The Elephant Curve of Global Inequality and Growth

Why it matters, in detail. Pure level shift of one of 15 subregional distributions in 1980-84 (shares unchanged). MENA residents are 17.8% of the 1980 global top 0.001% with the override and 35.8% without; a 45% cut of their 1980 incomes lowers 1980 top fractiles and raises 1980-2016 top-end growth. Direction: inflates the trunk (C2/C3) and the top-share trend (C4). Magnitude: top-1% growth +21 pp, top-0.001% growth +51 pp, world average growth +5.8 pp, top-1% share rise +1.27 pp (3.01 -> 4.28 pp); capture ratio +0.19 (2.00 -> 2.19). Three independent merges agree within ~1-2 pp.

Evidence. Code: computer-codes.zip, Do/'0c - aggregate-regions.do' lines 62-67. Adjudicator's Python translation of 0b/0c (scripts/rebuild_regions.py) reproduces the stored regions-aggregates.dta to 6.5e-8 only with the override; without it, only MENA 1980-84 differ. MENA income per adult (2016 PPP EUR) in the imported data: 20,566 (1980), 19,906, 18,349, 17,651, 17,454 (1984), 16,998 (1985); used: 11,332 for 1980-84. MENA growth 1980-2016: +4.1% in the data vs +88.8% used (Technical Note Table B1 'Middle-East 89%'). Saudi Arabia supplies 32.6% of MENA 1980 income (EUR 142,765 per adult in 1980, 72,876 in 1985). WDI real GDP per capita 1985/1980: MENA aggregate 0.85, Arab World 0.78, Saudi Arabia 0.51, Kuwait 0.62, UAE 0.69, Qatar 0.71. Current WID MENA (XN, bulk 2026-10-15): x0.835 over 1980-85, +4.7% over 1980-2016. Effect on world 1980-2016 growth (adjudicator's validated merge, scripts/experiments.py), published inputs -> MENA = national accounts: average 58.9 -> 53.2%; bottom 50% 94.1 -> 87.8%; middle 40% 40.9 -> 38.5%; top 10% 69.1 -> 60.1%; top 1% 101.1 -> 79.6%; top 0.1% 132.8 -> 93.8%; top 0.01% 183.9 -> 139.6%; top 0.001% 234.1 -> 183.1%. Global top-1% share 1980: 16.16 -> 17.43%, so the 1980-2016 rise falls from 4.28 to 3.01 pp (-30%). Capture top 1% / bottom 50%: 27.71 / 12.65 -> 26.10 / 13.03 (ratio 2.19 -> 2.00). Neutral 'flat at 1985' variant: top 1% 87.8%, top 0.001% 202%, ratio 2.09. The override also creates most of the 1984->85 jump in Figure 3's top-1% series (16.18 -> 16.96 with it; 16.88 -> 16.96 without). Both auditors obtained the same numbers independently (A: top 1% 79.7%, top 0.001% 184.7%; B: top-1% share rise -29.8%, capture 26.10/13.03).

Why this severity. Restoring the authors' own imported national accounts lowers the reported top-1% and top-0.001% growth rates by about a fifth (101% -> 80%; 234% -> 183%) and the 1980-2016 rise in the global top-1% share by 30%, i.e. roughly a quarter of core top-end magnitudes, and the bottom 50% then grows faster than the top 1% (88% vs 80%). The capture headline (2.0x) and the qualitative elephant shape survive, so the problem is major, not critical.

Why it matters, in detail. Static calibration transfers China+India share levels (including the within-pair between-country divergence) to a region with 60% mean growth, forcing negative absolute growth for ~470m bottom-half adults; this lowers global bottom-50% growth and capture. Range across defensible variants: capture ratio 1.46-2.19 (1.50 combined with F1), bottom-50% growth 94-127%, top-1% growth 91-101% (73% combined with F1). External check: current WID ratio 2.20, bottom-50% growth 95%, i.e. the published values are within the range and close to the later estimate.

