Thomas Piketty, Emmanuel Saez, Gabriel Zucman · Journal of Economic Inequality 20(1): 255-264 (special issue 'Finding the Upper Tail')

Twenty Years and Counting: Thoughts about Measuring the Upper Tail

16 problems found: 3 moderate · 13 minor

What the paper claims

The US top 1% receives almost 20% of total income and owns almost 40% of total household wealth, so measuring the top tail is crucial.
US top income shares followed a U-shape: high before the 1930s, falling to the 1970s, rising from the late 1970s. The U is 'a bit less pronounced' in pre-tax national income than in fiscal income. The US rise since 1980 is much larger than France's. Post-tax shares are well below pre-tax shares. US pre-tax inequality is 'almost as high now as ... in the early twentieth century', and French post-tax inequality is 'close to its all-time low'. Both countries saw a sharp drop in the first half of the century, 'particularly during World War II'.
Top income shares fell everywhere in the first half of the century, then diverged. English-speaking countries rose sharply after 1980; continental Europe and Japan did not. US and UK shares 'start increasing exactly in 1980 after Reagan and Thatcher come into power. No such break is visible in other countries.' This shows that institutions and policy, not only technology or globalization, drive top shares.
Methodology. Fiscal income misses a growing share of national income ('from 70% in the late 1970s to about 60% in 2018'). Distributional National Accounts (DINA) are 'the systematic solution'. Capitalization 'can work well' in the US. The corporate-individual interface is 'the most important blind spot'. Tax authorities should collect corporate ownership and asset balances (as Chile, Norway and Denmark do, and as the DTC already does).
Rich lists, independent of tax data, show the top .00001% wealth share (about 18 families today) following a U-shape. It 'jumped ten fold' from 0.13% in 1982 to about 1.35% on 1 July 2021, 'significantly higher than' 1913 (Rockefeller at $900m).
Tax progressivity at the very top: Saez and Zucman (2019) estimate that the US tax system was regressive above the top .01% in 2018, with the top 400 paying 23% of economic income against an economy-wide 28%. The ProPublica leak suggests the top 25 pay even less individual income tax relative to wealth.

Every problem found

1moderateconfirmed · previously known · selective presentation

The essay says the richest 1% get 'almost 20%' of income and own 'almost 40%' of wealth. The wealth number counts people in a way (tax-filing units) that gives a higher figure than the way the income number counts them. On the same basis the authors' own figure is about 35%. Other researchers estimate roughly 31-34% for wealth and about 14% for income, though those estimates are disputed. The top 1% clearly hold a very large share, but readers are not told that these exact numbers are contested.

Technical detail and evidence

Why it matters, in detail. 'Almost 40%' is SZ's tax-unit top-1% wealth share (37.9% in 2018). On the equal-split-adult unit used for the companion income figure, the authors' own value is 35.4% (-2.5 pp, about 7%). SZZ (2023) are 2.6 pp lower than revised SZ on the equal-split basis (33.7% vs 36.3% in 2016), which implies about 33% for 2018. For income, PSZ's 18.9% (2018, Sept-2020 vintage) compares with 14.2% (2014) and 13.8% (2019) in AS. Of the 6.0 pp 2014 gap, 2.0 pp comes from AS's allocation of under-reported income and 1.0 pp from retirement income. Both allocations are contested: Gale-Sabelhaus-Thorpe (2023) side mostly with PSZ, and Iselin-Reck (2025) find AS's implied falling misreporting unsupported. Like-for-like or alternative estimates lower the headline levels by about 7% (unit alone) to about 30% (full AS), but never to a small share.

Evidence. Essay p. 255. SaezZucman2020JEPData.xlsx, sheet DataF1-F2(Wealth), 2018 top 1%: revised SZ tax units 37.91%; revised SZ equal-split adults 35.36%; DFA households (Sept-2020 vintage) 32.39%; DFA converted to tax units, excluding durables and unfunded pensions, 38.14%. SZ (2020, JEP 34(4), pp. 8-9): 'the top 1 percent wealthiest tax units owned 38 percent of wealth in 2018'. PSZ Sept-2020 Table TB1: top-1% pre-tax income 18.93% (2018). SZZ (2023, QJE 138(1), Table I, p. 550; equal-split individuals, 2016): 33.7% baseline vs 36.3% revised SZ. AS (2024, JPE 132(7), Table 3, p. 2208): 2014 pre-tax top 1% 14.2% vs PSZ 20.2%; 13.8% in 2019. Fed DFA (2026Q2 vintage): 29.6-30.7% in 2018Q2-2021Q2. Scripts: scripts/headline_levels.py (logs/headline_levels_log.txt).

Why this severity. The figures match the sources cited, and every published estimate still leaves the top 1% with a very large share, so the qualitative point stands. But the wealth figure is about 2.5 pp above the authors' own like-for-like estimate. Credible, though disputed, alternatives would put the levels roughly 7-30% lower. Saying neither the unit nor the range is an important undisclosed caveat on the essay's most-quoted numbers.

