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Thomas Piketty, Gabriel Zucman · In A.B. Atkinson and F. Bourguignon (eds.), Handbook of Income Distribution, vol. 2B, ch. 15: 1303-1368, North-Holland
Wealth and Inheritance in the Long Run
18 problems found: 3 major · 9 moderate · 6 minor
What the paper claims
- Wealth-income ratios followed a U-shape over 1910-2010: very high in 18th-19th century Europe, collapsed after the world wars, recovered since the 1950s; less marked in the United States.
- Since 1970 private wealth-national income ratios rose in all eight largest rich economies; the growth slowdown is 'the central force' behind the rise.
- Wealth concentration followed a U-shape: Europe is much less concentrated than a century ago (with a recent rebound), while the US has almost returned to its early-20th-century level, a 'great inequality reversal'.
- Inherited wealth followed a U-shape: in France the annual inheritance flow and the share of inherited wealth fell sharply after 1914 and have risen again; similar U-shapes in the UK, Germany and Sweden.
- Over a wide range of models the long-run magnitude and concentration of wealth and inheritance increase with r - g (beta = s/g; Pareto tail set by omega = s e^{(r-g)H}; mu(g) falls with g); small changes in r - g make a huge difference to long-run wealth inequality.
- Current trends toward rising wealth-income ratios and wealth inequality might continue in the 21st century because of slower population and productivity growth and international tax competition; after-tax returns fell below growth after WWI and may exceed it again.
- Forbes data suggest higher returns for larger fortunes: top global wealth fractiles grew much faster than average wealth.
Every problem found
1majorconfirmed · newly identified here · speculative assumption
The chapter's best-known inheritance number, that roughly two-thirds to three-quarters of French wealth in 2010 was inherited, comes from a series built by multiplying another estimate by round factors typed into a spreadsheet, not from the micro data the text describes. The authors' own reproducible estimate is closer to one half. The broad pattern (high, then low, then rising) still holds, but the 2010 level is much less certain than presented.
Technical detail and evidence
Why it matters, in detail. phi_2010 = 66.6% = 1.08 x 61.7% (Modigliani); with k between 1.00 and 1.15, phi_2010 lies between 61.7% and 70.9%. The only reproducible series (simplified, H = 30 years) gives 52.4% for the year 2010 and 55.1% for the plotted decade point, which includes 2011-2019 extrapolations. The 'lower bound' property and the 'approximately constant' gap are untested, because no independent PPVR estimate for France exists. The same scaled series (k = 1.10) underlies the 80-90% projections of Fig. 15.30. The direction of the true bias is unknown: applying the Paris ratios of 1.27-1.51 would raise the level. So the finding is that the stated level is unsupported, not that it is demonstrably too high.
Evidence. PikettyZucman2014HIDSection4.xlsx, sheet DataFig4.1-4.3(b): H9:H34 (e.g. H25 '=1.08*B25' = 66.63%, H17 '=1.35*B17'); B9 '=0.05+72.6%'; B11:B15 typed -0.02/-0.03; Paris ratios U9:U15 = 1.27-1.51. Sheet DataFig4.4-4.7: E24 '=AVERAGE(DetailsDataFig4.4-4.7!F200:F209)' = 55.12%. DetailsDataFig4.4-4.7: F200 = 52.42%; rows 201-209 copy the 2010 inputs; E198:E200 = 14.53% (the 2008 value). Chapter pp.1334, 1337-1338, Fig. 15.20 and caption. Adjudicator recomputation: scripts/inheritance_share_recompute.py reproduces the sheet to 3e-16 (work/inheritance_share_recompute.json). Auditor A: I1, I2(a), I17(6). Auditor B: I3, I4.
Why this severity. The U-shape survives in every variant. But the headline 2010 level is reached only through an unexplained multiplier: k = 1 gives 61.7%, and the reproducible simplified estimate is 52-55%, roughly a quarter below the stated 65-75%. The implied recovery since 1970 shrinks from about 30 pts to 16-21 pts.
The authors' response. None located. The chapter calls the estimates approximate and says ongoing data collection 'suggests that the final estimates will not be too different' (p.1338). Alvaredo, Garbinti & Piketty (2017, Economica) later headline 'back to 50-60%' for Europe, using the simplified definition.
2majorlikely · previously known · external inconsistency
The chapter says the richest Americans now hold almost as large a share of wealth as on the eve of the 1929 crash. Later work, including the authors' own updated figures, still finds a large rise since 1980 and a US more unequal than Europe. But it puts today's top share clearly further below its 1920s peak, because the method used assumed the rich earn the same interest rate on their savings as everyone else.