Evidence. '1d - calibrate-subregions.do' (calibration=0 branch copies shares; the dynamic branch's header comment notes that otherwise the 'bottom 50% see its average income decrease'); Technical Note 2017/5 Section 3.5 and Appendix C (Tables C1-C2: world bottom-50% growth 115%, top 1% 94%, captured 25.77% vs 15%). Adjudicator recomputation (scripts/diagnostics.py, scripts/experiments.py): Other Asia static bottom-50% -19.8%, top 1% +247%; dynamic +24.4%; Other North America static bottom-50% -10.8%. World capture ratio: static 2.19; authors' dynamic file 1.67 (25.77/15.47; reproduces TN Appendix C exactly); dynamic + MENA national accounts 1.50 (24.03/16.04; bottom 50% grows 108% vs top 1% 73%); Other Asia held at the China+India 1980 shape 1.46 (24.83/17.03). Auditor A reports steep falls in World Bank $3/day poverty in Indonesia, Bangladesh, Pakistan and Thailand (not re-run here). Current WID (WO-PPP, bulk 2026-10-15): capture 27.15% vs 12.35% (ratio 2.20), bottom-50% growth 95%.

Why this severity. Within the 2018 inputs, the authors' own alternative cuts the headline capture ratio by about a quarter (2.19 -> 1.67) and raises bottom-half growth from 94% to 115%; but the later WID vintage, which uses direct data for more Asian countries, reproduces 27% vs 12% and 95% bottom-half growth, so no bias in the published headline is demonstrated. It is an important sensitivity that the paper does not disclose rather than a demonstrated error, and the top 1% captures far more than the bottom 50% in every variant (24-28% vs 12-17%). Auditor A rated it major.

The authors' response. Technical Note 2017/5 Section 3.5 acknowledges that the static method 'could lead to underestimating the growth rate of the average income of the Bottom 50%' and reports the dynamic alternative as 'qualitatively similar' ('the elephant curve is in fact even more pronounced'); the P&P (p. 104) calls the regional assumption 'obviously an over simplification'; Chancel & Piketty (2021, JEEA 19(6), pp. 3055-3056) state that reliance on a limited set of countries 'can certainly affect some of the finer decompositions for the more recent period'.

Why it matters, in detail. Clipping negative growth shares and rescaling raises the BAU 2050 bottom-50% mean by 16% relative to a floor-at-zero rule (EUR 6,219 vs 5,364) and its share by 1.2 pp; but the negative shares for Other Asia and Other North America are artefacts of the static proxy (F2), and replacing them with donor growth profiles raises the BAU 2050 bottom-50% share to 9.95% (+1.2 pp) and mean to EUR 7,095 (+14%). The BAU bottom-half trajectory is therefore not identified by the data.

Evidence. '6c - project-regions.do' lines 17-37 (replace share=0 if share<0) and 94-104 (rescaling); '0d - import-shares-growth.do' lines 141-149 (US donor is 1980-2015, not 1980-2016). The adjudicator's re-implementation of 6a (PPP) + 6c (scripts/proj6.py) reproduces the authors' project-regions.dta to 7e-7 in all three scenarios, and merged world results match gpinterized-projections.dta (BAU 2050 bottom-50% share 8.72%, top 1% 24.52%, bottom-50% income EUR 6,219). Variants (scripts/projection_variants.py): no clipping, final incomes floored at zero (rank weights repaired): BAU bottom-50% share 7.52%, top 1% 25.18%, bottom-50% income EUR 5,364 (Auditor B: 7.53%, EUR 5,373); Other Asia given the China+India 1980-2016 growth profile and Other North America the US profile: BAU bottom-50% share 9.95%, top 1% 23.52%, income EUR 7,095 (Auditor A: 9.95%, 23.5%, EUR 7,096). US and EU scenarios move by at most ~4%.

Why this severity. Affects a secondary (projection) result: the sign of the projected BAU change in the global bottom-50% share is not robust (7.5% to 10.0% in 2050 vs 9.7% in 2016) and BAU 2050 bottom-half income varies by about +/-14%; the rise of the top-1% share under BAU (23.5-25.4%) and the ranking of scenarios survive.