The authors' response. Saez & Zucman (2020, JEP pp. 8-9) reconcile the DFA with their series at 38% on tax units. Saez & Zucman, 'Comments on Smith, Zidar and Zwick (2020)' (14 May 2020), Saez & Zucman (2020, NBER w27921, 'Revising after the Revisionists') and Saez & Zucman (2022, NBER w30396) dispute the SZZ and AS alternatives. No response specific to this essay.

2moderatelikely · previously known · selective presentation

When the essay lists the hard problems in measuring the very rich, it mentions only missing data that would, if fixed, probably show even more inequality. It leaves out published criticisms arguing that the authors' methods overstate the top's share. Some of those criticisms led the authors themselves to revise their numbers in 2020. The main rival estimate finds the top 1%'s income share rose about half as much since 1979. That does not make the essay wrong, but it gives a one-sided picture of how settled the measurements are.

Technical detail and evidence

Why it matters, in detail. Roughly 40% of national income is not on tax returns and must be imputed. The essay discusses only imputations whose errors would bias top shares down (non-dividend-paying founders). It omits those argued to bias them up: - uniform fixed-income yields: in the original SZ (2016) series, capitalization factors for interest approached 100 in the low-rate 2010s (Kopczuk 2015; BHKS 2016); SZZ cut the 2016 top-0.1% share from 20.4% to 15.7%; - proportional allocation of under-reported business income and of pension income: 3.0 of the 6.0 pp 2014 level gap in AS. On trend, AS's 1979-2014 rise is 4.8 pp vs PSZ's 9.0 pp. Iselin-Reck (2025) bound the misreporting contribution to the 1962-2019 rise in pre-tax top-1% share at only +0.2 to +0.8 pp, so most of the trend gap lies in other contested allocations. The authors' own 2020 revisions moved the top-1% wealth share by 1-1.5 pp, with larger moves for the top 0.1%. The omission understates model uncertainty; it does not establish a specific bias.

Evidence. Essay pp. 258, 260-261. PSZ Sept-2020 update note (PSZUpdates_Sept2020.txt, Secs. 1.1.1, 1.1.7, 1.2.1): - top-group interest rate set at 1.15x the average (2003-07) and 1.4x (from 2008); - pension reallocation lowers the top-1% wealth share by 1-1.5 points and the top-1% income share by about 0.6 point (2016). AS (2024, Table 3, p. 2208): top-1% pre-tax share +9.0 pp in PSZ (11.2% -> 20.2%, 1979-2014) vs +4.8 pp in AS (9.4% -> 14.2%); after-tax +6.5 vs +1.7 pp. SZZ (2023, Table I): 33.7% / 15.7% (top 1% / top 0.1%, 2016) vs 38.9% / 20.4% under equal returns. Bricker-Henriques-Hansen (2018, FEDS 2018-024; per corpus us-wealth-taxes-03): top 1% in 2011 falls from 40.5% to 33.9% with heterogeneous returns. Kopczuk & Zwick (2020, JEP 34(4), pp. 38-39, 42).

Why this severity. The omission does not invalidate DINA as a framework; Auten-Splinter also distribute national income. Every published alternative still shows a substantial post-1980 rise. But a retrospective on measuring the top tail that omits the assumption-driven critiques gives readers a one-sided view of how reliable the levels and trends are. The main rival estimate halves the post-1979 rise, although that estimate is itself disputed.

The authors' response. Saez & Zucman (2020 NBER w27921; 2020 JEP) defend DINA as 'living series' and report agreement with the DFA once units and concepts are aligned. They incorporated a top interest-rate premium and pension reallocation (Sept 2020). Saez & Zucman (2022, w30396) argue the remaining SZZ gap is concentrated in the top 0.01%. PSZ's August-2026 comment and AS's September-2026 reply continue the dispute over allocations. No response specific to this essay.

3moderateplausible · previously known · external inconsistency

The essay's charts show US inequality falling steeply during World War II. A peer-reviewed 2022 study argues that the older tax-based figures overstate inequality before 1940. On its numbers the fall was about a third smaller and happened more during the Great Depression than during the war. The basic pattern (high, then low, then high again) survives, but the essay does not mention that its story of a wartime 'great levelling' has been challenged.

Technical detail and evidence

Why it matters, in detail. Geloso et al. lower 1928 levels by 4.4 pp (top 1%) and 6.8 pp (top 10%) in fiscal-income terms, with smaller corrections by 1944, so the 1928-44 fall shrinks by about 32%. PSZ's pre-1962 DINA shares are built on the PS tabulations, so the direction carries over to both plotted US series. The magnitude for DINA has not been re-estimated. The plotted DINA top-10% series puts all of its decline in 1939-44, while Geloso et al. assign the larger role to the Depression, so the 'particularly during World War II' claim is the most exposed. Lower early levels would make current US pre-tax concentration exceed, not merely approach, the 1910s-20s. Confidence is limited: the corrections involve judgement calls, have not been answered by PS, and were not reproduced here.

