obtain more precise estimates of absolute mobility in smaller CZs. However, because the goal of the exercise here is to evaluate the relationship between relative mobility �c and absolute mobility at each percentile nonparame- trically, we use �pc here.
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persistence) and the mean rank of children with parents at the p- th percentile of the national income distribution. A negative coefficient (�̂p < 0) implies that CZs with greater relative mobility generate better mean outcomes for children with parents at percentile p.
Figure VII Panel A plots the coefficients �̂p at each parent income percentile p along with a linear fit to the coefficients. The coefficients �̂p are increasing with p: CZs with greater relative mobility (lower �c) produce better outcomes for children from lower income families. The best linear fit crosses 0 at p¼85.1. Hence, increases in relative mobility are associated with better outcomes for children who grow up in families below the 85th percentile on average. For families at the 85th percentile, differ- ences in relative mobility across CZs are uncorrelated with a child’s mean rank. For families in the top 15%, living in a CZ with greater relative mobility is associated with worse outcomes on average for children. Observe that �p reaches only 0.2 for the richest families but is nearly �0.8 for the poorest families. This shows that differences in relative mobility across CZs are associ- ated with much larger differences in absolute mobility for chil- dren from low-income families than high-income families.40
Figure VII Panel B presents a schematic that illustrates the intuition underlying the preceding results. This figure plots hy- pothetical rank-rank relationships in two representative CZs, one of which has more relative mobility than the other. Figure VII Panel A implies that in such a pairwise comparison, the rank- rank relationship ‘‘pivots’’ at the 85th percentile on average. This is why the spatial patterns of absolute mobility at p¼25 and relative mobility in Figure VI look similar.
Because the pivot point is high in the income distribution, differences in relative mobility have a smaller effect on children’s percentile ranks in high-income families than low-in- come families.41 This may be because the rich are able to insulate themselves from differences in the local environment. If the
40. If the rank-rank relationship were perfectly linear, the relationship plotted in Figure VII Panel A would be perfectly linear and �100 – �0¼1 mechanically. The slight deviation from linearity at the bottom of the distribution evident in Figure V generates the slight deviation of �100 – �0 from 1.
41. It bears emphasis that this result applies to percentile ranks rather than mean income levels. Because the income distribution has a thick upper tail, a given difference in percentile ranks translates to a much larger difference in mean in- comes in the upper tail of the income distribution. The probability that children of
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differences in relative mobility across areas are caused by differ- ences in local policies, this result suggests that policies that im- prove relative mobility may be able to improve the outcomes of children from poor families without hurting children from high- income families significantly.
V.D. Robustness of Spatial Patterns
We assess the robustness of the spatial patterns in mobility along several dimensions. The results of this robustness analysis are reported in Online Appendix F and Appendix Table VII; we present a brief summary here.
We begin by considering changes in sample definitions: lim- iting the sample to male versus female children, married versus single parents, and later birth cohorts (for which we measure children’s location at earlier ages). Measures of both absolute and relative mobility across areas in these subsamples generally have a correlation of more than 0.9 with the corresponding base- line measures reported above. Restricting the sample to hold the parents’ ages at the birth of child fixed, limiting the sample to children who stay in the CZ where they grew up as adults, and limiting the sample to children linked to only one parent in all years yield very similar estimates of mobility across areas.
We also find that the spatial patterns are highly robust to using alternative measures of income used in Table I. For exam- ple, using individual income instead of family income or wage earnings instead of total income yields very spatial patterns.
We evaluate whether adjusting for differences in cost-of- living across areas affects our estimates by dividing parents’ income by a local price index (based on the ACCRA survey) for the CZ where their child grew up and the child’s income by the price index for the CZ where he lives in 2012 to obtain real income measures. Measures of intergenerational mobility based on real incomes are very highly correlated with our baseline measures. The degree of upward mobility—that is, the difference between the child’s rank and the parent’s rank—is essentially unaffected by adjusting for local prices because few children move to areas with very different levels of cost of living relative to their parents (see Online Appendix F for details).
affluent parents become very high-income ‘‘superstars’’ may therefore differ signif- icantly across areas.
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Because we measure parent income before 2000 and child income in 2011–2012, part of the variation in upward mobility across areas could be driven by shocks to local economic growth. While growth shocks—for example, from the discovery of a natu- ral resource such as oil—are a real source of upward mobility, one may be interested in isolating variation in mobility attributable to more stable factors that can be manipulated by policy. We assess the extent to which economic growth is responsible for the spatial variation in upward mobility in two ways. First, we define parent income as mean family income in 2011–2012, the same years in which we measure child income. Insofar as local economic growth raises the incomes of both parents and children, this measure nets out the effects of growth on mobility. Second, we regress upward mobility on the CZ-level growth rate from 2000 to 2010 and calculate residuals. Both of these growth-ad- justed mobility measures have a correlation of more than 0.8 with our baseline measures, indicating that most of the spatial varia- tion in upward mobility is not driven by differences in growth rates.
Finally, we consider a set of alternative statistics for relative and absolute mobility. Estimating relative mobility based on parent and child ranks in the local income distribution yields estimates that are very highly correlated with our baseline esti- mates based on national ranks. We also show that the two alter- native measures of upward mobility analyzed in Table III—the probability of rising from the bottom fifth to the top fifth and the probability of having income above the poverty line conditional on having parents at the 25th percentile – also generate very similar spatial patterns, with correlations above 0.9 with our baseline mean rank measure of upward mobility (Online Appendix Figure VI).
