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Measuring Income Concentration – A Guide for the Confused

Measuring Income Concentration – A Guide for the Confused

With the release of Emmanuel Saez and Gabriel Zucman’s (2019) new book, The Triumph of Injustice: How the Rich Dodge Taxes and How to Make Them Pay, income inequality is in the news again. The book includes a number of provocative claims about tax progressivity that have been viewed skeptically by a range of tax policy experts, who are poring through the methods and assumptions of Saez and Zucman (and their colleague, Thomas Piketty, a collaborator in the work on which the book is based).

The work of Piketty, Saez, and Zucman suggests sharply rising income and wealth inequality, falling tax progressivity, and stagnant income growth for the bottom half of Americans. But other researchers have reported modestly rising income inequality, growth in wealth inequality that is less sharp, rising tax progressivity, and more robust income growth for lower-income Americans. The question of who is right in these debates hinges on a variety of technical measurement questions and assumptions and the quality of various data sources. The debates have become inaccessible to even many observers with considerable economic training.

The current primer is intended to address the debate around income concentration specifically. It reviews the academic debates around how much income goes to the “top one percent,” conveying how we have arrived at the present, when one set of researchers can claim that this share rose by 8.5 percentage points from 1979 to 2015, while another can claim a rise of only 1.3 points. The primer will show the progress that has been made in terms of inequality measurement, and the considerable challenges that remain. For those most interested in the current controversy over measuring national income concentration, the penultimate section of the paper addresses the disagreements that are unresolved as of yet.

Fiscal Income Concentration among Tax Units

Understanding the state of the current debate on income concentration requires a review of attempts over the past twenty years to develop and refine measures of the share of income received by the top one percent. This history begins with a pioneering study by Piketty and Saez.

During the twentieth century, most inequality research focused not on the top one percent or on income concentration even higher up within this group but on inequality below the top. Researchers generally relied on easy-to-obtain household survey data, such as the Current Population Survey (CPS). The CPS has proven to be an invaluable data source for analyzing income inequality, however it badly understates income among the richest Americans. It does so for four reasons. First, out of privacy concerns, income reports are subsequently “top-coded,” or capped at some maximum before the data is released. Second, incomes often are underreported at the top.1 Third, refusing to participate in the CPS is more common at the very top.2 Finally, even in the absence of these problems, the CPS sample is not large enough to produce reliable income estimates very high up in the income distribution (say, for the top one percent of the top one percent).

While not the first to have the insight, Piketty and Saez recognized the potential of using tax data to better measure top incomes.3 Their first set of estimates were published in 2003, and they have been updated periodically over the years (most recently in March of 2019).4 Piketty and Saez analyzed what they then called “tax return gross income” and now (with Zucman) call “fiscal income”—essentially adjusted gross income reported on individual income tax returns but with the adjustments added back to AGI.5

Fiscal income is straightforward to measure for recent decades, since it mostly comes directly from tax return data.6 As a result, a variety of estimates of the concentration of fiscal income are consistent with one another. Figure 1 shows the share of fiscal income received by the top one percent of “tax units” as reported by Piketty and Saez (2003, updated in 2019), Piketty, Saez, and Zucman (2018, updated in 2019), Auten and Splinter (2019), and Larrimore et al. (2018).7 These estimates do not include capital gains in fiscal income, a point to which we will return below.

Figure 1. Share of Fiscal Income (Excluding Capital Gains) Received by the Top One Percent of Tax Units

Sources: Piketty-Saez from Emmanuel Saez’s website (, Table A1). Piketty-Saez-Zucman from Emmanuel Saez’s website (, PSZ2019Distributions.xlsx, tab TD2b). Auten-Splinter from David Splinter’s website (, tab C2-Shares, column BH). Larrimore et al. from personal communication with Jeff Larrimore.

Because most of the divergence in the major inequality series occurs after 1979, because the Congressional Budget Office estimates highlighted below begin in that year, and because 1979 is a peak year in the business cycle, all the charts in this memo begin in that year. The Piketty-Saez estimates indicate that the top one percent received 8 percent of fiscal income in 1979, 19 percent in 2012, and 18.5 percent in 2018.

The Piketty-Saez estimates have been subjected to a number of criticisms over the years. For one, many categories of income include taxable and tax-exempt sources, and the latter are not included in fiscal income. Obviously whether someone receives, say, interest from taxable or tax-exempt sources is arbitrary for purposes of estimating income inequality.

Of course, what is and is not tax-exempt need not stay the same over time. Changes in exemptions will lead to shifts in what does and does not show up on tax returns. For instance, investors may shift from assets that yield taxable interest or dividends to those that produce untaxed income in those forms.