Evidence. Essay p. 258 and Figs. 1-2 (p. 259). Geloso et al. (2022, Economic Journal 132(647): 2366-2391; accepted manuscript pp. 2-3): 1928 top 10/5/1% shares fall from 49.3/38.6/23.9% (PS) to 42.5/32.7/19.5%; the 1928-44 drop shrinks from 16.8/15.8/12.7 pp to 11.2/10.8/8.6 pp; PS 'overstate the magnitude of the observed leveling ... by roughly one third'. Plotted series: the US DINA top-10% pre-tax share (Fig. 2) is 48.2% in 1928, 48.6% in 1939 and 36.1% in 1944, so the entire 1928-44 fall (-12.2 pp) occurs in 1939-44. In the Fig. 1 fiscal top-1% series, 1928-39 is -5.5 pp and 1939-44 is -4.8 pp. logs/early_period_log.txt.

Why this severity. If correct, the revision shrinks the descending arm of the US U-curve by about a third and moves it from WWII to the Depression. That is a noticeable change to a secondary historical claim. The U-shape itself survives, and the comparison with today would favour the essay.

4minorconfirmed · newly identified here · documentation gap

The billionaire chart has no published data file. We rebuilt it from the authors' earlier spreadsheet and an archived copy of Forbes's live billionaire list for 1 July 2021, and it matches closely. The recent points mix two versions of the national wealth totals, which shifts them by a few hundredths of a percentage point. The 'tenfold' rise is measured at a stock-market high; using 2019 or 2020 instead it is about eightfold. These are bookkeeping issues that do not change the picture.

Technical detail and evidence

Why it matters, in detail. Mixing Sept-2020 denominators (1982-2019) with Feb-2022 ones (2020-21) lowers 2017-19 by about 0.02 pp relative to a consistent series and slightly exaggerates the 2019-21 jump. The 2020 value is 0.09 pp (7%) below the authors' own earlier figure. Choosing the 1 July 2021 real-time snapshot adds about 20% to the 1982-based multiple (10.1x vs 8.4x for 2020). The construction can be replicated only by combining a Wayback-archived Forbes API file, a later PSZ vintage and a fractional 18.83-unit rule, none of which the essay documents.

Evidence. Fig. 3 (p. 262), text p. 261. Adjudicator vector extraction of the 42 markers (scripts/fig3_extract.py; linear x-map residual <0.24 pt) and reconstruction (scripts/fig3_reconstruct.py, logs/fig3_reconstruct_log.txt): - 1982-2019 vs SZ (2020) DataF1(Forbes) col Y: max |diff| 0.003 pp; - 2020 plotted 1.125% = $1,177.3bn (SZ 2020 cells AR45:AR62) / $104,731bn (PSZ Feb-2022 TA0) = 1.124%; SZ (2020) X63 = (top 17 + 1.474 x 18th) x 1.02 over $100,016bn = 1.216%; - 2021 plotted 1.353% vs top 18.83 US citizens in the Forbes real-time API, Wayback snapshot 2021-07-01 22:45 UTC ($1,635.1bn), over $120,684bn = 1.355% (exactly 18 people: 1.332%); - with Feb-2022 denominators, 2019 would be 1.093% instead of 1.076%; - ratios: 2021/1982 = 10.1x, 2020/1982 = 8.4x, 2019/1982 = 8.1x.

Why this severity. Once reconstructed, all points except 1913 match public sources to within 0.02 pp. The vintage mixing moves recent points by about 0.02 pp. The endpoint dependence is disclosed by the 'as of July 1st, 2021' date. The roughly eightfold-to-tenfold rise since 1982 is robust.

5minorconfirmed · newly identified here · documentation gap

The 1913 point in the billionaire chart cannot be reproduced from the method the caption describes: standard stock-price data give about 0.95% rather than 0.85%. The claim that today's richest Americans hold a bigger share than the richest of 1913 still holds for July 2021 under any reasonable version. But the gap is smaller than the chart suggests, and before the 2020-21 stock boom it was modest.

Technical detail and evidence

Why it matters, in detail. The 1913 point anchors the left arm of the rich-list U and the 'significantly higher than 1913' claim. With S&P aging (0.955%) the July-2021 excess falls from +60% to +42%, the 2020 excess from +33% to +18%, and the 2019 excess from +27% to +13%. The equity index and denominator vintage actually used are unidentified. Codex's and Claude's reconstructions agree with this one within 0.04 pp. The decline from 1913 to 1957 to 1982 (about 0.85% to 0.30% to 0.13%) is robust to these choices.

