Wealth Inequality in the United States since 1913: Evidence from Capitalized Income Tax Data

Why it matters, in detail. Mechanism: each unit's taxable interest is converted to wealth with a single aggregate capitalization factor for a class that mixes near-zero-yield deposits with bonds and loans. As deposit yields collapsed relative to bond yields the factor rose from 24.0 (2000) to 96.6 (2012), and because yields rise with wealth (Table C6b mean group/aggregate ratio 1.16-1.38 in 2008-11, 1.54-1.68 for $20m+ estates; SCF 2013 top-0.1% yield 1.51x the average under the paper's own asset definition), interest received at the top is converted into too much wealth and deposit wealth is shifted away from the bottom 90%. The fixed-income component supplies +6.14 of the +6.02-pt rise in the top-0.1% share over 2000-12 and +7.53 of +14.94 pts over 1978-2012; SZ give the top 1% 64.2% of taxable fixed income in 2012 (SCF 2013 26.5-29.4%, DFA 31-35%; close to the SCF in 1989) and the bottom 90% 8.4% (SCF 29.1-32.0%, DFA 28-33%). Magnitude: defensible corrections put the 2012 top-0.1% share at about 16-20% (17-20% in tax units: B41c 18.7%, authors' 2020 rule 19.6%, authors' Feb-2022 series 20.3% including offsetting upward revisions; SZZ 16.3% vs 21.7% under equal returns, equal-split adults), cut the 1978-2012 rise by about 15-40% (authors' 2022 series -14%, B41c -22%, SZZ -36%), shrink the 2000-12 rise from +6.0 to +2.3-3.4 pts and leave 2012 at about 65-80% of the 1929 level (24.8%). Direction: the magnitudes in C1 and the 1929 comparison in C2 are overstated, part of the bottom-90% decline in C3 is inflated, and C6's claim of similar within-class yields is contradicted; every alternative still shows a large rise since 1978, so the qualitative findings survive.

Evidence. Verified by adjudicator (scripts/text_checks.py, components.py, scf_fi_shares.py, scf_yields.py, dfa_check.py; logs in output/): (1) Table B5b: top-0.1% fixed-income component 3.31% -> 9.45% of total wealth 2000-2012 (+6.14 of a +6.02-pt total rise); 1978-2012 +7.53 of +14.94 pts. Interest capitalization factor 21.2 (1978), 24.0 (2000), 96.6 (2012). (2) Table C6b (paper's own matched estate-income data): mean group/aggregate interest-rate ratio 1.13-1.21 in 2004-07 and 1.16-1.38 in 2008-11; $20m+ group 1.54-1.68 in 2008-11. (3) SCF 2013 public file: top-0.1%/all-household taxable-interest yield ratio 1.51 using the paper's own asset definition (scf(SZ).do line 181), 2.35 when fund assets are excluded; bottom 90% 0.48/0.36. (4) Shares of taxable fixed income in 2012 imputed by SZ: top 1% 64.2%, top 0.1% 41.5%, bottom 90% 8.4% (36.2% in 1986), vs SCF 2013 26.5-29.4% / 7.7-8.8% / 29.1-32.0% and Fed DFA 2012 31-35% / 12-15% / 28-33%; in 1989 SZ and SCF were close (top 1% 27.6% vs 24.3-24.5%). (5) Alternative 2012 top-0.1% estimates: Table B41c 18.70% (paper p.550); authors' 2020 rule (1.4x premium for top 1%) applied to SZ2016 holdings 19.6% (Auditor A, script reviewed); authors' Feb-2022 series, tax units, 20.33% (includes offsetting upward revisions); Smith-Zidar-Zwick (2023) baseline 16.33% vs 21.74% under equal returns on the same data (equal-split adults); DFA fixed-income distribution counterfactual 15.9% (lower bound). (6) 1978-2012 rise: 14.94 pts (SZ2016) vs 11.63 (B41c, -22%), 12.84 (authors' 2022 tax units, -14%), SZZ +9.19 vs +14.34 equal returns (-36%). 2000-2012 rise: +6.0 (SZ2016) vs +2.8 (B41c), +3.4 (authors' 2022), +2.3 (SZZ baseline).