Technical detail and evidence
Why it matters, in detail. Ratio of the current to the peak top-1% share: about 0.89 in the chapter (40/45), 0.81 in SZ 2016 (41.8/51.4), 0.75 in WID 2026 (36.6/48.7). Heterogeneous-yield levels (SZZ 33.7% in 2016) imply roughly 0.65-0.70, though these comparisons mix units (tax units vs households) and are not strictly like-for-like. The 1980s to 2010-12 rise falls from +12.0 pts (chapter) to +10.2 pts (WID decennial), and to roughly +6 pts under BHH-type yield premiums. SZ (2020) accept a modest premium (1.15x in 2003-07, 1.4x from 2008) and argue that the SCF and the Fed DFA show top-1% rises of 6.2 and 5.2 pts over 2001-2016, versus 1.4 pts in SZZ. The magnitude remains disputed.
Evidence. Chapter p.1325; Figs 15.15-15.16; Section3.xlsx DataFig3.5 B16:C26 and note A33 ('March 12, 2014 version'). SaezZucman2015MainData.xlsx DataFig1-6-7b, rows 18 (1928) and 102 (2012). NBER WP 20625, p.22 ('peaked at 84%'). WID 2026 bulk, US shwealj992 (scripts/wid_wealth_shares.py). SZ (2016) Appendix Table B41c (row 2012 = 18.70%). Bricker, Henriques & Hansen (2018), FEDS 2018-024, abstract. Smith, Zidar & Zwick (2023), QJE 138(1), Table I. Saez & Zucman (2020), NBER WP 27921, Sec. 5.1. Vector check of the printed figure: scripts/fig15_15_us_check.py.
Why this severity. The post-1980 US rise and the Europe-US reversal survive in every series. But the gap between today's US top-1% share and its 1920s peak is about 5 pts in the chapter, about 12 pts in the authors' own current series, and about 15 pts under heterogeneous-yield estimates. In linked-data and survey estimates the post-1980 rise is up to about half as large.
The authors' response. Saez & Zucman (2020, NBER WP 27921, Sec. 5.1) incorporate a top-1% interest premium (1.15x in 2003-07, 1.4x from 2008) but reject larger premiums. They argue that SZZ understate wealth above $50m by a factor of 1.7 relative to the SCF plus Forbes. Their revised series still shows a large rise.
3majorplausible · previously known · methodology
Much of the measured rise in French inheritance since the 1980s comes from gifts made during life, and these were measured in years when temporary tax breaks encouraged people to give early. A 2026 re-analysis of the same data puts the recent yearly inheritance flow at roughly 10% of national income instead of 15%. Inheritance still rose, but by less, and the chapter's 'two independent measures' both rely on the same gift data.
Technical detail and evidence
Why it matters, in detail. The economic flow is b_y = (1 + v) mu m beta. Most of the post-1980 rise in mu* = (1 + v) mu comes from v (about 0.28 -> 0.82), which is measured in six DMTG reference samples (1977-2006), several taken in years with gift incentives. In Piketty's own series, bequests alone rise only from 4.6% (1984) to 8.0% (2008) of national income (as reported by Geerolf 2026a). Excluding spouses (10% of the flow, Piketty's own assumption) lowers the 30-year simplified phi_2010 from 52.4% to 49.8% (adjudicator computation); adding the gift correction gives 46.1% (Geerolf 2026b). Agreement between the 'fiscal' and 'economic' series cannot validate the gift trend, because both embed v.
Evidence. Chapter pp.1334-1337 and the Fig. 15.17 caption. Section4.xlsx DataFig4.1-4.3(a), columns B, C, I, J: fiscal/economic ratio 0.59-0.97; v = J/I - 1 rises from about 0.28 (1970) to 0.82 (2010). DetailsDataFig4.4-4.7 E198:E200 = 0.1453 (2008-2010). Piketty (2011, QJE, p.1087 fn 19): the economic flow uses estate-tax relative age-wealth profiles and the observed fiscal gift-bequest ratio. Geerolf, F. (2026a), 'Les flux successoraux en France : mesurer les tendances de long terme a partir des donnees fiscales sur les successions et les donations', OFCE-Sciences Po working paper, January 2026, https://fgeerolf.com/flux-successoral.pdf, pp.2-4. Geerolf, F. (2026b), 'La part du patrimoine herite en France : reexamen des estimations fondees sur les flux', OFCE-Sciences Po, September 2026, https://fgeerolf.com/patrimoine-herite.pdf, pp.3, 8-9. Spouse-exclusion recomputation: scripts/inheritance_share_recompute.py.
