Top Incomes in the Long Run of History

Why it matters, in detail. Mechanism: the US magnitudes (Figs 1-3; Table 1; 'leading the way both in terms of timing and magnitude', p.5) are shares of fiscal income including realized gains in a tax-return-based control total, so trends in income that never reaches tax returns, or in the control total's coverage, move measured trends and not just levels; the JEL treats the omission of tax-exempt capital income only as a downward level bias (p.35). The control total's coverage of personal income less transfers falls from 0.811 (1946-59) and 0.808 (1960-79) to 0.765 (1980-99 and 2007). On the authors' own pre-tax national-income series (PSZ 2018/WID, tax units) the US top-1% share is 23.31 (1928), 16.63 (1949), 11.37 (1976) and 20.13 (2007) against fiscal 23.94, 11.73, 8.86 and 23.50: the 1928-49 fall shrinks from 12.2 to 6.7 points (45% smaller) and the 1976-2007 rise from 14.6 to 8.8 points (40% smaller), above the rubric's one-quarter threshold. On equal-split adults the US rise (+8.0) is no larger than the UK's (+8.1, 1978-2007) or Canada's (+7.8), so 'leading ... in magnitude' does not survive the change of concept. Direction: fiscal shares overstate both arms of the US U-shape, while the U-shape itself survives; PSZ concede that the top-10% share rose less than PS (2003) estimated. The bias is US-specific: national-income first-half declines are as large or larger in France (21.0 -> 10.3), the UK (26.9 -> 11.0) and Japan (20.7 -> 10.8) over 1919-49 and in Germany (21.9 -> 10.8) over 1913-50, so C1's cross-country pattern is untouched. Confidence is 'likely' rather than 'confirmed' because the gap between concepts is measured but which concept better captures economic income is contested (Auten & Splinter 2024 find an even smaller rise; PSZ's allocations are themselves disputed).

Evidence. WID 2026, US top 1%: fiscal (sfiinct992) 23.94 (1928), 11.73 (1949), 8.86 (1976), 23.50 (2007); pre-tax national income, tax units (sptinct992) 23.31, 16.63, 11.37, 20.13. 1928-49: -12.2 vs -6.7 pts (45% smaller); 1976-2007: +14.6 vs +8.8 (40% smaller); equal-split adults +8.0, no larger than UK (+8.1, 1978-2007) or Canada (+7.8), so 'leading in magnitude' does not survive. PS control total / (BEA A065RC - A577RC): 0.811 (1946-59), 0.808 (1960-79), 0.765 (1980-99), 0.765 (2007). PSZ, NBER WP 22945 Sec. 6.2: 'the top 10% income share has increased less than estimated by Piketty and Saez (2003)'; PS figures 'exaggerate the share of growth going to top groups'. National-income first-half declines are as large or larger outside the US: France 21.0 -> 10.3 (1919-49), UK 26.9 -> 11.0, Germany 21.9 -> 10.8 (1913-50), Japan 20.7 -> 10.8. Scripts: final/scripts/check_wid_compare.py, check_us_denominator.py.

Why this severity. The US supplies the paper's most-quoted magnitudes, and on the authors' own later concept both the post-1976 rise and the 1928-49 fall shrink by 40-45%, above the rubric's one-quarter threshold. The qualitative US U-shape survives and the problem is US-specific: the cross-country first-half declines and the UK/Canadian rises are as large on the national-income basis, so C1's cross-country pattern is untouched.

The authors' response. PSZ (2018; NBER WP 22945 Sec. 6.2) concede that fiscal data exaggerate the share of growth going to the top and that the top-10% share rose less than PS (2003) estimated, but conclude 'Rising inequality is not an illusion of tax data'. The JEL (Sec. 3.2.2) states that its series follow the tax law.

Why it matters, in detail. Mechanism: the abstract says the recent rise occurred 'but not in continental European countries or Japan', whereas the body is hedged ('no or modest increases', p.5) and the German, Dutch and Swiss series end in the late 1990s. Table 8 measures France (1998-2005) and Japan (1999-2005) over late sub-periods only, which keeps each below the paper's own change thresholds of 2 points for the top 1% and 0.65 point for the top 0.1% (p.48). Measured from the trough, Japan's top 1% rises from 6.77 (1977) to 9.20 (2005), +2.43, and its top 0.1% by 0.92; France's top 0.1% rises from 1.63 (1983) to 2.48 (2005), +0.85, while its top 1% (+1.74 to 2005, +1.95 to 2006) stays just under 2 points; Sweden, classed 'U-shaped', rose less than Japan (3.97 in 1981 to 5.72 in 2004). Later data narrow the contrast further: on WID pre-tax national income (equal-split adults, trough to 2007) France rose 4.9, Germany 4.8 and Japan 3.8 points vs US 8.0, UK 8.1 and Canada 7.8; WID's revised fiscal series show Germany 8.16 (1995) -> 14.04 (2007) and France 8.20 (1983) -> 10.90 (2007). Direction: the abstract overstates the signature U-versus-L contrast; the ordering survives in every dataset, with continental and Japanese rises roughly half as large as the English-speaking ones, so the second half of C3 is materially softened rather than reversed. The internal inconsistency is confirmed; the later-data comparison carries concept and vintage caveats.