More generally, tax policy changes can lead to artificial changes in fiscal income concentration. The relative levels of individual income tax rates and corporate tax rates can lead to more or less corporate profit being distributed to shareholders and executives (which generally shows up on individual income tax returns) rather than being retained as corporate earnings (which appears on corporate tax returns). Because pass-through entities distribute income to their owners in forms that show up on individual returns, the difference between individual and corporate rates can lead to more or fewer pass-throughs and, hence, more or less fiscal income. The difference between individual capital gains tax rates and ordinary income tax rates can lead to different investment allocations and to changes in executive compensation (such as greater use of stock options). If fiscal income estimates do not include capital gains in income, as in Figure 1, then those effects can artificially alter the level and distribution of fiscal income.

To see how dramatically tax policy changes can affect fiscal income concentration estimates, consider the jump in the top one percent’s share shown in Figure 1 between 1986 and 1988. That increase accounts for 40 percent of the 1979-to-2018 increase in income concentration. However, it is largely artificial, resulting from the Tax Reform Act of 1986. This law lowered top marginal tax rates on ordinary individual income from 50 percent to 28 percent while lowering the corporate tax rate from 46 percent to 34 percent. It also raised the top tax rate on long-term capital gains from 20 percent to 28 percent. These changes led affluent Americans to move income from retained earnings to executive pay, alter the way in which they received stock options, and incorporate their businesses as pass-throughs rather than traditional C corporations. All these effects led to more income showing up on tax returns, producing an illusory “increase” in the share of income going to the top.

Increases in the top ordinary income tax rate in 1990, 1992, and 2012 also visibly affect the fiscal income concentration trend, producing one-time spikes. These result from upper-income taxpayers opting to receive income in advance of the tax increase rather than in the following year; fiscal income concentration then looks higher in 1990, 1992, and 2012 and lower in 1991, 1993, and 2013, rather than smoothly moving over time.

More importantly, tax policy changes affect the long-term trend in fiscal income concentration too. As different tax rates have changed, behavioral incentives have changed, and not just for a year or two. Some of those behaviors have produced new income and actually altered the income distribution. But others have simply shifted more income onto individual income tax returns instead of being invisible from the perspective of fiscal income. For example, Cooper et al. (2016) find that the 10-point rise in income concentration from 1979 to 2013 that Piketty and Saez report (for a series to be discussed next) would have been just a six-point rise if not for the increase in pass-through income.

Piketty and Saez also have provided a second set of fiscal income concentration estimates that include realized capital gains in income. The thick green line in Figure 2 (extending to 2018) displays the share of fiscal income received by the top one percent according to this series. Setting aside the Bricker et al. and CBO trendlines for the moment, the chart also shows tax-unit-based estimates from Piketty, Saez, and Zucman (2018, updated 2019) and Larrimore et al. (2018).8 These three trends practically lie on top of each other, except that the Piketty-Saez-Zucman estimate for 2017 is unusually high. When capital gains are included, the trend in income concentration is more volatile than the trend excluding capital gains, and it indicates higher concentration at the top. The Piketty-Saez series show the top one percent share rising from 10 percent in 1979 to 24 percent in 2007 and then falling to 22 percent in 2018. The PSZ series indicate a rise from 10 percent to 24 percent in 2017.

Figure 2. Share of Fiscal or Market Income (Including Capital Gains) Received by the Top One Percent

Sources: Piketty-Saez from Emmanuel Saez’s website (, Table A3). Piketty-Saez-Zucman from Emmanuel Saez’s website (, PSZ2019Distributions.xlsx, tab TD2b). Larrimore et al. from personal communication with Jeff Larrimore. Bricker et al. from the Brookings Institution website (, tab “Data Figure 2 (income shares)”). CBO from the Table Builder tool at (ranking by market income).

Clearly, the boom and bust of equities and housing markets affects this trend. The tech-stock boom peaked in 2000, and 2007 marked the peak of the housing bubble and another stock-market boom.

Like the series that exclude capital gains, the estimates in Figure 2 also are affected by changes in top tax rates. There are obvious one-time jumps related to increases in top capital gains tax rates. In 1986 and 2012, investors rushed to realize capital gains ahead of tax increases, artificially raising the top one percent share and lowering it the next year. This kind of artifact raises the concern that tax policy changes also can have longer-term effects in terms what shows up on individual tax returns—altering top income share series in ways that do not reflect real changes in inequality.