Why this severity. Defensible corrections put the 2012 top-0.1% share at roughly 16-20% (about 17-20% in tax units) instead of 22%, cut the 1978-2012 rise by roughly 15-40%, remove most of the post-2000 increase, and leave 2012 at about 65-80% of the 1929 peak rather than 'almost as high'. Every alternative still shows a large rise since 1978, so the qualitative finding survives.

The authors' response. In the paper (pp.549-551, fn 42, Table B41c) the authors report the estate-premium variant (18.7%) and a 10-year-Treasury variant, but keep the baseline because few estates exceed $20m, and say the premium may lead to 'some overestimation of top wealth shares since 2008, but there is no doubt that top wealth shares have increased sharply since the late 1970s' (p.551). In Sept 2020 (NBER w27921; PSZUpdates.pdf section 2.1.1) they adopted a 1.15x (2003-07) / 1.4x (2008+) interest premium for the top 1% and split dividend-paying bond/money-market funds; SZ (2020 JEP p.9) say the SZ2016 series 'might overestimate the rise of the top 0.1 percent wealth share' but that it is 'at least equally likely' the SCF underestimates it. SZ (2022, NBER w30396) argue SZZ's top yields are overstated and billionaire equity understated, and that the series are otherwise 'reconciled'.

Why it matters, in detail. The SCF, linked estate-income and foundation tests are the paper's evidence that equal within-class yields do not bias top shares (C6), but they report long-period averages (SCF 1989-2013) or levels in selected samples, and the paper's own tables contradict the assumption in the period that generates the headline trend: capitalized minus direct SCF top-1% shares are -2.3 to -3.3 pts in every wave from 1995 to 2010 but +2.8 pts in the 2013 wave (income year 2012); the direct SCF top 0.1% rises from 17.8% (1989) to 22.2% (2013) rather than being 'flat'; estate groups earn above the aggregate rate in most years (mean ratio 1.16-1.38 in 2008-11) rather than 'closely tracking' it; and SCF 2013 group yields show a 1.51x top-0.1% premium even under the paper's own asset definition. The estate comparison described as 'remarkably similar ... in both level and trend' has SZ above Kopczuk-Saez by 4.5 pts on average in 1930-39 (max 7.7) with a 2.8-pt mean absolute gap in 1916-29, and the p.569 reconciliation leaves no room for capitalization error in explaining the SCF gap (C7). No series changes, so there is no direct effect on C1-C3; the effect is to remove the claimed independent corroboration of the post-2000 magnitude that F1 shows to be fragile, while the tests remain informative about levels before the low-rate era.

Evidence. Table C1 (verified): capitalized minus direct SCF top-1% share is -2.3 to -3.3 pts in every wave 1995-2010 but +2.8 pts in the 2013 wave (income year 2012); the direct SCF top 0.1% rises from 17.8% (1989) to 22.2% (2013), not 'flat'. SCF 2013 group yields under the paper's own definition: top 0.1% 1.51x the all-household rate (codex computation, re-run by adjudicator). Table C6b: wealthy estate groups earn above the aggregate capitalization rate in most years (mean ratio 1.16-1.38 in 2008-11). Foundations are tax-exempt with a 5% payout rule (caveat noted p.544). Table C4: SZ minus Kopczuk-Saez top 0.1% averages +4.5 pts in 1930-39 (max +7.7) and mean absolute gap 2.8 pts in 1916-29. BHKS (2016) and BHH (2018) identify capitalized fixed income as the source of the post-2000 SCF gap.

Why this severity. Does not change the series, but removes the claimed independent validation of the post-2000 magnitude that F1 shows is fragile; the tests remain informative about levels before the low-rate era.

The authors' response. The paper acknowledges the foundation caveats (p.544), the decedent-sample caveats and the $20m+ premium since 2008 (p.549), and that the SCF gap is only partly explained (p.567). No later response on the specific points located.

