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Thomas Piketty, Emmanuel Saez, Gabriel Zucman · Quarterly Journal of Economics 133(2): 553-609

Distributional National Accounts: Methods and Estimates for the United States

16 problems found: 1 major · 9 moderate · 6 minor

What the paper claims

Every problem found

1majorlikely · previously known · speculative assumption

About two-fifths of national income never appears on anyone's tax return, so the authors had to decide who receives it, and their choices tend to give more of it to the richest. With other reasonable choices, the rise in the top 1%'s share since 1980 ranges from about half as large to nearly as large as reported. Under the main critics' choices, the top 1% never overtakes the bottom half. The paper gives single numbers with no ranges, so figures like '81 times' are one estimate among several, even though the overall direction is not in doubt.

Technical detail and evidence

Why it matters, in detail. The top-1% pretax share equals observed fiscal income plus imputed components. The imputation keys (positive business income, total pension distributions, capitalized equity) load imputed income on the top, so the bias relative to audit- or owner-linked keys is upward for both level and trend. Serious estimates of the 1979/80-2014 rise: 9.5 pp (PSZ 2018; 9.0 pp from 1979), 8.5 pp (PSZ Feb-2022), 4.8 pp (AS 2024). The 2014 level is 20.2%, 19.0% and 14.2% respectively. The headline ratio is 80.5x (2018 vintage) and 72.3x (2022). In AS's series it rises from about 23x to about 47x, and the bottom-50% share (15.2%) stays above the top-1% share (14.2%). Neutral assessors put the truth between the camps and nearer PSZ on misreporting. The most likely overstatement is therefore well below AS's ~45% of the trend, but could plausibly reach a quarter. No source pins down where in this range the truth lies. Bottom-50% pretax stagnation is far less sensitive: growth stays between about -2% and +15% across vintages, base and end years and deflators, against ~60% average growth.

Evidence. (i) Authors' Feb-2022 vintage (Distrib TB1/TB3, verified): 2014 top-1% share 20.20% -> 18.98%; bottom-50% share 12.55% -> 13.12%; ratio 80.5x -> 72.3x; 1980-2014 top-1% rise 9.5 -> 8.5 pp; bottom-50% pretax growth +1.4% -> +4.9%. (ii) Auten & Splinter (2024, JPE 132(7)): Table 3 (p.2208) top-1% pretax share 1979-2014 +4.8 pp vs PSZ +9.0 pp, 2014 level 14.2% vs 20.2%. Table 4 (p.2210) attributes the 6.0-pp 2014 gap to underreporting 2.0, retirement 1.0, corporate 0.7, other taxes 0.7 and tax-return corrections 0.4. AS's online data (Figure 4 sheet) put their bottom-50% pretax share at 20.6% (1979) and 15.2% (2014), so under AS conventions the two groups do not 'switch', and the top-1%/bottom-50% average ratio rises from about 23x to about 47x (different unit: size-adjusted individuals). (iii) Neutral assessments: Gale, Sabelhaus & Thorpe (2023, Brookings) say PSZ's choices 'tended to push measured inequality higher' while AS's 'push top income share estimates down', and that 'the preponderance of evidence suggests that income inequality has increased'. Iselin & Reck (2025) place PSZ's misreporting treatment at the upper end of the plausible range and caution against 'reversing or moderating the consensus' (verified in their text). (iv) Adjudicator re-run on the Feb-2022 external micro-files: allocating public goods equally per adult raises bottom-50% posttax growth 1980-2014 from +22.9% to +30.5% (F5). (v) Kopczuk & Zwick (2020, JEP 34(4), pp.38-42) and Deaton (2020) call for explicit uncertainty.

Why this severity. Not critical: the direction of every core finding survives in all vintages and alternatives, including Auten-Splinter's. But the size of the top-1% surge and of the redistribution offset rests on unvalidated conventions. Across the range spanned by the authors' own revision and serious published alternatives, the 1980-2014 top-1% rise is about 10% to 50% smaller and the 81x ratio 10% to 40% lower. That meets the rubric's 'a quarter or more within a defensible range'.

The authors' response. The paper calls DINA a 'prototype' whose goal is 'not to provide definitive answers ... but to be comprehensive, consistent, and explicit' (p.556). Code and tables are public, and later vintages are documented in the Updates log. Saez & Zucman (2020, NBER w27921) accept the pension correction and defend the other conventions. PSZ (2026 comment) attribute 41% of the 1979-2019 trend gap with AS to AS's allocation of partnership excess depreciation and S-corporation exempt income, and call AS's comparison with the 2018 version 'partly obsolete'.

2moderateconfirmed · newly identified here · arithmetic or transcription

The spreadsheet formula that computes government transfers to the middle class leaves out a needed weight and overstates them by about a quarter. Corrected, the poorer half and the middle class receive about the same per person in 2014, and in most earlier years the poorer half received more. So the paper's claim that transfers mainly go to the middle class is not supported. The paper's estimates of incomes after taxes and transfers are not affected.