Why this severity. If the corrections hold, the qualitative U-shape survives (the critic confirms it). But the recent level is about 30% lower (10.3% vs 14.5% of national income in 2008) and the recovery since the mid-1980s more than 40% smaller: a material change in the size of the 'return of inheritance'.
The authors' response. None located. Geerolf (2026a, p.4) quotes Piketty's (2010) data appendix acknowledging that gift flows are 'structurally more volatile' and that simulations suggest a slight 'overshooting' in the rise of gifts since the 1980s, 'perhaps due to tax incentives'; these are translated quotations not checked against the original appendix.
4moderateconfirmed · previously known · data error
For recent years the chapter's UK figures count only the wealth of people whose estates go through probate and treat everyone else as owning nothing, which makes the richest tenth appear to hold 70% of wealth instead of roughly 55%. This error creates most of the apparent recent rise in European wealth concentration in the chapter's data. It does not affect the large historical decline, or the conclusion that the US is now more unequal than Europe.
Technical detail and evidence
Why it matters, in detail. Top-10% share = 0.707 / (1 + w), where w = excluded wealth / identified wealth: 0.707 (w = 0), 0.561 (w = 0.26), 0.484 (w = 0.46, the Series C total). Europe (FR+UK+SE)/3 in 2010: 63.9% becomes 59.1% (UK at 56.1%) or 58.8% (UK from WID). The 1980-2010 change falls from +4.6 pts to between -0.2 and +1.7 pts. With WID France (50.5% -> 57.8%) and UK, the change is +3.9 pts and the 2010 level 57.3%. The bias also drifts upward as HMRC coverage falls (35% -> 31% -> 27% of adults).
Evidence. Section3.xlsx DataFig3.1-3.6: F24:G26 hard-coded (0.64/0.24, 0.685/0.27, 0.705/0.28); notes A33-A37. HMRC Table 13.8, 2008-10 row (69% of adults not in the identified population). HMRC, 'Personal Wealth Statistics 2008 to 2010' (2012), section 6 'Quality'. Alvaredo, Atkinson & Morelli (2017), CSEF WP 464, pp.11 and 35; published in J. Public Econ. 162: 26-47 (2018). WID 2026, GB shwealj992. scripts/europe_concentration_uk.py (work/europe_concentration_uk.json).
Why this severity. The UK level is overstated by about 15 pts and its post-1980 rise is an artefact. This lowers the European 2010 top-10% average from 63.9% to about 59%, below the stated 60-70%, and removes most of the European rebound in the chapter's own data. The long-run European decline and the Europe-US reversal are unaffected (both widen), and the authors' later French series restores a modest European rebound (+3.9 pts using WID France and UK). Hence moderate rather than major.
The authors' response. Piketty's response to the FT (28 May 2014) defends estate-tax data against the Wealth and Assets Survey (low response rates, poor coverage of the top). It does not address the excluded-population denominator. The chapter, completed later in 2014, kept the 70.5% value.
5moderateconfirmed · newly identified here · overclaiming
The chapter says the share of inherited wealth fell and then rose again in four European countries. Its own figures show a clear rebound only in France and Germany: in Sweden the share has been flat since 1950, and in Britain it is still below its 1970 level.
Technical detail and evidence
Why it matters, in detail. Change in phi from the 1970s to 2010: France +21.2 pts, Germany +28.3, Sweden +1.1, UK -5.8 (UK +3.2 from the 1990s trough). Sweden falls from 77.6% (1900) to 44.7% (1950) and is flat thereafter.
Evidence. Section4.xlsx DataFig4.4-4.7, columns E-H (rows 13-24) and D13:D14 '=0.1441*1.2'. Chapter pp.1306, 1340-1341. Captions of Figs 15.22-15.23. scripts/inheritance_share_recompute.py ('plotted_decennial_phi').
Why this severity. The French and German U-shapes stand, but the generalisation to four countries holds for the stock share in only two of them. Flows are reported as U-shaped in all four, so this narrows rather than reverses C4.
The authors' response. The Fig. 15.23 caption concedes that 'the Swedish inheritance stock increased relatively little', attributing this to a rise in the private saving rate.
6moderateconfirmed · newly identified here · internal inconsistency
To show how a small rise in the gap between returns and growth can sharply concentrate wealth, the chapter gives a numerical example. Worked out exactly, the example raises the top 1% share by about 11 percentage points, not the roughly 30 points the text claims, and its numbers would require people to save more than everything they have.