Why it matters, in detail. Top-end growth is the ratio of 2016 to 1980 top-fractile incomes; more than half of the 1980 denominator for the global top 0.001% consists of Latin American and MENA tails extrapolated from 2001 and 1990 shapes, so any true 1980-2001 change in Latin American (or 1980-90 MENA) top shares passes almost one-for-one into the global trunk. Sign and size unknown.

Evidence. wid2017_subset (extract of the frozen 2017 WID input database): Brazil top-10% share observed 2001-2015; UK 1990-2014 (individual series only); Germany 18 years between 1961 and 2013. Authors' inputs (1d-calibrate-subregions.dta): Brazil top-10% share 54.34% in every year 1980-2001; MENA 65.11% in 1980-89. Workbook Figure1A-data C14:C24: Brazil 58.09% (1990) -> 54.03% (2000). Composition of the 1980 global top 0.001% (adjudicator merge, scripts/diagnostics.py): Other Latin America 26.5%, MENA 17.8%, Brazil 12.8% (together 57.1%); of the top 1%: 25.0%. The P&P (p. 104) gives 1990 as 'the first year for which we can construct estimates' for the Middle East, Brazil and sub-Saharan Africa.

Why this severity. The 1980 base of the trunk and of the top-1% share rests mostly on assumed (constant-share) distributions; the direction of any bias is not demonstrated (constant shares are conservative where inequality rose, but this is untested for Latin America and MENA), so this is an important undisclosed caveat on the magnitudes in C2-C4 rather than a demonstrated error.

The authors' response. Technical Note 2017/5 Section 2.4 describes the constant-share extrapolation and calls it 'conservative' 'in the context of a general rise in inequality since the 1980s'.

Why it matters, in detail. The later vintage (new country DINA series, revised PPPs and national accounts, a MENA series without the 1980-84 cut) lowers top-group growth by 26-44% and middle-40% growth by 11 pp; the top 0.001% now grows about as much as the hump of the curve (131% vs ~120% in the paper), i.e. the 'long trunk' largely disappears, while capture shares (27.2% vs 12.4%) are unchanged.

Evidence. WID bulk download 2026-10-15, WO-PPP, sptincj992 x anninci992 (scripts/current_wid_check.py): average growth 46.2% (paper 60%), bottom 50% 95.2% (94%), middle 40% 32.2% (43%), top 10% 52.0% (70%), top 1% 74.6% (101%), top 0.1% 97.5% (133%), top 0.01% 121.4% (185%), top 0.001% 131.5% (235%); capture top 1% 27.15%, bottom 50% 12.35%; top-1% share 16.8% (1980), 21.6% (2007), 20.1% (2016); bottom-50% share 6.0% (1980) -> 8.0% (2016) vs 8.0% -> 9.7%. Auditor A obtained the same (top 0.001% 124.9% using a slightly different bracket construction).

Why this severity. The authors' own later estimates put top-1% growth about a quarter lower and top-0.001% growth about 45% lower, so the trunk magnitudes in C2/C3 must be read as fragile; the C1 headline is corroborated. Not counted as an error of the 2018 paper.

The authors' response. Technical Note 2017/5 (p. 5) advises replicators to use the frozen September 2017 database because the online version 'is regularly updated' and 'may generate slightly different estimates'; Chancel & Piketty (2021, pp. 3055-3056) say new country series can affect 'finer decompositions for the more recent period'.

Why it matters, in detail. Block-merging removes within-subregion between-country dispersion (Japan had 19% of Other Asia's adults but 46% of its income in 1980) and substitutes the donor's dispersion. With country means, the 1980 global bottom half is poorer and the 2016 middle richer, shifting the hump right and deepening the trough. Upper-bound caveat: applying the China+India shape (which already contains the China-India gap) country by country double counts part of the between-country dispersion.