Why it matters, in detail. The 1930s values in the published figures contain an estimation error that the authors acknowledged in 2020 (NBER WP 27921, Figure 1 notes). Against their corrected Feb-2022 tax-unit series, SZ2016 overstates the top-0.1% share by 3.0 pts in 1930, 5.0 in 1931, 5.1 in 1932 and 2.9 in 1934 (e.g., 22.4% vs 17.3% in 1932), up to about a quarter of the level, while 1929 is essentially unchanged (24.8% vs 24.9%). The published series therefore shows almost no fall from 1929 to 1934 (24.8% to 21.8%), whereas the corrected series falls by a third by 1931; this misstates Depression-era dynamics in C2 and the 'negative saving at the top' narrative (p.563), and it inflates the 1930s gap with the Kopczuk-Saez estate series (SZ above KS by 4.5 pts on average in 1930-39) that bears on C7. The long-run U-shape, the 1929 peak and the 1929-1978 decline are unaffected.

Evidence. Saez & Zucman (2020), NBER WP 27921, Figure 1 notes: 'The correction for the 1930s was already done in Piketty, Saez, and Zucman (2018) and due to an error in our initial estimation.' Adjudicator comparison, top 0.1% (SZ2016 Table B1 vs authors' Feb-2022 series, tax units): 1929 24.8 vs 24.9; 1930 23.0 vs 20.0; 1931 21.6 vs 16.6; 1932 22.4 vs 17.3; 1934 21.8 vs 18.9.

Why this severity. Materially wrong 1930s levels (up to ~25% of the level) and Depression dynamics, but the long-run U-shape and the 1929-1978 decline are unaffected.

The authors' response. Corrected in Piketty, Saez & Zucman (2018) and later updates.

Why it matters, in detail. Bond and money-market mutual funds distribute dividends, not interest, for tax purposes (IRS Pub. 550), yet the macro mapping puts taxable bonds held through mutual funds ($1,851bn at end-2011, $2,248bn at end-2012, before netting fund munis) in the fixed-income class capitalized with taxable interest; this inflates the interest capitalization factor, and hence the wealth imputed per dollar of interest, which is concentrated at the top, feeding the F1 mechanism behind C1. In the SCF validation the taxable-interest yield is computed over an asset base that includes money-market and bond-fund holdings; removing them raises the SCF 2013 top-0.1%/all yield ratio from 1.51 to 2.35 and the top-1% ratio from 1.39 to 1.86, so the mapping biases the test toward the 'flat yields' conclusion in C6 (IRS 2008 linked-estate yields move little: $20m+ estates 3.52% to 3.55-3.64%). The separate effect on top shares was not quantified (it depends on how concentrated non-qualified dividends are) and overlaps F1; the authors split these fund assets out in their Sept-2020 revision.

Evidence. Table A1 col 11 formula includes DataWealth!R = directly held bonds + bonds held through mutual funds (DataWealth!T: $1,851bn end-2011, $2,248bn end-2012, before netting fund munis). scf(SZ).do line 181: intinc_wscf = liq+cds+savbnd+bond-notxbnd+nmmf-stmutf-tfbmutf-.5*comutf. Adjudicator re-run on SCF 2013: top-0.1%/all yield ratio 1.51 -> 2.35 and top-1% 1.39 -> 1.86 when fund assets are removed (matches codex). IRS 2008 linked estates ($20m+): 3.52% -> 3.55% (excl. bond funds) / 3.64% (also excl. unclassified funds) (codex).

Why this severity. A confirmed mapping error that biases the validation evidence toward flat yields and feeds the F1 mechanism; its separate effect on top shares was not quantified (it depends on how concentrated non-qualified dividends are) and overlaps F1.

The authors' response. In the Sept-2020 revision the authors decompose fixed income into interest-generating assets and dividend-generating fund assets allocated by non-qualified dividends (PSZUpdates section 2.1.1; credited to SZZ).