Technical detail and evidence
Why it matters, in detail. S_k = [(1-p) omega^k - (1-omega) p^k] / (omega - p). With p = 0.1, S_2 = 0.9 omega + 0.1. omega = 0.2e^0.6 = 0.364 and 0.2e^0.9 = 0.492 give 42.8% and 54.3%. The bottom 90% hold zero wealth, so the top-10% share is 100% in both cases. The proportional change is +27% (exact) or +56% (feasible p = 0.25), versus roughly +100-150% implied by the text.
Evidence. Chapter pp.1352-1356 (eqs 15.1-15.5, fn 40). scripts/theory_checks.py (work/theory_checks.json); the exact shares agree with summation to 1e-15. Auditor A: I6. Auditor B: I2.
Why this severity. The qualitative theorem (a higher r - g fattens the Pareto tail) is correct. But the chapter's only quantitative illustration of 'huge' effects overstates the effect on the top-1% share by a factor of about 2.5 in percentage points.
The authors' response. The sentence is hedged ('say'), and footnote 40 notes that the discrete distribution and the continuous Pareto approximation differ. Piketty (2015, AER P&P) repeats the 2.28 -> 3.25 illustration.
7moderateconfirmed · previously known · speculative assumption
The chart showing that, after taxes and war losses, returns on wealth fell below economic growth for most of the 20th century is not built from measured after-tax returns. It applies round-number assumptions, and for 1950-2012 a slightly lower assumed tax rate would reverse the conclusion.
Technical detail and evidence
Why it matters, in detail. 1913-50: r-bar = 0.7 x 5.15% - 2.5% = 1.10% vs g = 1.81%, a gap of -0.70 pts. It is +1.80 pts without the loss deduction, and negative only if losses exceed 1.80%/yr. 1950-2012: r-bar = 0.7 x 5.33% - 0.5% = 3.23% vs g = 3.78%, a gap of -0.55 pts. It is -0.05 pts without the deduction; the tax-only break-even rate is 29.1%, and the gap is +0.22/+0.49 pts at 25%/20% tax rates. The 2012-2100 values are scenarios (10% and then 0% tax).
Evidence. Section5.xlsx DataFig5.4-5.5: C12 '=0.7*B12-0.025', C13 '=0.7*B13-0.005', C14 '=0.9*B14', B7:B9 = 0.045; note A20. Chapter p.1358, Figs 15.27-15.28. Auditor A: I8. Auditor B: I7.
Why this severity. Pre-tax r > g is independently supported (Jorda et al. 2019). But the sign of the post-WWI after-tax gap, used as an explanation of 20th-century deconcentration, hinges on the assumed 30% tax rate and on the extra 0.5%/yr deduction for 1950-2012.
The authors' response. The assumptions are disclosed in the appendix note (Section5.xlsx DataFig5.4-5.5, A20), and the future paths are described in the text as scenarios.
8moderateconfirmed · newly identified here · arithmetic or transcription
The chapter's table says the world's very richest people grew their wealth by 6-7% a year after inflation from 1987 to 2013. Spreadsheet errors inflate that figure; the corrected rate is about 4.5% a year, still more than twice as fast as average wealth but much less dramatic.
Technical detail and evidence
Why it matters, in detail. Real CAGR, 1987-2013: published 6.77% / 6.42%; with the backcast fixed, 5.39% / 5.05%; with both fixes, about 4.47% / 4.50%. Average wealth per adult 2.01% (printed 2.1%); income per adult 1.34% (printed 1.4%).
Evidence. Chapter12TablesFigures.xlsx TS12.3: Z7:Z9 '=Z8*N7/N$10' etc., U7:U9, T31:V33 and Y31:AA33; T12.1 B9 '=0.001+TS12.3!AP37' and B10 '=0.0004+TS12.3!AO37'. Forbes 2010/2013 lists (/mnt/zdata/downloads/forbes-billionaires). scripts/table151_forbes_check.py (work/table151_forbes_check.json). Auditor A: I4. Auditor B: I6.
Why this severity. The direction survives: the top fractiles grew about twice as fast as average wealth. But their excess growth over average wealth falls from about 4.5 to about 2.5 pts a year (roughly 45% smaller). This is secondary evidence for the claim that larger fortunes earn higher returns.
The authors' response. The chapter warns that Forbes-type data are 'of relatively low quality' and 'likely ... suffer from various biases' (pp.1359-1360).
9moderateconfirmed · newly identified here · misrepresentation of source
The chapter says one simple model, started in 1820, reproduces two centuries of French inheritance. In fact the plotted line joins two different models, one of which the original study says fits the nineteenth century poorly. The model behind the forecasts has been checked against about one century of data, not two.
