Emmanuel Saez, Gabriel Zucman · Journal of Public Economics 259: 105675

Distributional Tax Analysis in Theory and Practice: Harberger Meets Diamond-Mirrlees

21 problems found: 9 moderate · 12 minor

What the paper claims

The effective tax rate of the top 1% of US adults (all taxes, all levels of government, divided by pre-tax national income plus pure realized capital gains; equal-split adults) fell from about/nearly 50% in the early 1950s to 32% in 2021; it is about the same as in 1932.
High mid-century progressivity was achieved through the corporate tax (plus estate tax), not the individual income tax, which absorbed a roughly constant share of top incomes since 1930.
The conventional CBO allocation of the corporate tax understates mid-century progressivity and biases trends (C-to-S conversions, pensions); with it the 1950-2021 decline is 'only 7 points' instead of 'nearly 13'.
Theory: in the Diamond-Mirrlees model with pure profits fully taxed and other taxes adjustable (or optimal), mechanical changes in liabilities by group plus aggregate revenue effects of household behavioural responses are sufficient statistics for reform analysis; pre-tax price (Harberger incidence) effects are normatively irrelevant; in Harberger's model the corporate tax is production-inefficient.
Applied reform analysis (2021): a 10% federal corporate-rate increase and a 10% increase in top-1% federal individual income tax are both desirable under geometric welfare weights; the corporate increase is desirable even with equal domestic weights because ~39% is paid by non-residents.
The 2021 US tax system (all levels) is only mildly progressive; the federal system is more progressive.

Every problem found

1moderateconfirmed · previously known · methodology

The paper counts every dollar of corporate tax as paid by the companies' shareholders. Government agencies instead assume part of it is paid by workers and by other investors. Under the agencies' rules the top 1%'s tax rate still falls a lot after 1950, but by about 8-10 points instead of 13. So roughly a fifth to a third of the measured fall comes from this accounting choice.

Technical detail and evidence

Why it matters, in detail. The 12.63 pp decline (45.30% -> 32.67%) decomposes almost entirely into the corporate component (K: 23.27% -> 2.79% of top-1% pre-tax income). With CBO-type shares (Data!I: 41.4% of the corporate tax to the top 1% in 1950 vs 57.9% under SZ) and the denominator O = N(1-K) + I*AW, the 1950 rate is 41.41%. The micro-based 2021 CBO-method rate is 33.11%, a decline of 8.30 pp (up to about 9.0 pp allowing for re-ranking and corporate-only-component uncertainty). A TPC 60/20/20 split gives 10.1 pp. Convention therefore accounts for about 20% (TPC) to 34% (CBO) of the measured trend. The level effect is concentrated in mid-century, when the corporate tax was 6-7% of NI and equity ownership was concentrated.

Evidence. Workbook Data!C,K,L,N,O,I,W,X (row 44 = 1950) and cbo-vs-sz!H61 (33.11%). Adjudicator scripts/incidence_variants.py: SZ 45.30 -> 32.67 (12.63 pp); CBO-consistent 41.41 -> 33.11 (8.30 pp; 8.88 pp if the 1950 corporate-only component is 22.34% rather than 23.27%); TPC-style 42.61 -> ~32.50 (10.11 pp). Auditor A (R8, I1) obtained the same CBO-method figures and the same 1950 TPC-style rate. scripts/cbo_check.py: in 1962-80 the consistent formula under-predicts the micro-based CBO-method rate by 0.3-0.7 pp.

Why this severity. The paper's estimand is explicitly the current-tax wedge. It argues the convention and itself presents the CBO comparison. The direction of C1-C2 survives every convention tested. Under agency conventions, though, the decline is about 8-10 pp rather than 12.6 pp, so the magnitude moves by 20-35%: a disclosed but material qualification.

The authors' response. Sec. 2.2 and 3.2: current-tax analysis measures price wedges rather than counterfactual incidence. The CBO method is internally inconsistent (it shifts taxes while holding aggregate income fixed) and non-neutral to C-to-S conversions. The paper shows the comparison in Fig. 3 and Fig. A2 (but see F2 for the size it reports).

2moderateconfirmed · newly identified here · arithmetic or transcription

The paper says the agencies' method would show the top 1%'s tax rate falling by only 7 points instead of 13. The 7 comes from a spreadsheet shortcut that mixes two different measures of income. Done consistently, the agencies' method shows a fall of about 8.3-9 points. The gap between the two methods is real but about a third smaller than the paper says.