Evidence. Workbook: Japan top 1% 6.77 (1977) -> 9.20 (2005), +2.43 (> 2-pt criterion); top 0.1% 1.48 -> 2.40 (+0.92). France top 0.1% 1.63 (1983) -> 2.48 (2005), +0.85 (> 0.65); top 1% 6.99 -> 8.73 (8.94 in 2006). Sweden, classed 'U-shaped', rose less than Japan (3.97 in 1981 -> 5.72 in 2004). WID 2026, pre-tax national income, equal-split adults, trough -> 2007: France 6.98 -> 11.85 (+4.9), Germany 8.78 -> 13.61 (+4.8), Japan 9.79 -> 13.58 (+3.8), vs US +8.0, UK +8.1, Canada +7.8. WID revised fiscal series: Germany 8.16 (1995) -> 14.04 (2007), France 8.20 (1983) -> 10.90 (2007). Scripts: final/scripts/check_table8_9.py, check_wid_compare.py.

Why this severity. The ordering (much larger rises in the US, UK and Canada) survives in every dataset, but the abstract's categorical 'not' is contradicted by the paper's own Table 8 and criterion for Japan, and on later evidence continental Europe and Japan rose by roughly half as much as the English-speaking countries, a material softening of the signature U-versus-L contrast.

The authors' response. The body hedges ('no or modest increases') and notes that the German, Dutch and Swiss data end in the late 1990s.

Why it matters, in detail. Mechanism: Table 1's share of growth captured by the top 1%, (m1 s1 - m0 s0)/(m1 - m0) with m real mean fiscal income per tax unit and s the top-1% share, has a small denominator because average real income grew only 1.16%/yr over 1976-2007 (bottom 99%: 0.59%/yr), so the split moves strongly with the deflator and the income concept; the table uses CPI-U-RS and income including realized gains with no sensitivity analysis, and its note misdescribes the deflator (the source uses CPI-U-RS from 1978, not 'before 1992'). Recomputed from TabFig2007 (baseline exact at 57.6/44.7/64.7% for 1976-2007/1993-2000/2002-07): PCE deflator 49.5/41.8/60.7% (bottom-99% growth 0.88%/yr); GDP deflator 47.0/41.6/62.5%; excluding gains 50.0/32.3/61.7%; excluding gains with PCE 41.3%; start years 1977-82 give 51-60%. The authors' own national-income analog (WID, equal-split adults) gives 29.7/31.0/44.0%, with bottom-99% growth of 1.44%/yr. Direction and size: the 58% headline falls by about 15-50% under defensible alternatives (to 41-50% with standard deflators or definitions, about 30% on the national-income basis), which weakens the p.9 reading that Table 1 explains 'the gap between the economic experiences of the public and the solid macroeconomic growth'; PSZ (2018) concede that the PS figures 'exaggerate the share of growth going to top groups'. Under every variant the top 1% still captures many times its population share, so C5's qualitative point stands.

Evidence. Recomputed from TabFig2007 Tables A0, A1, A3 and BEA DPCERG/A191RD: baseline 57.6/44.7/64.7% (exact). PCE deflator 49.5/41.8/60.7%; GDP deflator 47.0/41.6/62.5%; excl. KG (CPI-U-RS) 50.0/32.3/61.7%; excl. KG with PCE 41.3%; bottom-99% growth 0.59%/yr (paper) vs 0.88%/yr (PCE). Start years 1977-1982: 51-60%. DINA analog (WID aptincj992/sptincj992): 29.7/31.0/44.0%, bottom-99% growth 1.44%/yr. Scripts: final/scripts/check_table1.py, check_dina_table1.py.

Why this severity. A widely quoted secondary statistic falls by 15-50% (to 41-50% under standard alternative deflators or definitions and about 30% on the authors' national-income basis), while the top 1% still captures many times its population share under every variant.

The authors' response. PSZ (2018; NBER WP 22945 Sec. 6.2) concede that the PS figures 'exaggerate the share of growth going to top groups'. JEL fn 3 caveats only the international comparison.