Technical detail and evidence

Why it matters, in detail. The missing weight inflates the middle-40% mean by 0.25 x the bottom-90% mean: +$1,766 (+23.9%) in 2014. Corrected per-adult transfers excluding Social Security (posttax ranks, 2014) are 10.5% for the bottom 50%, 11.4% for the middle 40% and 7.9% for the top 10% of average national income, against 10.5/14.1/7.9 published. That is nearly flat: the middle-class advantage falls from 3.6 to 0.9 points (-76%). Including Social Security the corrected figures are 15.0/18.8/15.9%. In 1970-2012 the bottom 50% received more per adult than the middle 40%. Ranked by pretax income, the bottom 50% receives about twice the middle 40%'s per-adult transfers. So the 'targeting' result also depends on ranking recipients by an income measure that includes the transfers themselves.

Evidence. TG4!G64 formula '=(E64-F64*0.5)/0.4', with headers E = Bottom 90%, F = Bottom 50%, G = Middle 40%. In 2014: E = 7,063.44, F = 6,810.59, H (top 10%) = 5,082.47, D (all) = 6,864.90. The published G = 9,145.37 implies 0.5F + 0.4G + 0.1H = 7,571.7, not D. The corrected G = (0.9E - 0.5F)/0.4 = 7,379.51 satisfies the identity (the authors' own check, 0.9E + 0.1H - D ≈ 0, holds). Corrected 2014 middle-40% transfer: 11.4% of per-adult national income, not 14.1%; including Social Security, 18.8%, not 22.9%. Year by year (adjudicator): with the published formula the middle 40% exceeds the bottom 50% in 1962-69, 1974 and 1998-2014 (excluding Social Security), and in 1981-2014 (including it). Corrected, it does so only in 1962-68 and 2013-14 (excluding Social Security), and in 2006-14 (including it). Ranked by pretax income (TG4d, 2014), the bottom 50% receives $9,216 (14.3% of per-adult national income) against $4,654 (7.2% corrected; 10.0% published) for the middle 40%. The bottom panel of Figure X (cols EX-EZ) satisfies the population identity and is unaffected. Scripts: tg4_check.py, tg4_years.py.

Why this severity. The error does not touch the posttax income series, which are built from micro-files, so C5's main claim stands. But it removes or reverses, for most of 1970-2012, the evidence for a claim the introduction lists among the paper's main findings, and roughly equalizes the 2014 comparison.

3moderateconfirmed · previously known · methodology

The authors used records of tax-free retirement payouts to work out who owns retirement savings. Many of those 'payouts' were just wealthy people moving money between accounts. This gave the top 1% too much retirement income. The authors have acknowledged and fixed it, which lowers the top 1%'s share by around half a point to one point.

Technical detail and evidence

Why it matters, in detail. Putting non-taxable distributions into the key that allocates 60% of pension wealth and all private pension benefits shifts retirement income toward rollover-heavy top returns. The authors' fix (a 10% weight) lowers the 2016 top-1% pretax share by about 0.6 pp. AS attribute 1.0 pp (2014 level) and 1.2 pp (1979-2014 change) to their broader retirement treatment, which also covers unfunded plans; part of that is disputed.

Evidence. build_usdina.do lines 368-371 (totpeninc = peninc + penincnt; 60% of pension wealth allocated by totpeninc) and 1347-1349 (plpbe = peninc + penincnt + ssinc_oa, scaled to the NIPA total). Saez & Zucman (2020, NBER w27921, §3.3): PSZ (2018) 'put too high a weight on non-taxable distributions ... inflated by rollovers. This led to allocating too much retirement income to the top', revised to a constant 10% weight. PSZ Updates (Sept 2020, §2.2.1): about -0.6 pp on the top-1% pretax share in 2016. AS 2024 Table 4: 1.0 pp of the 2014 level gap and 1.2 pp of the 1979-2014 trend gap. AS fn 33: 79% of pension distributions on returns with AGI of $1m or more were tax-exempt in 2014 (Auditor B re-derived 79.3% from IRS SOI Table 1.4). Gale et al. (2023): 'PSZ mistakenly assumed too large a share of non-taxable rollovers were income'.

Why this severity. A conceded error worth about 0.6-1.0 pp of the 2014 top-1% share and up to about 1.2 pp of its 1979-2014 rise (roughly 3-6% of the level and up to ~13% of the trend). It does not change direction.

The authors' response. Acknowledged and corrected in the Sept-2020 update (SZ 2020, §3.3: 'We are grateful to AS'); the authors say the revision 'closes about 10% of the gap between AS and PSZ (2018)'. PSZ dispute AS's remaining allocation of pension income to holders of unfunded plans.