Market Income Concentration among Families and Households

The inequality estimates discussed thus far have been limited to measuring the fiscal income of tax units. Fiscal income, however, misses some forms of income that are tax exempt or that are taxed away in corporate income taxes or business property taxes before they are ever enjoyed. It also misses underreported income. In response, researchers have tried to develop fuller measures of “market,” or pre-tax and -transfer, income.

Further, the Piketty and Saez series have been criticized for their focus on tax units. Tax units may be thought of as tax returns (plus the tax returns we would see if non-filers filled out Form 1040s). A married couple filing jointly constitutes a tax unit, as does a single filer. Tax units, then, are different than individuals because some consist of married couples. They are different from families because spouses are the only family members whose incomes are combined, and then only if they file jointly. Dependent children who file their own returns are treated as separate tax units. Finally, tax units are different than households because, for instance, a cohabiting couple or pair of roommates is treated as two tax units. For these reasons, the number of tax units significantly exceeds the number of families or households, and tax units tend to be poorer (because their incomes are not combined within families or households and because of young dependents with little income). Further, the distinction between tax units and families or households is empirically larger below the top one percent.9 That means that income concentration across tax units is larger than income concentration across families or households.

Finally, the decline in marriage—greater below the top than in the top one percent—has increased the number of tax units and thus the number of tax units that are in the top percentile. Without any other changes in inequality, that would increase the top one percent’s share.10

Figure 2 includes other income concentration trends from the Congressional Budget Office (2019) and from a team of researchers at the Federal Reserve Board (Bricker et al., 2016). These series both include realized capital gains in fiscal income, like the other estimates in Figure 2. The Bricker et al. estimates examine inequality across families, and they include employer-provided health insurance in market income. Unlike the other estimates discussed so far, they come from the Survey of Consumer Finances rather than administrative income tax data. The trend the Fed researchers estimate, nonetheless, is similar to those for the tax unit estimates from tax data in Figure 2, except in 1988.11

The CBO trendline, however, indicates less income concentration and rises less steeply than the tax unit estimates. This difference may arise because the CBO series focuses on the household income of individuals ranked by size-adjusted household income (rather than the tax unit income of tax units ranked by tax-unit income).12 However, another difference is that the CBO series incorporates additional market income that is tax-exempt (such as employer contributions to health insurance) or that does not show up on individual returns because it is taxed away (such as income lost because of corporate income taxes or the employer’s share of payroll taxes).13 Finally, the CBO series is produced by statistically merging the Current Population Survey data with the tax records, which could also create discrepancies with the series solely based on tax data.

Post-Transfer and Post-Tax & -Transfer Income Concentration among Families and Households

Some researchers have criticized the Piketty and Saez series for not taking account of taxes and transfers. For many purposes, it is strange to consider inequality of fiscal or market income, since they take account of no redistribution. After all, policymakers could choose to eliminate post-tax and -transfer inequality entirely through redistribution, but fiscal or market income concentration estimates might still indicate substantial “inequality.”

For other questions—such as how equally markets distribute income—fiscal or market income concentration is more sensible to analyze, though this rationale raises an issue when retirees are included in analyses. Retirees tend to rely strongly on Social Security benefits. More generally, they often require less income to maintain their pre-retirement living standards. (Many own their homes outright, for instance.) As the baby boomers have aged, retirees have become a growing share of tax units, which means fiscal or market income concentration has become more ambiguous as an inequality measure over time.

For these reasons, some researchers have estimated income concentration trends using either pre-tax, post-transfer income or post-tax and -transfer income. Figure 3 shows how incorporating transfers lowers the CBO and Bricker et al. income concentration levels, carrying over the market-income-based estimates from Figure 2 (dashed lines). Once again, all these trends include realized capital gains in income.

Figure 3. Share of Post-Transfer Income (Including Capital Gains) Received by the Top One Percent

Sources: CBO from the Table Builder tool at (ranking by market income or by pre-tax income) and from (for the post-transfer series). Bricker et al. from the Brookings Institution website (, tabs “Data Figure 2 (income shares)” and “Data Figure 11”).

Unsurprisingly, transfers reduce income concentration, and they reduce the increase in inequality over time (though only modestly in the CBO data). More surprisingly, essentially all the reduction in inequality from transfers appears to come from social insurance benefits rather than means-tested transfers.14

The dashed line in Figure 4 carries over the CBO post-social-insurance trend from Figure 3. Comparing it with the CBO post-tax and -transfer line shows how taking taxes into account affects income concentration. Doing so reduces income concentration more than accounting for transfers does, and it reduces the rise in inequality much more. The CBO market income estimates in Figure 2 indicate that between 1979 and 2016 the top one percent’s share rose by eight points (from 9.6 to 17.5 percent). After transfers, the increase was seven points (9.0 to 15.8), but after both taxes and transfers, the increase was only five points (7.4 to 12.6). By contrast, the Piketty-Saez estimates for fiscal income in Figure 2 indicate an 11-point rise (10.0 to 20.7).