Evidence. Fig. 3 and caption (p. 262). Forbes 1918 list (Forbes 2002 reprint): Rockefeller $1,200m, Frick $225m, Carnegie $200m, Baker $150m. PSZ 1913 household wealth $158.07bn and 37.7m tax units (3.77 units in the top 1e-7). Shiller S&P Composite annual average 8.508 (1913) vs 7.539 (1918). Chernow (CNN interview, 1998): Rockefeller 'reached the peak of his net worth in 1913. He was worth $900 million'. Results (logs/fig3_reconstruct_log.txt): no aging 0.911%; S&P annual 0.955%; S&P vs Q1-1918 0.967%; household-wealth ratio 0.804%; plotted 0.847% requires a factor of 0.813. Codex obtained 0.958% (annual) and 0.920% (December prices).

Why this severity. The 1913 value is a disclosed construction. Plausible implementations bracket it (0.80-0.97%), and the essay's comparison for 1 July 2021 holds under all of them. Only the size of the margin, and the comparison for years other than 2021, are affected.

6minorconfirmed · newly identified here · overclaiming

The essay says US and British top incomes started rising 'exactly in 1980' after Reagan and Thatcher took power, and that nothing similar happened elsewhere. In fact the US rise began before Reagan took office, and countries such as Canada and Australia also turned up around then. The bigger point, that English-speaking countries saw much larger increases than France or Japan, still holds, but the timing argument is overstated.

Technical detail and evidence

Why it matters, in detail. The US fiscal series rises 0.8 pp in 1978-80, before the inauguration. Excluding capital gains, the sustained rise starts in 1982, alongside ERTA81. The 1986-88 jump (9.1% to 13.2%, excluding capital gains) coincides with TRA86 and C-to-S conversions, which Kopczuk-Zwick (2020) and AS (2024) attribute partly to reporting shifts. Several non-English-speaking countries have shallow troughs in 1981-83. The divergence argument rests on rise magnitudes (US +4.8 pp from 1980 to 1990 vs France +0.6 pp), not on a unique 1980 break.

Evidence. Essay p. 257 vs p. 258. SZ (2020) DataF3(Income): fiscal 8.36% (1978), 9.00% (1979), 9.15% (1980), 8.93% (1981), 9.76% (1982); national 10.77% (1979), 10.35% (1980). APS (2011) top 1%, excluding capital gains: US trough 1973 (7.74%), 8.2% (1980), 8.0% (1981), 8.4% (1982); UK trough 1978 (5.72%); Canada 1978 (7.60%); Australia 1981 (4.61%); Ireland 1977 (5.64%); France 1983 (6.99%); Italy 1983 (6.34%); Spain, Sweden and Finland 1981. scripts/wtid_timing_b.py, logs/wtid_timing_b_log.txt. Reagan Presidential Library inaugural record (20 Jan 1981), per Codex.

Why this severity. The measured series are unaffected. The cross-country contrast in magnitude (large rises in English-speaking countries, small ones in France and Japan) survives. Only the precise-timing evidence for a policy-triggered break fails.

7minorconfirmed · newly identified here · internal inconsistency

The essay says the share of national income that shows up on tax returns fell from 70% in the late 1970s to about 60% in 2018. The authors' own data give a starting point closer to 64-68%, and depending on the definition the fall is anywhere from about 3 to 10 points. The direction is right; the numbers are generously rounded.

Technical detail and evidence

Why it matters, in detail. Depending on concept, the late-1970s level is 63-68%, not 70%, and the decline is 2.5-9.8 pp. Only the Fig. I concept reproduces a roughly 10 pp fall, and its end level is 53%, not 60%. The case for DINA does not depend on the exact numbers.

Evidence. Essay p. 257. PSZ Sept-2020 Tables TA0, TC1, TSA8, TSA8b, 1976-79 average vs 2018: - PS income control excluding capital gains / national income: 65.7% -> 60.3% (-5.5 pp); - including capital gains: 68.3% -> 65.8%; - positive market income: 67.9% -> 64.6%; - declared labor + capital (% of personal factor income): 63.3% -> 53.4% (-9.8 pp). PSZ (2018) QJE-vintage Figure I data: 65.3% (1976-79) -> 56.2% (2014). Scripts: scripts/fiscal_share_sept2020.py, scripts/fiscal_share_psz2018.py; logs/fiscal_share_*.txt. Codex: 65.9% (1979) -> 60.3% (2018).

Why this severity. It is a rounded motivating statistic whose direction (fiscal income captures a falling share of national income) holds for every definition excluding capital gains. The overstatement of the late-1970s level, by 2-7 pp, does not affect any conclusion.

8minorconfirmed · newly identified here · documentation gap

In the France-US chart, the two US lines come from two slightly different versions of the authors' data, though the caption names only one. The difference is under one percentage point and, if anything, makes taxes and transfers look a little less equalizing than they are. It does not affect any conclusion.