V.E. Intermediate Outcomes: College Attendance and Teenage Birth
To better understand the sources of the spatial variation in intergenerational income mobility, we characterize spatial vari- ation in the three intermediate outcomes analyzed in Figure IV: college attendance rates, college quality rank, and teenage birth rates. We first regress each of these outcomes on parent na- tional income rank in each CZ c using specifications analogous to equation (2). We then characterize spatial variation in two
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measures of mobility for each outcome using the regression esti- mates: the slope coefficient, which is analogous to our measure of relative mobility, and the predicted outcome for children with parents at the 25th percentile, which is analogous to our measure of absolute mobility.42
We present heat maps for the relative and absolute mobility measures for the three intermediate outcomes in Online Appendix Figures VII–IX; the CZ-level data underlying these maps are reported in Online Data Table V. There is substantial spatial variation in all three intermediate outcomes and the var- iation is highly correlated with the variation in the intergenera- tional income mobility. For example, college attendance rates for children with parents at the 25th percentile vary from less than 32.4% in bottom decile of CZs to more than 55.6% in the top decile of CZs. The unweighted correlation between college attendance rates at the 25th percentile and mean income ranks at the 25th percentile (absolute upward mobility) across CZs is 0.71 (Online Appendix Table VII, row 23). Similarly, teenage birth rates for female children whose parents are at the 25th percentile vary from less than 15.4% in the bottom decile of CZs to more than 29.4% in the top decile. The correlation between teen birth rates and absolute upward mobility is �0.61.
An important implication of these results is that much of the difference in intergenerational mobility across areas emerges while children are teenagers, well before they enter the labor market as adults.43 This suggests that the spatial variation in income mobility is driven by factors that either directly affect children at early ages (such as the quality of schools or social structure) or anticipatory behavioral responses to subsequent dif- ferences (such as returns to education in the local labor market). We explore mechanisms that have such properties in the next section.
42. Because the relationship between college quality rank and parent rank is not linear, we regress college quality ranks on a quadratic function of parent income rank and define the relative mobility measure for college quality as the difference in the predicted college quality rank for children with parents at the 75th percentile and children with parents at the 25th percentile, as in Figure IV Panel A.
43. Further supporting this claim, we find a strong positive correlation of 0.63 between teenage labor force participation rates (between the ages of 14 and 16) and upward mobility (see Figure VIII and Online Appendix H).
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VI. Correlates of Intergenerational Mobility
Why do some areas of the United States exhibit much higher rates of upward mobility than others? As a first step toward an- swering this question, we correlate our measures of intergenera- tional mobility with local area characteristics. Naturally, such correlations cannot be interpreted as causal mechanisms. Our goal is merely to document a set of stylized facts to guide the search for causal determinants and the development of new models of intergenerational mobility.
We correlate our mobility statistics with various factors that have been discussed in the sociology and economics literature, such as segregation and inequality. Because most of these factors are slow-moving and we have estimates of intergenerational income mobility for essentially one birth cohort, we focus on cross-sectional correlations rather than changes over time. For most covariates, we use data from the 2000 census and other publicly available data sets because many variables cannot be consistently measured in earlier years. See Online Appendix G for details on the construction of the covariates analyzed in this section and Online Data Table VIII for CZ-level data on each of the covariates.
Figure VIII presents a summary of our correlational results. It plots the unweighted univariate correlation between absolute upward mobility and various CZ-level characteristics, using all CZs with available data for the relevant variable. We consider sev- eral proxies for each broad factor (segregation, inequality, etc.). The dots show the point estimate of the correlation and the hori- zontal lines show a 95 percent confidence interval, based on stan- dard errors clustered at the state level. The sign of the correlation is shown in parentheses next to each variable. In Online Appendix Table VIII, we report these correlations as well as estimates from several alternative specifications including state fixed effects, weighting CZs by population, restricting to urban areas, and con- trolling for differences in racial demographics and income growth (see Online Appendix H for details). These alternative specifica- tions generally yield very similar results to the baseline estimates shown in Figure VIII. Most important, the correlations discussed below hold even in specifications with state fixed effects, showing that the results are not just driven by broad regional differences across the South versus other parts of the country. We also show in Online Appendix Table VIII that the factors that are positively
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associated with absolute upward mobility are generally positively associated with relative mobility (i.e., are negatively correlated with rank-rank slopes).
In the remainder of this section, we discuss correlations of mobility with the categories in Figure VIII that have the stron- gest relationship with mobility: racial demographics, segregation, income inequality, school quality, social capital, and family struc- ture. We discuss results for four other broad categories for which we find weaker correlations – local tax policies, higher education, labor market conditions, and migration – in Online Appendix H.
FIGURE VIII
Correlates of Spatial Variation in Upward Mobility
This figure shows the correlation of various CZ-level characteristics with absolute upward mobility (r25) across CZs. For each characteristic listed on the y-axis, the dot represents the absolute value of the unweighted correlation of the variable with r25 across CZs. The horizontal bars show the 95% confidence interval based on standard errors clustered at state level. Positive correlations are shown by (þ) on the y axis; negative correlations are shown by (–). We consider covariates in 10 broad categories: racial demographics, segregation, properties of the income distribution, K–12 education, social capital, family structure, local tax policies, college education, labor market conditions, and migration rates. The categories with the highest correlations are highlighted. See column (1) of Appendix Table VII for the point estimates corresponding to the correlations plotted here. See Section VI, Online Data Table IX, and Online Appendix G for definitions of each of the correlates. CZ-level data on the covar- iates used in this figure are reported in Online Data Table VIII.