4moderateconfirmed · previously known · overclaiming

Spending on schools, roads and defence has to be assigned to someone. The authors assign it in proportion to people's cash income and say that assigning it equally would barely change the growth picture. When we re-ran their data with equal shares, after-tax income growth for the poorer half rose from about 23% to about 31% over 1980-2014. Government still offset only part of the widening gap, but noticeably more than the paper says.

Technical detail and evidence

Why it matters, in detail. Proportional allocation ties the bottom 50%'s public-goods receipts to its falling share of cash income. An equal per-adult allocation instead grows with average income. Collective consumption is 18.8% of national income in 1980 and 16.9% in 2014. Top-1% posttax share on the external files: 7.3% -> 14.7% at baseline, 6.1% -> 12.3% with equal allocation. The paper's share-neutrality statement is algebraically inexact but empirically close.

Evidence. Code build_usdina.do lines 1502-1504 and 1547-1550 (colexp = dicsh x total / sum of dicsh). Adjudicator re-run on the authors' Feb-2022 external micro-files (1980, 2014; equal-split; re-ranked; interest and deficit terms rescaled), bottom-50% posttax real growth 1980-2014: - baseline +22.9%; - equal per adult +30.5% (+31.5% without rescaling the interest and deficit terms); - half equal, half proportional +27.1%; - the authors' education-per-child variant +23.8%. The bottom-50% posttax share goes 26.5% -> 20.3% at baseline and 30.9% -> 25.1% with equal allocation. Auditor A obtained +22.6% -> +31.7% on the April-2019 files (2017 methodology). The share of the macro vs bottom-50% growth gap closed by redistribution rises from ~29% to ~44% on the external files; in the published figures it would go from one third to roughly half. Neutrality: Auditor B's algebraic point holds (proportional allocation to cash income is share-neutral only if the rest of posttax income is distributed like cash income). Empirically the deviation is ≤0.25 pp for the top-1% share and ≤0.02 pp for the bottom 50%. Gale et al. (2023): fully proportional allocation is 'likely too extreme'. AS 2024 Table 4: 1.3 pp of the 2014 posttax top-1% level gap. Scripts: micro_publicgoods.py, micro_neutrality.py.

Why this severity. A compromise allocation raises bottom-50% posttax growth by about 4 pp and the polar equal allocation by about 8 pp (+35-40% relative). 'Transfers erased about a third of the gap' becomes 'up to about half'. The conclusion that redistribution offset only part of the divergence survives: posttax bottom-50% growth is about 30% against 61% average.

The authors' response. PSZ (2026) call their treatment of government consumption 'neutral', in line with most inequality studies, and argue that AS's half-per-capita lump sum (8% of national income in 2019) mechanically lowers inequality and its rise. Saez & Zucman (2020) object that per-capita allocation would make, e.g., spending on mass incarceration funded by a proportional tax look equalizing.

5moderateconfirmed · previously known · methodology

The paper says that since 2000 the richest 1% have gained mainly from owning capital, especially from profits kept inside corporations, and that capital provides over half their income. The 'mainly capital since 2000' pattern holds in every version we checked. But whether capital provides more than half their income depends on how profits of owner-run businesses are counted, and the paper's own two charts of this differ by four points. In the authors' later data, profits kept inside large corporations are no longer the main driver.

Technical detail and evidence

Why it matters, in detail. Treating all S-corporation profit as capital and using panel A's hard-coded 78.7% capital fraction of top-1% pension income gives 58.9% capital. Panel B's own components give 54.6%; reclassifying 54% or 75% of S-corporation profit gives 50.4% or 48.7%; SYZZ's full corrections about 47%; Smith-Zidar-Zwick assumptions 41%. The post-2000 direction is robust: capital +3.07 pp vs labor -1.14 pp in the 2017 vintage, +2.20 vs -0.56 pp in 2022, and the capital contribution still exceeds the total rise with 75% reclassification (+2.93 pp). The mechanism is not: C-corporation retained earnings explain 1.21 of 1.93 pp in the 2017 tables, but 0.49 of 1.63 pp (2000-14) and 0.09 of 1.73 pp (2000-19) in the 2022 vintage.

Evidence. MainData: panel A (col GD) 58.9% vs panel B (CA/BZ) 54.6% in 2014; 49.5% vs 43.6% in 2000. In TB2d (panel A) the top-1% capital share uses a hard-coded 78.7% capital fraction of pension income, and the 2010 value is carried forward into 2011-14 (R111 = R$107). Panel B's pension components imply about 43%. Top-1% S-corporation profits are 1.58% of national income in 2014 (col IV, author-site file). Reclassifying 54% or 75% of them as labor lowers the panel-B capital share to 50.4% or 48.7%. SYZZ (2019, QJE; NBER WP 25442 pp.5-6): top-1% labor share 45.4% -> 52.9% in 2014, with a 'qualitatively similar' time pattern. Kopczuk & Zwick (2020, p.44): 56% (PSZ) vs 41% capital. Retained earnings, 2000-14: 1.21 pp of the 1.93-pp rise in the Nov-2017 TB2f (Appendix C.2 says 1.2), against 1.4 in the text. Feb-2022 TB2f: C-corporation undistributed profits contribute +0.49 of +1.63 pp (2000-14) and +0.09 of +1.73 pp (2000-19); C+S retained earnings (memo) +0.93 and +0.60 pp; capital +2.20 pp vs labor -0.56 pp (2000-14). Scripts: tb2f_vintages.py.

