Thomas Piketty, Emmanuel Saez · Science 344(6186): 838-843

Inequality in the Long Run

17 problems found: 8 moderate · 9 minor

What the paper claims

A century ago (on the eve of WWI) top-decile income shares were higher in Europe than in the United States.
Income and wealth inequality dropped dramatically in the first half of the 20th century: in Europe the top-decile income share fell from 45-50% to about 30%, and the top-decile wealth share 'from about 90% to less than 60%', between 1914 and the 1950s-1960s.
US income inequality surged back from the 1970s, so the US is now much more unequal than Europe; on the fiscal measure US concentration is higher than ever in US history and slightly higher than pre-WWI Europe.
Wealth shows the same 'great inequality reversal': the top-decile wealth share was higher in Europe than in the US a century ago and is lower today; US wealth concentration never reached Europe's pre-WWI level; the bottom 50% always owns less than 5%.
Private wealth/national income followed a pronounced U-shape in Europe and a flatter path in the US; interpreted through beta = s/g ('Capital is back because low growth is back') and a capital share rising with beta (sigma > 1).
Wealth-concentration interpretation: r - g was large throughout history; the after-tax-and-loss return fell below growth in the 20th century, which 'simple simulations' show explains why concentration did not return to pre-WWI levels; r - g is likely to widen again in the 21st century; Forbes rankings show top global wealth growing 6-7% a year in real terms over 1987-2013, more than three times average wealth (~2%).
Income-dynamics interpretation: the first-half-century compression came primarily from the fall of top capital incomes, with 'no structural decline in the inequality of labor income' (against Kuznets); the recent US rise is driven by top labor incomes and executive pay; SOM: top-tax-rate cuts correlate with rising pre-tax top shares, which 'must reflect' behavioural responses, and the absence of growth effects is consistent with rent-seeking.

Every problem found

1moderateconfirmed · newly identified here · internal inconsistency

The paper says the richest tenth's share of European wealth had already fallen from about 90% to under 60% by the 1950s-60s. Its own chart shows the share was still about 75% in the 1950s and 68% in the 1960s, and only dropped below 60% around 1980. Europe's wealth equalization was real, but slower and more of it happened in peacetime than the text says.

Technical detail and evidence

Why it matters, in detail. On the paper's decennial series the European top-decile wealth share falls 14.2 pp by the 1950s and 21.3 pp by the 1960s (claimed: >= 29.5 pp); the first decade below 60% is the 1980s; WID-2026 gives the same chronology, with 60% of the 1910-1980 fall after 1950. The first-half-century wealth compression is therefore about half the size the text states. The remainder coincides with 1950-1980 (high growth, high taxation, r - g low in the paper's own Fig. 4), so the error does not contradict the r - g mechanism, but it does contradict the implied attribution of most of the fall to the 1914-45 shocks. 2010 levels and the reversal are unaffected.

Evidence. PikettySaez2014Science.xlsx DataF2!O16,O20:O23 = 0.8955, 0.7536, 0.6822, 0.6027, 0.5928 (= (B+F+L)/3); chart2.xml plots DataF2!$O$12:$O$26; HAL halshs-01053609 identical sentence; Piketty (28 May 2014) 'Technical appendix... Addendum: Response to FT', p. 3; WID-2026 shwealj992 p90p100 Europe-3: 91.8 (1910-13), 76.6 (1950s), 69.0 (1960s), 59.6 (1970s), 54.0 (1980s); AAM (2017) CSEF WP 464 abstract. Adjudicator scripts: scripts/science_core_checks.py, scripts/wid_key_numbers.py.

Why this severity. Fig. 2, the paper's evidence, is correct, and the century-scale decline and the Europe-US reversal are untouched, so the core finding survives. But the text overstates the decline achieved by the 1950s-60s by 8-15 pp (30-50% of the stated fall) and moves about half of Europe's wealth de-concentration from the post-1950 decades into the war era. This is the upper end of moderate: it misinforms readers about timing, which bears on the shocks-versus-postwar-policy interpretation, without altering the data.

The authors' response. None specific. Piketty's 28 May 2014 FT response, written about the same data, describes the European decline as lasting 'until the 1960s-1970s (down to about 50-60%)', consistent with the data and not with the Science sentence.

2moderateconfirmed · newly identified here · arithmetic or transcription

The paper says the world's very richest grew their fortunes by 6-7% a year after inflation from 1987 to 2013, more than three times faster than average wealth. Fixing two spreadsheet mistakes gives about 4.5% a year, roughly twice as fast as average wealth. The richest still pulled ahead, but by much less than claimed.