Technical detail and evidence

Why it matters, in detail. The hybrid ignores that reallocating the corporate tax also reallocates pre-tax income (O44 = N44(1-K44) + I44*AW44 = 15.44% vs N44 = 16.54% of NI), so the non-corporate taxes of the top 1% must be rescaled by N/O = 1.071. The consistent 1950 CBO rate is 41.4%; applying the formula's validated residual bias (-0.3 to -0.7 pp in 1962-80) or an alternative corporate-only component (22.3% instead of 23.3%) raises it to about 41.7-42.1%. The CBO-method decline is therefore 8.3-9.0 pp versus the paper's 6.9 pp ('7 points'), and the gap between methods is 3.6-4.3 pp versus 5.7 pp.

Evidence. Workbook: C121 = -12.63, K121 = -20.48, L121 = -14.75; 1950: C44 = .4530, K44 = .2327, L44 = .1781, N44 = .1654, O44 = .1544. Consistent rate (C-K)N/O + L = 41.41%; hybrid C-K+L = 39.84%; 2021 hybrid 32.94% vs micro-based 33.11% (cbo-vs-sz!H61). scripts/cbo_check.py: across 1962-1980 the hybrid under-predicts the micro-based CBO-method rate (cbo-vs-sz!H) by 1.2-2.6 pp, the consistent formula by 0.3-0.7 pp. Both auditors reproduced 6.90 vs 8.30 pp.

Why this severity. This is the paper's main quantitative evidence that the method choice 'has large implications' for trends. Corrected, the method gap is about 3.6-4.3 pp rather than 5.7 pp, an overstatement of roughly a third to a half. The paper's own headline (C1) is untouched, and a smaller but real gap remains.

3moderateconfirmed · previously known · documentation gap

The paper's 2021 figures were not computed from 2021 tax records. They are projections from older files grown in line with the economy, and the paper does not say so. Newer official statistics show 2021 corporate taxes about 20% higher, which would raise the 2021 top-1% rate by about half a point. The long-run story is unchanged, but the end point is an estimate.

Technical detail and evidence

Why it matters, in detail. The 2021 rate inherits the 2017 fiscal-income distribution, aggregate growth assumptions and TAXSIM-simulated taxes. The workbook's 2021 realized gains ($2,028bn; 10.25% of NI) enter only through aggregates. Updating the corporate-tax aggregate to the current vintage (+19.9% federal) raises the corporate component of the top-1% rate from 2.79% to about 3.35% of income, i.e. the 2021 rate to about 33.1-33.3%. The decline shrinks by about 0.5 pp. Table 2A's mechanical gain becomes about $33.5bn instead of $27.9bn.

Evidence. PSZ2022Programs/runusdina.do lines 27-39; PSZUpdates.txt Sec. 3.3 ('Preliminary distributional series for most recent years'); PSZ2022AppendixTablesII TG1 covers 1913-2019 only; FRED/ALFRED FCTAX vintages (2021: 279.897 vs 335.476); Claude R6 (fed+state corporate tax 1.96% vs 2.35% of NI). Paper p.5: micro-files 'taken from the February 2022 release'; data statement 'available on request'.

Why this severity. The endpoint of the headline trend is an estimate presented as data. The revised corporate-tax vintage alone would raise the 2021 top-1% rate by about 0.4-0.6 pp and Table 2A's mechanical gain by about 20%. Neighbouring years (2016: 34.9%; 2018-2020: 32.2-33.8%) bracket the 2021 value, so the qualitative decline is unaffected.

The authors' response. Not addressed in the paper. The PSZ notes (Sec. 3.3) describe the projection procedure and say the assumptions 'will be revisited as more data become available'.

4moderateconfirmed · newly identified here · replication failure

We could not rebuild the paper's numbers from the public data files. In some years, especially around 1980, the public files give top tax rates 2-2.5 points higher than the published ones, and the files behind the 1950 and 2021 end points are not public at all. Nothing suggests the published numbers are wrong, but outsiders cannot fully check them.

Technical detail and evidence

Why it matters, in detail. Differences between public and internal files (aggregated extreme-value records, blurring), plus unpublished processing, are the likely sources. They cannot be diagnosed without the internal files. The 1950 value is anchored to 1962-63 internal micro fractions (taxrates.do), so the public-file 1962 gap (+0.83 pp, all in the income tax) would carry into the pre-1962 series if the public file were used. The sign of the 1950-2021 trend effect is therefore indeterminate, and probably small.