Why it matters, in detail. In a component decomposition of the 1986-2012 fall in the bottom-90% share (-13.3 pts, component sum, internal SOI files), debt accounts for -3.30 pts (owner mortgages -3.41, non-mortgage debt +0.11), about a quarter, and in share terms does not offset the +4.66-pt rise in pensions as p.555 states; the largest negative items are taxable bonds and deposits (-6.24; with currency -0.64, about half of the fall) and gross owner-occupied housing (-6.50). Holding the bottom-90 debt/total-wealth ratio at its 1986 level would leave the 2012 share at 26.2% instead of 22.9%. The fixed-income item is largely the F1 imputation: the bottom 90%'s imputed share of taxable fixed income falls from 36.2% to 8.4%, whereas the SCF goes from 37.9-38.2% (1989) to 29.1-32.0% (2013) and the DFA from 34-40% (1989) to 28-33% (2012); and the '90% of non-mortgage debt' offered as evidence is a constant imposed in the code. Roughly a quarter to a third of the decline's magnitude mirrors F1, yet the inverted U in C3 survives (DFA -8.7 pts 1989-2012; SZZ -9.4 and the authors' 2022 tax-unit series -12.0 pts 1986-2012, vs -13.6 in SZ2016). The debt narrative holds in dollar levels (bottom-90 debt +$6.4tn vs pensions +$6.0tn, 2010$) and for 2000-12 (debt ~60% of the decline) but not for the share decline since the mid-1980s, which also weakens the debt-and-saving account in C4.

Evidence. Adjudicator re-computation (scripts/components.py; output/components.log), % of total wealth, SOI 1986 -> 2012: total -13.3 (component sum); taxable bonds & deposits -6.24, currency -0.64, gross owner housing -6.50, owner mortgages -3.41, non-mortgage debt +0.11, pensions +4.66; debt = -3.30 (~25%). Holding the bottom-90 debt/total-wealth ratio at its 1986 level gives a 2012 share of 26.2% instead of 22.9%. Bottom-90 share of taxable fixed income 36.2% (1986) -> 8.4% (2012); SCF 37.9-38.2% (1989) -> 29.1-32.0% (2013); DFA 34-40% (1989) -> 28-33% (2012). Table B12: bottom-90 share of non-mortgage debt fixed at ~90.0% every year; aggregate non-mortgage debt/wealth 6.1% (1986) vs 6.0% (2012).

Why this severity. The inverted U survives (DFA -8.7 pts 1989-2012; SZZ -9.4 pts 1986-2012; authors' 2022 tax-unit series -12.0 pts), but the stated cause is not what the paper's own accounting shows and roughly a quarter to a third of the decline's magnitude mirrors the F1 artifact.

Why it matters, in detail. Synthetic saving is backed out from eqs. (1)-(3) as the change in a group's wealth not explained by asset-class price indices, so the C4 decomposition assigns to 'saving' every share change not due to income shares, including mobility, within-class return differences and imputation error; it is an accounting identity and does not identify behavior. Because F1/F3 understate bottom-90 fixed-income wealth increasingly after 2000, bottom-90 saving is biased down and top saving up: had the bottom 90% kept its 2000 share of taxable fixed income it would hold ~5.3% rather than 1.7% of total wealth in 2012, roughly 2% of bottom-90 income per year, the same order as the negative bottom-90 saving rates of 2000-12 (approximate). Top saving is also sensitive to the price assumption: adding 1 pt to assumed annual appreciation lowers mean top-1% synthetic saving over 2000-11 from 35.1% to 25.5%. The saving rates and the 29.7%/32.7% counterfactuals reproduce exactly, so the problem is interpretive: the causal claims in C4 ('due to', 'key driver', 'primarily explained') are weakened, not overturned.

Evidence. Algebra and residual status verified (eqs. 3-5; both auditors reproduced the 2000-11 synthetic saving rates and the 29.7%/32.7% simulations exactly). Auditor A: had the bottom 90% kept its 2000 share of taxable fixed income, it would hold ~5.3% instead of 1.7% of wealth in 2012, ~2% of bottom-90 income per year, the same order as the negative bottom-90 saving rates of 2000-2012 (approximate). Auditor B: adding 1 pt to assumed annual appreciation lowers mean top-1% synthetic saving 2000-11 from 35.1% to 25.5%.