Technical detail and evidence
Why it matters, in detail. Table D5 (1820-initialised): the 1900 flow is 22.0% under class saving and 20.9% under uniform saving, vs 24.1% observed, and uniform saving misses the steep old-age wealth profile. The projections (16-17% and 22-23% of national income) come from the 1900-initialised uniform-saving run.
Evidence. Section4.xlsx DataFig4.1-4.3(a) L11:L39 (header 'Tables D5-D6'). Piketty2010-Simulations.xls: TableD5 D10 = 0.2101 = L11 and D20 = 0.2196 = L12; for 1900, D90 = 0.2200 (class) vs F90 = 0.2093 (uniform) vs 0.2410 observed; TableD6 D10 = 0.2374 = L19. Piketty (2011), QJE 126(3), pp.1118-1121. Auditor B: I5.
Why this severity. The plotted aggregate flows differ by only about 1 pt between saving regimes, and the 1900-2010 fit and the projections are as described. But the claimed two-century validation of the simple uniform-saving model used for the 2010-2100 projections is overstated, and the chapter omits its source's finding that uniform saving fails in the high r - g nineteenth century.
The authors' response. The source article is transparent about the two regimes (Piketty 2011, pp.1118-1121). The chapter notes that the simulations ignore within-cohort inequality, which it calls 'a major limitation' (p.1365).
10moderateconfirmed · previously known · selective presentation
The chapter shows the share of national income going to capital rising strongly from 1975. But 1975 was an unusually low year: measured from 1970, where the authors' own data begin, the rise is about a third as large, which weakens the evidence for the chapter's assumption about how easily capital substitutes for labour.
Technical detail and evidence
Why it matters, in detail. Mean alpha: 0.250 (1970), 0.205 (1975), 0.272 (2010). Mean beta: 2.87 (1970), 3.08 (1975), 5.16 (2010). The endpoint sigma is 1.18 vs 2.23, the fixed-effects slope implies 1.55 vs 1.87, and the net-vs-gross and housing objections apply on top.
Evidence. Section5.xlsx DataFig5.2 (PZ2014 Table A48, 1970-2010); Section2.xlsx DataFig2.8. Chapter pp.1350-1351. scripts/capital_share_start.py. Rognlie (2015); Gechert et al. (2022, RED 45). Auditor A: I11.
Why this severity. A secondary empirical support for the theory (capital share rising with beta) is overstated about threefold by the choice of start year. The co-movement survives in the chapter's own accounting, and the text does say 'since the mid-1970s'.
The authors' response. Piketty (2015, AER P&P; JEP pp.81-82) appeals to multi-sector models with high inter-sectoral substitution. PZ2014 acknowledge that housing accounts for most of the 1970-2010 rise in domestic capital in several countries.
11moderatelikely · previously known · methodology
The estimate of how much French wealth is inherited depends on how many years of past inheritances and savings are added up. The chapter uses 30 years without testing alternatives. Longer periods make the post-1970 increase shrink or disappear, while a choice consistent with the authors' own life-cycle assumptions keeps a smaller increase.
Technical detail and evidence
Why it matters, in detail. Out of steady state, phi_t depends on how past flows are weighted. The flat 30-year window gives no weight to pre-1980 labour savings of cohorts still alive in 2010, nor to pre-1940 inheritances still held in 1970. This deepens the 1970s trough and steepens the rebound. The model-consistent variant puts flat 30-year weights on inheritances and triangular 60-year weights (60 - tau)/60 on labour savings. It yields +10.7 pts for France over 1970-2010 and +16.2 pts from the 1979 trough. The UK share falls over 1970-2010 under every window.
Evidence. Section4.xlsx DetailsDataFig4.4-4.7: annual columns B, C, E (France), O, P, R (Germany), I, J, L (UK). scripts/inheritance_share_recompute.py and scripts/inheritance_window_modelconsistent.py (work/inheritance_share_recompute.json, work/inheritance_window_modelconsistent.json). Geerolf (2026b), pp.3 and 11 (same window results for France).
Why this severity. The 1910-1970 decline is robust to the window. The size of the recovery is not (from +23 to -7 pts across 20-60-year windows). But under a weighting consistent with the chapter's own demography the recovery is still about +11 pts, so the U-shape survives with a smaller right arm.
The authors' response. None located. The 30-year window follows the generation-length convention of the KSM literature and of the chapter's own definition (p.1328).
12moderatelikely · previously known · speculative assumption
The chapter argues that slower economic growth will widen the gap between the return on wealth and growth, and so concentrate wealth further. In the chapter's own textbook models, slower growth also lowers the return on wealth, usually by more, so the gap narrows unless machines and workers are extremely easy to substitute. The historical record, in which returns stayed high when growth changed, partly supports the authors.