Evidence. Code 1b, 1c, 1d, 1g; 0c lines 27-37 (USSR fill). Technical Note Section 3.1 ('the between-country component of inequality is properly estimated') and Section 3.3 ('We performed tests where we combined a larger number of countries, and as expected, results were very similar'). Adjudicator test (scripts/country_means.py: each country's own 1980/2016 national income per adult and adult population from the authors' files, donor shape unchanged): bottom-50% share 7.92% -> 6.80% (1980) and 9.67% -> 8.88% (2016); top-1% share 2016 20.44% -> 21.07%; bottom-50% growth 94% -> 108%; hump 120% at p25 -> 124% at p38; median growth 62% -> 110%; mean growth p40-p60 68% -> 106%; trough 36.7% at p75 -> 31.6% at p81; capture ratio 2.19 -> 2.30 (dynamic calibration 1.67 -> 1.83). Auditor A's E8 gave the same within ~1 pp.

Why this severity. Moves the hump of Figure 2 from p25 to p38, raises median growth from 62% to 110% and lowers the bottom-50% share level by about 1 pp, which are noticeable features of Figures 2-3; the change makes the elephant more pronounced and leaves the capture headline essentially unchanged, so it does not undermine the core findings.

The authors' response. Technical Note 2017/5 Section 3.3: merging country by country 'would be computationally very intensive and would not add much'; tests combining more countries gave 'very similar' results.

Why it matters, in detail. The archive's EU8016 growth profile gives a 2050 bottom-50% share of 11.7% and mean of EUR 8,350 (EU/US 1.86); the published 12.9%/EUR 9,138 lies between the archive's EU8016 and FR8015 results and is unreconciled. Other world-level differences (<= 2 pp) are consistent with a later final run.

Evidence. World column, archive vs published: average 58.9 vs 60, middle 40% 40.9 vs 43, top 10% 69.1 vs 70, top 0.01% 183.8 vs 185, top 0.001% 234.4 vs 235; capture 27.71/12.65 vs 27/12 (the technical note's Figure B2 key says 28%/13%; workbook-implied values 27.32/12.45). EU scenario 2050: bottom-50% share 11.71% (archive; adjudicator merge of project-regions.dta identical) vs 12.88% (workbook Figure3-data C75); bottom-50% income EUR 8,350 vs 9,138 (Figure4-data E74), -8.6%; EU/US income ratio 1.86 vs 2.04 ('twice higher'); top 1% 19.35% vs 19.05%. Neither archived European profile reproduces the published values (EU8016: 11.71%, EUR 8,350; FR8015: 14.51%, EUR 10,353). BAU EUR 6,219 vs 6,299; US EUR 4,479 vs 4,479 (exact). Figure 1's Europe top-10% series differs from the archive's Europe aggregate by up to 2.4 pp (other regions match within 0.15 pp); Brazil 1990-2000 differs (F4). DataCite: deposit created 2025-05-31; openICPSR returned HTTP 403 (Cloudflare) to the adjudicator and to both auditors.

Why this severity. Core world numbers reproduce within 1-2 pp, but the European-scenario numbers quoted in the text (about 13%, EUR 9,100, 'twice higher') cannot be obtained from the posted materials, and no reconciling package is accessible; this weakens a secondary result and the paper's statement that 'all data and programs are available online at WID.world'.

Why it matters, in detail. Global top-1% share -0.53 pp over 2000-2016 and -1.76 pp over 2007-2016; bottom-50% share +0.98 pp over 2000-2016; top-10% share -3.2 pp. The defensible statement (within-country inequality kept rising while between-country inequality fell) is in the WP abstract but not in the P&P.

Evidence. Workbook Figure3-data: top-1% share I25 = 20.97% (2000), I31 = 22.22% (2006), I32 = 22.20% (2007), I41 = 20.43% (2016); bottom-50% share E25 = 8.68% (2000), E41 = 9.66% (2016). Archive: global top-10% share 55.3% (2000) -> 52.1% (2016); Gini 0.677 -> 0.652 (Auditor B). WP 2017/20 (long version) abstract: 'We observe a trend-break after the financial crisis, but this is only due to between-country reduction in inequality, as within-country inequality continued to rise'; Section 4: 'the situation more or less stabilized beginning in the early 2000s'. Chancel & Piketty (2021, Figure 8 caption): 'the decline in global inequality observed since 2008'. Current WID: top-1% share 21.6% (2007) -> 20.1% (2016).