Why it matters, in detail. Mechanism: after TRA86, business income shifted from corporate to individual returns, mechanically raising fiscal top shares. The JEL accepts that almost half of the 4-point 1986-88 jump in the series excluding gains is such shifting, but argues that the series including gains is immune because retained earnings 'translate into capital gains that are eventually realized' and because CPS top shares rose as fast as the tax-based share including gains 'in the medium run from 1985 to 1990' (p.32). That comparison is window-specific: of 25 windows (start 1982-86, end 1988-92) it holds in 8, all starting in 1985 (a CPS dip) or 1986 (a realization spike: top 1% including gains 12.67 in 1985, 15.92 in 1986, 12.66 in 1987, 15.49 in 1988); e.g. 1984-90 CPS x1.110 vs tax x1.195, and 1983-90 x1.117 vs x1.240. The CPS also excludes capital gains, so it cannot test that series, and realization is not an identity (step-up at death, fn 26; in a stylized example, moving never-realized retained profits onto personal returns lifts a 10% fiscal share to 14.3%). In the authors' favour, the series including gains shows little excess over its own 1979-85 trend (+0.37 point in 1988-90, vs +3.17 for the series excluding gains). Magnitude: if the series including gains were affected like the series excluding gains, whose 1976-2006 rise the authors' own correction cuts from 10.1 to 7.0 points (-31%), the US rise would be about 20% smaller; this is a scenario, not a demonstrated bias, and it overlaps with F1. Direction: the immunity claim for the preferred series (behind C3's US rise and the C5 statistics built on it) is weakly supported rather than shown to be wrong.

Evidence. Workbook 'Data for Fig 5': of 25 windows (start 1982-86, end 1988-92) the claim holds in 8, all starting in 1985 or 1986; e.g. 1984-90 CPS x1.110 vs tax x1.195; 1983-90 x1.117 vs x1.240. Incl.-KG top 1%: 12.67 (1985), 15.92 (1986), 12.66 (1987), 15.49 (1988). In the authors' favour, the incl.-KG series shows little excess over its 1979-85 trend (+0.37 pt in 1988-90 vs +3.17 excl. KG; Auditor A). Codex counterexample: fiscal share 10% -> 14.3% when never-realized retained profits move onto personal returns. The authors' own correction cuts the excl.-KG 1976-2006 rise from 10.1 to 7.0 pts. Script: final/scripts/check_gini_tra86.py.

Why this severity. The evidence offered for the incl.-KG series' immunity to TRA86 is fragile; if that series were affected like the excl.-KG one (-31% after the authors' own correction), the US rise would be about 20% smaller, though the impact is not demonstrated and overlaps with F1.

The authors' response. Piketty & Saez (2006 reply to Reynolds) point to the doubling of the incl.-KG series and of W-2 wage shares; PS (2003) acknowledged TRA86 shifting; PSZ (2018) add corporate retained earnings.

Why it matters, in detail. (a) Mechanism: the paper backs out a bottom-99% Gini G0 from G = (1-S)G0 + S, combining the official Census household Gini (cash income including transfers) with the pre-transfer tax-unit CPS top share S of Burkhauser, Feng, Jenkins & Larrimore (BFJL), and reads the absence of a 1992-93 break in G0 as showing that the CPS redesign discontinuity is 'entirely due to measurement changes within the top 1 percent' (p.32; Fig. 6 note: 'demonstrating'). Because G and S refer to different units and income concepts (as fn 23 concedes), the cancellation cannot locate the break: the implied G0 moves by 4e-7 (0.3835930 to 0.3835935) against a median year-to-year change of 0.003, a numerical coincidence (the CPS shares reproduce BFJL's published +42.5% change in 1992-93). Consistently defined bottom-99% Ginis (BFJL 2012, REStat, Appendix Table C1) jump by 1.0 point in 1992-93 (.382 -> .392 post-transfer household; .520 -> .530 pre-transfer tax units), 37-40% of the full-population jump, and the jump-removed bottom-99% rise over 1976-2006 is 4.87 points on the pre-transfer tax-unit basis vs the hybrid's 3.2, so the hybrid's bottom-99% rise is not robust to consistent definitions. (b) 'CPS data that do not measure top incomes fail to capture about half of this increase' holds for the preferred series including gains (51%; 54% with the F7 normalization) but not for the other variants in the same table: 40% excluding gains and 25% for the TRA86-corrected series excluding gains. Direction: both conclusions are overstated; the share of the adjusted Gini rise attributable to missing top incomes ranges from 25% to 54% across the paper's own variants, and part of the redesign jump lies in the bottom 99%. C5's message that the top 1% accounts for a large part of the rise in the Gini survives.

Evidence. Workbook: implied bottom-99% Gini 0.3835930 (1992) vs 0.3835935 (1993), a change of 4e-7 vs a median year-to-year change of 0.003; the CPS shares reproduce Burkhauser et al.'s published +42.5% 1992-93 change, so this is a numerical coincidence. BFJL (2012, REStat 94(2), Appendix Table C1, p.388): bottom-99% Gini .382 -> .392 (CPS-Post-HH) and .520 -> .530 (CPS-Pre-TU) in 1992-93, i.e. 37-40% of the full-population jump; jump-removed bottom-99% (Pre-TU) rise 1976-2006 4.87 vs APS 3.2. Share of the adjusted Gini rise missed by the CPS: 51% (incl. KG), 40% (excl. KG), 25% (TRA86-corrected excl. KG), 54% (incl. KG, normalized formula). Script: final/scripts/check_gini_tra86.py.