Why this severity. The direction (capital-driven rise after 2000) holds in every vintage and under SYZZ's reclassification. But the 'over half from capital' level is fragile (41-59% across conventions and panels), and the named driver, C-corporation retained earnings, is not robust to the authors' own revisions.

The authors' response. p.597 and Appendix C.2: other tax-induced shifting (firms with passive owners, closely held C-corporations) runs the other way, so the net bias is unclear and the standard national-accounts split is preferred. SZ (2020, §4) argue that a 75% labor share implies implausibly low returns on business capital and estimate about 50% capital. The Sept-2020 update adopted heterogeneous S-corporation splits and a 50% capital share for partnerships.

6moderateconfirmed · newly identified here · internal inconsistency

To show that the poorer half's stagnation is not just population ageing, the paper says the poorer half of working-age adults saw their incomes 'collapse' after 1980: down 20% for those under 45 and 8% for those aged 45-64. The paper's own chart shows falls of about 15% and 2.5%, and for the older group the change is close to zero depending on the starting year. Part of the fall also reflects how the paper counts pension and Social Security contributions, which rose over the period. The broader point, that working-age people in the bottom half gained little, still holds.

Technical detail and evidence

Why it matters, in detail. Text -20%/-8% against plotted -14.7%/-2.5% (1980-2014); the text figures are close to a 1979 base (-18.6%/-7.3%). Between about a third (published 20-64 group) and two-thirds (2022 external files, ages 20-44) of the measured pretax decline reflects the pretax concept netting pension and social-insurance contributions (which rose, notably Social Security payroll taxes) against benefits that mostly accrue to the elderly in the same concept. Posttax, the working-age bottom 50% grew +12.6%, not 'close to zero'. A pure life-cycle explanation is still not supported, but the evidence shows stagnation, not collapse.

Evidence. MainData FH/FI (plotted in Figure IV, chart F4a) = Appendix TB7b: ages 20-44 $15,091 -> $12,866 (-14.7%); ages 45-64 $23,569 -> $22,971 (-2.5%). From 1979: -18.6%/-7.3%; from 1981: -12.2%/0.0%; Feb-2022 vintage: -10.9%/+0.2% (Auditor A). Adjudicator: part of the pretax decline is pension accounting. Pretax income deducts pension and social-insurance contributions, which rose (notably Social Security payroll taxes), and adds benefits, which go mostly to the elderly. Published working-age (20-64) bottom 50%: factor income -4.0% vs pretax -6.2% (MainData DE/DT). Feb-2022 external files, ages 20-44: factor -3.3% vs pretax -10.0%. Posttax, the working-age bottom 50% (MainData EO) rose +12.6%; within-age +5.8% (20-44) and +11.3% (45-64) (FL/FM). The same sentences appear in NBER WP 22945 (Dec 2016).

Why this severity. The evidence offered against an ageing explanation of the bottom-50% stagnation is overstated about threefold for ages 45-64 and its sign is not robust. The qualitative point (no working-age bottom half gained much) survives, so C1 is not undermined.

7moderatelikely · previously known · speculative assumption

Some business income escapes tax records, and the authors assume it is spread like the profits people do report, which go mostly to the very rich. Tax-audit data suggest it is more spread out, which would lower the top 1%'s 2014 share by one to two points. The effect on the trend since 1980 is small, and experts disagree about which assumption is better.

Technical detail and evidence

Why it matters, in detail. Proportional-to-positive-income allocation implies a relative misreporting rate of about 1 for pass-through income. It gives the top 1% about 47-50% of misreported business income, against about 15% after re-ranking under audit-based keys (AS). Level effect on the 2014 top-1% share: 1.17 pp (authors' own calculation vs AGI-proportional) to 2.0 pp (AS). Trend effect: 0.7 pp of the 1979-2014 rise (AS). In pretax national income, PSZ's rule adds +0.76 pp to the 1962-2019 rise against +0.09 to +0.66 pp under Iselin-Reck's plausible range, i.e. at or just above its upper end. The bias is upward and moderate in level, small in trend, and negligible for the bottom 50%.