Why this severity. Weakens the identification of the saving channel rather than overturning it: the bottom-90 saving decline is partly an artifact of F1 and the decomposition cannot separate behavior from measurement error; the paper does label saving 'synthetic'.

The authors' response. The paper defines saving as 'synthetic' (p.560), discusses within-class price effects (eq. 5) and presents the simulations as counterfactuals.

Why it matters, in detail. Each asset class is allocated with a different income flow, so revisions to the composition of the Z.1 control totals change the distribution and not just the level (contrary to the p.528 argument about hedge funds). Household-and-nonprofit corporate and foreign bonds, a residual series, have been revised from $2,641bn to $1,180bn at end-2012 and from $1,961bn to $850bn at end-2007 (Treasuries at end-2007 from $207bn to -$318bn), and fixed income is imputed heavily to the top (41.5% of taxable fixed income to the top 0.1% in 2012). An approximate re-benchmarking of the authors' group-by-component holdings to the current vintage (Auditor A; script reviewed, not re-derived) lowers the 2012 top-0.1% share in C1 from 22.0% to 20.3% and the top 1% from 41.8% to 39.4%, raises the bottom 90% (C3) from 22.8% to 25.0%, and cuts the 1978-2012 rise by about 10%. The effect runs through the same fixed-income channel as F1 and is not additive with it, and it is not an author error: fn 43 anticipated revisions in either direction.

Evidence. Adjudicator check of Z.1 vintages: corporate & foreign bonds held by households & nonprofits (FL153063005) end-2012 $2,641bn (Mar-2014 vintage) vs $1,180bn (2026Q2 vintage); end-2007 $1,961bn vs $850bn; Treasuries end-2007 $207bn vs -$318bn. Auditor A's approximate re-benchmarking of the authors' group-by-component holdings (script reviewed, not independently re-derived): top 0.1% 2012 22.0 -> 20.3, top 1% 41.8 -> 39.4, bottom 90% 22.8 -> 25.0; 1978-2012 rise -10%. Authors' Feb-2022 log (PSZUpdates fn 1): household bond figures in recent releases 'cannot be reconciled' with hedge-fund holdings.

Why this severity. A noticeable but not transformative change (about -1.7 pts on the 2012 headline, -10% of the rise) operating through the same fixed-income channel as F1 (not additive with it); not an error by the authors, who anticipated revisions (fn 43).

The authors' response. fn 43 (p.551): future FA revisions 'might find less fixed income wealth than currently published, but they could also find more'; later updates use revised FA data and call the estimates 'living series'.

Why it matters, in detail. Table I's population average ($343,000) and thresholds are in current 2012 dollars, whereas every group average is taken from Table B3 in 2010 dollars, so the group averages are 3.7% below their current-dollar values (top 0.1%: $72.8m printed vs $75.6m) and, read at face value, the table implies a top-0.1% share of 21.2% rather than 22.0%; p.551 repeats the mix. Shares and thresholds are correct, so no core estimate changes; the effect is confined to the dollar levels reported alongside C1.

Evidence. Table A0 2012: $343,307 (current) vs $330,907 (2010$); Table B3 top-0.1% average $72,825,966 (2010$); thresholds from Table B2 current-dollar columns ($20,561,000). Implied top-0.1% share with the printed averages 21.2% vs 22.0%; implied current-dollar group averages 3.7% higher (e.g., $75.6m).

Why this severity. Presentation only; shares and thresholds are correct.

Why it matters, in detail. Over 1986-2012 the top 0.1% accounts for 31.3% of the growth in aggregate real household wealth ((0.22008 x 53,170 - 0.09293 x 22,500)/(53,170 - 22,500), 2010 $bn; 26% in nominal terms), not 'almost half'; the 42.3% figure obtains only for growth in average wealth per tax unit, which ignores the 45% growth in the number of tax units, and both measures include asset revaluation as well as saving. The sentence (p.521) overstates the top group's share of aggregate accumulation, but it is illustrative; the share series behind C1 are unaffected.