Evidence. scripts/micro_rates.py; outputs/micro_rates.txt; published values from cbo-vs-sz!G and PSZ2022AppendixTablesII TG1/TG2b. Both auditors obtained 43.55% (1962) and 33.07% (2019); Claude obtained 42.5% for 1980. Ranking by peinc instead of peinc_kg gives 32.64% in 2019 and 34.13% in 2014. PSZUpdates Sec. 3.1.3; paper fn 17 ('All vintage releases and corresponding code are also published').

Why this severity. Neither the start nor the end of the headline series can be regenerated from public material, and intermediate years differ by 0.4-2.5 pp. There is no evidence the published series is wrong. The public files give higher, not lower, top rates, so this is not evidence that the decline is overstated.

The authors' response. Data availability statement: 'Data will be made available on request'. Fn 17 points to the PSZ website for vintages and code.

5moderateconfirmed · previously known · internal inconsistency

The paper says taxes like sales taxes are counted against the people who buy the goods. The data it uses instead charge 30% of these taxes in proportion to everyone's earnings and investment income, which adds about a point to the top 1%'s tax rate. Fixing this barely changes the long-run decline. It slightly lowers today's top rates and makes the current system look a little flatter.

Technical detail and evidence

Why it matters, in detail. The factor slice adds about 1.4 pp (1962) and about 1.0 pp (2014-19) to top-1% rates. Pre-1962 sales-tax shares are frozen at 1962-63 values, so 1950 carries roughly the 1962 effect scaled by the sales-tax level (about 1.1 pp). The trend effect is therefore about 0.1-0.4 pp. With both stated rules applied, the 2019 bottom-50% rate rises by about 0.6 pp and the top 1% falls by about 1.0 pp, narrowing Table 1's spread by about 1.5 pp. Pandemic transfers would make the A.2 adjustment larger in 2021.

Evidence. PSZ2022Programs/build_usdina.do l.2155-2187 ('assume 70% shifted to prices, 30% to factors'; salestax_on_factor = 0.3*ttsalestax*fainc/total_fainc; dicsh2 = dicsh + ditax - difoo); PSZUpdates Sec. 3.1.1. Adjudicator scripts/micro_salestax_rules.py on public files. Moving the factor slice to consumers changes the top-1% rate by -1.37 pp (1962), -0.97 (2014), -0.96 (2019), and the bottom-50% rate by +1.56 / +1.93 / +1.92 pp. The A.2 rule (cash transfers ex-SNAP) changes the bottom-50% rate by -0.42 (1962) and -0.95 (2014, 2019). Auditor A's larger A.2 estimate (-2.0 to -2.2 pp) uses a broader transfer definition.

Why this severity. This departs, without disclosure, from the allocation rule the paper presents as its core principle. It raises top-1% levels by about 1 pp (about 3% of the 2021 rate) and changes Table 1's bottom-to-top gradient by about 1-1.5 pp. The effect on the 1950-2021 trend is at most about 0.4 pp.

The authors' response. Not addressed in the paper. The PSZ notes justify the 30% factor slice as covering indirect taxes (licences etc.) that the ITEP analysis does not capture.

6moderateconfirmed · newly identified here · speculative assumption

The paper calculates that a corporate tax increase is worthwhile even for a government that does not care about redistribution. That rests on a figure from unpublished work: that 39% of the corporate tax is paid by foreigners. It also rests on an assumed degree of taxpayer response. If foreigners paid under about 13%, or companies responded strongly, that particular conclusion would reverse.

Technical detail and evidence

Why it matters, in detail. With equal domestic weights the welfare cost is the mechanical gain times (1 - s), where s is the foreign share. Net value = 24.13 - 27.86(1 - s), which is positive only if s > 0.134. The JCT allowance (10.8% of the 75% not shifted to labour, about 8%) gives -$1.50bn. The paper argues JCT is too low (portfolio-only, 2005-12 data), and the ~40% foreign ownership of US equity supports a large s, but the mapping from equity ownership to tax shares is unpublished. The individual reform's net revenue is sensitive to the MTR (30% vs a 37% statutory top rate: $75.1bn vs $66.7bn) and to the elasticity (Codex: $49.1bn at e = 0.8).

Evidence. Workbook Table2A!D12, W16 (0.5), Table2B!X10:X11 (0.30) and note A22; paper p.11 and fn 33; Rosenthal & Burke (2020, NYU colloquium draft) text verified. Adjudicator scripts/table2_thresholds.py: equal-weights net value $7.19bn; zero at a foreign share of 13.4%; -$1.50bn at JCT's ~8%; break-even e = 1.48 (workbook formula) or 1.35 (exact). Individual reform net revenue $66.7bn at a 37% MTR (vs $75.1bn).