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VI.A. Race
Perhaps the most obvious pattern from the maps in Figure VI is that intergenerational mobility is lower in areas with larger African American populations, such as the Southeast. Indeed, the unweighted correlation between upward mobility and the frac- tion of black residents in the CZ (based on the 2000 census) is �0.580, as shown in the first row of Figure VIII.
This correlation could be driven by two very different chan- nels. One channel is an individual-level race effect: black children may have lower incomes than white children conditional on parent income, and hence areas with a larger black population may have lower upward mobility. An alternative possibility is a place-level race effect: areas with large black populations might have lower rates of upward mobility for children of all races.
To distinguish between these two channels, we would ideally control for race at the individual level, essentially asking whether whites have lower rates of upward mobility in areas with a larger black population. Unfortunately, we do not observe each individ- ual’s race in our data. As an alternative, we predict race based on the parent’s five-digit ZIP code (in the year they first claim their child as a dependent). We use data from the 2000 census to mea- sure racial shares by ZIP code. Figure IX Panel A replicates the map of absolute upward mobility (r25;c) by CZ, restricting the sample to ZIP codes within each CZ in which at least 80% of the residents are non-Hispanic whites.44 In this subsample, 91% of individuals are white. The spatial pattern in Figure IX Panel A is very similar to that in the original map for the full sample in Figure VI Panel A. Most notably, even in this predom- inantly white sample, rates of upward mobility remain low in the Southeast and are much higher in the West. Among the 604 CZs for which we are able to compute upward mobility measures for predominantly white individuals, the unweighted correlation be- tween upward mobility for the predominantly white sample and the full sample is 0.91.
44. We continue to estimate r25;c at the CZ level in this map, but we only include ZIP-5s within each CZ in which 80% or more of the residents are white. To facilitate comparison to Figure VI, we color the entire CZ based on this statistic, including ZIP-5s whose own white share is below 80%. CZs that have fewer than 250 children who grew up in ZIP codes where more than 80% of the residents are white are omitted (and shown with cross-hatch shading).
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.
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In Figure IX Panel B, we generalize this approach to assess how the spatial pattern of upward mobility changes as we restrict the sample to be increasingly white. To construct this figure, we first compute upward mobility in each CZ, restricting the sample to individuals living in ZIP codes that are more than w% white, which we denote by rw25;c. We then regress r
w 25;c on r25;c, our base-
line estimates of upward mobility based on the full sample, using an unweighted OLS regression with one observation per CZ with available data. We vary w from 0% to 95% in increments of 5% and plot the resulting regression coefficients in Figure IX Panel B against the fraction of white individuals in each of the subsam- ples. When w¼0, the regression coefficient is 1 by construction
because r25;c ¼ r w¼0 25;c . Since 68 percent of the U.S. population is
white, the first point on the figure is (0.68, 1). The point generated by the w¼80% threshold is (0.91, 0.84), consistent with the map in Figure IX Panel A. The dotted lines show a 95% confidence interval for the regression coefficients based on standard errors clustered at the state level.
If the variation in upward mobility across areas were entirely driven by heterogeneity in outcomes across race at the individual level, the coefficient in Figure IX Panel B would fall to 0 as the fraction white in the sample converged to 1, as illustrated by the dashed line. Intuitively, if all of the spatial variation in Figure VI Panel A were driven by individual-level differences in race, there would be no spatial variation left in a purely white sample. The data reject this hypothesis: even in the subsample with more than 95 percent white individuals, the regression coefficient remains at 0.89.
The main lesson of this analysis is that both blacks and whites living in areas with large African American populations have lower rates of upward income mobility.45 There are many potential mechanisms for such a correlation, including differ- ences in the institutions and industries that developed in areas with large African American populations. We are unable to dis- tinguish between these mechanisms in our data; instead, we next turn to one such mechanism that has received the greatest atten- tion in prior work: segregation. The United States has a historical legacy of greater segregation in areas with more blacks. Such
45. To be clear, this result does not imply that race does not matter for children’s outcomes at the individual level, as shown, for example, by Mazumder (2011). Our finding is simply that there is spatial heterogeneity in upward mobility even con- ditional on race.
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segregation could potentially affect both low-income whites and blacks, as racial segregation is often associated with income segregation.
VI.B. Segregation
Prior work has argued that segregation has harmful effects on disadvantaged individuals through various channels: reducing exposure to successful peers and role models, decreasing funding for local public goods such as schools, or ham- pering access to nearby jobs (Wilson 1987; Massey and Denton 1993; Cutler and Glaeser 1997). In this section, we evaluate these hypotheses by exploring the correlation between intergenera- tional mobility and various measures of segregation (shown in the second panel of Figure VIII and Online Appendix Table VIII).