Technical detail and evidence

Why it matters, in detail. The plotted pre-post gap in 2018 (6.46 pp) is 0.64-0.86 pp smaller than either internally consistent pair. Using PSZ's preferred pre-tax series would raise US pre-tax top-10% levels by up to 0.76 pp. No verbal claim about Fig. 2 changes.

Evidence. Fig. 2 and caption (p. 259). Adjudicator check (scripts/fig1_fig2_sources.py, logs/fig1_fig2_sources_log.txt): - saez-AEAlecture.xlsx US pre-tax vs Bozio datafile2 US P90-100: 0 of 104 years differ; - vs PSZ Sept-2020 TB1 top 10%: 55 of 104 differ (max -0.761 pp, 2014); - US post-tax vs PSZ TC1: 0 of 106 differ; - vs Bozio US post-tax V1: 104 of 104 differ (max 0.997 pp). 2018: plotted 44.91% / 38.45% (gap 6.46 pp); PSZ pair 45.55% / 38.45% (7.10 pp); Bozio pair 44.91% / 37.59% (7.32 pp).

Why this severity. Both series are legitimate DINA estimates. The discrepancy is under 1 pp, slightly understates redistribution, and leaves the 1980-2018 US rise essentially unchanged (11.57 vs 11.78 pp).

9minorconfirmed · newly identified here · misrepresentation of source

The chart caption says 'pre-tax' income leaves out all government transfers. In fact the authors' definition includes Social Security pensions and unemployment benefits. The numbers are fine, but the description is wrong in a way that matters to readers comparing incomes 'before' and 'after' government.

Technical detail and evidence

Why it matters, in detail. Counting social-insurance benefits in pre-tax income means the pre-to-post-tax gap omits the redistribution done through Social Security, DI and UI. A reader taking the caption literally would treat the pre-tax line as pre-government income and overstate how much of the Social Security redistribution the gap shows. The factor vs pre-tax difference in the 2018 top-10% share is about 0.4 pp.

Evidence. Fig. 2 caption (p. 259). Saez & Zucman (2020, JEP p. 14): pre-tax national income 'includes all pension income (from Social Security and private pensions) and subtracts all corresponding pension contributions'; p. 21, on Social Security (retirement and disability) and unemployment insurance: 'We include these transfers in our measure of pre-tax income.' Saez (2021, AEA P&P 111, Fig. 1 notes) uses the same caption wording. Codex, public 2018 DINA microfile: top-10% factor income 45.33% vs pre-tax 44.91%.

Why this severity. A labelling error. The series follow the documented DINA convention, and nothing in the comparison changes.

10minorconfirmed · newly identified here · arithmetic or transcription

A footnote says a key inequality measure is 'typically between 2 and 3' and uses 3 to show that the top 0.1% get almost half of the top 1%'s income. In the authors' own international data that measure is usually below 2, which would give about a quarter. It is a footnote illustration, not a result.

Technical detail and evidence

Why it matters, in detail. Typical post-war b of about 1.7-1.8 implies the top 0.1% hold 26-28% of top-1% income. 46% applies to b = 3, a value seen in the pre-1940 era and in the contemporary US (2.8-2.9 in 2005-07). The range is closer to typical for wealth.

Evidence. Essay p. 256, fn. 1. APS (2011, JEL 49(1), p. 15): 'beta coefficients typically vary between 1.5 and 3'. APS Table A24 (1,165 country-years): median b = 1.82; b between 2 and 3 in 36% of cases (87% before 1940, 18% in 1940-79, 24% from 1980); b < 2 in 81% (1940-79) and 72% (1980+). 0.1^(1/b) = 46.4% at b = 3, 27.8% at b = 1.8. scripts/wtid_timing_b.py.

Why this severity. An expository footnote. No finding depends on it.

11minorconfirmed · newly identified here · misrepresentation of source

The essay says Pareto discovered his famous law using Swiss tax data. The 1896 paper it cites relies mostly on English, German and Italian income-tax statistics, with only one Swiss city. A small historical slip.

Technical detail and evidence

Why it matters, in detail. The cited source's evidence is predominantly German, English and Italian income-tax tabulations. Swiss data (Basel) are one of eight series, and no wealth-tax data appear in the article.

Evidence. Essay p. 256. Pareto (1896), 'La courbe de la répartition de la richesse': it opens 'L'impôt sur le revenu nous fournit, pour plusieurs pays...'. The alpha table on p. 3 covers Angleterre 1843 and 1879-80, Prusse 1876-1894, Saxe 1880/1886, villes italiennes and Paris (loyers), and the data tables include Bâle (source K. Bücher) and Oldenbourg 1890 (figs/pareto96-03.png).