Figure 4. Share of Post-Tax and Transfer Income (Including Capital Gains) Received by the Top One Percent

Sources: CBO from the Table Builder tool at (ranking by pre-tax or post-tax income). Larrimore et al. from personal communication with Jeff Larrimore.

Figure 4 sheds light on another criticism of income concentration series that include capital gains. Capital gains show up on tax returns only when they are realized. Gains that accrue as people hold assets are not included in the Piketty-Saez or CBO income estimates until the assets are sold. Consider two shareholders with the same amount of ownership in a company, purchased at the start of the year. If one sells her stock at the end of the year, she will report income (the difference between the value of the stock when she sold it versus when she purchased it). If the other investor holds her stock, she will report no gain on her tax return for the year. However, the two shareholders arguably have become richer by the same amount.

It is true that if the second shareholder eventually sells her stock, the gain that accrued to her in the earlier year might show up on her tax return as income in a subsequent year. But this points out the potential problem of counting gains as income not in the year they accrue but in the year they are realized. Someone holding stock for 30 years before selling has three decades’ worth of accrued gains counted in that final year of ownership, which could push income concentration higher than it would be if gains were counted as they accrue, year-by-year. This possible effect might be further exacerbated to the extent that investors are able to time their sales near asset market peaks. And it might be exacerbated even further in that only a limited amount of capital losses show up on tax returns.

Another potential problem is that capital gains are included as income by Piketty-Saez and CBO only if they are taxable. Home ownership is a primary source of wealth for most Americans. However, capital gains from the sale of a home are taxable only above levels few Americans enjoy. The combination of taxable gains being counted in a single year when realized and non-taxable gains not being counted as income at all could very well overstate income concentration.

Figure 4 includes two sets of post-tax and -transfer estimates from Larrimore et al. (2018) that show how this issue affects income concentration trends.15 The first of these series counts taxable capital gains as income as they are realized. Despite their estimates applying to tax units, the trend lines up extremely well with the CBO numbers based on ranking individuals by size-adjusted household income.

Rather than counting taxable capital gains all at once, when realized, and ignoring non-taxable gains, the second Larrimore series attempts to count all gains as they accrue to tax units, year-by-year.16 It is more volatile than the other series, and it produces peaks in inequality that precede by several years the peaks in those other series. According to this second set of estimates, the top one percent’s share of income was 9.9 percent in 1990, 9.5 in 1994, 9.9 in 2002, 12.1 in 2009, and 12.2 in 2011. Comparing peaks, the share was 14.3 in 1989, 16.3 in 1998, 15.9 in 2004, and 18.1 in 2013. In other words, Larrimore et al. indicate a rise of three or four percentage points in the top one percent’s share from 1989 or 1990 to 2011 or 2013.17 That is a period during which time the CBO post-tax and -transfer series rises by one or two points and the Piketty-Saez fiscal income series in Figure 2 rises by five points.18 So this issue of when capital gains are counted turns out to affect the year-to-year pattern of inequality trends, but its impact on long-term trends is ambiguous.

National Income Concentration

Moving from Figure 1 to Figure 4 documents researchers’ attempts to create more meaningful income measures by which to consider inequality. Fiscal income is essentially income received as cash, but only from sources that are taxable. The studies using expanded definitions of market income capture more of the resources that flow to people. Pre-tax, post-transfer income incorporates cash and non-cash transfers, and post-tax and -transfer income accounts for taxes too.

However, even the studies reviewed above that look at market income miss a substantial share of it, and the studies accounting for taxes address only some of them. In recent years, Piketty, Saez, and Zucman (henceforth, PSZ) and Auten and Splinter (AS) have attempted to improve on the earlier work by distributing all national income across rich and poor. Among the types of income accounted for in their analyses are corporate retained earnings, corporate taxes that would have been received as income absent taxation, underreported income, employer-provided health, life, and other insurance, employer payroll taxes that would otherwise have been received as income, business property taxes, and the imputed rent of homeowners (who would have to pay rent to a landlord if they did not own). (Capital gains are included as they accrue only insofar as they reflect greater retained earnings. Any pure gains due solely to asset price increases are not included in income, because—being unrelated to production—they are not included in national income.)

The studies include not just federal and state income taxes, but local income and property taxes, payroll taxes, estate taxes, sales taxes, and business taxes. They also account for government transfers. And the two papers allocate national deficits as negative income across Americans and government spending other than transfers as positive income.