Evidence. Code build_usdina.do (Nov 2017): lines 313-321 build partnership and sole-proprietor wealth from positive income (comment '0 value when negative business income'); lines 1234-1238 allocate flmil by partpinc_l + schcincp_l + rylinc_l. Online Appendix C.1 (p.35 and fn 30): $538bn misreported business income plus $80bn wages in 2013 (4.3% of national income). The top 1% gets $262bn, against $93bn under an AGI-proportional allocation, a difference of 1.17% of national income. AS 2024 Table 4: 2.0 pp of the 2014 top-1% level gap and 0.7 pp of the 1979-2014 trend gap. Iselin & Reck (2025, Table 1, pretax national income, PSZ assumptions, Feb-2022 files): misreporting adds +0.76 pp to the 1962-2019 top-1% rise under PSZ's rule, against +0.09 to +0.66 pp under their plausible relative misreporting rates (0.3-1); the 2019 level is 19.08% against 17.83-18.94%. Gale, Sabelhaus & Thorpe (2023): audit-based allocations 'will tend to understate the share of pre-tax income going to the top 1%'.

Why this severity. It moves the 2014 top-1% level by about 1-2 pp (of 20.2%) but the 1980-2014 trend by at most ~0.7 pp (of 9.5 pp). Independent evidence places PSZ at the upper end of the plausible range for the trend, not outside it.

The authors' response. Appendix C.1: random audits 'severely under-estimate tax evasion at the top-end', and 30% of partnership income is untraceable (Cooper et al. 2016). PSZ (2026) say evasion explains only 5% of the 1979-2019 trend gap with AS, and that partnership excess depreciation belongs to partnership owners. AS (2026, Table 1) reply with confidential linked-owner data implying a much smaller top-share effect for partnership excess depreciation (+0.16 pp vs PSZ's +1.2 pp in 2019); these data have not been independently replicated.

8moderatelikely · previously known · overclaiming

The famous finding that the bottom half 'stagnated at $16,000' is true for the specific measure the authors chose: income before taxes and benefits, per adult, from 1980 to 2014. Counting taxes and government benefits, the bottom half's income rose about a fifth. Researchers who count children and household size find faster growth. In every version the bottom half fell far behind the average, but phrases like 'shut off from economic growth for over 40 years' go further than the data show.

Technical detail and evidence

Why it matters, in detail. Bottom-50% growth ranges from about 0% (the paper's pretax concept, 1980-2014) to +14.5% (to 2019), +21% (posttax) and +40%/+66% (AS's per-capita, size-adjusted pretax/aftertax, 1979-2019). The gap with average growth persists under every concept, so the qualitative finding stands, but 'stagnation' is a statement about one concept and window. Health transfers account for about half to three-quarters of the posttax gain, not almost all.

Evidence. Bottom-50% pretax growth (MainData DX): -2.4% from 1979, +1.4% from 1980, +2.6% from 1981. 1980-2019: +14.5% (Feb-2022 TB3). With the PCE deflator +4.5%, with the GDP deflator +6.5%. Posttax +21% (Table II). Health accounts for 49% (from 1970), 57% (1976), 71% (1978) and 63% (1980) of the bottom-50% posttax gain (cols FK/FP), not 'almost all'; excluding health the series still rose 19% from 1970. AS (2024, pp.2204-2205; per capita, size-adjusted, PCE): bottom-half real pretax income +40% and aftertax income +66% over 1979-2019. CBO (2022, cited there): +61% for the bottom two quintiles after taxes and transfers.

Why this severity. Under the paper's own concept the stagnation is robust (growth stays within about -2% to +15%, against ~60% average), so C1 survives. But the unqualified rhetoric ('shut off from growth', 'almost all from health') goes beyond what the evidence shows under other reasonable concepts and windows.

The authors' response. The concept is defined explicitly. Equal-split adults are argued to neutralize trends in marriage and household size (fn 53; Appendix B.7.1). Lifetime and mobility issues are discussed (pp.583-584, citing Kopczuk, Saez & Song 2010), and posttax series are reported. SZ (2020) argue that equivalence scales mix income and consumption concepts.

9moderateplausible · previously known · methodology

The top 1%'s share jumps sharply in 1986-88, right after a major tax reform that changed how high earners reported income. Part of that jump may be income relabelled or shifted between years rather than real gains. The demonstrated effect is small (about half a point of a nine-point rise), but the paper does not examine it.

Technical detail and evidence

Why it matters, in detail. TRA86 cut the top rate from 50% to 28% and triggered income retiming and C-to-S elections. The DINA jump persists after 1988, so it is not pure retiming. DINA's retained-earnings imputation neutralizes part of the C-to-S effect but allocates retained earnings by dividends and gains, not by the actual owners of converting firms, so a reclassification component may remain. The bias on the trend is upward and of uncertain size; about 5% of the trend is demonstrated.

Evidence. MainData BP: 12.55% (1985), 12.21% (1986), 13.31% (1987), 14.88% (1988), 14.46% (1989). Labor component (CG): 5.74% -> 7.46% of national income over 1985-88. AS (2024, fn 30): a smaller jump remains in their series, partly from retiming and new S-corporation elections. AS Table 4: 'various corrections to tax income definition' account for 0.4 pp of the 2014 level gap and 0.5 pp of the 1979-2014 trend gap. Kopczuk & Zwick (2020, p.36) on C-to-S conversions.