Why this severity. The message that the top 1% accounts for a large part of the rise in the Gini survives, but the 'demonstration' is invalid and contradicted by consistent-definition data, and the 'about half' magnitude ranges from 25% to 54% across the paper's own variants.

The authors' response. Fn 23 notes the method 'is not perfect' because of the household/family and transfer mismatch; Burkhauser et al. (2012, p.381) endorse combining a CPS bottom-99% Gini with tax-based top shares.

Why it matters, in detail. Mechanism: the pre-1944 US shares rest on a control total fixed at 80% of personal income less transfers (p.17), fixed net-to-gross deduction multipliers (pp.18, 36) and very low filing coverage, with no sensitivity analysis although the JEL itself doubts that a constant percentage is appropriate (p.18). Geloso, Magness, Moore & Schlosser (2022, EJ) re-estimate from the same SOI sources and find lower pre-war shares: top 1% including gains 19.47 vs 23.94 in 1928 (about 4.5 points, nearly a fifth, lower), 12.63 vs 16.48 in 1940, 10.84 vs 11.28 in 1944 and 10.57 vs 11.73 in 1949. The 1928-44 fall shrinks from 12.66 to 8.63 points (32% smaller) and the 1940-44 fall from 5.20 to 1.79 points (66% smaller); the top-decile fall over 1940-45 drops from 10.9 to 2.9 points (74% smaller), against Fig. 1's 'precipitous (10 percentage point) decline during World War II'. Since the 80% rule is close to current BEA data (0.793 in 1929-43 vs 0.811 in 1946-59), most of the revision comes from the numerator adjustments (the 1928 numerator stage alone gives 21.92). Direction: the PS construction overstates the pre-war level and, above all, the WWII compression, so less of the US decline is concentrated in the war years than Fig. 1 shows. Bound: the 1919-49 comparison used in Table 7 barely moves (1949/1919 ratio 0.715 vs 0.739), and no other country behind C1 depends on the US series, hence moderate rather than major. Confidence is 'likely': the GMMS comparator and endpoints reproduce from its data appendix, but the alternative was not independently rebuilt and its own corrections are contestable.

Evidence. GMMS data appendix (DataAppendix-6-7-21.xlsx, TopIncomeShares; PS 'latest updated file (with full K-gains)' vs 'Corrected - Cumulative + full K-gains'): top 1% 1928 23.94 vs 19.47; 1940 16.48 vs 12.63; 1944 11.28 vs 10.84; 1949 11.73 vs 10.57. Fall 1928-44 -12.66 vs -8.63 (32% smaller); 1940-44 -5.20 vs -1.79 (66% smaller). Top decile 1940-45 -10.9 vs -2.9 (74% smaller), against Fig. 1's '10 percentage point' WWII decline. But 1949/1919 ratio 0.715 (Table 7: '70 per cent of 1919') vs 0.739. The 80% rule is close to current BEA data (0.793 in 1929-43 vs 0.811 in 1946-59; Auditor A), so most of the revision comes from numerator stages (Codex: 1928 numerator stage alone 21.92). Scripts: final/scripts/check_gmms.py; codex/scripts/gmms_checks.py.

Why this severity. A credible peer-reviewed re-estimate cuts about a third of the US 1928-44 fall and most of the US WWII compression highlighted in Fig. 1, but leaves the US 1919-49 decline used in Table 7 almost intact and does not affect the other countries behind C1.

The authors' response. None located; the JEL (p.18) itself flags the constant-percentage concern.

Why it matters, in detail. Mechanism: with the infinitesimal-top approximation G = (1-S)G0 + S, replacing the CPS top share S by the tax-based share T at a fixed bottom-99% Gini G0 gives G' = G + (T-S)(1-G)/(1-S); the Fig. 6 note and the workbook instead use (1-D)G + D with D = T-S, omitting the 1/(1-S) factor, so the adjusted Gini does not deliver the target top share (implied 2006 top share 21.6% vs target 22.8%). Published vs normalized adjusted Ginis including gains: 0.4109 vs 0.4118 (1976) and 0.5186 vs 0.5263 (2006); the 1976-2006 rise becomes 11.44 rather than 10.77 points (+0.68, about +6%), and 9.10 rather than 8.79 excluding gains. Direction: the slip understates the top-adjusted Gini rise, so correcting it slightly strengthens C5's point that top incomes matter for overall inequality (it also moves the 'share missed by the CPS' including gains from 51% to 54%; F6).