Evidence. Adjudicator: (0.22008 x 53,170 - 0.09293 x 22,500)/(53,170 - 22,500) = 31.3% (Tables B1, A0, 2010 $bn); per tax unit 0.001 x (72.83m - 18.89m)/(330,907 - 203,281) = 42.3% (Table B3).

Why this severity. A supporting illustrative statement in the introduction; the top-share series are unaffected.

Why it matters, in detail. The slips are in supporting text, not in the series: top-0.01% real wealth growth 'since 1988' is given as 7.8% a year vs 5.8% for 1988-2012 in Table B3 (7.9% applies only to 1988-2000), overstating recent growth at the very top in the text; the 2012 top 0.1% is quoted as 22.1% (baseline) and 23.0% (offshore) vs 22.0% and 22.9% in Tables B1/B6; SCF and foundation figures in the validation and reconciliation sections differ from the tables by 0.2-1.0 pts (fn 57: 39.5% not 38.5%, 37.4% not 37.2%; p.544: 50.6% not 50.8%; p.542: 4.1/4.9/6.6% not 3.9/4.5/6.3%); two different SCF baselines are used for the same comparison (p.566 vs fn 58); the top-0.01% 'from 3.5%' (p.573) is the 1985 value; and the Kopczuk-Saez (2004) NTJ volume is 57, not 52. Several are leftovers from the 2014 working paper; none feeds the published estimates, so the effect on C1, C2, C6 and C7 is limited to the accuracy of individual statements.

Evidence. Adjudicator re-checked (i)-(v) against Tables B1, B3, B6, C1, C4, C14 (output/text_checks.log); (vi)-(viii) from Auditor A, consistent with the tables and the NTJ citation.

Why this severity. Small slips in supporting statements; several are leftovers from the 2014 working-paper vintage. None affects the series.

Why it matters, in detail. All noncorporate mortgage liabilities (FL113165005), including $1,390.6bn of commercial mortgages in mid-2012 (2.52% of household wealth), are netted from tenant-occupied housing and thereby implicitly added back to business wealth; aggregate wealth is unchanged, but the two classes are allocated with different income flows. Because both are top-concentrated (in 2012 the top 0.1% holds 16.6% of net rental and 18.9% of business wealth), reclassifying with within-class group shares held fixed moves the top-0.1% share by +0.43 pts (1986), +0.33 (1989), +0.11 (2000) and -0.06 (2012), so the 1986-2012 rise in C1 is overstated by about 0.5 pt (~4%), and the bottom-90% level in C3 is overstated by 0.3-0.5 pts. The authors corrected the classification in their Sept-2020 revision.

Evidence. DataWealth!AJ = FL113165005.A feeds Table A1 col 6 'Mortgages, tenant-occupied' ($2,806.5bn mid-2012). Commercial component FL113165505 (Mar-2014 vintage): $1,390.6bn mid-2012 = 2.52% of household wealth; $397bn end-1986. Adjudicator estimate with within-class group shares held fixed (scripts/commercial_mortgage.py): correcting it changes the top-0.1% share by +0.43 pts (1986), +0.33 (1989), +0.11 (2000) and -0.06 (2012) (in 2012 the top 0.1% holds 16.6% of net rental vs 18.9% of business wealth), so the 1986-2012 rise is overstated by ~0.5 pt (~4%); bottom 90% -0.3 to -0.5 pts in levels.

Why this severity. Confirmed and author-acknowledged, but net rental and business wealth are both concentrated at the top, so the effect on top shares is a fraction of a point in any year (codex graded it moderate; downgraded after quantification).

The authors' response. Fixed in the Sept-2020 revision ('mortgages on commercial real estates were included under tenant-occupied-housing mortgage debt ... now correctly subtracted from business equity wealth').