Why this severity. A stated conclusion about the post-2000 trend is the opposite of what the paper's own Figure 3 series show; it does not affect the 1980-2016 estimates, so its impact on the core findings is limited, but it misstates a secondary result and frames the projections.

The authors' response. The working paper's own abstract acknowledges 'a trend-break after the financial crisis', attributing it to between-country convergence; Chancel & Piketty (2021) refer to 'the decline in global inequality observed since 2008'.

Why it matters, in detail. Donor-tail and proportional-scaling assumptions determine where the national-accounts/survey gap is allocated; in MENA the Lebanese tail shapes a population that is a large share of the global top in 1980. Direction and size for the global curve are not established; Yonzan et al. (2022) support tax-based corrections for the top 1% in rich countries but not wholesale replacement of upper-decile survey data.

Evidence. P&P p. 103 and footnote 2; Technical Note Section 2.3. MENA residents are 17.8% of the 1980 global top 0.001% (35.8% at national-accounts incomes, F1) and 8.7% in 2016 (adjudicator merge). The current WID MENA top-1% share falls from 33.7% (1980) to 22.9% (2016), indicating large later revisions to these tails. Kharas & Seidel (2018, Brookings WP 114): WID uses distributional data 'for just 53 countries covering 65 percent of the world's population'; Lebanon's top data 'applied to all other countries' of the Middle East and Cote d'Ivoire's to Africa (fn 28).

Why this severity. Plausibly affects the level and growth of the global top, which drives the trunk and part of the capture headline, but neither the critics nor this adjudication quantify the effect on the global curve, and the survey-based comparators are not concept-matched; an important caveat rather than a demonstrated bias.

The authors' response. Chancel & Piketty (2021, JEEA, pp. 3055-3056) acknowledge that corrections 'often rely on a limited set of countries' but say their robustness checks show this does not affect the general long-run conclusions; per the critique corpus, Alvaredo, Assouad & Piketty (2019, fn 10) reply that Hlasny & Verme's survey-based Pareto benchmarks are 'artificially low' (not re-verified here).

Why it matters, in detail. Denominator error in projected income per adult: 2050 adult counts understated by ~13% in aggregate, so per-adult means and bottom-50% means are overstated by 7-10%; distributional shares are essentially unaffected because growth shares are applied to totals. Magnitude approximate (current WPP age structures stand in for WPP 2017).

Evidence. projections.dta, 2016: China 1,403.5m, India 1,324.2m, US 322.2m, Nigeria 186.0m (total population) vs WID adults 1,067.3m, 826.3m, 234.8m, 85.4m (populations.dta); '6a - import-projections.do' line 18. World Bank (WPP-based, current revision) 2016-2050: total population x1.280, adults 20+ x1.427 (ratio 1.115; India 1.22, Nigeria 1.30). Re-running 6a/6c with 20+ growth (scripts/projection_variants.py, P3): world adults 2050 6.06bn -> 6.95bn; world average per adult EUR 35,661 -> 32,800; 2050 bottom-50% income BAU EUR 6,219 -> 5,692, US 4,479 -> 4,180, EU 8,350 -> 7,542; shares nearly unchanged (BAU top 1% 24.71%, bottom 50% 8.68%). Auditor A obtained the same within 1%.

Why this severity. Lowers projected 2050 bottom-half incomes by 7-10% ('double again' becomes about +85%) but leaves shares, the scenario ranking and all conclusions unchanged; Auditor A rated it moderate.

Why it matters, in detail. Inverse scaling misallocates income between the bottom 90% and top 10% of Germany and the UK in opposite directions; the errors largely cancel in the FR-DE-UK donor and in world aggregates (<0.3 pp on top-1% growth; capture unchanged) but understate European top-end growth.