Why this severity. A historical-background slip with no bearing on any finding.

12minorconfirmed · newly identified here · misrepresentation of source

The essay says a US securities clearing house, the Depository Trust Company, already keeps track of who ultimately owns shares. The company itself says it only knows which brokers and banks hold the shares, not their customers. The information is spread across many financial firms, so the proposed reform is possible but harder than the essay suggests.

Technical detail and evidence

Why it matters, in detail. Building a beneficial-ownership register for listed equity would require reporting by every participant and custodian down the custody chain, not a single DTC extract. Non-listed firms would need registry or K-1-type reporting. The essay understates implementation cost but not the merit of the proposal.

Evidence. Essay p. 260. DTC Blanket Letter of Representations (SEC EDGAR exhibit 99(k)(4)(b)): 'DTC has no knowledge of the actual Beneficial Owners of the Securities; DTC's records reflect only the identity of the Direct Participants ... The Direct and Indirect Participants will remain responsible for keeping account of their holdings on behalf of their customers.' The same claim appears in SZ (2020, JEP p. 14: DTC 'de facto acts as the ultimate bookkeeper for the ownership of securities').

Why this severity. This affects how easy the proposed data reform looks, not any estimate. The policy point, that tax authorities could collect ownership data from financial intermediaries, still stands.

13minorconfirmed · previously known · selective presentation

The essay says the 400 richest Americans paid 23% of their income in taxes in 2018, less than the 28% average. That figure was a projection made before 2018 tax data existed, and in earlier years the authors' own figures had the richest paying about the average. Later IRS-based work, partly by the same authors, found about 24%, so the 2018 claim has held up.

Technical detail and evidence

Why it matters, in detail. At the time of writing, the 2018 top-400 rate (23.0%) was about 8 pp below TOI's last actual-data year (2016, 30.7%). The post-2017 regressivity was model-projected, and the TCJA cut corporate taxes, which are 10.0 of the 23.0 pp. BSYZ (2025) later find 23.8%/24% for 2018-20 vs 30% overall. Incidence choices cut both ways: shifting part of the corporate tax to labour would lower the top-400 rate further.

Evidence. Essay p. 262. TOI appendix (SZ2019AppendixTables.xlsx), Table C8 (2018): top 400 23.04%; P99.99-top 400 30.36%; P99.9-99.99 33.15%; all 27.70% of pre-tax income (28.29% of national income). Table B1 top-400 rate: 30.7% (2014), 30.8% (2015), 30.7% (2016), 26.9% (2017), 23.0% (2018); all groups 29.3-29.9% (2014-16). Balkir, Saez, Yagan & Zucman (2025, NBER w34170, abstract): top 400 averaged 24% in 2018-20 vs 30% for the population, and 30% in 2010-17. scripts/toi_rates.py, logs/toi_rates_log.txt.

Why this severity. The figures are dated, accurately quoted and later broadly corroborated with IRS data. The omitted caveat bears on robustness, not on the stated 2018 conclusion.

The authors' response. Balkir, Saez, Yagan & Zucman (2025, NBER w34170) match the Forbes 400 to IRS individual, business, estate and gift tax returns for 2010-2020 and report about 24% for 2018-20 vs 30% for the full population.

14minorconfirmed · newly identified here · documentation gap

There are a handful of typos and citation errors, including a percentage in a chart caption that is off by a factor of ten. None changes any result.

Technical detail and evidence

Why it matters, in detail. The '.0001%' typo is a factor-of-ten label error. The title, text and family counts make clear that the figure uses the 1e-7 group. The reference errors complicate source tracing but do not misattribute results.

Evidence. Fig. 3 caption (p. 262): 'The top .0001% includes 3.8 families in 1913, and 18 families today' (at 1e-6 these would be 38 and 180 families). Reference list pp. 263-264. Essay p. 255.

Why this severity. Typographical and referencing slips with no effect on findings.

15minorlikely · newly identified here · misrepresentation of source

The essay gives one reason why the two lines in Figure 1 differ: profits kept inside companies. The authors' own data show that corporate taxes mattered more in the 1950s, and that other differences, such as how married couples are counted, explain the recent gap. It is an oversimplified explanation, not a data error.

Technical detail and evidence

Why it matters, in detail. The national-fiscal top-1% gap peaked at about +4.8 pp in 1950-55, when the corporate tax was the larger untaxed corporate component (6.6% vs 3.8% of personal factor income in 1950). After 1990 the gap turns negative (-1.5 pp in 2018). That reflects equal-split units, realized capital gains included in the fiscal numerator, and tax-exempt pension and fringe income, not retained earnings. The ownership-concentration story may still hold for undistributed profits as a whole.