As should be clear, it is much more difficult to allocate many of these sources of income and taxes between poor, middle-class, and rich people than is the case for forms of income that are unambiguously received by taxpayers. While national income may represent a more coherent income concept in theory, in practice it presents enormous measurement challenges.

In Figure 5, the two middle lines carry over from Figure 1 the income concentration estimates from the two research teams that examine the fiscal income of tax units. As noted earlier, those trends lie very close to one another. The two thick solid lines show trends in the top one percent’s share when using pre-tax income and assessing inequality across individuals rather than tax units.19 (The other dashed lines show intermediate steps in moving from tax-unit fiscal income to individual pre-tax income. For the PSZ estimates, the intermediate step moves from tax-unit fiscal income to tax-unit pre-tax income. For the AS estimates, it moves from tax-unit fiscal income to individual fiscal income.) Note that the “pre-tax” estimates use the PSZ definition, which is actually more like pre-tax, post-social-insurance income, since it counts Social Security and unemployment insurance but no other transfers. (AS do not include social insurance in their pre-tax measure, but it is possible to allocate it using their spreadsheet.)

Figure 5. Share of Pre-Tax National Income Received by the Top One Percent

Sources: Piketty-Saez-Zucman from Emmanuel Saez’s website (, PSZ2019Distributions.xlsx, tabs TD2b and TB10). Auten-Splinter from David Splinter’s website (, tab C2-Shares, columns BH, BP, and FH).

PSZ find that the top one percent’s share of pre-tax income was 12 percent in 1979 and 20 percent in 2015. The AS estimates suggest an increase from 9 percent to 13 percent in 2015. Thus, inequality is lower in the AS data than in the PSZ data, and it rises less (a four-point rather than an 8.5-point increase from 1979 to 2015).

What accounts for these differences? In their paper, AS attempt to reconcile their estimates with those of PSZ.20 They find that over half of the difference in the 1979-to-2014 increase between the two papers (2.4 points of the 4.3-point gap) derives from differences in how underreported income and retirement income are treated. Discrepancies between how non-retirement corporate income and sales taxes are allocated explain another one point. Together, these four categories explain 80 percent of the gap in inequality growth between the two papers.

That leaves the question of which team is closer to the truth. Regarding underreporting, both PSZ and AS allocate unreported income that is incorporated in the US national accounts.21 AS rely heavily on IRS audit studies, which they note are the basis for the national accounts estimates of underreported income. PSZ have argued that the audit studies fail to account for the underreported income of complex partnerships, citing Cooper et al. (2016). However, in their appendix, AS show that even if half of the income of such partnerships estimated by Cooper et al. was unreported and it all belonged to the top one percent, the top one percent share would only rise by 0.3 percentage points in 2014. In response to PSZ claims that accounting for income from offshore wealth would raise inequality, AS conduct a sensitivity check using estimates of offshore wealth from Saez and Zucman (2016) and rates of return the exceed estimates in the literature. They find that the top one percent’s share would be raised by only a couple of tenths of a percentage point.

For their part, AS fault PSZ for allocating too little underreported business income to people with negative reported business income (and thus too much to people with already-high reported business income).22 PSZ has not responded to this criticism in their papers.

Regarding the discrepancies related to retirement income allocation, in the online appendix to their paper23, AS cite Devlin-Foltz, Henriques, and Sabelhaus (2016), who find the top one percent own 8 percent of retirement wealth—much closer to AS’s estimate of the top’s share of retirement income (6 percent) than PSZ’s (16 percent). AS note a clear error on the part of PSZ in that they include rollovers on tax returns as income when they back into aggregate retirement wealth, to which they then apply a rate of return to estimate full retirement income.24 Rollovers in a given year do not represent income generated by wealth in that year and received by retirees; rather they represent wealth itself being transferred between accounts. PSZ has not responded to this criticism in their papers.

Regarding sales tax allocation, AS note that PSZ do so on the basis of labor and business income less savings, which takes no account of retirement income, taxes, or transfers and their impact on purchasing power. Arguably, however, rather than coming from the pockets of consumers, sales tax ultimately may come from the pockets of workers and business owners who would see higher pay or profits if not for the taxation. PSZ updated their estimates in 2019, and in their latest version they allocate 70 percent of sales taxes across consumers (taking into account retirement income, some taxes, and some transfers), and 30 percent according to labor and business income.

Finally, regarding nonretirement corporate income, Smith, Zidar, and Zwick (2019) point out that PSZ likely overstate income concentration by allocating corporate retained earnings on the basis of dividends and realized capital gains (both forms of taxable income from C-corporations), since only some—perhaps a minority—of realized gains come from sale of corporate stock (real estate sales being a primary alternative source of gains). In effect, they are giving corporate retained earnings to well-off people who don’t have ownership in corporations.