Why it matters, in detail. In the 2012 rows of the alternative-specification tables B41 and B43, bottom-90 composition is computed from 2010 aggregates (Table A1 row 107 instead of 109), and total top-group equity is subtracted from aggregate non-S-corporation equity while S-corporation equity is added to business; B39 has the wrong-year reference only. The result is a published bottom-90 equity component of -1.71% of total wealth (printed as -2%) instead of about +1.56%, with business at 2.54% once corrected (B41). The formulas do not feed B1 or the headline top shares (the control tables B5, B35 and B37 use the correct row and column), so the error is confined to bottom-90 composition in these robustness tables (C3) and alters no core estimate.

Evidence. Adjudicator inspection of formulas: TableB41!C108 = ([1]TableA1!$I107 - J108*[1]TableA1!$B107)/[1]TableA1!$B107 (value -1.71%); B43 identical; B39 uses $H107; controls B5, B35, B37 correctly use row 109 and column H. Codex: corrected equity residual +1.56%, business 2.54% (B41).

Why this severity. Confined to bottom-90 composition in alternative appendix specifications; does not feed the headline top shares.

Why it matters, in detail. Fn 36 reports 'little discontinuity' around the Tax Reform Act of 1986, but the top-0.1% share rises from 9.29% to 11.63% over 1986-88 (+2.34 pts, +25%), the largest two-year rise in 1962-2012 (next: 2006-08 +2.21, 2008-10 +1.73 pts), with equities contributing +0.91 and fixed income +1.13 pts as imputed S-corporation equity rises from $99bn to $265bn. To the extent the jump reflects income moving from corporate to individual returns rather than a change in wealth, the timing and size of the rise in C1/C2 are slightly overstated; even if it were wholly an artifact it would be at most ~2.3 pts, about 15% of the 1978-2012 rise, and it is likely partly genuine.

Evidence. Table B1 (adjudicator): largest two-year rises 1986-88 +2.34, 2006-08 +2.21, 2008-10 +1.73 pts. Table B5b 1986-88: equities +0.91, fixed income +1.13 pts. Auditor A: Table A1 S-corp equity $99bn -> $265bn.

Why this severity. Even if wholly an artifact it would be at most ~2.3 pts (~15%) of the 1978-2012 rise; likely partly genuine.

The authors' response. Sec. IV.E (p.546): capitalization factors rescale when reported income shifts between corporate and individual returns.

Why it matters, in detail. Components without a taxable income flow are allocated with time-invariant rules documented only in the code, although p.538 says they are allocated 'so as to match their distribution in the SCF': the bottom 90% receives ~90% of non-mortgage debt in every year (Table B12), all non-itemizers receive identical housing and mortgage amounts, itemizers own a fixed 75% of homes and 80% of mortgages, and pensions follow a constant 60/40 rule. These rules shape bottom-90 composition (C3) mechanically, but the demonstrated impact is small: the bottom-90 share of primary housing matches the SCF closely, and because the SCF bottom-90 share of non-mortgage debt rises from 76% (1989) to 87% (2013), the fixed 90% overstates early bottom-90 debt and so biases against, not toward, the measured bottom-90 decline.

Evidence. Table B12: bottom-90 share of non-mortgage debt 89.8-90.0% in every year; build_usdina(SZ).do non-itemizer block (Auditor A). SCF checks (Auditor A, partially re-run): bottom-90 share of primary housing matches the SCF closely; the SCF bottom-90 share of non-mortgage debt (76% in 1989, 87% in 2013) implies the fixed 90% is conservative for the bottom-90 decline.

Why this severity. Limited demonstrated impact; the debt assumption biases against, not toward, the bottom-90 decline.

Why it matters, in detail. The 1916 and 1929 levels (24.8%) against which 2012 is judged 'almost as high' in C1 come from group-level capitalization of Piketty-Saez tabulations with re-ranking corrections fixed at 1962/64 ratios, non-taxable components fixed at 1962-66 shares, 1913-15 composition copied from 1916 and full reporting of dividends and interest assumed from 1917, all documented only in spreadsheet notes; the authors' notes say they 'need to better understand the large variations in top wealth shares in 1913-1933'. The Kopczuk-Saez estate series puts the top 0.1% about 4 pts lower in those years (21.0% in 1916, 20.8% in 1929), so the early-century benchmark is uncertain by a few points in either direction; this affects the 2012-versus-peak comparison and the early level of the U-shape in C2, whose existence the estate data corroborate.