Technical detail and evidence
Why it matters, in detail. Dynastic: r - g = theta + (gamma - 1) g, which rises with g for gamma > 1. CES (beta = s/g, r = a beta^(-1/sigma)), calibrated at beta = 5, r = 5%, g = 2%: halving g gives r - g = 0.86/1.50/2.15/2.54/2.97% for sigma = 0.7/1.0/1.5/2.0/3.0, all below the initial 3.0%. Rognlie: the net elasticity is about 0.74 times the gross one, and only 2 of 31 estimates surveyed imply a net sigma above 1. Gabaix et al.: random-growth models have a half-life of at least about 26 years, too slow for the recent US rise. Jorda et al.: corr(r - g, g) is between -0.2 and -0.6 historically, so r did not track g, which partly supports the authors.
Evidence. Chapter pp.1307, 1343-1349, 1356-1359, 1365. scripts/theory_checks.py (dynastic, CES and gross-saving blocks). Rognlie (2015), BPEA, pp.31-35. Krusell & Smith (2015), JPE 123(4). Jones (2015), JEP 29(1). Gabaix et al. (2016), Econometrica 84(6). Acemoglu & Robinson (2015), JEP 29(1). Jorda et al. (2019), QJE 134(3). Auditor B (report Sec. 6) computes the same CES and Ramsey results but chose not to count them as an issue.
Why this severity. The steady-state comparative statics are correct conditional on r. But the growth-slowdown channel for rising concentration rests on an assumption that the chapter's own closures contradict at its illustrative parameters. The tax-competition channel and the effect of slower growth on beta are unaffected, and historical return data partly support the assumption.
The authors' response. Piketty (2015, JEP pp.81-82) concedes that net saving is not constant and that beta = s/g does not go to infinity. He argues that r shows 'limited systematic variations in the long run' and that multi-sector elasticities can exceed one. Piketty (2015, AER P&P) presents r - g as a steady-state amplifier rather than a driver of short-run changes.
13minorconfirmed · previously known · selective presentation
The chapter attributes the recent rise in wealth relative to income mainly to slower growth and steady saving. The authors' own earlier paper finds that about 40% of the rise came from higher asset prices, mostly housing, a factor the chapter mentions only in passing.
Technical detail and evidence
Why it matters, in detail. Volume (saving) about 60% and price (capital gains) about 40% of the 1970-2010 rise in beta_n on average, in PZ2014's preferred specification including R&D. PZ2014 interpret the gains mainly as a recovery from earlier capital losses.
Evidence. Chapter p.1347 and fn 27 (p.1340). Piketty & Zucman (2014), QJE 129(3), p.1288 and Table VI. Auditor A: I9.
Why this severity. The rise in beta is measured, not modelled, and saving remains the larger component. Only the causal emphasis on s/g is overstated, and the chapter does mention the asset-price recovery.
The authors' response. PZ2014 (QJE, Sec. V) argue that the 1970-2010 capital gains are mostly a recovery from earlier twentieth-century losses and that relative prices wash out over 1870-2010.
14minorconfirmed · previously known · documentation gap
Several historical points in the wealth-concentration charts are typed-in estimates or carry unexplained adjustments, and the printed US chart does not exactly match the posted data. These move individual points by a few percentage points but do not change the overall story.
Technical detail and evidence
Why it matters, in detail. The France 1910 top 1% is 60.5% as built vs 58.8% under the sheet's own fixed-uplift rule. The US printed-vs-posted gap is up to 2.7 pts in the 1910s-1930s top 10%, and within 0.8 pts elsewhere and for the top 1%.
Evidence. Section3.xlsx DataFig3.1-3.6 F6 '=0.28+G6', F12 '=0.26+G12', L6 '=0.28+M6', L17:M17; DetailsDataFR F16:G16, F22:G26 and note A57; DataFig3.5. Roine & Waldenstrom (2009), SJE, Table A1. scripts/fig15_15_us_check.py. WID 2026 FR shwealj992. Auditor A: I10(i) and I13.
Why this severity. Each adjustment moves individual points by 1-4 pts and none changes the long-run patterns. Sutch's 1870 re-estimate (27.8% for households, 39.8% for adults) still leaves the 19th-century US well below Europe's roughly 55-60%.
The authors' response. Piketty's FT response (28 May 2014) explains the Swedish 1908/1920 bridge, the French 1910 factor (year-specific differential mortality) and the UK 19th-century Pareto interpolation, and concedes they 'should have been explained more clearly'.
15minorconfirmed · previously known · internal inconsistency
The text says world wealth would reach 7-8 years of income by 2100, but the chapter's own chart and spreadsheet show about 6.7 years. The historical world figures outside the rich countries are mostly round-number guesses.