In the online appendix to their 2018 paper25, PSZ enumerated several issues with an earlier draft of the AS paper. Most of these objections were addressed in the latest AS paper. In some cases AS changed their methods in response; in others (noted above) they defended their choices. PSZ’s revised appendix26 no longer includes the section addressing the earlier AS paper, and it has not been replaced by a new response. Instead, PSZ (2019) approach the revised AS paper through several general criticisms.

First, they compare the aggregate amount of national income AS estimate going to the top one percent in 2015 to the amount of fiscal income Piketty and Saez (2003) estimate going to it. They note that AS find less income going to the top than Piketty and Saez, despite national income being more comprehensive than fiscal income. But this is an inappropriate comparison because the Piketty-Saez estimates they cite include realized capital gains. Realized gains reflect undistributed retained earnings (included in national income) but also pure price changes in assets that are unrelated to production (excluded from national income). The latter constitute a substantial amount of fiscal income.

PSZ also conduct a back-of-the-envelope exercise suggesting that AS must be allocating untaxed income (as opposed to fiscal income) in ways that imply dramatically falling inequality in untaxed income over time. However, their exercise proceeds from the Piketty-Saez fiscal income estimates (looking at tax units ranked by tax-unit income) as if AS were also looking at tax units ranked by tax-unit income. In actuality, the AS national income estimates report the share of income received by the tax units containing the top one percent of individuals, ranked by size-adjusted tax unit income. The estimates in AS’s Table 1 suggest that a sizable proportion of the reduced rise in inequality they find, relative to the Piketty-Saez estimates, can be attributed to this change in the unit of analysis and ranking methodology—roughly one-fourth of reduction from 1960 to 2015.

In their response to PSZ, AS show that the assumptions PSZ use in their back-of-the-envelope exercise about how untaxed income is distributed in the AS estimates are simply wrong.27 PSZ’s exercise assumes that the share of 2016 untaxed capital income not earned on pension plans that AS give to the top one percent is 10 percent (versus the 40 percent that PSZ use to reproduce their own estimates in a similar exercise). But AS report that this amount is actually 29 percent in their data in 2015.28

Using the equation on page 26 of AS’s online appendix, one can confirm that the PSZ exercise produces the result that it does (low concentration of untaxed capital income outside pension plans) because they ignore that AS are looking at individuals ranked by size-adjusted income. Setting the top one percent shares of imputed rent and private capital (which, together, constitute capital income outside pension plans) to 10 percent, as in the PSZ exercise, and zeroing out the decline in the top share that is attributable to the change of units and ranking methodology, the aggregate income amount going to the top one percent is consistent with the amount AS actually allocate to them. PSZ have only shown one way to produce, from the distribution of fiscal income by tax unit, a national income concentration trend that happens to align with the AS trend based on ranking individuals by size-adjusted income.

To close out this primer, Figure 6 carries over the pre-tax trends from Figure 5 and also displays the post-tax estimates from PSZ and AS. Most of the difference between the post-tax series, in terms of how much inequality rises, is due to the pre-tax estimates diverging. The way that AS allocate government consumption (non-transfer expenditures) and government deficits leads their inequality measure to decline by around one point more than it would if they used the PSZ approach. AS argue that by allocating government consumption strictly by after-tax income, PSZ reject the possibility that public goods benefit everyone equally or that some government consumption expenditures redistribute well-being downward. Regarding (non-Social Security) deficits, AS allocate by federal income taxes. PSZ allocate half by government transfers and half by taxes, which seems a compromise between allocating by who pays for deficits and by who benefits from them.

Figure 6. Share of Post-Tax National Income Received by the Top One Percent

Sources: Piketty-Saez-Zucman from Emmanuel Saez’s website (, PSZ2019Distributions.xlsx, tabs TB10 and TC10). Auten-Splinter from David Splinter’s website (, tab C2-Shares, columns AB, EZ, and FH).

PSZ find the top one percent share rising 6.5 points, from 9.1 percent to 15.6 percent from 1979 to 2015. In contrast, AS report it increasing only from 7.2 to 8.5 percent.


The latest project of inequality measurement—attempting to allocate all national income—is ambitious. If it can be reliably achieved, we will be able to understand how economic growth is shared across poor, middle-class, and well-off Americans. However, as the discussion above should be clear, we have a long way to go before the kind of consensus can be developed that exists for the measurement of gross domestic product. It is simply inappropriate at this stage to make strong claims about the level or trend of income concentration, without heavy caveats. It is certainly inappropriate to justify preferred policies on the basis of national income distribution figures and tax distribution figures that are very much contested and under continual development.