Evidence. '1a - prepare-data.do' line 232: replace ainc = afr * (avg90fr/avg90) if p<90000. Adjudicator check (scripts/degb_fix.py): UK 1980 top-10% share 28.3% in the inputs vs 37.1% intended; Germany 1980 35.8% vs 31.9% (WID-2017 31.86%); UK 1980 bottom-90% average EUR 22,858 vs 15,327 intended. Correcting it: world top-1% growth 101.1 -> 101.3%, top-0.001% 233.9 -> 239.1%, capture unchanged (27.74/12.65); Europe column of Table 1: bottom 50% 26.3 -> 28.8%, top 10% 58.0 -> 55.3%, top 1% 71.9 -> 73.6%, top 0.1% 76.3 -> 84.8%, top 0.01% 87.7 -> 101.7%, top 0.001% 118.7 -> 137.7%. Both auditors found the same error (B: European bottom-50% growth 26.28 -> 28.42%).

Why this severity. A confirmed coding error with negligible effect on world results and a modest effect on the Europe column (top-end growth up by 2-19 pp); Europe still has the smallest gap between bottom and top growth. Auditor B rated it moderate.

The authors' response. Technical Note Section 2.2 calls the UK/Germany imputation provisional and says alternative specifications 'had only very little impacts'.

Why it matters, in detail. The world merge embeds ~8 pp faster US-Canada average growth than Table 1 reports and treats Russia+Ukraine as one block; consistent harmonization would lower world average and top-group growth slightly and leave capture shares unchanged.

Evidence. Technical Note Table B1 (archive): North America 71%, Ex-USSR 16% (with group rows 8/50/135/224/347/488/684 and -36/-9/151/579/2200/7105/21820), vs P&P Table 1 US-Canada 63/5/44/123/206/320/452/629 and Russia 34/-26/5/190/686/2562/8239/25269. wid2017_subset: US anninc992i +72.2% (1980-2014), +74.5% (1980-2016); Ukraine -41.7%. Auditor A: PSZ (2018) US +60.8% over 1980-2014; harmonizing US-Canada to 63% gives world average 57.3%, top-1% growth 97.9%, capture 27.8%/12.9% (A's E7, not re-run).

Why this severity. An undisclosed inconsistency between a reported regional table and the inputs of the world computation, with small effects on world results (per Auditor A's harmonization, top-1% growth -3 pp) and no effect on conclusions.

Why it matters, in detail. Higher imposed mean growth in poorer subregions mechanically raises global bottom-half levels (+13-24% by 2050) and the bottom-50% share (+0.8 pp in BAU), and slightly raises the BAU top-1% share because of the Other Asia growth-share profile (+0.3 pp).

Evidence. '6a - import-projections.do' lines 31-48; adjudicator variant without the overrides (scripts/projection_variants.py, P4): 2050 bottom-50% income BAU EUR 5,241 (vs 6,219), US 3,959 (vs 4,479), EU 6,754 (vs 8,350); BAU bottom-50% share 7.96% (vs 8.72%); BAU top-1% share 24.22% (vs 24.52%). Auditor A obtained identical figures.

Why this severity. The assumption is disclosed and is indeed conservative for inequality shares; the only problem is that the headline income levels ('double again, to EUR 6,300') depend on it, which the footnote does not make clear.

The authors' response. Disclosed in footnote 4 and Technical Note Section 4.1 ('We view this relative optimism as a conservative assumption').

Why it matters, in detail. The data repair concentrates MENA 1980 income at the top (+5.8 pp top-10% share), raising 1980 global top fractiles; correcting it would raise world top-1% growth by ~3 pp (Auditor A).

Evidence. Data/Added/middle-east.dta: 112 inconsistent brackets in 1980 (e.g. bracket average above the next threshold); top-10% share 65.1% in the source vs 70.9% after the force-format step (1984: 65.6%; 1985: 65.0%; 1990: no inconsistencies). Auditor A: correcting it raises world top-1% growth to 104% and, combined with F1, gives 85%.

Why this severity. Small and in the direction opposite to F1 (it raises the 1980 global top and so lowers measured top-end growth).

Why it matters, in detail. Scenario differences in the bottom-50% mean are established; mapping them to poverty requires a poverty line and the within-bottom-half distribution, neither of which is reported.

Evidence. P&P p. 108 (opening paragraph) and Figure 4. All three scenarios raise the bottom-50% mean above its 2016 level (EUR 4,479-9,138 vs 3,082). Auditor B's illustrative counterexample: two distributions with identical bottom-half means (EUR 4,500) but 0% vs 25% below an illustrative threshold. Concept difference: Kharas & Seidel (2018) on pre-tax income vs consumption.