Technical detail and evidence

Why it matters, in detail. Real growth 1987-2013: 6.42%/6.77% -> 4.50%/4.47%. Fixing only the back-cast gives 5.05%/5.39%; fixing only the 2013 endpoint gives 5.86%/5.83%. The ratio to average-wealth growth falls from 3.2-3.4x to 2.2x, and excess growth from 4.4-4.8 pp to about 2.5 pp. Upper bound from the sheet's 1987 count and total plus the actual 2013 means: 4.80%. The same numbers appear in Capital Table 12.1 and Piketty-Zucman (2015, Handbook Table 15.1). The 1987 base remains a back-cast because no machine-readable 1987 list exists.

Evidence. Chapter12TablesFigures.xlsx (md5 81aad200...) TS12.3 U7:U9, Z7:Z9, N7 (= 1.3*2.1), U33 = T33*V33, Z33 = Y33*AA33, B7 = 140, C7 = 295, S7 = 142.54; T12.1!B9 = 0.001 + TS12.3!AP37; Forbes API lists 2013 (1,426 entries, $5,432bn) and 2010 (sheet reproduces: 9.31 vs 9.31; 20.81 vs 20.90). Adjudicator script scripts/forbes_recompute.py (output work/forbes_recompute.txt) reproduces both auditors' corrected values.

Why this severity. The Forbes figure illustrates the r > g interpretation; it is not one of the paper's three basic facts. Corrected, top global fortunes still grew about twice as fast as average wealth, so the qualitative point survives. But the stated growth rate is about 2 points a year too high, and the excess over average wealth growth is roughly halved.

3moderateconfirmed · newly identified here · speculative assumption

The paper's chart says that in the 20th century the after-tax return on wealth fell below the economy's growth rate worldwide, and uses this to explain why the rich never regained their pre-1914 share of wealth. In fact the 'world' return is a French series with several assumed deductions. Whether it falls below growth after 1950 depends on an assumed 30% tax rate; with a somewhat lower rate it would not. The chart is an illustration built on assumptions, not a measurement.

Technical detail and evidence

Why it matters, in detail. 1950-2012: with pre-tax r = 5.33% (French 'pure') and world g = 3.78%, r_after < g requires an average capital tax rate of at least 29% (no loss adjustment) or 19.7% (0.5 pp loss). Any average rate below those thresholds reverses the sign (e.g. 25% without the loss adjustment: +0.22 pp), as does using France's observed rather than 'pure' returns (+0.95 pp at the published assumptions). 1913-50: the 2.5 pp/yr loss alone produces the inversion. Forward-looking: r > g in 2050-2100 follows from the UN growth slowdown regardless of taxes, but in 2012-50 only if capital taxes fall. Pre-tax total returns exceed g in nearly all peacetime years 1870-2015 (Jorda et al. 2019), so the 20th-century reversal is entirely a tax-and-loss construct.

Evidence. PikettySaez2014Science.xlsx DataF4 B11:D15; C12 = 0.7*B12-0.025, C13 = 0.7*B13-0.005, C14 = 0.9*B14; notes A18-A20. Chapter6TablesFigures.xlsx TS6.2 D7:E26; E32 = AVERAGE(E17:E19)-0.01; E31 = 4.937% vs 4.997% hard-coded in DataF4 B11. Adjudicator script scripts/science_core_checks.py.

Why this severity. Fig. 4 carries the paper's main interpretive mechanism but none of its descriptive facts. The 1913-50 inversion reflects documented wartime capital losses (Piketty-Zucman 2014, Table VIII) and is plausible. The 1950-2012 inversion is knife-edge, resting on tax and loss parameters that defensible alternatives reverse, so 'r fell below g in the 20th century' is a calibrated conjecture, not a measurement. It is not classed as circularity because the caption does say 'after tax and capital losses' and the paper calls its interpretations 'little more than an informed discussion'.

The authors' response. The spreadsheet note (DataF4!A20) discloses the 30%/10%/0% tax and capital-loss assumptions; Capital ch. 10 presents the series as illustrative. No response specific to the Science figure was located.

4moderateconfirmed · previously known · methodology

For the US before 1960 the paper had no direct data on the richest tenth's share of wealth. It estimated that share by adding a fixed 36 points to the richest 1%'s share, and some points labelled 1980 and 2010 are really 1989 and 2007 survey figures. These shortcuts make the early US numbers uncertain, but later and better data still show Europe was more unequal than the US a century ago and less unequal today.