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Larrimore, Jeff (2014). “Accounting for United States Household Income Inequality Trends: The Changing Importance of Household Structure and Male and Female Labor Earnings Inequality.” Review of Income and Wealth 60(4): 683-701.

Piketty, Thomas, Emmanuel Saez, and Gabriel Zucman (2019). “Simplified Distributional National Accounts.” American Economic Association Papers and Proceedings 109: 289-295.

_____ (2018). “Distributional National Accounts: Methods and Estimates for the United States.” Quarterly Journal of Economics 133(2): 553-609.

Piketty, Thomas and Emmanuel Saez (2007). “How Progressive is the U.S. Federal tax system? A Historical and International Perspective.” Journal of Economic Perspectives 21(1): 3-24.

_____ (2003). “Income Inequality in the United States, 1913-1998.” Quarterly Journal of Economics 118(1): 1-39.

Saez, Emmanuel and Gabriel Zucman (2019). The Triumph of Injustice: How the Rich Dodge Taxes and How to Make Them Pay (New York: W. W. Norton & Co.).

_____ (2016). “Wealth Inequality in the United States since 1913: Evidence from Capitalized Income Tax Data.” Quarterly Journal of Economics 131(2): 519-578.

Smeeding, Timothy M. and Jeffrey P. Thompson (2011). “Recent Trends in Income Inequality: Labor, Wealth and More Complete Measures of Income.” Research in Labor Economics 32: 1-50.

Smith, Matthew, Danny Yagan, Owen M. Zidar, and Eric Zwick (2019). “Capitalists in the Twenty-First Century.” Quarterly Journal of Economics 134(4): 1675-1745.

Smith, Matthew, Owen M. Zidar, and Eric Zwick (2019). “Top Wealth in the United States: New Estimates and Implications for Taxing the Rich.” Working paper.

Wolff, Edward N. and Ajit Zacharias (2009). “Household Wealth and the Measurement of Economic Well-Being in the United States.” Journal of Economic Inequality 7:83-115.


1. Though many also over-report income. See Dennis Fixler, Marina Gindelsky, and David Johnson (2018). “Improving the Measure of the Distribution of Personal Income.” Paper prepared for the 35th IARIW General Conference, Copenhagen, Denmark, August 20-25, 2018.

2. Christopher R. Bollinger, Barry T. Hirsch, Charles M. Hokayem, and James P. Ziliak (2019). “Trouble in the Tails? What We Know about Earnings Nonresponse 30 Years after Lillard, Smith, and Welch.” Journal of Political Economy 127(5): 2143-2185.

3. Earlier research was conducted by Daniel Feenberg and James Poterba. See Feenberg and Poterba (1993). “Income Inequality and the Incomes of Very High Income Taxpayers: Evidence from Tax Returns.” In Poterba, ed., Tax Policy and the Economy (Cambridge, MA: MIT Press) and Feenberg and Poterba (2000). “The Income and Tax Share of Very High Income Households, 1960-1995.”
American Economic Review 90: 264-270.

4. Thomas Piketty and Emmanuel Saez (2003). “Income Inequality in the United States, 1913-1998.” Quarterly Journal of Economics 98(1): 1-39.

5. Taxable Social Security and unemployment benefits are excluded.

6. Some imputation is required for the income of nonfilers.

7. Auten and Splinter make small modifications to the definition of fiscal income to make the estimates more consistent over time. The estimates up to 1986 are primarily affected, reflecting the tax changes in the Tax Reform Act of 1986.

8. Updated results from this paper were generously provided by Jeff Larrimore.

9. Jesse Bricker, Alice Henriques, Jacob Krimmel, and John Sabelhaus (2016). “Measuring Income and Wealth at the Top Using Administrative and Survey Data.”
Brookings Papers on Economic Activity. Spring: 261–312. Jeff Larrimore, Jacob Mortenson, and David Splinter (Forthcoming). “Household Incomes in Tax Data: Using Addresses to Move from Tax Unit to Household Income Distributions.” Journal of Human Resources.

10. See Larrimore (2014).

11. They are lower than estimates that Bricker et al. present that are intended to resemble a tax-unit-based series, but the latter are actually based on families, with the number of families included in the top one percent altered to mimic the number that would be included if the SCF families were actually tax units.

12. Specifically, the top one percent of individuals are identified on the basis of size-adjusted household income, and the total income of the households containing those people is compared to total household income in the entire population. That is, the “top one percent share of income” is technically the share of household income received by households containing the top one percent of individuals as ranked by size-adjusted household income.