Evidence. Workbook 'Data for Fig 5' rows 13 and 43: published adjusted Ginis 0.4109/0.5186 (incl. KG) vs normalized 0.4118/0.5263; 1976-2006 rise 10.77 -> 11.44 (+0.68, +6%); excl. KG 8.79 -> 9.10. Script: final/scripts/check_gini_tra86.py.

Why this severity. An algebraic slip in an illustrative calculation; correcting it slightly strengthens the paper's own conclusion.

Why it matters, in detail. Equation (4) (p.59; WP eq. 6) gives the Simon-Lydall hierarchy's 'inverse Pareto exponent' as log[1 + increment]/log[span] and labels it beta. Since the hierarchy's Pareto exponent is alpha = log(span)/log(1 + increment), the expression equals 1/alpha, whereas beta everywhere else in the paper is the inverted Pareto coefficient alpha/(alpha-1) (eq. 2, p.14) used for the empirical beta values (e.g. Table 6). With span 4 and a 100% increment, the printed expression gives 0.5 while beta is 2. Both quantities rise with the promotion increment and fall with the span, so the model's comparative statics keep their sign; no empirical estimate uses the formula, so the slip affects only the theoretical illustration attached to C4.

Evidence. Span 4 and increment 100%: the printed expression gives 0.5, the defined beta is 2. PDF visually checked by Codex (page59.png).

Why this severity. A notational error in an illustrative model; the comparative statics have the same sign and no empirical estimate uses the formula.

Why it matters, in detail. Recount from the printed Table 6: 1949 top-0.1% shares within 2.6-3.9%: 11 (text 12); 1949 beta within 1.88-2.00: 9 of 20 (text 10); 2005 top-1% shares outside 9% +/-20%: 11 of 21 (text 9); 2005 top-0.1% income relative to the average, excluding two outliers at each end: 19-56 times (text 13-56), 1949: 24-52 (text 20-52), 1949 excluding three at each end: 26-40 (text 26-39); 2005 beta above 2.5: 4 (text 5); number of 2005 beta values 21 (text 22); beta changes larger than 0.1: 12-13 of 19 pairs with 9-10 rises (text 15 of 20 with 12 rises); p.48 has 'nine U-shaped' followed by 'the ten countries'. Counts are off by one to three countries and range bounds by up to six times the average. Direction is mixed: the 2005 dispersion count understates the wider dispersion the text describes for 2005 relative to 1949, while the beta-change count overstates the number of rises in concentration within the top, though rises still dominate (9-10 of 12-13 changes). The figures the text leans on most, the 1949 median top-1% share (10.82) and the 6/5/6 split of 1949-2005 changes, are exact, so neither C2 nor C3 changes.

Evidence. Recount (final/scripts/check_table6_counts.py): 1949 top-0.1% shares within 2.6-3.9: 11 (text 12); 1949 beta within 1.88-2.00: 9 of 20 (text 10); 2005 top-1% shares outside +/-20%: 11 of 21 (text 9); 2005 top 0.1% excluding two outliers each end: 19-56 times the mean (text 13-56); 1949: 24-52 (text 20-52); 1949 excluding three: 26-40 (text 26-39); 2005 beta > 2.5: 4 (text 5); 2005 beta values: 21 (text 22); beta changes > 0.1: 12-13 of 19 pairs with 9-10 rises (text 15 of 20, 12); 'nine U-shaped' then 'the ten countries' (p.48). The 1949 6/5/6 split and the median (10.82) are exact.

Why this severity. None changes a conclusion; the 2005 miscount understates the dispersion being described.

Why it matters, in detail. Table 6 'around 2005' cells: New Zealand's 8.76/2.51 are its 2001 values (2005: 8.98/2.66); Sweden's are its 2005 values although the note says 2004 (the 2004 values are 5.72/1.73); Finland's are 2004 HES/IDS survey values (F12) and China's are 2003, neither flagged. Table 9: UK 2005 next 4%/second vintile printed 14.5/11.2 vs 15.32/12.05 in the series; Australia 2002 next 4% 11.2 vs 12.11; Italy 2004 next 4% 12.3 vs 13.29, i.e. printed cells 0.8-1.0 point below the data. Table 8's UK 'rose 7.5' (top 1%) and 'rose 3' (top 0.1%) match the series only to 2003-04 (to 2005: +8.5/+4.0), pointing to an older UK vintage than in Table 6. Direction: the Table 9 slips understate end-period shares of the groups just below the top 1%, tilting Table 9 slightly toward C4's 'concentrated in the top 1%' reading, and the Table 8 UK entries understate the UK rise by about one point, which is conservative for C3. Each discrepancy is about a point or less, and none overturns C4 or C3.