Technical detail and evidence

Why it matters, in detail. 1910 Europe-US gap: 8.4 pp published; 1.4 pp with a 43-point P90-99 share; about 16 pp without the household factor; 13.3 pp in WID-2026. The WID US figures are capitalization-based and contested on return heterogeneity (us-wealth-taxes-03, -06). 2010: 71.5% plotted (2007 SCF) vs 74.4% in the actual 2010 SCF and 73.0% in WID. The unit mismatch (US households vs European individuals) biases US shares up relative to Europe by an unquantified amount; on equal-split adults (WID) the 2010 US-Europe gap is still +13.3 pp.

Evidence. Chapter10TablesFigures.xlsx TS10.1DetailsUS G6:K16 and notes I17:I21; DataF2 I12:I26 and note A28; chart2.xml range DataF2!$I$12:$I$26; Sutch (2017) pp. 595-597; Kennickell (2009) Table 4. Adjudicator SCF recomputation (scripts/scf_top10.py): 2010 SCF top 10% 74.39%, top 1% 34.07%, matching Auditor B.

Why this severity. The US side of the a-century-ago wealth comparison is largely assumed. Using Soltow's 43-point 1870 gap instead of the 36-point markup would shrink the 1910 Europe-US gap from 8.4 to 1.4 pp. But independent later evidence (Saez-Zucman/WID: US 78.5% vs Europe 91.8% in 1910-13) supports the gap, and the modern US endpoint is if anything understated, so the reversal survives while the historical US levels are imprecise.

The authors' response. Piketty's 28 May 2014 FT response concedes the 1970 estimate is 'relatively uncertain' and 'could have been explained more clearly', and designates the Saez-Zucman capitalization series, which shows a larger recent rise, as the reference US series. No response to Sutch was located.

5moderateconfirmed · previously known · data error

The paper's UK figure for the richest tenth's share of wealth (about 70%) comes from estate records covering only about 3 in 10 adults, and effectively treats everyone else as owning nothing. Better estimates from the same kind of records put it at about 52-56%; one of their authors (Atkinson) built the original UK estate-based series. Europe is therefore somewhat less unequal today than the paper says, which actually makes the US-Europe contrast stronger.

Technical detail and evidence

Why it matters, in detail. Equating the top 9.3% of all adults with the top 30% of the identified population is an upper bound that is exact only if excluded adults hold zero wealth. With excluded wealth at 15-25% of the total, the share is 53-60%. EU-3 2010: 63.9% -> about 58.6% with the UK at its WID value, and the Europe-US gap widens from 7.6 to about 12.9 pp. In WID-2026 a European rise after 1980 persists (54.0% -> 59.7%), driven by France and Sweden, but from a lower level than plotted.

Evidence. HMRC Personal Wealth Statistics Table 13.8 (2008-10 row; 69% of adults not in the identified population), cached at /mnt/zdata/downloads/hmrc-personal-wealth/Table_13.8.xlsx; DataF2 F24:F26 and notes A36-A37; Alvaredo, Atkinson & Morelli (2017), CSEF WP 464, p. 34 (published J. Public Econ. 162: 26-47, 2018, https://doi.org/10.1016/j.jpubeco.2018.02.008); WID-2026 shwealj992 GB. Adjudicator script scripts/science_core_checks.py.

Why this severity. The UK level is overstated by about 15-19 pp, moving Europe's 2010 average by about 5 pp. That undermines the secondary claims about Europe's current level, its post-1980 rise in the paper's own series, and the UK being above continental Europe. It strengthens rather than weakens the central US-Europe wealth reversal.

The authors' response. Piketty's 28 May 2014 FT response defends the ~71% estate-based figure against the ONS Wealth and Assets Survey (44%), arguing that surveys miss the top. The problem here, however, is the treatment of the population outside probate, and the estate-based AAM estimate (~52%) is far below 71%.

6moderatelikely · previously known · external inconsistency

The paper's US numbers come straight from tax returns, which captured more top income after 1986 partly because tax rules and filing patterns changed, not only because top incomes grew. The authors' own later, broader measure still shows a big rise in US inequality and a US well above Europe, but the rise is roughly a fifth to a third smaller than in this paper's chart.

Technical detail and evidence

Why it matters, in detail. PSZ (2018) decomposition of the 1980-2014 rise: 15.7 pp (fiscal, tax units) -> 14.0 pp (national income, tax units) -> 12.8 pp (national income, equal-split adults). About half of the shortfall comes from the income concept (retained earnings, tax-exempt capital income) and half from the unit. Consistent-unit DINA cross-country comparison, 2010: US 43.8% vs EU-4 34.2% (gap 9.6 pp, vs 13.2 pp plotted). Realized capital gains add 1.6 pp to the plotted US 2010 value. AS (2024, JPE) put the 1979-2019 rise in the top-1% pre-tax share at about half the fiscal-income rise (their allocations are disputed: us-income-10 to -13).