Why this severity. A robustness concern with limited demonstrated impact: the demonstrated correction is about 0.5 pp of the ~9-pp rise, but how much of the 2.3-pp jump is reclassification rather than real gains is unknown.

The authors' response. Not addressed for DINA in the paper. PSZ argue that including retained earnings and corporate taxes deals with corporate-form shifting (pp.567-569; Appendix C.2), and that pre-1986 retained earnings may hide labor income, so they may understate the earlier labor share (fn 61).

10moderateplausible · previously known · external inconsistency

For years before 1962 the paper reuses an older series of top incomes built from early tax tables. A newer study argues that series exaggerates 1920s inequality and the drop during World War II by about a third. If so, today's top shares would be above, not just equal to, their 1920s peak, and the mid-century fall less dramatic. The findings for 1962 onward are unaffected.

Technical detail and evidence

Why it matters, in detail. Pre-1962 DINA top shares are PS fiscal shares adjusted to national income. GMMS's numerator corrections (low filing coverage; net-income-to-AGI multipliers that add 1-3 pp to pre-war top-1% fiscal shares) would carry over. If they do, DINA's 1928 top 1% (21.39%) could fall below its 2014 level (20.20%), and the WWII compression would be shallower and more gradual. There is no effect on post-1962 results.

Evidence. Online Appendix A.1.2 and A.2.4 (pre62.do). MainData: top 10% 47.96% and top 1% 21.39% in 1928, against 47.01% and 20.20% in 2014. GMMS (2022, Economic Journal 132(647); accepted manuscript pp.2-3): the 1928 fiscal top-1% share falls from 23.9% to 19.5%, and the 1928-44 drop from 12.7 to 8.6 pp ('roughly one third' smaller). Their denominator correction (a fixed 80% of personal income) does not carry over to DINA's national-income denominator; their numerator corrections would.

Why this severity. It affects only the secondary long-run result (C7); the post-1962 core findings are untouched. If GMMS's numerator corrections carry over, 2014 would exceed rather than merely match the 1920s peak. The DINA-specific magnitude is not established.

The authors' response. No response by the authors located. GMMS themselves retain the U-shape.

11minorconfirmed · newly identified here · internal inconsistency

A number of figures quoted in the article's text do not match the data files published with it, apparently because the text was carried over from an earlier draft. Most differences are small and none changes the main conclusions. But anyone quoting the text could be off by a few points.

Technical detail and evidence

Why it matters, in detail. The discrepancies range from rounding (0.1-0.3 pp in tax rates) to sizeable relative errors: retained earnings overstated by 16%; median labor-income growth 10% vs 4.4%; health share of posttax growth 'almost all' vs about half to three-quarters. The p.577 comparison mixes posttax 1946-80 with pretax 1980-2014 growth, though the contrast holds on either basis (pretax +109% vs -25%; posttax +179% vs +4%).

Evidence. Text vs data (adjudicator-verified, MainData/Distrib Nov 2017 unless noted): (a) p.598: retained earnings explain '1.4 points' of the 1.9-pp rise; TB2f gives 1.21 pp, Appendix C.2 says 1.2, and only the Dataverse file gives 1.41. (b) p.595: capital income +2.2%/yr and labor +0.1%/yr (2000-14); Table S.2 gives 1.98% and 0.05%. (c) p.595: capital share 23% -> 30%; data 23.3% -> 28.8% (col GA). (d) p.595: bottom-90% capital share 'close to 20% today'; data 15.4% (col GB), and p.581 itself says 15%. (e) p.580: tax-exempt labor 13% -> 23% of bottom-90% income; data 11.5% -> 21.2%. (f) fn 44: bottom-90% posttax income 'about 3%' above pretax after the war and 13% today; data 4.8-7.0% (1946-70) and 14.9% (2014). (g) p.594: all-working-age median pretax labor income $27,500 in 2014, +10% since 1989; the plotted series (Figure VII, col FW) gives $31,450 and +4.4%. The men's and women's figures match. (h) p.601: bottom-50% payroll, income and sales tax rates 11.3/6.6/4.7%; data 11.4/6.4/5.0%. (i) p.603: middle 40% +8% (1999-2014) with transfers +32%, and the 2007-09 fall 'limited to 3%'; data +9.4%, +36.1% and -4.9%. (j) p.601: Medicaid 3.4% of national income; Dec-2016 NIPA gives $487.4bn / $15,153.9bn = 3.2%. (k) p.564: share of national income reported on returns '70% in the late 1970s to about 60% today'; Figure I series give 64.6-65.6% (1977-79) -> 56.2% (2014). (l) p.557: '$64,500' (Table I $64,600); top-1% average '$420,000' in 1980 ($428,781); top-1% share 'almost twice' the bottom-50% share (actual ratio 1.6). (m) p.583: 'almost all' bottom-50% posttax growth from Medicare/Medicaid; data 49-73% depending on base year. (n) fn 49: elderly bottom-50% income excluding health 'stagnated at $20,000 since the early 2000s'; data $17.1-18.5k (2000-07) -> $20.3k (2014). (o) p.577: the 1946-80 gains quoted (+179% bottom quintile, +117% next 30%) are posttax Table II figures, set against pretax 1980-2014 figures (-25%, +7%). Pretax 1946-80 gains are +109% and +101%. The 1946-62 bottom-group growth is assumed equal to the bottom-90% rate (disclosed in the Table II note). Scripts: text_claims.py.