Evidence. Essay p. 258. SZ (2020, JEP p. 13): 'only the fraction of corporate profits paid out as dividends are included in fiscal income statistics, while all corporate profits are included in national income'. PSZ (2016 NBER w22945, Sec. 6.1): the gap reflects undistributed profits, the rise of pension-fund income and untaxed fringe benefits, and the equal-split unit. PSZ Sept-2020 Table S.A8 (% of personal factor income), retained earnings / corporate tax: 3.8 / 6.6 (1950), 5.0 / 5.7 (1955), 4.1 / 4.5 (1960), 7.3 / 2.1 (2010), 4.0 / 1.6 (2018). National minus fiscal top-1% share: +4.8 pp (1950), -1.5 pp (2018). scripts/corp_components.py, logs/corp_components_log.txt.

Why this severity. This affects only the explanation offered for a figure. The figure's data, and the observation that the national-income U is somewhat flatter, are correct.

16minorlikely · newly identified here · overclaiming

The essay credits the authors with pioneering the idea of spreading national accounts totals across the population. Government statisticians in the US, Australia and at the OECD were already working on this, as the authors' own 2018 paper acknowledges. The authors' approach was new; the idea was not.

Technical detail and evidence

Why it matters, in detail. The distinctive PSZ features are a tax-data base rather than CPS scaled to personal income, coverage of 100% of national income including retained earnings and corporate taxes, and a long historical span. 'Pioneered ... the idea' conflates the method with the concept, which statistical agencies were already implementing.

Evidence. Essay p. 258. PSZ (Nov-2017 version, Sec. I): 'In response to this report, on [sic] OECD Expert Group on the Distribution of National Accounts was created. A number of countries, such as Australia, have introduced distributional statistics in their national accounts (Australian Bureau of Statistic, 2013) ... Furlong (2014), Fixler and Johnson (2014), McCully (2014), and Fixler et al. (2015) describe the ongoing U.S. effort'; fn. 4: 'Earlier attempts include King (1915, 1927, 1930)'.

Why this severity. Credit attribution only; no empirical claim is affected.

Claims examined and rejected

Problems one auditor raised that did not survive checking.

Figure 3 cannot be reproduced from public materials (moderate): the 0.13%, the 1.35% (1 July 2021) endpoint and the tenfold trend cannot be independently certified. — Largely rejected and downgraded. The adjudicator reproduced the July-2021 endpoint: an archived Forbes real-time snapshot (Wayback, 2021-07-01 22:45 UTC; top 18.83 US fortunes, $1,635bn) over PSZ Feb-2022 2021 household wealth ($120.7tn) gives 1.355% vs 1.353% plotted. The 2020 point (1.124% vs 1.125%), the 1957 point (0.300%) and the 1982-2019 points (exact match to SZ 2020) also reproduce. The tenfold arithmetic is correct. What remains (the 1913 point and undocumented vintages) is kept as minor issues F4-F5.
With Forbes's own 1918 valuation of Rockefeller ($1.2bn, aged back), the 1913 share would be 1.24%, so July 2021 is only 9% above 1913 and 2019-2020 are below it. — Not evidence of an error. The essay explicitly uses Chernow's $900m peak for 1913 (confirmed in Chernow's 1998 CNN interview). This is the better-documented figure, and B.C. Forbes's 1918 $1.2bn exceeds it. Swapping in a less credible input is an alternative assumption, not a reproduction failure. The non-reproducibility under the stated method is retained in F5.
Footnote 3 overstates US information on pass-through ownership, given that '20% of the income goes to unclassifiable partners, and 15% ... is earned in circularly owned partnerships' (Cooper et al. 2015/16). — The footnote says the US 'already collects such information' for partnerships and S-corporations, and calls them 'sometimes very large and complex'. That is accurate: Cooper et al. themselves use IRS K-1 records to 'identify pass-through business owners'. Multi-tier opacity limits tracing but does not make the statement false. Only the DTC part is retained (F13).
Fig. 2 caption says 'from 1910' although the US series starts in 1913. — The figure includes the French series, which starts in 1910 (saez-AEAlecture.xlsx), so the caption's range is accurate for the figure.
Group sizes are inconsistent across the authors' documents (SZ 2020 text '17 tax units today and 10 in 1982' vs 18.47 and 11.05 in their sheet), and '18 people' (text) vs '18 families' (caption). — The 17/10 vs 18.47/11.05 inconsistency is in Saez-Zucman (2020), not in this essay. The essay's '18' is a rounding of 18.8 (2021 PSZ tax units x 1e-7). The July-2021 point reproduces best with 18.83 units. 'People' and 'families' both loosely describe tax units here.
The Fed DFA's 30-31% top-1% share is a competing estimate against which 'almost 40%' is 15-25% too high. — Partially rejected. The DFA is household-based and, in the Fed concept, includes durables and unfunded pensions. Saez-Zucman (2020, pp. 8-9; DataF1-F2 col R) convert it to tax units, excluding those items, and obtain 38.1% for 2018. The like-for-like competitors are the authors' own equal-split figure (35.4%) and SZZ (2.6 pp lower than SZ on that basis), which F1 uses. The 2026 DFA vintage cited (29.6-30.7% in 2018-21) also post-dates the essay.
(Examined and not scored by Codex) The essay misrepresents Feldstein (1995) as 'celebrating' top-income growth as proof that 1980s tax cuts succeeded. — Agreed with Codex: a rhetorical characterization, not a misquotation. Feldstein (1995) does interpret the post-TRA86 rise in high-income taxable income as a behavioural response to lower rates with favourable efficiency and revenue implications.
(Examined and not scored) Fig. 3 is not 'totally independent from tax data', or is circular. — Agreed with Codex: no circularity. The numerators come from Forbes and Fortune lists and the denominators from national-accounts household wealth; tax-unit counts are used only to size the group.
(Both auditors examined) Ravallion (2022) and Yonzan et al. (2022), in the same JOEI issue, undercut the essay's claim that surveys cannot capture the top tail. — Both auditors judged it weak and we agree. The essay's claim concerns the very top (top 0.1% and 0.01%) and correct sampling arithmetic (10 and 1 units in a sample of 10,000). Yonzan et al. themselves find tax-survey gaps concentrated in the top 1% in the US. The essay also explicitly credits the SCF's tax-based oversample.