Evidence. PSZ2018MainData.xlsx sheet 'Data' col 67 (top 10% pre-tax, equal-split), col 98 (pre-tax national income per tax unit), col 99 (fiscal income incl. KG); WID-2026 sptincj992 and sfiinct992 p90p100 for US, FR, GB, DE, SE; DataF1 cols D, I; Chapter9 CopyTS8.2 cols B (incl. KG) vs G (excl. KG). Adjudicator scripts: scripts/psz_decompose.py, scripts/wid_key_numbers.py.

Why this severity. C3's direction holds under every measure checked, including the authors' own DINA and a consistent-unit cross-country comparison: a large US surge since the 1970s, with the US now well above Europe. The surge and the gap are 18-33% smaller on the authors' later preferred concept, and plausibly smaller still on Auten-Splinter's. That is a noticeable but not transformative qualification of a series the paper explicitly labels as fiscal income.

The authors' response. PS (2003) acknowledged the 1986-88 jump as partly due to 'fiscal manipulation'. PSZ (2018) moved to national-income totals and equal-split adults, partly to neutralize falling marriage, and still find a large rise. PSZ and Saez-Zucman dispute Auten-Splinter's allocations.

7moderatelikely · previously known · speculative assumption

The paper's slogan 'capital is back because low growth is back' rests on a simple formula that assumes people keep saving the same share of income and that asset prices don't drift. Under other reasonable assumptions, slower growth raises wealth relative to income by much less. A good part of Europe's recent rise in wealth came from rising house and asset prices rather than slow growth. The rise in wealth is real; the explanation is less certain than presented.

Technical detail and evidence

Why it matters, in detail. Constant net s: halving g doubles beta (3.33 -> 6.67). Constant gross s matched to the same starting point: beta -> 3.94-4.90 (+18% to +47%) for delta = 10%-2%. PZ Table V: residual capital gains explain 25-58% of 1970-2010 national-wealth growth in France, Italy and the UK (-14% in Germany, 28% in the US). The sigma > 1 inference holds only in a one-sector competitive model with gross concepts; net and housing-adjusted evidence points below 1.

Evidence. Science pp. 840-841; Piketty & Zucman (2014) QJE 129(3) Table V, p. 1286; gross-saving sensitivity K/Y_net = s_G/(g + delta(1 - s_G)) computed by both auditors (Codex: +18.2% to +37.9% for delta 10%-3%; Claude: +32% to +47% for delta 4%-2%) and re-derived by the adjudicator.

Why this severity. The descriptive U-shape (C5) is unaffected. The causal reading, and the forecast that low growth will push beta up sharply, rest on a contestable saving assumption: under constant gross saving, halving growth has about a fifth to a half of the implied effect. A quarter to over half of the 1970-2010 rise came from asset-price gains. The paper does state the no-relative-price-change assumption, so this is an overstated interpretation rather than an error.

The authors' response. Piketty (JEP 2015, pp. 81-82) concedes that net saving need not be constant and that beta will not explode as g -> 0, and moves toward multi-sector, relative-price and bargaining explanations (AER P&P 2015). Piketty & Zucman (2014) acknowledge large capital-gains contributions in some countries.

8moderateplausible · previously known · external inconsistency

Another research team redid the early US tax-data calculations and found that inequality in the 1920s-30s was lower than Piketty and Saez estimated. If they are right, the fall in US inequality around World War II was about a third smaller, though the overall U-shape remains, and today's US inequality looks even more exceptional by comparison.

Technical detail and evidence

Why it matters, in detail. Annual, PS vs GMMS: 1928 49.29% vs 42.47%; 1944 32.51% vs 31.25%. Decennial: 1930s 45.11% vs 38.91%; 1950s 33.69% vs 31.12%. The pre-1960 peak falls from 49.3% to 42.5%, below the 2010 fiscal value (47.9%). GMMS's 1917 value (35.2%) suggests the imputed US 1910-13 point (40.9%) may also be high, which would widen Europe's lead in 1910.

Evidence. GMMS replication workbook DataAppendix-6-7-21.xlsx, sheet 'TopIncomeShares' (col D 'PS latest updated file (with full K-gains)' vs col I 'Corrected - Cumulative + full K-gains'); DataF1 col D. Adjudicator script scripts/gmms_effect.py (output work/gmms_effect.txt). PS harmonization schedules in Comp1398.xls were inspected by Auditor B.