Why this severity. The main geometric-weight verdicts are robust: the corporate reform stays desirable to e of about 2.6-2.9, and the authors publish thresholds and an editable sheet. A headline policy statement, however, depends on an unpublished parameter and on an uncited elasticity. It reverses for a foreign share below 13% or e above about 1.35-1.48.

The authors' response. Thresholds are reported (2.9/3.9 and 1.6/1.9) and a companion spreadsheet allows other parameters. Fn 33 explains why JCT's foreign allowance is considered too low.

7moderateconfirmed · newly identified here · internal inconsistency

An appendix example about funding health insurance with a payroll tax treats money that workers themselves pay toward premiums as if employers paid it, and lets a third of it go to company profits. Corrected, the example's warning that the reform could hurt low earners mostly disappears for the bottom half, though it still mildly favours the top. This is a side example, not a main result.

Technical detail and evidence

Why it matters, in detail. With employee share s = 0.268 assumed equal across groups, the corrected effect is (1 - s) times the rigid-wage effect plus s times the conventional effect. About $95bn of the implied profit windfall is spurious. The qualitative lesson that wage rigidity can change incidence survives. The magnitude and the sign for low earners depend on the omitted employee/employer split.

Evidence. Workbook TableA4!G16 (1,068.3), notes J16, J20, G21 (11.83%); totals show the full head tax re-entering pre-tax income (K12 = 0). CMS NHE Table 24, 2021 (current vintage): ESI $1,120.9bn = employer $820.8bn + employee $300.1bn (26.8%). Adjudicator scripts/appendix_checks.py, following Codex's decomposition: after-tax effects become -0.93 -> -0.04 pp (bottom 50%), -1.05 -> -0.48 (middle 40%), +2.52 -> +1.51 (top 0.1%). The employer-only rate is about 8.7% on the paper's base.

Why this severity. This is a secondary appendix illustration and does not touch C1-C6. Its central distributional result (the reform 'becomes regressive' under rigid wages) roughly halves and nearly vanishes for the bottom half once the error is corrected.

8moderatelikely · newly identified here · overclaiming

The paper's theory says knock-on effects of taxes on wages and investment returns can be ignored when judging reforms, because the government could always undo them with other taxes. That holds in the textbook model, but only if the government actually makes those offsetting changes, and the summary states it as a general rule. For a real corporate tax rise without such adjustments, effects on workers' pay would matter.

Technical detail and evidence

Why it matters, in detail. In Prop. 1 the dp terms cancel through 100% profit taxation and the free adjustability of all t_j. When instruments are restricted (e.g. Mirrlees taxation with unobserved types and endogenous relative wages, as in Stiglitz/Naito), production efficiency and price-irrelevance fail. The incidence of the corporate tax on wages then enters welfare unless separately offset. Table 2A's $17.2bn net value and the equal-weights $7.2bn assume a costless offset that the reform does not include. The direction of the correction depends on the wage incidence (e.g. Fuest, Peichl & Siegloch 2018 find workers bear about half in Germany) and on welfare weights.

Evidence. Paper p.10 (Proposition 1; 'Importantly, this analysis hinges on the key assumption...'), p.11, p.13 and Table 2 notes; Conclusion p.13. Literature (verified via Crossref): Stiglitz (1982) JPubE 17:213-240; Naito (1999) JPubE 71:165-188; Sachs, Tsyvinski & Werquin (2020) Econometrica 88(2) (NBER w22646). Codex R11 numerical example: with the labour tax above its optimum, raising a below-optimal capital tax lowers welfare (derivative -0.019).

Why this severity. The theorem stands and the body states its conditions. But one of the paper's two main lessons is framed as general. The applied reform verdict (net value $17.2bn) is the value of a compensated, pure-wedge reform rather than of the statutory change itself.

The authors' response. Sec. 4.1, Sec. 5 and App. A.4 state the conditions and argue that 'the optimal tax approach tells the policy maker which direction to go; the tax incidence analysis can provide the technical pathway'. They note that 'having the full suite of distributional tax reform for each type of tax is actually useful'.

9moderateplausible · previously known · external inconsistency

A tax rate is taxes divided by income. The paper counts as income several items that do not appear on tax returns and whose assignment to the rich is disputed by other researchers. This makes today's top tax rates look lower than official estimates: 22% versus 30% for federal taxes in 2021. How much it affects the comparison with the 1950s is not known.