Why this severity. An interpretive overreach in a concluding sentence; the conditional result it rests on (bottom-half average income differs about 1.9-2x between the EU- and US-style scenarios) is reproduced and is the defensible statement. Auditor B rated it moderate.

Why it matters, in detail. The trough mixes the collapse of ex-Soviet incomes, the imputed Other Asia distribution and rich-country stagnation; attribution to the US/Western Europe alone overstates their role.

Evidence. Adjudicator composition of the 1980 global p70-p90 band (scripts/diagnostics.py): Other Asia 22.0%, Russia+Ukraine 19.2%, Other Western Europe 12.1%, US 11.1%, Eastern Europe 7.3%, Germany 5.4%, UK 4.0%, France 3.7%, Other North America 1.3% (US+Canada+Western Europe 37.7%); 2016: China 27.6%. Table 1 does show low US-Canada and European bottom-50% growth (5%, 26%).

Why this severity. A labelling simplification common to anonymous growth curves; the underlying pattern (slow growth for rich-country lower and middle classes) is real in Table 1, and the trough's position relative to the mean is not an artefact of population growth (see rejected claims).

Why it matters, in detail. No effect on estimates; the abstract's 'at the median' would only be accurate under country-level means (F6) or in the later vintage (hump at p46).

Evidence. P&P p. 107 Figure 4 (page image checked) vs workbook Figure4-data D74 = 6,299.2, C74 = 4,479.2 and text p. 107; P&P p. 107 text vs Figure 3-4 legends; AEA abstract vs workbook Figure2-data B44 = 62.04 (p50), B19 = 119.96 (p25); workbook Figure1A-data F37:F40 = 55.456; WP 2017/20 (December 2017, long version, eml.berkeley.edu/~saez/ACPSZ2018WIDWP.pdf), Section 3: 'income growth was lower than 100% (40%, 34%, and 74%, respectively)', 'the global average (+66%)' and Europe 'excluding Ukraine, Belorussia, and Russia'; '0b - import-regions.do' line 20; User Guide 2017/9 description of 1d (calibration = 1 described as rescaling) vs its own option list (static 0, dynamic 1) and the code.

Why this severity. Presentation slips with no effect on computed results; the text values are the correct ones.

Why it matters, in detail. No propagation into any estimate.

Evidence. Technical Note 2017/5, Section 3.5 (p. 15 of the PDF), worked example; the formula in the code ('2a - world-shares-growth.do', '1d') and in the adjudicator's recomputation is correct.

Why this severity. An arithmetic slip in an illustrative example in the companion note; the empirical 27%/12% use the correct formula.

Why it matters, in detail. Omitting a small high-income region slightly lowers world mean levels; including it changes world group growth by <0.7 pp and capture shares by <0.1 pp.

Evidence. 'runwir-program.do' line 92 ($countries = AF AS BR CN DE EE FR GB IN ME NA RU SA US WE); '0c - aggregate-regions.do' lines 54-60 keep only listed regions; regions-aggregates.dta contains no OC rows. Dropped: 13.7m adults (0.57%) and 1.17% of world income in 1980; 26.9m adults (0.55%) and 1.09% in 2016 (Australia 18.1m adults at EUR 38,977; New Zealand 3.3m; Papua New Guinea 4.1m) (scripts/rebuild_regions.py). Technical Note Table A1 (Scenario 4: 100% of population and income); P&P p. 103. Adding Oceania with the Western European shape (scripts/experiments.py, E5): capture ratio 2.19 unchanged; top-1% growth 100.9%; top-0.001% 233.4%.

Why this severity. A coverage misstatement with no material effect on any reported result.

Why it matters, in detail. Cross-sectional co-movement of inequality and policy across five or six regions cannot separate policy from other region-specific shocks; no identification is offered.

Evidence. P&P p. 104, first column; Figure 1.

Why this severity. An interpretive claim outside the paper's quantitative findings; it may be defensible on the basis of the authors' country studies but is not established here.