Why this severity. If correct, the US leg of the 'dramatic first-half drop' is about a third smaller, a noticeable change to part of C2. The European decline and the abstract's other claims are unaffected or strengthened, and the correction itself is contested and unanswered.

The authors' response. No response by Piketty or Saez located. PS (2003) annotations describe the harmonization multipliers as rounded 'reasonable' values informed by composition tables.

9minorconfirmed · newly identified here · documentation gap

Several of the 'a century ago' income numbers for the US, UK and France are estimates filled in before proper income-tax statistics existed, not figures read off tax returns as the caption suggests. The available hard data and the authors' later reconstructions still show Europe was more unequal than the US around 1910, so the conclusion stands; the caption oversells the data.

Technical detail and evidence

Why it matters, in detail. Full-decade 1910s means give Europe 44.7% vs US 41.0% (gap 3.7 pp vs 4.9 pp published); WID fiscal series (France, Germany, Sweden; WID has no UK top-decile data before 1918) give 45.1% vs US 40.7%. At the very top, observed 1913 top-0.1% shares are UK 11.2%, Sweden 9.0% (1912), US 8.6%, Germany 8.1%, so the ordering at the top 0.1% rests mainly on the UK; at the top 1%, Germany (17.8%) is roughly equal to the US (18.0%). GMMS (F8) would lower the US further.

Evidence. Chapter8TablesFigures.xlsx DetailsTS9.2 B6 = AVERAGE(B14:B19); DetailsWTIDSeries AH45:AH54 (= AE*(U$55/AE$55)/100); Chapter9TablesFigures.xlsx CopyTS8.2 B6 = 0.405 and B16:B22; Capital technical appendix pp. 50-53; DataF1 D6, D16, E6, E16.

Why this severity. The imputations set the size of the 1910 gap (4.9 pp) but not its direction. Observed German (43.7%) and Swedish (44-46%) top-decile shares exceed the first observed US values (40.3% in 1917-19), and the authors' later DINA gives Europe 50.1% vs US 42.6%. This is a caption/documentation problem.

The authors' response. Capital's technical appendix (pp. 50-53) discloses that pre-income-tax US and French values are adjusted contemporary estimates. The 2014 FT response explains that decennial values use the closest available years.

10minorconfirmed · newly identified here · external inconsistency

The paper says US income concentration is now the highest in US history and a bit above Europe's before World War I. That is true on the tax-return measure it uses. On the authors' own later and broader measure, today's US is slightly below its 1920s-30s peak and below 1913 Europe, so these two eye-catching comparisons depend on how income is measured.

Technical detail and evidence

Why it matters, in detail. Record margin (US now vs its pre-war peak): +1.1 pp fiscal annual, +0.5 pp DINA per tax unit, -1.0 pp PSZ-2018 equal-split, -3.4 pp WID-2026. Margin over 1913 Europe: +2.1 pp fiscal incl. capital gains, +0.5 pp excluding them, about -6 pp DINA.

Evidence. Chapter9 CopyTS8.2 cols B and G; Saez TabFig vintages (Auditor A); PSZ2018MainData 'Data' cols 67, 98, 99; WID-2026 sptincj992 p90p100. Adjudicator scripts scripts/psz_decompose.py and scripts/wid_key_numbers.py.

Why this severity. The text explicitly qualifies the record claim ('According to this measure'). Both claims are secondary to the abstract's 'much more unequal than Europe'. On equal-split DINA the US remains within about 4-6 pp of 1913 Europe ('approximately the same level', as the paper puts it), so no conclusion changes.

The authors' response. The paper itself says 'According to this measure'; the DINA series post-date the article.

11minorconfirmed · newly identified here · misrepresentation of source

The paper says that when inequality fell in the first half of the 20th century, the wage gap between top earners and everyone else did not lastingly shrink. That is true for France, but the authors' own earlier US study shows top US wage shares fell sharply during World War II and stayed low for about 30 years. The main point, that collapsing fortunes rather than a natural development process drove the decline, still holds.

Technical detail and evidence

Why it matters, in detail. 1940-45: US top-decile wage share -6.8 pp (-22%), top-1% -2.6 pp (-32%); top-1% wage share still 5.2% in the 1960s, with pre-war levels regained only in the 1980s. 'Primarily capital' holds for 1920s->1950s (72% of the top-decile fall in the top 1%), but not for 1940-45 (64% in P90-99, a wage-dominated group).

Evidence. Piketty & Saez (2003) QJE 118(1): abstract and pp. 29-31, 36-37 (cached /mnt/zdata/downloads/ps2014-science/PikettySaez2003QJE.pdf); Capital Chapter8 TS8.2 J46/K46 vs J51/K51 (Auditor B); decennial decomposition by Auditor A (72% of the 1920s->1950s US top-decile fall in the top 1%).