Technical detail and evidence
Why it matters, in detail. s/g = 12%/1.5% = 8.0 vs 10%/1.5% = 6.67; the simulated 2100 value is 6.67.
Evidence. Section5.xlsx DataFig5.1: B28 = 6.67; saving assumptions H30:U38; regional columns H5:U19. Chapter pp.1348-1349, Fig. 15.24. Auditor A: I14.
Why this severity. The projection is explicitly labelled 'specific and uncertain'. The text overstates the chapter's own figure by 5-20%.
16minorconfirmed · previously known · selective presentation
The early British inheritance figures are averaged over slightly shifted years and raised by 10%, which makes them look like France's 20-25%. On standard calendar decades and without the uplift they are closer to 17-20%.
Technical detail and evidence
Why it matters, in detail. Raw fiscal flow: 20.6% (1896-1902 average) vs 17.2% (1910-13 average).
Evidence. Section4.xlsx TS11.3 B8 '=1.1*AVERAGE(F8:F14)/100' and B9 '=1.1*AVERAGE(F16:F22)/100'; DataFig4.4-4.7 C13:C14; DetailsDataFig4.4-4.7 column L '=1.1*N'. Auditor A: I15.
Why this severity. This masks a pre-war decline and slightly overstates the UK-France similarity. The UK U-shape in flows survives.
17minorconfirmed · newly identified here · arithmetic or transcription
The chapter contains a number of typos, swapped numbers, garbled sentences and small unexplained spreadsheet tweaks. None of them changes its conclusions.
Technical detail and evidence
Why it matters, in detail. All underlying calculations use the correct formulas; the errors are in the prose and labels, apart from small typed adjustments.
Evidence. Section2.xlsx DataFig2.10 Q145:R145 and DataFig2.1 F14; Section4.xlsx DataFig4.4-4.7 E14:E15 and DataFig4.1-4.3(a) columns I-J; chapter text at the pages cited. Auditor A: I17. Auditor B: I8. Items (8) and (12) checked by the adjudicator.
Why this severity. None changes a conclusion.
18minorlikely · previously known · version instability
The chapter says Germany had about as much wealth relative to income as Britain and France before 1914. Revised figures from the authors' own institute put Germany about a third below them, so the British-French pattern is a less general European story, although Europe's overall rise-fall-rise pattern is unchanged.
Technical detail and evidence
Why it matters, in detail. German beta for 1910-13 is 6.08 in the chapter vs 4.69 in WID 2026 (-23%). The European (DE, FR, UK) average for 1870-1910 falls from 6.6-6.8 to 6.4-6.6.
Evidence. Section2.xlsx DataFig2.6-2.7 (D11:F15). WID 2026 wpweali999 (scripts/wid_beta_compare.py, work/wid_beta_compare.json). Waldenstrom (2017), JEH 77(1). Auditor A: I12.
Why this severity. The European average and its U-shape barely move (1910: 6.60 -> 6.38). Only the representativeness claim is weakened.
Claims examined and rejected
Problems one auditor raised that did not survive checking.
- I16: the exclusion of pay-as-you-go pension and social-security wealth biases the chapter's concentration levels and trends (minor, plausible). — The exclusion is stated and justified (p.1309) and matches the chapter's estimand: marketable, transmissible wealth, which is what matters for inheritance. Roine-Waldenstrom's 'augmented wealth' variant changes the concept rather than correcting a measurement error, whereas the offshore adjustment the chapter cites stays within the concept. This is a scope caveat for welfare interpretation, not an error. Auditor B reached the same conclusion.
- I2(b): the post-1970 rise in the simplified inherited share is not robust because a 30-year window 'truncates inheritances still held by the living'; the rise survives only for windows of 40 years or less (graded major). — Partly rejected. The window numbers are confirmed, but Auditor A's own data (inheritance at about age 49, death at about 78) imply holdings of about 30 years, so flat windows of 50 years or more overweight inheritances of people already dead. A weighting consistent with the chapter's demography keeps a +10.7 pt rise (France, 1970-2010). The point is retained as a moderate robustness issue (F5).
- I1: the Modigliani series is closer to the PPVR series than the simplified series is (mean gaps of 7.7 vs 9.8 pts), contradicting the chapter's statement that KSM estimates are 'far too small' for France. — The gap numbers are correct, but the PPVR series is constructed as k x Modigliani, so the closeness is mechanical and says nothing about the true accuracy of the Modigliani measure. In the only genuine PPVR data (Paris 1872-1937), Modigliani shares are 21-34% below PPVR shares (PPVR/Modigliani ratios 1.27-1.50).