Why this severity. Individually small, from 0.1 pp to a few points, and none reverses a conclusion. Collectively they show the text was not updated when the series were revised, which matters for anyone quoting the paper.

12minorconfirmed · newly identified here · documentation gap

The most precise results rely on confidential tax data, so outsiders can only approximately reproduce them; the public files give somewhat different numbers. The data file deposited with the journal also differs from the one on the authors' website in a block of figures, and the article quotes both versions in different places. This does not change the conclusions but makes exact checking harder.

Technical detail and evidence

Why it matters, in detail. External micro-files approximate the internal series within about 0.2-1.0 pp in shares, but bottom-50% growth differs by several points. Users of the journal deposit get a different S-corporation/retained-earnings decomposition from users of the author-site file.

Evidence. A full cell-by-cell comparison finds 532 differing cells in the Data sheet, all in cols IS-JD (the S-corporation/retained-earnings robustness block). Top-1% retained-earnings rise 2000-14: 1.41 pp in the Dataverse file vs 1.21 pp in the author-site file. Top-1% S-corporation profits 2014: 0.90% vs 1.58% of national income. The text quotes the Dataverse value on p.598 ('1.4') and the author-site value in fn 61 ('about 1.5%'). MainData T2's growth cells are hard-coded numbers. External vs internal series (Feb 2022): 2014 bottom-50% share 13.88% vs 13.12%; bottom-50% growth 1980-2014 +7.3% vs +4.9%. Scripts: compare_wb.py, micro_shares_eq.py.

Why this severity. No effect on the findings as such, but exact verification is impossible, and the official replication deposit is an earlier, partly different vintage than the files on the authors' site.

The authors' response. Codebook: the external files 'track the results from internal files closely' for most series. The authors publish an unusually rich set of code, tables, later-vintage micro-files and an updates log.

13minorconfirmed · newly identified here · arithmetic or transcription

A worked example in the appendix contains a small arithmetic mistake (96% instead of 94%). It does not affect any of the paper's results.

Technical detail and evidence

Why it matters, in detail. 1 - 0.02 x 3 = 0.94. The recurrence is correct; only the numerical substitution is wrong. No effect on any estimate.

Evidence. PSZ2017DataAppendix.txt, Section B.6.3 and fn 20 (both the Nov 9 and Nov 10, 2017 versions).

Why this severity. Expository only; the empirical series use measured aggregates, not this example.

14minorlikely · newly identified here · data error

The number of adults the authors divide national income by differs slightly from Census figures (about 2 million fewer adults in 2014). Using Census counts would trim average income growth from about 61% to 59%. That is a small change, and if anything it strengthens the finding that the bottom half stagnated.

Technical detail and evidence

Why it matters, in detail. With Census adults, average real national income per adult grows about 59.0% rather than 60.8% over 1980-2014, and the 2014 average is about $64,100 rather than $64,600. Bottom-50% growth is roughly +0.3% rather than +1.4% if the extra adults scale proportionally (an approximation).

Evidence. PSZ (Distrib TG4 col B): 155.268m (1980) and 234.444m (2014). Census: 154.824m (July 1980, file e8081rqi) and 236.441m (July 2014, NC-EST2016-AGESEX-RES). Adjudicator recomputed both Census totals.

Why this severity. The effect is about 1-2 pp on 60% growth and, if anything, strengthens the stagnation finding.

15minorplausible · newly identified here · speculative assumption

People who do not file tax returns make up a large part of the poorer half. The authors boost their survey-reported wages with a correction measured only for 1999-2014 and apply it back to 1962. If the right correction was different in earlier decades, the poorer half's growth could be off by one or two percentage points, small next to its 60-point gap with average growth.

Technical detail and evidence

Why it matters, in detail. The x2/x2 adjustment roughly quadruples CPS non-filer wages. If the true 1980 shortfall differed by ±50%, bottom-50% income in 1980 would move by about ±1-2%, i.e. ±1-2 pp of 1980-2014 growth.

Evidence. Online Appendix B.1 (pp.19-20). Feb-2022 external micro-files (adjudicator): non-filers are 19.9% (1980) and 27.9% (2014) of bottom-50% adults, and their wages are 3.0% and 6.2% of bottom-50% pretax income.

Why this severity. Plausible effect of about 1-2 pp on bottom-50% growth, small relative to the ~60-point gap with average growth.