Why this severity. Downgraded from both auditors' 'moderate'. The paper's conclusion, that the compression was mainly a capital-income phenomenon not explained by a Kuznets process, is consistent with ref. 11, which attributes the persistent US wage compression to wartime controls and norms rather than technology. 'Structural' can also be read in that Kuznets sense. The sentence misstates the US labor-income record but changes no conclusion.

12minorconfirmed · newly identified here · documentation gap

The paper says 'simple simulations' show that low after-tax returns explain why the rich never regained their pre-1914 share of wealth. It neither shows nor cites those simulations, and we could not find them in the authors' related publications. The explanation may be right, but readers cannot check it.

Technical detail and evidence

Why it matters, in detail. Only comparative statics exist (inverted Pareto coefficient rising with r - g). No transition simulation calibrated to 1914-2010 was found. Given Fig. 4's assumed inputs (F4) and convergence half-lives of decades (GLLM 2016), whether r - g quantitatively accounts for the post-1945 non-recovery is untested.

Evidence. Science p. 842; Capital technical appendix (ch. 10 notes on Pareto coefficients: 'For numerical simulations see Dell 2005. See also the numerical simulations presented in Piketty-Zucman, Wealth and Inheritance in the Long Run, p. 42-47'); Piketty & Zucman (2015) Handbook ch. 15, Secs. 15.5.4-15.5.5. Auditor B re-derived the Handbook's binomial model (inverted Pareto b = 2.28 vs 3.25 for r - g = 2% vs 3%).

Why this severity. The steady-state link between r - g and the Pareto tail is standard, and the paper frames its interpretations as 'little more than an informed discussion'. The gap is that a specific quantitative claim cannot be checked; that limits the interpretation but does not overturn it.

The authors' response. Piketty (JEP 2015) frames r - g as a determinant of long-run wealth inequality with long lags rather than of short-run changes; no simulation was located.

13minorconfirmed · previously known · overclaiming

The supplement says the link between lower top tax rates and higher top incomes 'must' be caused by the rich responding to tax rates. It could also run the other way (richer elites lobbying for lower taxes), or reflect income simply being reported differently, alternatives the paper's own source discusses. The policy conclusion is less firmly grounded than the wording suggests.

Technical detail and evidence

Why it matters, in detail. Logical overreach: removing the mechanical channel leaves reverse causality, common shocks and reporting responses. The 1986-88 TRA86 jump (+4.0 pp in the top-1% share excluding capital gains) is a documented reporting-sensitive margin. Short-run reported-income elasticities of about 1.2-1.5 with positive GDP effects (MMO 2018) cut against inferring a near-zero real elasticity from flat cross-country growth correlations.

Evidence. SOM pp. 2-3; PSS (2014) AEJ:EP 6(1) pp. 248-251, 255-257 (read by Auditor B); Chapter8 TS8.2 rows 92-94; TabFig2012prel income-growth table (Auditor A).

Why this severity. Downgraded from Auditor B's 'moderate'. The issue is confined to the supplementary policy discussion, which elsewhere hedges ('consistent with'; 'a difficult empirical problem'). It overstates identification but changes no descriptive finding.

The authors' response. PSS (2014, pp. 255-257) state that the correlation 'does not prove a causal link' and that growth regressions are not fully robust. The PS (2006) reply to Reynolds argues that the broad rise also appears in wage income.

14minorconfirmed · documentation gap

'Europe' in the paper means different groups of countries in different charts, and one chart quietly adds Italy, the country with the most wealth relative to income, partway through. Keeping the same countries throughout makes Europe's recent rise in wealth relative to income about 13% smaller, but the overall pattern is unchanged.

Technical detail and evidence

Why it matters, in detail. Composition effect on Fig. 3: +0.42 years in 2010 and +0.41 in 2000 from adding Italy, i.e. 13% of the 1950-2010 rebound. 'Now back to about 5 to 6 years' becomes about 5.0 (and 4.5 in 2000) on fixed composition. Weighting effects are 1.7-2.0 pp on the income and wealth shares, which leaves the US-Europe orderings unchanged.

Evidence. DataF3 F16 = AVERAGE(C16:E16) vs F17:F20 = AVERAGE(C:E, R); chart3.xml plots DataF3 col F; Capital technical appendix p. 26; adjudicator script scripts/science_core_checks.py; Auditor A outputs/europe_weighting.txt.

Why this severity. The U-shape appears in every country and survives fixed composition and population weighting. The European rebound changes by about 13% and no qualitative conclusion is affected.