We begin by measuring racial segregation using a Theil (1972) index, constructed using data from the 2000 census as in Iceland (2004). Let �r denote the fraction of individuals of race r in a given CZ, with four racial groups: whites, blacks, Hispanics, and others. We measure the level of racial diversity in the CZ by an entropy index: E ¼
P �rlog2
1 �r
, with �r log2
1 �r ¼ 0 when �r ¼ 0. Letting j¼1, . . . , N index census tracts
in the CZ, we analogously measure racial diversity within each
tract as Ej ¼ P �rjlog2
1 �rj
where �rj denotes the fraction of individ-
uals of race r in tract j. We define the degree of racial segregation in the CZ as
H ¼ X
j
popj poptotal
E � Ej E
� � ; ð4Þ
where popj denotes the total population of tract j and poptotal denotes the total population of the CZ. Intuitively, H measures the extent to which the racial distribution in each census tract deviates from the overall racial distribution in the CZ. The segregation index H is maximized at H¼1 when there is no racial heterogeneity within census tracts, in which case Ej¼0 in all tracts. It is minimized at H(p)¼0 when all tracts have racial composition identical to the CZ as a whole, so that Ej¼E.
Column (1) of Table IV reports the coefficient estimate from an unweighted OLS regression of absolute upward mobility r25;c on the racial segregation index, with one observation per CZ. In
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this and all subsequent regressions, we standardize the depen- dent variable and all independent variables to have mean 0 and standard deviation 1 within the estimation sample. Hence, the coefficients in the univariate regressions can be interpreted as correlation coefficients. Standard errors are clustered by state to account for spatial correlation across CZs.
More racially segregated areas have less upward mobility. The unweighted correlation between upward mobility and the racial segregation index in Column 1 is �0.361.46 Column (2) shows that the correlation remains at �0.360 in urban areas, that is, CZs that overlap with MSAs.
TABLE IV
SEGREGATION AND INTERGENERATIONAL MOBILITY
Dep. var.: Absolute upward mobility
(1) (2) (3) (4) (5) (6) (7)
Racial segregation �0.361 �0.360 (0.045) (0.068)
Income segregation �0.393 �0.058 (0.065) (0.090)
Segregation of poverty (<p25)
�0.508 �0.408 (0.155) (0.166)
Segregation of affluence (>p75)
0.108 0.216 (0.140) (0.171)
Share with commute < 15 mins
0.605 0.571 (0.126) (0.165)
Urban areas only x x R-squared 0.131 0.130 0.154 0.167 0.052 0.366 0.368 Observations 709 325 709 709 325 709 709
Notes. Each column reports coefficients from an OLS regression with standard errors clustered at the state level reported in parentheses. All independent and dependent variables are normalized (in the relevant estimation sample) to have mean 0 and standard deviation 1, so univariate regression coefficients equal correlation coefficients. The regressions are run using data for the 709 CZs with at least 250 chil- dren in the core sample. The dependent variable in all columns is our baseline measure of absolute upward mobility, the expected rank of children whose parents are at the 25th national percentile. Columns (2) and (5) restrict to the sample of CZs that intersect an MSA. Racial segregation is measured by the Theil index defined in Section VI.B using racial shares at the census tract level. Income segregation is measured by a weighted average of two-group Theil indices, as in Reardon (2011). Segregation of poverty is a two-group Theil index, where the groups are defined as being above versus below the 25th percentile of the local household income distribution. Segregation of affluence is defined analogously at the 75th percentile. Share with commute < 15 minutes is the fraction of working individuals in each CZ who commute less than 15 minutes to work. See Online Appendix G for details on the definitions of the independent variables.
46. Online Appendix Figure X Panel A presents a nonparametric binned scatter plot corresponding to this regression; see Online Appendix H for details on the construction of this figure.
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Next, we turn to the relationship between income segrega- tion and upward mobility. Following Reardon and Firebaugh (2002) and Reardon (2011), we begin by measuring the degree to which individuals below the p-th percentile of the local house- hold income distribution are segregated from individuals above the p-th percentile in each CZ using a two-group Theil index H(p). Here, entropy in a given area is EðpÞ ¼ plog2
1 p þð1 � pÞlog2
1 1�p
and the index H(p) is defined using the formula in equation (4). Building on this measure, Reardon (2011) defines the overall level of income segregation in a given CZ as
income segregation¼ 2logð2Þ
Z p EðpÞHðpÞdp: ð5Þ
This measure is simply a weighted average of segregation at each percentile p, with greater weight placed on percentiles in the middle of the income distribution, where entropy E(p) is maxi- mized. We implement equation (5) using data from the 2000 census, which reports income binned in 16 categories. Following Reardon (2011, Appendix 3), we measure H(p) at each of these cutoffs and take a weighted sum of these values to calculate income segregation.
In column (3) of Table IV, we regress absolute upward mobility on the income segregation index; see Online Appendix Figure X Panel B for the corresponding nonparametric binned scatter plot. The correlation between income segregation and upward mobility is �0.393, consistent with the findings of Graham and Sharkey (2013) using survey data. Interestingly, areas with a larger black population exhibit greater income segregation: the correlation be- tween the fraction of black individuals in a CZ and the income segregation index is 0.264 (std. err. 0.082). Hence, the negative relationship between income segregation and upward mobility could partly explain why low-income white children fare more poorly in areas with large African American populations.
In column (4), we decompose the effects of segregation in different parts of the income distribution. Following Reardon and Bischoff (2011), we define the ‘‘segregation of poverty’’ as H(p¼25), that is, the extent to which individuals in the bottom quartile are segregated from those above the 25th percentile. We analogously define the segregation of affluence as H(p¼75). Column (4) regresses upward mobility on both segregation of pov- erty and affluence. Segregation of poverty has a strong negative
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association with upward mobility, whereas segregation of afflu- ence does not. Column (5) shows that the same pattern holds when restricting the sample to urban areas. These results suggest that the isolation of low-income families (rather than the isolation of the rich) may be most detrimental for low-in- come children’s prospects of moving up in the income distribution.