Evidence. AppendixTables(Distributions).xlsx, sheet 'Pre-62' notes (verified); paper p.539-540 and fn 31 say pre-1962 imputations are 'cruder'. Kopczuk-Saez estate levels for 1916/1929 are ~4 pts lower (21.0%/20.8% vs 24.8%/24.8%, Table C4).

Why this severity. Adds uncertainty of a few points to the early-century benchmark in either direction; the U-shape is corroborated by estate data.

The authors' response. The paper states that pre-1962 imputations are cruder (p.539).

Why it matters, in detail. Fn 13 attributes '1.5 million non-resident citizens' filing a 1040 to Hollenbeck & Kahr (2014, Figure B, col. 2), which shows 449,277 returns with Form 2555; 1.5 million matches only a dollar column (col. 10, 2006 housing exclusion, $1,491,218 thousand). Fn 29 turns Senate PSI shares of undeclared accounts (e.g., Credit Suisse 'between 85 and 95%' of accounts) into shares of wealth, and fn 30 rounds the tax-haven equity series loosely (TIC values not re-verified). These peripheral footnotes enter no estimate, so there is no effect on C7 or any other core finding beyond the accuracy of the citations.

Evidence. Adjudicator check of Hollenbeck & Kahr (2014) Figure B (pp.142-143); Senate PSI (2008; 2014) count accounts (e.g., Credit Suisse 'between 85 and 95%' of accounts). TIC series values from Auditor A (not re-verified).

Why this severity. Peripheral footnotes; no effect on any estimate.

Why it matters, in detail. When groups are formed by ranking on capitalized wealth, idiosyncratic return heterogeneity does not average out: ranking selects units with high realized returns into the top, which biases top shares upward (r_a/r = 2/(1+a)^(1/a) = 1.086 for Pareto a = 1.5 and returns uniform on [0, 2r], as Sec. IV.A itself derives), and the bias grows with return dispersion, e.g. with a widening deposit-bond spread (the F1 mechanism). The introduction's 'the noise cancels out' (p.522) therefore mischaracterizes the method's validity (C6), but under the paper's own calibration the bias is modest, so the inconsistency is presentational and does not change the estimates.

Evidence. p.522 vs pp.540-541 and fn 32; with returns uniform on [0, 2r], r_a/r = 2/(1+a)^(1/a) = 1.0858 for a = 1.5 (re-derived by both auditors and the adjudicator).

Why this severity. Presentational; Sec. IV.A itself quantifies the idiosyncratic bias as modest.

Why it matters, in detail. Pension wealth is allocated 60% by pension income and 40% by wages above the median, a split calibrated only to the SCF top-10% pension share (fn 24) and not checked against the top 1%; since pensions are 14.2% of top-1% wealth in 2012 but only ~7% of top-0.1% wealth, misallocation matters mainly for the top 1%. The authors' Sept-2020 revision (60% taxable pension distributions, 30% wages, 10% non-taxable distributions), which targets the top-1% pension share, lowers the top-1% wealth share by 1-1.5 pts in recent years, so the 41.8% top-1% figure for 2012 in C1 is overstated by about that much, while the top-0.1% series is hardly affected.

Evidence. Paper fn 24 (p.537); PSZUpdates section 2.1.7 (Sept 2020): 'This revision reduces the top 1% wealth share by 1-1.5 points in recent years.' Table B5b: pensions are 14.2% of top-1% wealth in 2012 (codex) but only ~7% of top-0.1% wealth.

Why this severity. Affects the 42% top-1% figure by about 1-1.5 pts and the top 0.1% hardly at all.

The authors' response. Revised in Sept 2020 (60% taxable pension distributions, 30% wages, 10% non-taxable distributions).