The authors' response. The 2014 FT response states that population or GDP weighting 'does not make a big difference'.

15minorconfirmed · documentation gap

A handful of numbers in the charts were nudged up or down by hand without explanation. Each nudge is small and none changes what the charts show, but it makes the work harder to reproduce exactly.

Technical detail and evidence

Why it matters, in detail. Magnitudes: +/-0.1 in beta (2-3% of the affected levels), 0.06 pp in r, 0.1 pp in average-wealth growth (which slightly narrows the published Forbes-vs-average gap; see F3), 2-4.5 pp in two Swedish annual top shares that feed the Fig. 1 decennial means.

Evidence. DataF3 B9, B10, F13 (Chapter5 CTS4.5 unadjusted for B9:B10); DataF4 B11 vs Chapter6 TS6.2 E31; Chapter12 T12.1 B9:B10; Chapter8 DetailsTS9.2 H22, I9, I22, J22.

Why this severity. The adjustments are small, visible in the published spreadsheets, and change no conclusion. The problem is that they are unexplained.

The authors' response. The 2014 FT response concedes that some adjustments (e.g. Sweden 1908/1920) 'should have been made more explicit'.

16minorconfirmed · newly identified here · arithmetic or transcription

Several numbers in the text are rounded or generalized in ways the authors' own data don't support. For example, Europe's income concentration fell by about a quarter, not 'almost a third'. And the poorer half of the population held about 10% of wealth in Scandinavia in the 1970s-80s, not 'always less than 5%'. None of these changes the paper's main story.

Technical detail and evidence

Why it matters, in detail. (a) 24% vs ~33% decline (19.6% without Sweden; 20.7% adult-weighted). (b) A bottom-50% wealth share of 8-14% in 1980s-90s Europe (WID) contradicts 'always <5%' outside the US. (c)-(d) The US beta and middle-class-share ranges understate mid-century variation.

Evidence. DataF1 I6:I116; DataF2 col I; DataF3 col B; Capital Chapter7 T7.2 (L14 = 0.5, L32 = 0.1, note A41); WID-2026 shwealj992 p0p50; Capital Chapter13 TS13.1; adjudicator SCF recomputation (bottom 50% 1.19% in 2010). Adjudicator scripts scripts/science_core_checks.py, scripts/wid_key_numbers.py, scripts/scf_top10.py.

Why this severity. These are loose phrasings and rounding in a broad review; none changes a qualitative conclusion. The largest, (a) and (b), overstate the secular decline in European income concentration and the universality of the bottom-half's tiny wealth share.

17minorconfirmed · newly identified here · data error

Two individual tax rates in the supplementary charts are slightly wrong: the 2013 US estate tax and the 2001 US top income tax. This does not affect the paper's conclusions.

Technical detail and evidence

Why it matters, in detail. 2013 estate-tax endpoint understated by 5 pp; 2001 income-tax rate by 0.5 pp. Neither changes the 1980-2012 declines described in the SOM.

Evidence. DataF_A2 row 2013 (US = 0.35); DataF_A1 row 2001 (0.386); IRS Instructions for Form 706 (Rev. Aug 2012 and Aug 2013), Table A; IRS SOI Historical Table 23 (2001: 39.1; 2002: 38.6), cached in /mnt/zdata/downloads/ps2014-science/.

Why this severity. These are single data points at the edge of supplementary figures, and they do not affect any stated comparison.

Claims examined and rejected

Problems one auditor raised that did not survive checking.