Evidence. Table 6: NZ 8.76/2.51 = 2001 values (2005: 8.98/2.66); Sweden = 2005 (note says 2004: 5.72/1.73); Finland = 2004 HES/IDS; China = 2003. Table 9: UK 2005 14.5/11.2 vs 15.32/12.05; Australia 2002 next 4% 11.2 vs 12.11; Italy 2004 next 4% 12.3 vs 13.29. Table 8 UK 'rose 7.5' (top 1%) and 'rose 3' (top 0.1%) match the series only to 2003-04 (to 2005: +8.5/+4.0). Scripts: final/scripts/check_table6_counts.py, check_table8_9.py.

Why this severity. Transcription and labelling slips that mostly understate rises below the top 1% and in the UK; they do not overturn C4.

Why it matters, in detail. Table 6 compares Finland's tax-based 1949 top-1% share (7.71%) with 'around 2005' values (7.08/2.65; beta 2.34) that are 2004 HES/IDS household-survey values, without saying so in the table (Table 4 does disclose survey use for 1966-2004). The workbook's tax-linked series rescales HES/IDS by a constant factor of 1.2148 for 1993-2004, giving 8.60 for 2004. On the linked series Finland's 1949-2004 change is +0.9 points rather than the printed -0.6, and its recent rise +5.1 rather than Table 8's +3.5. Direction: the unflagged survey endpoint understates Finland's recent level and rise and flips the sign of a small long-run change; it concerns one country's entries behind C2 and C3 and no cross-country conclusion.

Evidence. Workbook 'Table A18 Finland': tax-linked top 1% = HES/IDS x 1.2148 for 1993-2004 ('pasted' note); 2004 linked 8.60 vs HES 7.08. On the linked series Finland's 1949-2004 change is +0.9 pts (printed -0.6) and the recent rise +5.1 (Table 8: +3.5). Table 4 discloses that survey data are used for 1966-2004.

Why this severity. A documentation gap for one country that flips the sign of a small change but no conclusion.

Why it matters, in detail. In the workbook and in the source chapter (Jaentti et al. 2010, Table 8A.2), Finland's top shares fall by exactly 0.780 points a year from 1938 (13.04) to 1947 (6.01), with further straight-line runs over 1923, 1925, 1927-28, 1930, 1932-33 and 1936; the chapter's list of tax tabulations (Table 8A.8) has none for 1923, 1925, 1927-28, 1930, 1932-33, 1936, 1939-41, 1944 and 1946, and the 1942, 1943 and 1945 values also lie on the line, so 16 of the 85 annual values sit on straight-line runs without being flagged (only Finland among the 22 series shows such runs). Consequences in the JEL: Table 4's '1920-2004 (85 years)' overstates observed coverage, Fig. 10 plots the line as data, and Table 7's Finland 'WW2: loss of 5 points' is a difference between interpolated years (1939 12.26 -> 1945 7.57, -4.7), whereas the observed change is -7.0 over 1938-47. Direction: the timing and size of the wartime part of Finland's decline are not observed; the observed endpoints confirm a large war-period fall, so C1 is unaffected.

Evidence. final/scripts/detect_interpolation.py (only Finland shows such runs among the 22 series). Jaentti, Riihelae, Sullstroem & Tuomala (2010), 'Trends in Top Income Shares in Finland', in Atkinson & Piketty (eds) Top Incomes: A Global Perspective, Table 8A.2 (p.413) and Table 8A.8 (p.441; list of tax tabulations: none for 1923, 1925, 1927-28, 1930, 1932-33, 1936, 1939-41, 1944, 1946; the 1942, 1943, 1945 values also lie on the line); https://wid.world/www-site/uploads/2016/06/Jantti_Riihela_Sullstrom_Tuomala_Chapter8_2010.pdf. Interpolated 1939 12.26 -> 1945 7.57 (-4.7) vs observed 1938 13.04 -> 1947 6.01 (-7.0).

Why this severity. Affects the presentation of one country's coverage and WWII entry; the observed endpoints confirm a large war-period decline, so C1 is unaffected.