Another mechanism by which segregation may diminish upward mobility is through spatial mismatch in access to jobs (Kain 1968; Kasarda 1989; Wilson 1996). We explore this mech- anism in column (6) by correlating upward mobility with the frac- tion of individuals who commute less than 15 minutes to work in the CZ, based on data from the 2000 census. Areas with less sprawl (shorter commutes) have significantly higher rates of upward mobility; the correlation between commute times and upward mobility is 0.605. Column (7) shows that commute times remain a significant predictor of upward mobility in a mul- tivariable regression but income segregation does not.
These results are consistent with the view that the negative effects of segregation may operate by making it more difficult to reach jobs or other resources that facilitate upward mobility. But any such spatial mismatch explanation must explain why the gradients emerge before children enter the labor market, as shown in Section V.E. A lack of access to nearby jobs cannot di- rectly explain why children from low-income families are also more likely to have teenage births and less likely to attend college in cities with low levels of upward mobility. However, spatial mismatch could produce such patterns if it changes children’s behavior because they have fewer successful role models or redu- ces their perceived returns to education.
VI.C. Income Levels and Inequality
In this subsection, we explore the correlation between prop- erties of the local income distribution—mean income levels and inequality—and intergenerational mobility.
1. Mean Income Levels. The third section of Figure VIII shows that the mean level of household income in a CZ (as measured in the 2000 census) is essentially uncorrelated with upward mobility (see Online Appendix Figure XI Panel A for the corresponding nonparametric binned scatter plot). Children in low-income
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families who grow up in the highest-income CZs (with mean in- comes of $47,600 a year) reach almost exactly the same percentile of the national income distribution on average as those who grow up in the lowest-income areas (with mean incomes of $21,900).
2. Income Inequality. Prior work has documented a negative correlation between income inequality and intergenerational mo- bility across countries (Corak 2013). This ‘‘Great Gatsby’’ curve (Krueger 2012) has attracted attention because it suggests that greater inequality within a generation could reduce social mobil- ity. We explore whether there is an analogous relationship across areas within the United States by correlating upward mobility with the Gini coefficient of parent income within each CZ. We compute the Gini coefficient for parents in our core sample
within each CZ as Gini ¼ 2 X c
CovðXic; PicÞ, where X c is the mean
family income (from 1996 to 2000) of parents in CZ c and Cov(Xic, Pic) is the covariance between the income level (Xic) and the percentile rank (Pic) of parents in CZ c. The correlation be- tween the Gini coefficient and upward mobility is �0.578 (see also Online Appendix Figure XI Panel B).
An alternative measure of inequality is the portion of income within a CZ that accrues to the richest households, for example, those in the top 1%. This measure is of particular interest because the rise in inequality in the United States over the past three decades was driven primarily by an increase in top income shares (Piketty and Saez 2003). We calculate top 1 percent income shares using the distribution of parent family income within each CZ. The correlation between upward mobility and the top 1 percent income share is only �0.190 (see also Online Appendix Figure XI Panel C), much weaker than that with the Gini coefficient.
We investigate why the Gini coefficient and top 1% share pro- duce different results in Table V, which is constructed in the same way as Table IV. Column (1) replicates the regression correspond- ing to the raw correlation between the Gini coefficient and upward mobility as a reference. We decompose the Gini coefficient into inequality coming from the upper tail and the rest of the income distribution by defining the bottom 99% Gini as the Gini coefficient minus the top 1% income share. The bottom 99% Gini can be in- terpreted as the deviation of the Lorenz curve from perfect equal- ity among households in the bottom 99%. Column (2) of Table V
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shows that a 1 standard deviation increase in the bottom 99% Gini is associated with a 0.634 standard deviation reduction in upward mobility. In contrast, a 1 standard deviation increase in the top 1% share is associated with only a 0.123 standard deviation reduction in upward mobility. Column (3) shows that in urban areas (CZs that overlap with MSAs), the pattern is even more stark: upper tail inequality is uncorrelated with upward mobility, whereas the Gini coefficient within the bottom 99% remains very highly strongly correlated with upward mobility.