I17: later revisions of the underlying national series (WID-2026: German pre-WWI beta 4.6 vs 6.0; German pre-1950 fiscal top shares 5-6 pp lower; French pre-1915 shares about 5 pp higher) constitute 'version instability' of the paper. — Not a defect of the paper: the Science numbers never changed across versions (HAL and published texts and the 2014-2015 Capital workbooks are identical), and later re-estimates by other researchers do not show 2014 errors. The revisions partly offset (Europe's 1910 fiscal average stays near 45%; EU-3 beta 1910 is 6.35 in WID) and leave the qualitative facts intact. The level effects are noted under F14 and in the reproduction summary.
I2: Fig. 4's 20th-century r < g is 'circular' (the conclusion is assumed rather than shown). — Reclassified, not dismissed. The construction is assumption-driven and knife-edge for 1950-2012, which survives as F4 ('speculative_assumption', moderate). It is not circular in the rubric's sense. The caption labels the series 'after tax and capital losses', and the 1913-50 capital losses are independently documented (Piketty-Zucman 2014, Table VIII; European wealth-income ratios more than halved). The problem is sensitivity to unvalidated parameters, not reasoning that assumes its conclusion.
I15(f): the text's statement that the US top decile 'fell in the 1930s-1940s' is contradicted by the data because the 1930s decennial value (45.1%) exceeds the 1920s (44.65%). — The annual series falls from its 1928 peak (49.3%) to about 45% in the 1930s and to 32.5% by 1944; the sentence describes the path from the late-1920s peak, for which decade averages are not the right benchmark.
I4 (sub-claim): realized capital gains account for 'all of the above-pre-WWI-Europe margin'. — True for the 2000s decade average (44.2% excluding gains vs 45.8%), but not for the 2010 benchmark the text uses ('currently'): excluding gains the US 2010 share is 46.3%, still 0.5 pp above Europe's 1910 value. The surviving concept-dependence point is F10.
I14 (sub-claim, following Giles 2014): France's 1910 decedent-to-living adjustment factors (1.02/1.08 instead of 1.01/1.05) are an unexplained tweak. — Piketty's 2014 FT response documents a year-specific rationale (rising differential mortality, Piketty-Postel-Vinay-Rosenthal 2006, Table A4, reproduced in TS10.1DetailsFR); this is a documented modelling choice, not an undisclosed adjustment, and its effect is small.
I3 (sub-claim): 'no other inequality metric exists for 1910', so the text's 'true for every inequality metric' cannot hold. — Partly rejected: top-percentile and top-0.1% shares exist for 1910-13 for several countries and broadly confirm the ordering. No distribution-wide metrics exist, so 'every inequality metric' remains an overstatement; this is recorded under F9.
I15(h): 'population growth... even today represents about half of global GDP growth' is wrong because the recent-decade share is about 38%. — Capital Table 2.1 gives population 1.39% of 3.04% world growth over 1913-2012 (46%), so 'about half' is reasonable for the paper's long-run frame. The recent-decade figure was not verified and is immaterial.

Audit notes

What reproduced. Reproduced: all six figures from the authors' workbook (exact), including Fig. 1's decennial and European means; the Fig. 2 European average and the US construction formulas; the Fig. 3 averages (including the Italy switch) and the Fig. 4 tax/loss formulas. The US fiscal top-decile series was matched to Piketty-Saez vintages (Auditor A) and approximately to IRS SOI 2010 tables (Auditor B). Independent data confirm the qualitative facts: the authors' later WID-2026 fiscal, DINA and wealth series, PSZ (2018) DINA, the 2010 SCF (top 10% 74.39%, top 1% 34.07%, bottom 50% 1.19%, recomputed by the adjudicator) and Forbes 2010/2013 lists. Not reproduced (text vs data): Europe's wealth share 'less than 60%' by the 1950s-60s (data 75.4%/68.2%); the Forbes 6-7%/yr, 'more than three times' (corrected about 4.5%/yr, about 2.2x; both auditors and the adjudicator obtain 4.50%/4.47%); 'almost one-third smaller' (24%); bottom-50% wealth 'always <5%' (about 10% for Scandinavia in the authors' own Capital Table 7.2); the UK 2010 wealth share of 70.5% (about 52-56% in later estate-based estimates). Concept-dependent: on the authors' DINA (equal-split adults) the 1980-2014 US surge is 18% smaller (24% from the 1970s), the 2010 US-Europe gap is 9.6 rather than 13.2 pp, and the 'record high' and 'above 1913 Europe' claims fail. Could not be reproduced at all: the 'simple simulations' (none published) and the 1987 Forbes base from list data (no machine-readable 1987 list).

Limits of this audit. The text of Capital in the Twenty-First Century (book pp. 353-358 on the r-vs-g assumptions) was not available; the technical appendix and workbooks were used instead. No machine-readable 1987 Forbes list exists, so the corrected 1987 base remains a back-cast, bounded by the sheet's own 1987 count and total. Auten-Splinter's top-10% series and the PSS (2014) regressions were not re-estimated, and the Geloso et al. corrections were re-tabulated but not independently validated. WID-2026 (the successor to the now-offline WTID) was used for comparisons; it reflects later methodological revisions, so differences are not all 2014 errors. Survey-based SCF shares carry sampling and imputation error that was not estimated. The SCF and DINA comparisons use the authors' marketable-wealth concept; including Social Security or pension wealth (Weil 2015; Catherine, Miller & Sarin 2025) would change the levels and trends of US wealth concentration, but the paper explicitly defines wealth as non-human marketable net worth (Box 1), so this was not counted as an issue. Auditor A's report.md was missing; its scripts and outputs were read and its key numbers independently re-checked where they mattered. Auditor B's IRS SOI reconstruction and Auditor A's figure digitization were not re-run.