Why it matters, in detail. A set of independent slips, mostly carried over unchanged from the 2009 working paper: p.8 swaps the Clinton (1993-2000) and Bush (2002-07) top-1% real growth rates relative to Table 1 (10.3 and 10.1%/yr); p.9 calls 64.7% 'over two-thirds'; p.15 gives the 2007 top-1% share excluding gains as 18.9% (data 18.29%) and a beta of 2.89 that is the share-ratio value (2.74 at the P99 threshold); p.15 dates New Zealand's change to individual units to 1963 (1953 in Table 4 and Atkinson & Leigh 2008); p.32 says the CPS 'misses 10.4 points' (13.96 - 4.08 = 9.9) and puts the 1992-93 CPS jump at 3.4 (3.5 in the Fig. 5 note; data 3.41); the Table 5 notes cite column (4) for a correction shown in column (3) and call point changes 'percentage increase'; fn 4 uses 8.8 for the 1976 share (data 8.86) and 'about 74 percent' where 17.34/23.7 = 73.2%; Table 4 gives India '1922-1988' (the series runs to 1999), the US '96 years' (95) and China 18 years vs 15 on p.4; p.12 credits the US with 'half of the worldwide increase' in the globally rich, whereas Fig. 4's data imply about 38% (42% in population-share terms); p.39 gives France 1998 as 'about 7.7 percent' (revised series 7.94); fn 8's '(see equation (4) below)' is a stale WP cross-reference. The largest gaps (the US 'half' vs about 38-42%; 10.4 vs 9.9 points) concern illustrative statements, and the swapped Clinton/Bush rates differ by only 0.2 point and are correct in Table 1, so no core magnitude in C1 or C5 moves.

Evidence. p.8: Clinton/Bush top-1% growth rates swapped vs Table 1 (10.3/10.1). p.9: 64.7% called 'over two-thirds'. p.15: 2007 excl.-KG top-1% share '18.9 percent' (data 18.29%); beta 2.89 is the share-ratio value, 2.74 at the P99 threshold. p.15: 'New Zealand from 1963' (Table 4 and Atkinson & Leigh 2008: 1953). p.32: 'misses 10.4 points' (13.96 - 4.08 = 9.9). CPS jump 3.4 (text) vs 3.5 (Fig. 5 note; data 3.41). Table 5 notes: column (4) for a correction shown in column (3); point changes called 'percentage increase'. fn 4: 1976 share 8.8 (data 8.86); 'about 74 percent' (17.34/23.7 = 73.2%). Table 4: India '1922-1988' (series to 1999); US '96 years' (95); China '15 years' (p.4) vs 18 (Table 4). p.12: US 'half of the worldwide increase' in the globally rich (Fig. 4 data x world population: ~38%, ~42% in population-share terms). p.39: France 1998 'about 7.7 percent' (revised series 7.94). fn 8: '(see equation (4) below)' is a stale WP cross-reference (JEL eq. 4 is the hierarchy formula). Scripts: final/scripts/check_gini_tra86.py, check_table1.py; claude/scripts/check_text_numbers.py, misc_checks.py; codex/scripts/final_checks.py.

Why this severity. Typographical and transcription errors, mostly carried over from the 2009 working paper; none affects a conclusion.

Why it matters, in detail. Three documentation slips. (i) Fn 4 computes the top 1%'s income net of federal taxes (5.8% of total pretax income in 1976 and 17.3% in 2007, 'about 74 percent' of all federal taxes) from average tax rates attributed to 'Piketty and Saez (2006)', which in the reference list is the AER P&P top-incomes paper; the 1976 rates (26.2/1.6/6.8; total federal rate 24.7%) match Piketty and Saez's 2006 NBER WP on tax progressivity (published in JEP 2007), whose tables end in 2004, so the 2007 rates (22.5/3/2.2; total 23.7%) are undocumented. (ii) Table 1's note says CPI-U-RS is used 'before 1992', whereas the source uses CPI-U-RS from 1978 (F4). (iii) The text gives a 20% nonfiler income imputation since 1944, whereas the source uses 50% for 1944-45 (per Auditor A; not re-verified in the adjudication). No item is shown to move a number: the 1976 tax figures match their source and the 2007 ones are plausible, so the tax-capacity point in C5 stands, but these inputs cannot be fully traced from what is cited.

Evidence. piketty-saezNBER06taxprog: 1976 P99-100 rates 26.2/1.6/6.8, total 24.7 (match fn 4); latest year 2004. 2007 rates in fn 4: 22.5/3/2.2, total 23.7. TabFig2007 notes on CPI-U-RS from 1978.

Why this severity. Citation and documentation slips; the 1976 figures match the source and the 2007 ones are plausible.

Why it matters, in detail. Between NBER WP 15408 and the JEL, the illustrative US-France growth comparison changed from 1975-2005 (average income US +29.8% vs France +19.3%; excluding the top 1%, +16.5% vs +19.7%) to 1975-2006 (US +32.2% vs France +27.1%; excluding the top 1%, +17.9% vs +26.4%), without disclosure. The JEL workbook gives France +23.9%/+23.6% for 1975-2005, so about 60% of the change in the French figures comes from the November 2009 revision of the French series ('REVISE 11/2009 using Landais new excel file') and the rest from the extra year. Direction: the revision raised French growth by about 4.6 points over the same window and widened France's lead excluding the top 1% from 3.2 to 8.5 points, strengthening the reversal; the qualitative result holds in both versions and fn 3 calls such comparisons 'primarily illustrative', but the shift shows how sensitive this C5 illustration is to data revisions.