Another measure of inequality within the bottom 99% is the size of the middle class in the CZ, which we define as the fraction of parents in the CZ who have family incomes between the 25th
TABLE V
INCOME INEQUALITY AND INTERGENERATIONAL MOBILITY: THE ‘‘GREAT GATSBY’’ CURVE
Dep. var.:
Across CZs within the United States Across countries
Absolute upward mobility
Relative mobility
Log-log Log-log elasticity elasticity
1985 inequality
2005 inequality
(1) (2) (3) (4) (5) (6) (7) (8)
Gini coefficient �0.578 (0.093)
Gini bottom 99% �0.634 �0.624 0.476 0.72 0.62 0.78 (0.090) (0.113) (0.088) (0.21) (0.27) (0.27)
Top 1% income share �0.123 0.029 �0.032 0.17 �0.11 (0.035) (0.039) (0.032) (0.27) (0.28)
Frac. between p25 and p75
0.679 (0.111)
Urban areas only x R-squared 0.334 0.433 0.380 0.462 0.224 0.518 0.536 0.531 Observations 709 709 325 709 709 13 13 12
Notes. Each column reports regression coefficients from an OLS regression with all variables normal- ized to have mean 0 and standard deviation 1 in the estimation sample, so univariate regression coeffi- cients are equal to correlation coefficients. Columns (1)–(5) are estimated using data for the 709 CZs with at least 250 children in the core sample. The dependent variable in columns (1)–(4) is our baseline CZ-level measure of absolute upward mobility, the expected rank of children whose parents are at the 25th national percentile in the core sample. In column (5), the dependent variable is relative mobility, the rank-rank slope within each CZ. In column (3), we restrict to CZs that intersect MSAs. In columns (1)–(5), the Gini coefficient is defined as the Gini coefficient of family income for parents in the core sample in each CZ; the top 1% income share is defined as the fraction of total parent family income in each CZ accruing to the richest 1% of parents in that CZ; the Gini bottom 99% is defined as the Gini coefficient minus the top 1% income share; and the fraction between p25 and p75 is the fraction of parents in each CZ whose family income is between the 25th and 75th percentile of the national distribution of parent family income for those in the core sample. In columns (6)–(8), the dependent variable is the log-log IGE estimate by country from Corak (2013, Figure 1). The Gini coeffi- cients across countries are obtained from the OECD Income Distribution Database (series ‘‘Income Distribution and Poverty: by country’’). We interpret these coefficients as applying to the bottom 99% because the surveys on which they are based are typically top-coded. The top 1% income share across countries is from the World Top Income Database (series ‘‘Top 1% Income Share’’). The independent variables are measured in 1985 in columns (6) and (7) and in 2005 in column (8).
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and 75th percentiles of the national parent income distribution. Column (4) of Table V shows that upward mobility is strongly positively correlated with the size of the middle class.
Finally, column (5) of Table V replicates column (2) using relative mobility �c as the dependent variable. The bottom 99% Gini coefficient is strongly positively associated with this mea- sure. That is, greater inequality in the bottom 99% is negatively related to relative mobility. 47 But once again, the top 1% share is uncorrelated with relative mobility.
3. Comparison to Cross-Country Evidence. Next, we explore whether the size of the middle class is more strongly correlated with intergenerational mobility than upper tail inequality in the cross-country data as well. In column (6) of Table V, we replicate Corak’s (2013, Figure 1) result that there is a strong positive correlation between the Gini coefficient (as measured in survey data on income in 1985) and the IGE using data from 13 devel- oped countries compiled by Corak (2013).48 In column (7), we in- clude the top 1% income share in each country, based on statistics from the World Top Incomes Database. As in the within–United States analysis, there is little correlation between the top 1% income share and intergenerational mobility across countries. Column (8) shows that results are similar if one uses inequality measures from 2005 instead of 1985.
We conclude that there is a robust negative correlation between inequality within the current generation of adults and mobility across generations. However, intergenerational mobility is primarily correlated with inequality among the bottom 99% and not the extreme upper tail inequality of the form that has increased dramatically in recent decades. Interestingly, this pat- tern parallels the results we obtained for segregation above: seg- regation of affluence is not significantly correlated with intergenerational mobility, whereas segregation of poverty is negatively associated with mobility.
47. Because parent and child ranks are measured in the national income dis- tribution, there is no mechanical relationship between the level of inequality within the CZs income distribution and the rank-rank slope.
48. We obtain estimates of the Gini coefficient by country from the OECD Income Distribution Database. We interpret these estimates as applying to the bottom 99% because surveys typically do not capture the thickness of the top tail due to top-coding.
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VI.D. School Quality
In the fourth panel of Figure VIII, we study the correlation between mobility and various proxies for school quality. We first consider two proxies for inputs into school quality: mean public school expenditures per student and mean class sizes based on data from the National Center for Education Statistics (NCES) for the 1996–1997 school year. We find a positive correlation be- tween public school expenditures and upward mobility, but the correlation is not as strong or robust as with measures of inequal- ity or segregation. There is a strong negative correlation between class size and upward mobility (columns (1) and (2) of Online Appendix Table VIII) when pooling all CZs. However, there is no correlation between upward mobility and class size in more urban areas (columns (3) and (4)).
One shortcoming of input-based measures of school quality is that they may capture relatively little of the variation in school quality (Hanushek 2003). To address this problem, we construct output-based proxies for school quality based on test scores and dropout rates adjusted for differences in parent income. We obtain data on mean grade 3–8 math and English test scores by CZ from the Global Report Card. The Global Report Card con- verts school district–level scores on statewide tests to a single national scale by benchmarking statewide test scores to scores on the National Assessment of Educational Progress (NAEP) tests. We obtain data on high school dropout rates from the NCES for the 2000–2001 school year, restricting the sample to CZs in which at least 75 percent of school districts have nonmiss- ing data. We regress test scores on mean parent family income (from 1996 to 2000) in the core sample and compute residuals to obtain an income-adjusted measure of test score gains. We con- struct an income-adjusted measure of dropout rates analogously.
The income-adjusted test score and dropout rates are very highly correlated with upward mobility across all specifications, as shown in the fourth panel of Figure VIII. In the baseline spe- cification, the magnitude of the correlation between both mea- sures and upward mobility is nearly 0.6. These results are consistent with the hypothesis that the quality of schools—as judged by outputs rather than inputs—plays a role in upward mobility. At a minimum, they strengthen the view that much of the difference in intergenerational income mobility across areas emerges while children are relatively young.
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VI.E. Social Capital
Several studies have emphasized the importance of social capital—the strength of social networks and engagement in com- munity organizations in local areas—for social and economic out- comes (Coleman 1988; Borjas 1992; Putnam 1995). We explore the relationship between mobility and measures of social capital used in prior work in the fifth panel of Figure VIII.