Audit notes

What reproduced. Reproduced: - Versions: the three versions (online-first, paginated issue, HAL accepted manuscript) are textually identical apart from pagination. - Fig. 1: national-income series = PSZ Sept-2020 TB1 top 1%, 106/106 years exact; fiscal series = PS 'mix method' (SZ 2020 DataF3). Falls of 12.8 pp (fiscal) and 12.0 pp (national); rises of 12.1 and 8.6 pp ('a bit less pronounced' holds). - Fig. 2: France lines and the US pre-tax line = Bozio et al. (2020) datafile2 exactly; US post-tax = PSZ TC1 exactly. All verbal claims hold: US pre-tax 44.9% (2018) vs 45.5% (1913-29 average); post-tax 38.4% vs 42.9%; since 1980, US +11.6 pp vs France +4.4 pp; French post-tax 25.0% vs record low 23.75% (1983). - Headline levels: 18.9% income (PSZ 2018, Sept-2020) and 37.9% wealth (SZ 2020, tax units, 2018) match the cited sources. - Fig. 3: 1982-2019 = SZ (2020) Forbes series (max |diff| 0.003 pp); 1957 = Fortune bracket midpoints (0.300%); 2020 = Forbes real-time of 24 June 2020 over Feb-2022 2020 wealth (1.124% vs 1.125%); 1 July 2021 = archived Forbes real-time snapshot, top 18.83, over Feb-2022 2021 wealth (1.355% vs 1.353%); 2021/1982 = 10.1x. - Tax rates: TOI C8(2018) 23.04% (top 400) and 27.70% (all). ProPublica: top 25's $13.6bn of income tax on $401bn of wealth growth; 0.25-0.39% of wealth per year vs about 0.75-1.0% (TOI top 400, federal plus state income tax, relative to Forbes-400 or TOI wealth). - Arithmetic: footnote-1 Pareto algebra and the survey-sample arithmetic. Not reproduced: - Fig. 3's 1913 point: 0.91-0.97% under the stated method vs 0.85% plotted. - '70% -> 60%' on any single definition: 65.7 -> 60.3 (excluding capital gains), 68.3 -> 65.8 (including), 63.3 -> 53.4 (PSZ Fig. I concept). - The b 'typically 2-3' range: median 1.82 in WTID. - 'Exactly in 1980' timing. Not attempted: re-estimating the PSZ/AS/SZZ disputes (these need confidential IRS data) and the Geloso et al. corrections.

Limits of this audit. - No replication package exists. Fig. 3 values come from vector extraction of the published PDF (error about ±0.003 pp). - The equity index and vintage behind the 1913 point are unknown. - The Forbes real-time snapshot used (Wayback, 1 July 2021 22:45 UTC) may differ in timing from the authors' own. - The 1957 Fortune brackets come from a secondary (Wikipedia) transcription. - The PSZ vs Auten-Splinter and SZ vs SZZ disputes rest on confidential IRS microdata and are reported, not adjudicated. Several critique magnitudes (BHH 2018, FGMP 2016, Deaton 2020, Iselin-Reck 2025) rely on corpus entries and auditor reading rather than fresh re-reading. - Geloso et al.'s corrections were not re-estimated, and their effect on the DINA series in Figs. 1-2 is inferred in direction only. - Reagan's inauguration date and DFA vintages were taken from the auditors' cached sources. - Severity is judged relative to this short perspective essay. The same disputes may be more serious for the underlying papers (PS 2003, SZ 2016, PSZ 2018), which are audited separately.