Evidence. WP p.7: 1975-2005 US +29.8% vs France +19.3%; excluding top 1% +16.5% vs +19.7%. JEL p.9: 1975-2006 US +32.2% vs France +27.1%; excluding top 1% +17.9% vs +26.4%. JEL workbook gives France 1975-2005 +23.9/+23.6%; France sheet note 'REVISE 11/2009 using Landais new excel file' (cell N100). Claude script check_growth.py.

Why this severity. The qualitative reversal holds in both versions and fn 3 calls the comparison illustrative, but it shows the comparison's sensitivity to data revisions.

Why it matters, in detail. The abstract presents the evidence as series built 'using income tax statistics' and lists China among the countries where top shares rose substantially, but China's series comes from urban household-survey tabulations for 1986-2003 (Table 4: 'Urban Household surveys used (not tax statistics)'; p.50: levels 'probably underestimated'). The rise itself, top 1% from 2.65% (1986) to 5.87% (2003), reproduces from the workbook, and later WID estimates confirm the direction. Direction: a framing issue that blurs the evidential basis for one country in C3; it is disclosed in the body and does not change the finding that China's top share rose.

Evidence. Table 4 China: 'Urban Household surveys used (not tax statistics)'; p.50: levels 'probably underestimated'. Workbook China top 1% 2.65 (1986) -> 5.87 (2003). Later WID estimates confirm the direction.

Why this severity. A framing issue disclosed in the body; the direction is confirmed by later data.

Why it matters, in detail. p.58 uses the UK as an example of a large top-rate cut after which top shares would keep rising until a new equilibrium was approached, stating that the top rate 'was cut from 98 percent to 40 percent in the first half of the 1980s'. The 98% applied only to investment income (83% plus a 15% surcharge); the top rate on earnings fell from 83% to 60% in 1979 and to 40% only in the March 1988 budget (Hansard, HC Deb 15 March 1988, vol. 129, col. 1012), consistent with the JEL's own reference on p.66 to 'the twenty years since the top rate ... was reduced to 40 percent'. The misdating sits in an illustrative remark in the capital-accumulation modelling discussion; no empirical estimate or core finding uses it.

Evidence. Hansard, HC Deb 15 March 1988, vol. 129, col. 1012 (Codex); Adam, Browne & Heady, IFS 'Taxation in the UK' (Auditor A).

Why this severity. An illustrative remark in a modelling section; no empirical result depends on it.

Why it matters, in detail. Mechanism: Table 8's Norway 'rose 8 points' and Table 6's 2004 values (top 1% 11.82%; beta 3.08, the highest in the table) rest on the post-1992 dividend surge, which the source (Aaberge & Atkinson 2008, Statistics Norway DP 552, pp.12-14) attributes partly to income shifting; its shifting-robust 'Hicksian' series 'rises less fast, particularly after 2001'. Workbook top 1%: 4.24 (1989), 8.49 (1999), 10.44 (2000), 7.48 (2001), 11.82 (2004), 16.78 (2005), 8.06 (2006); top 0.1%: 0.94 (1989), 5.59 (2004), 2.70 (2006); the source links 2001 to a temporary dividend tax and the 2005 spike to the 2006 dividend tax. At face value Norway's +8 exceeds every English-speaking rise in Table 8 except the US's +10 (UK +7.5, Canada +6, Australia and New Zealand +4), contradicting p.5's statement that Nordic increases are 'less in magnitude than in English speaking countries'; from the 1989 trough to 2006 the rise is about 3.8 points, below the UK and Canadian rises and close to Australia's and New Zealand's. Table 9's Norway '2005' cells (11.3/9.4) are the 2006 values (11.32/9.41; 2005: 11.84/9.06). Direction: the face-value years overstate Norway's sustained rise and, read literally, would blur C3's contrast between English-speaking and other countries. Minor because it concerns one country, the authors avoided the 2005 spike and the source itself reports the 1991-2004 rise at face value.

Evidence. Workbook Norway top 1%: 4.24 (1989), 8.49 (1999), 10.44 (2000), 7.48 (2001), 11.82 (2004), 16.78 (2005), 8.06 (2006); top 0.1% 0.94 (1989) -> 5.59 (2004) -> 2.70 (2006). Table 9 Norway '2005' 11.3/9.4 = 2006 (11.32/9.41), 2005 = 11.84/9.06. Aaberge & Atkinson (2008, Statistics Norway DP 552, pp.12-14): rise 'taken at face value' of about 7 pts 1991-2004; temporary 2001 dividend tax; 2005 spike from the 2006 dividend tax; Hicksian series 'rises less fast, particularly after 2001'. From the 1989 trough to 2006 the rise is about 3.8 pts.

Why this severity. One country; the authors avoided the 2005 spike and their source reports 2004 at face value.