Our primary proxy for social capital is the social capital index constructed by Rupasingha and Goetz (2008), which we aggregate to the CZ level using population-weighted means. This index is com- prised of voter turnout rates, the fraction of people who return their census forms, and various measures of participation in community organizations. The correlation between upward mobility and social capital is 0.641 in our baseline specification, an estimate that is quite robust across alternative specifications. Interestingly, one of the orig- inal measures proposed by Putnam (1995)—the number of bowling alleys in an area—has an unweighted correlation of 0.562 with our measures of absolute upward mobility.
We also consider two other proxies for social capital: the frac- tion of religious individuals (based on data from the Association of Religion Data Archives) and the rate of violent crime (using data from the Uniform Crime Report). Religiosity is very strongly pos- itively correlated with upward mobility, while crime rates are negatively correlated with mobility.
VI.F. Family Structure
Many have argued that family stability plays a key role in children’s outcomes (see Becker 1991; Murray 1984, 2012). To evaluate this hypothesis, we use three measures of family struc- ture in the CZ based on data from the 2000 census: (i) the fraction of children living in single-parent households, (ii) the fraction of adults who are divorced, and (iii) the fraction of adults who are married. All three of these measures are very highly correlated with upward mobility, as shown in the sixth panel of Figure VIII.
The fraction of children living in single-parent households is the single strongest correlate of upward income mobility among all the variables we explored, with a raw unweighted correlation of �0.76 (see Online Appendix Figure XII Panel A for the corre- sponding nonparametric binned scatter plot). One natural expla- nation for this spatial correlation is an individual-level effect: children raised by a single parent may have worse outcomes
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than those raised by two parents (Thomas and Sawhill 2002; Lamb 2004). To test whether this individual-level effect drives the spatial correlation, we calculate upward mobility in each CZ based only on the subsample of children whose own parents are married. The correlation between upward mobility and the frac- tion of single parents in their CZ remains at �0.66 even in this subgroup (Online Appendix Figure XII Panel B). Hence, family structure correlates with upward mobility not just at the individ- ual level but also at the community level, perhaps because the stability of the social environment affects children’s outcomes more broadly. The association between mobility and family struc- ture at the community level echoes our findings in Section VI.A on the community-level effects of racial shares.
VI.G. Comparison of Alternative Explanations
In Table VI, we assess which of the five factors identified above—segregation, inequality, school quality, social capital, and family structure—are the strongest predictors of upward mo- bility in multivariable regressions that control for race and other covariates. Based on the analysis, we first identify the proxy that has the strongest and most robust univariate correlation with upward mobility in each category: the fraction of working indi- viduals who commute less than 15 minutes to work (segregation), the bottom 99% Gini coefficient (inequality), high school dropout rates adjusted for income differences (school quality), the social capital index, and the fraction of children with single parents (family structure).49 As in preceding regression specifications, we normalize all the dependent and independent variables to have a standard deviation of 1 in the estimation sample for each regression in Table VI.50
We begin in column (1) with an unweighted OLS regression of absolute upward mobility r25;c on the five factors, pooling all CZs. All of the factors except the Gini coefficient are significant predictors of the variation in absolute upward mobility in this
49. We obtain similar results if we combine the various proxies into a single index for each factor using weights from an OLS regression of absolute upward mobility on the proxies within each category.
50. We code the high school dropout rate as 0 for 126 CZs in which dropout rate data are missing for more than 25% of the districts in the CZ and include an indi- cator for having a missing high school dropout rate. We do the same for 16 CZs that have missing data on social capital. We normalize these variables to have mean 0 and standard deviation 1 among the CZs with nonmissing data.
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specification. Together, the five factors explain 76 percent of the variance in upward mobility across areas. Column (2) shows that the coefficients remain similar when state fixed effects are in- cluded. Column (3) shows that the estimates are roughly similar when restricting the sample to urban areas (CZs that intersect MSAs). Across all the specifications, the strongest and most robust predictor is the fraction of children with single parents.