13. Auten and Splinter (2019) reconcile the Piketty-Saez fiscal income estimates with CBO pre-tax estimates (including social insurance benefits). They find that after accounting for the social insurance benefits (not included in fiscal income), the different units and ranking in the CBO estimates explain much of the difference between the two sources’ 2014 estimates.
Larrimore, Mortenson, and Splinter (forthcoming) find that switching from tax units to households reduces the top one percent share in 2010 from 15.6 to 13.5, or two percentage points. The 2010 difference between the Piketty-Saez and CBO lines is about three points. However, the Larrimore-Mortenson-Splinter paper compares the share of tax unit income received by the top one percent of tax units (as do the tax unit estimates in Figure 2) to the share of household income received by the top one percent of households (unlike the CBO estimates). The Larrimore-Mortenson-Splinter paper uses an income measure that adds non-taxable Social Security and unemployment benefits to fiscal income and excludes capital gains.
Piketty, Saez, and Zucman (2018) find very little difference in the top one percent’s share of national income whether they use the tax-unit income of tax units or the tax-unit income per individual of individuals.Piketty and Saez (2007) report results that add to fiscal income additional income that is taxed away. They find very little impact on their baseline income concentration estimates.

14. Fixler, Gindelsky, and Johnson (2019). Examine the distribution of personal income, which is similar to the CBO post-transfer income definition. The biggest differences are that it does not include realized capital gains and does not count employee or employer payroll taxes as income taxed away. They find the personal income received by the households with the top one percent of individuals (ranked by size-adjusted household income) rose from 12.5 percent in 2007 to 13.3 percent in 2012.

15. Their estimates include imputed rent of homeowners as income, as well as employer-provided health insurance.

16. The basic trend is driven by accrued gains from equities, but the authors also include gains from business and home ownership.

17. In 2008, accrued capital gains were negative due to the financial crisis, and they were almost as large as the sum of other post-tax and -transfer income. As a result the 2008 share—44 percent—is omitted from Figure 4 so as not to throw off the scale of the chart.

18. Wolff and Zacharias (2009) use a pre-tax, post-transfer income measure that imputes flows of income from wealth (realized or not). They find an increase in the share of income going to the top one percent of families from 14 percent in 1982 to 17 percent in 1988 and to 20 percent by 2000. Smeeding and Thompson (2011) conduct a similar imputation exercise to estimate pre-tax, post-transfer income concentration. They find that it rose from 18 percent in 1988 to around 21.5 percent in 2000 and to 22 percent in 2007. This four-point rise from 1988 to 2007 compares with an eight-point rise in the Piketty-Saez series that includes realized gains and a five-point rise in the series that excludes gains. The Larrimore et al. (2018) estimates are the same in 1989 and 2007.

19. In the PSZ estimates, they are splitting the tax unit income of married couples equally between spouses, then ranking individuals by this individual income. In the AS estimates, they are ranking individuals by size-adjusted tax unit income, then estimating the share of tax unit income received by the tax units that contain the top one percent of individuals.

20. The top one percent shares using the updated PSZ data from 2019 are very close to those from the 2018 paper, so the reconciliation exercise remains relevant.

21. PSZ allocate unreported wages on the basis of reported wages and unreported business profits on the basis of reported business profits. AS estimate unreported income for wages and four types of business income as the residual after subtracting their pre-tax income from national account totals. They allocate 15 percent of underreported income to nonfilers, citing evidence from Johns and Slemrod (2010). Based on the same study, they allocate the rest of underreported income between tax units with negative AGI, other tax units in the bottom 50 percent of AGI, and tax units in income groups within the top half of the distribution. Within each AGI group, underreported wages are allocated according to reported wages. Underreported business income (for each of the four types of business income) is allocated by the absolute value of reported business income (to deal with negative incomes) within AGI groups, but it is allocated only to half the tax units in the bottom 95 percent and 10 percent in the top five percent.

22. Specifically, they argue that unreported passthrough business income is allocated on the basis of positive reported passthrough business income, whereas tax units with negative reported business income tend to have higher underreporting than other “low income” tax units.

24. They also include other nontaxable amounts reported on tax returns, such as the basis portion of Roth conversions.

27. Gerald Auten and David Splinter (2019). Online Appendix to “Top 1 Percent Income Shares: Comparing Estimates Using Tax Data.” AEA Papers and Proceedings 109: 307-311.

28. AS report 40 percent for nontaxed capital income excluding imputed rent, but the equation they give allows for the computation including imputed rent.

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