The authors' response. The appendix notes (fn 12) that non-filers can be built from tax data only for 1999-2014, and that tax data do not link spouses for non-filers.

16minorplausible · previously known · methodology

The paper finds the rich now pay a smaller share of their income in taxes than in the 1950s, while the poorer half pays more, mainly through payroll taxes. That holds under the authors' definitions. Other reasonable choices, such as how refundable tax credits are counted and who is assumed to bear the corporate tax, give different trends, and federal-only studies find federal taxes became more progressive after 1979.

Technical detail and evidence

Why it matters, in detail. Measured progressivity depends on (i) refundable credits counted as transfers rather than negative taxes; (ii) corporate-tax incidence (the shareholder-only convention raises 1950s top rates and steepens the decline); (iii) imputed top-end income in the denominator, which lowers recent top-1% rates; and (iv) the federal-only vs all-government scope. The paper's direction holds within its concept; other conventions can give rising federal progressivity since 1979.

Evidence. MainData HN/HI: top 1% 39.6-43.4% (1950s) vs 31.3-36.4% (2010-14); bottom 50% 15.5-17.4% vs 22.9-24.4%. PSZ Updates (Oct 2019, §3.1.2): shareholder-only incidence makes top effective rates 'now higher than in PSZ (2018) in the 1950s-1960s'. Splinter (2020, NTJ 73(4)): the federal Kakwani index rose 46% over 1979-2016 (CBO data). Splinter & Auten (2019) on PSZ-style denominators (corpus us-wealth-taxes-15).

Why this severity. Within PSZ's all-government, all-tax concept the direction is robust, and the later incidence change strengthens it; the magnitude, and the contrast with federal-only studies, is largely definitional.

The authors' response. PSZ include all taxes at all levels of government, and their later incidence change strengthens the decline. Federal-only measures that count refundable credits as negative taxes answer a different question.

Claims examined and rejected

Problems one auditor raised that did not survive checking.

Audit notes

What reproduced. From the authors' November-2017 files, the following reproduce exactly (both auditors, spot-checked by the adjudicator): Tables I-II; the 27x/81x ratios (26.8 / 80.5); +60.8% average and +1.4% bottom-50% pretax growth; +41.8% middle 40%; +204% top 1%; the Figure II growth-incidence statements; the gender shares (27.4/16.5/11.5%); tax-rate levels; and the France comparison. Independently, Dec-2016 NIPA national income ($2,426.8bn in 1980, $15,153.9bn in 2014) divided by PSZ's adult counts gives $15,630 and $64,638 per adult, exactly the MainData values, and +60.8% real growth with PSZ's deflator (+65.8% PCE). On the authors' Feb-2022 external micro-files (1979, 1980, 2014, fetched by range requests), the adjudicator reproduced: the external-file shares (bottom 50% 20.8% -> 13.9%, top 1% 10.0% -> 18.8%); Auditor A's imputed-item sensitivities (bottom-50% pretax growth +7.3%, up to +10.5%); and the public-goods sensitivity (bottom-50% posttax growth +22.9% -> +30.5% to +31.5% with equal per-adult allocation; +27.1% half/half). Formula inspection confirmed the TG4 middle-40% formula error, the Figure VIII panel discrepancy (58.9% vs 54.6%; hard-coded 78.7% pension capital fraction carried forward from 2010) and the 532-cell difference between the Dataverse and author-site MainData. Not reproducible: the internal-IRS-data construction (exact published micro-files are not public, and external files differ by 0.2-1 pp in shares and several points in bottom-50% growth); the AS, SYZZ and GMMS alternative series (taken from their publications and checked against the texts); and the December-2016 data files.

Limits of this audit. No access to internal IRS data or the licensed PUF, so the micro-construction (non-filers, imputations, re-ranking) could not be rebuilt. The exact published-vintage micro-files are not public. The adjudicator's micro tests used the authors' Feb-2022 external files (1979, 1980, 2014), whose levels differ from the published internal series and whose methodology includes the 2019-2022 updates (e.g. neutral deficit allocation). Auditor A's April-2019 (2017-methodology) results were not re-run. The AS, SYZZ, Kopczuk-Zwick, Iselin-Reck, GMMS, Gale-Sabelhaus-Thorpe, PSZ (2026) and AS (2026) figures were checked against the published texts, but their estimates were not reproduced; AS's linked-owner estimates are confidential. The effect of the Geloso et al. corrections on DINA's pre-1962 series was not quantified, and the immigration and incarceration composition of the bottom 50% was not analysed. The December-2016 data files were not retrieved, so the hypothesis that the text discrepancies stem from that vintage is unverified, although the same sentences do appear in NBER WP 22945. Current WID series were not re-downloaded; vintage comparisons use the authors' Feb-2022 Distrib workbook. Judgments about where the truth lies between PSZ and AS rest on published third-party assessments, not on new estimation.