In column (4), we use relative mobility �c as the dependent variable instead of absolute upward mobility. The fraction of
TABLE VI
CORRELATES OF INTERGENERATIONAL MOBILITY: COMPARING ALTERNATIVE HYPOTHESES
Dep. var.: Absolute upward
mobility Relative mobility
Absolute upward mobility
(1) (2) (3) (4) (5) (6) (7) (8)
Fraction short commute
0.302 0.227 0.314 �0.290 �0.325 0.331 0.319 (0.065) (0.077) (0.052) (0.061) (0.064) (0.070) (0.065)
Gini bottom 99% �0.009 �0.017 0.060 0.006 0.343 �0.287 �0.021 (0.053) (0.043) (0.097) (0.071) (0.095) (0.059) (0.054)
High school dropout rate
�0.147 �0.120 �0.109 0.010 0.181 �0.288 �0.140 (0.055) (0.038) (0.085) (0.064) (0.056) (0.059) (0.055)
Social capital index
0.169 0.065 0.173 0.154 0.154 0.168 0.168 (0.047) (0.050) (0.060) (0.060) (0.070) (0.059) (0.045)
Fraction single mothers
�0.487 �0.477 �0.555 0.591 �0.808 �0.579 (0.062) (0.071) (0.089) (0.049) (0.085) (0.061)
Fraction black 0.056 0.132 (0.073) (0.051)
State fixed effects x Urban areas only x R-squared 0.757 0.859 0.671 0.48 0.324 0.651 0.584 0.763 Observations 709 709 325 709 709 709 709 709
Notes. Each column reports coefficients from an OLS regression with standard errors clustered at the state level reported in parentheses. The regressions are run using data for the 709 CZs with at least 250 children in the core sample. The dependent variable in columns (1)–(3) and (6)–(8) is our baseline measure of absolute upward mobility, the expected rank of children whose parents are at the 25th national per- centile. The dependent variable in columns (4) and (5) is relative mobility, the rank-rank slope within each CZ. All independent and dependent variables are normalized (in the relevant estimation sample) to have mean 0 and standard deviation 1. Column (1) reports unweighted estimates across all CZs. Column (2) includes state fixed effects. In column (3), we restrict to CZs that intersect MSAs. Columns (4)–(8) rep- licate the unweighted specification in column (1) with different dependent and independent variables. The fraction with short commutes is the share of workers that commute to work in less than 15 minutes calculated using data for the 2000 census. Gini bottom 99% is the Gini coefficient minus the top 1% income share within each CZ, computed using the distribution of parent family income within each CZ for parents in the core sample. Income-residualized high school dropout rate is the residual from a re- gression of the fraction of children who drop out of high school in the CZ, estimated using data from the NCES Common Core of Data for the 2000–2001 school year, on mean household income in 2000. Social capital index is the standardized index of social capital constructed by Rupasingha and Goetz (2008). Fraction single mothers is the fraction of children being raised by single mothers in each CZ. Fraction black is the number of people in the CZ who are black alone divided by the CZ population. We code the high school dropout rate as 0 for 116 CZs in which dropout rate data are missing for more than 25% of the districts in the CZ, and include an indicator for having a missing high school dropout rate. We do the same for 16 CZs with missing data on social capital. See Section VI, Online Data Table IX, and Online Appendix G for additional details on the definitions of each of these variables.
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single parents and commute times are strong predictors of differ- ences in relative mobility across areas, but the other factors are not statistically significant. To understand why this is the case, in column (5) we replicate column (4) but exclude the fraction of children with single parents. In this specification, all four of the remaining factors—including the Gini coefficient—are strong predictors of the variation in relative mobility across CZs. Column (6) replicates the specification in column (5) using abso- lute upward mobility as the dependent variable. Once again, all four factors are strong predictors of upward mobility when the fraction of single parents is excluded. These results suggest that the fraction of single parents may capture some of the variation in the other factors, most notably the level of income inequality.
In the last two columns of Table VI, we explore the role of racial demographics versus the other explanatory factors. Column (7) shows that when we regress absolute upward mobility on both the fraction of single-parent families in the CZ and the share of black residents, black shares are no longer significantly correlated with upward mobility. Column (8) shows that the cor- relation of upward mobility with black shares is slightly positive and statistically significant when we include controls for all five explanatory factors. These results support the view that the strong correlation of upward mobility with race operates through channels beyond the direct effect of race on mobility.
Overall, the results in Table VI indicate that the differences in upward mobility across areas are better explained by a combi- nation of the factors identified above rather than any single factor. However, the regression coefficients should be interpreted with caution for two reasons. First, the regression may place greater weight on factors that are measured with less error rather than those that are truly the strongest determinants of mobility. Second, all of the independent variables are endogenously determined. These limitations make it difficult to identify which of the factors is the most important determinant of upward mobility.
VII. Conclusion
This article has used population data to present a new por- trait of intergenerational income mobility in the United States. Intergenerational mobility varies substantially across areas.
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For example, the probability that a child reaches the top quintile of the national income distribution starting from a family in the bottom quintile is 4.4% in Charlotte but 12.9% in San Jose. The spatial variation in intergenerational mobility is strongly correlated with five factors: residential segregation, income inequality, school quality, social capital, and family structure.
In this article, we have presented a cross-sectional snapshot of intergenerational mobility for a single set of birth cohorts. In a companion paper (Chetty et al. 2014), we study trends in mobility over time. We find that the level of intergenerational mobility (national rank-rank slope) has remained stable for the 1971– 1993 birth cohorts in the United States, especially in comparison to the degree of variation across areas. A natural question given the results of the two papers is whether the cross-sectional cor- relations documented here are consistent with the time trends in mobility. To answer this question, we predict the trend in the rank-rank slope implied by changes in the five key correlates over time (see Online Appendix I and Appendix Figure XIII). The predicted changes are quite small because the factors move in opposing directions. For example, the increase in inequality and single parenthood rates in recent decades predict a small decline in mobility in recent decades. In contrast, the decline in racial segregation and high school dropout rates predict an in- crease in mobility of similar magnitude. Overall, the cross-sec- tional correlations documented here are consistent with the lack of a substantial time trend in mobility in recent decades.
The main lesson of our analysis is that intergenerational mo- bility is a local problem, one that could potentially be tackled using place-based policies (Kline and Moretti 2014). Going for- ward, a key question is why some areas of the United States gen- erate higher rates of mobility than others. We hope that future research will be able to shed light on this question by using the mobility statistics constructed here (available online at the county by birth cohort level at www.equality-of-opportunity.org) to study the effects of local policy changes.
Harvard University and NBER
Harvard University and NBER
University of California, Berkeley, and NBER
University of California, Berkeley, and NBER
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Supplementary Material
An Online Appendix for this article can be found at QJE online (qje.oxfordjournal.org).
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