- I3: once the UK series is corrected, most of Europe's post-1980 rebound in wealth concentration disappears (graded major). — Partly rejected. This is true of the chapter's own data (+4.6 pts becomes about 0). But the authors' later French series (WID: 50.5% in the 1980s, 57.8% in 2010-12) restores a European rebound of about +3.9 pts when combined with the corrected UK series. The UK error is retained as moderate (F4).
- I10: today's US top-1% share is 'roughly 0.65-0.75' of the 1920s peak, using SZZ and Fed DFA levels. — Partly rejected. The 0.75 ratio (WID 2026: 36.6/48.7) is like-for-like. The 0.65-0.70 figures divide SZZ (2016) or DFA household-based (2014) levels by a tax-unit 1929 peak that was not re-estimated with heterogeneous returns, so they are not like-for-like.
- I17 items: b_w 'over 3.5%' is really 3.46% (1910); b_w differs from mu*m in 1940. — These are rounding and decennial-averaging differences (a ratio of averages vs a product of averages in the war decade), not errors.
- I5 sensitivity: the 1820-initialised 1900 flow is 21.46% under class saving vs 20.26% under uniform saving (auditor's own recursion). — Not material, and superseded: the archived Piketty (2010) Table D5 gives 22.0% vs 20.9% for 1900. The qualitative point (both saving regimes give similar aggregate flows; the misdescription concerns the claimed validation) is retained in F11.
- The general-equilibrium objections (r responding to g, gross vs net saving) should not be counted as an issue because the chapter's statements are conditional. — Not accepted. The chapter's own dynastic and CES closures imply that r - g falls when g falls at its illustrative parameters, while the abstract attributes a possible rise in inequality to the growth slowdown. Retained as moderate (F8), with the supporting historical evidence of Jorda et al. (2019) noted.
Audit notes
What reproduced. Reproduced exactly: the French wealth-income ratios and the beta ranges quoted in the text (from PZ2014); the European concentration averages; the UK 2010 shares from HMRC Table 13.8 (70.7%, which requires zero wealth for the 69% of excluded adults); the simplified inherited share for France, the UK and Germany (to 3e-16); the multiplier construction of the 'PPVR' series; the fiscal and economic inheritance flows (Auditor B); all theoretical numbers; the published Table 15.1 arithmetic; and the after-tax r-bar formulas. Not reproduced as printed: the text's 65-75% French inherited share for 2010 (the data give 52.4% annual, 55.1% plotted, 66.6% scaled); the Japan/Germany NFA values (swapped); the binomial top-1% mapping (exact model 42.8% -> 54.3%, not 20-30% -> 50-60%); Table 15.1 growth (6.8%/6.4% become about 4.5% after fixing the backcast and using the actual 2013 Forbes list); the world beta for 2100 (667% plotted vs 700-800% in the text); the printed US curve for 1910-1930 (1.9-2.7 pts below the posted data); and the 'uniform-saving from 1820' simulation (actually class saving before 1900 and a 1900 restart). Sensitivities computed by the adjudicator: cumulation windows of 20-60 years and a demography-consistent weighting (France 1970-2010 rise +10.7 pts vs +15.6); spouse exclusion (phi_2010 49.8%); the European average with the corrected UK and WID series (57.3-59.1%); and the r - g response to g in the chapter's own models. Not independently reproduced: Geerolf's (2026) gift and spousal flow corrections, the BHH/SZZ confidential re-estimates, Sweden's inheritance inputs, and the 19th-century source data.
Limits of this audit. CEPR DP 10072 was not obtained (neither auditor could access it); the March and June 2014 manuscripts were compared by the auditors and are numerically identical to the published chapter apart from the Swedish material. Geerolf's (2026a, 2026b) gift and spousal corrections are recent, non-peer-reviewed OFCE working papers; they were read but not reproduced, which is why F3 is rated 'plausible'. The UK correction uses HMRC's 2005 reconciliation ratio and later AAM/WID series rather than year-specific excluded-wealth estimates. The US alternatives (BHH, SZZ, DFA) rely on confidential data and differ in units, so cross-series ratios are approximate. WID comparisons use cached 2026 bulk extracts. The demography-consistent window weighting is a diagnostic based on the chapter's stylised benchmark (inheritance at 50, death at 80), not an estimate. Upstream inputs (Piketty 2010 tables, Schinke 2013, Atkinson 2013, Ohlsson-Roine-Waldenstrom 2013, the 19th-century US sources, Forbes 1987-89 lists) were checked only for internal consistency. No series in the chapter carries uncertainty bands, and none were estimated here.