Technical detail and evidence

Why it matters, in detail. The SZ top-1% federal rate is 21.95% vs CBO's 29.8%, with near-identical federal tax dollars and a denominator ratio of 1.31. Of the PSZ-vs-AS difference in top-1% income, a sizeable part is allocation of untaxed income (underreporting, depreciation, retirement), which is disputed and unvalidated against linked owner data. Mechanically, a 10-20% smaller 2021 top-1% denominator would raise the 2021 rate by about 3.5-8 pp, holding taxes fixed. The 1950 denominator's imputations (retained earnings, corporate tax, underreporting) are of comparable or larger relative size, so the net effect on the trend is indeterminate.

Evidence. tab1 (federal taxes incl. estate tax $1,104.5bn on $5,031.3bn; Table A1 basis). CBO, Distribution of Household Income in 2021 (Sept 2024), Table A-1 (1,231,562 households), Table C-1 ($3,126,400 average income; $929,600 federal taxes), Table C-2 (29.8%). Splinter (2020) NTJ online appendix Sec. 6: removing imputed retirement and underreported income raises SZ rates by about 6 pp for the top 5% (2010). Corpus: AS (2024) attribute 2.0 pp of a 6.0 pp 2014 top-1% share gap to underreporting; AS (2026) put partnership excess depreciation at +1.2 pp (PSZ) vs +0.16 pp.

Why this severity. The level effect is potentially large. The trend effect is unknown because imputations enter both the 1950 and 2021 denominators. If the contested items grew mainly after 1980, they would make the measured decline too large, but this is not demonstrated.

The authors' response. Saez & Zucman (2020, NBER w27921) and Piketty, Saez & Zucman (comments on Auten & Splinter, 2023-2026, e.g. https://gabriel-zucman.eu/files/PSZ2026.pdf) defend allocating untaxed partnership/S-corporation income, retirement income and underreporting to the top. Gale, Sabelhaus & Thorpe (2023) largely side with PSZ on underreporting. The paper's trend comparisons hold the denominator concept fixed.

10minorconfirmed · newly identified here · arithmetic or transcription

The paper's example of Warren Buffett's tax rate uses the wrong ownership share and, apparently, Amazon's equipment figure instead of Berkshire Hathaway's. Corrected, his estimated rate is about 19-21% rather than 18.4%, and his income about $4.6 billion rather than $8.2 billion. The example's point, that corporate taxes are most of what he pays, still holds.

Technical detail and evidence

Why it matters, in detail. Ownership scales numerator and denominator almost equally (rate 18.51% with the stake fixed alone), but dollar levels fall by 45%. The PP&E error understates imputed business property taxes ($618m vs $1,524m) and so the rate. Using tax-basis realized gains (about $3.3bn) instead of GAAP figures would lower the corrected rate to about 18.9% (Codex), so the illustrative rate is about 19-21% depending on the gains convention.

Evidence. Berkshire 2018 annual report (balance sheet and Note 10: 20,628 and 131,780; investment and derivative gains/losses (22,455); unrealized losses (22,729)); 2019 proxy ('approximately 31.4% of the voting interest and 16.5% of the economic interest'); Amazon 2018 10-K net PP&E 61,797. Adjudicator scripts/appendix_checks.py: rate 18.44% (paper) -> 21.08% (PP&E fixed) -> 21.15% (both fixed); income $8.18bn -> $4.62bn.

Why this severity. These are transcription errors in an appendix illustration. They raise Buffett's illustrative rate by about 2.7 pp and nearly halve his attributed income, but the example's point (the corporate tax is his main tax) is unchanged and no core finding uses it.

11minorconfirmed · newly identified here · selective presentation

The paper says the income tax took a roughly constant share of top earners' income since 1930. In its own data that share fell in the 1950s-60s and then rose by 5-9 points. The fall in corporate taxes is still the main story, but it was partly offset by higher income taxes.

Technical detail and evidence

Why it matters, in detail. The 'little change since 1930' counterfactual depends on the high 1930 base (21.3%). Measured from 1950 or 1960, individual income+payroll taxes at the top rise 5-9 pp, offsetting about 17% of the 28.7 pp corporate+business-property decline for the top 0.1% (1951-2021). This is consistent with Splinter's (2020) evidence of rising top income-tax rates.

Evidence. Workbook DataF1B col D and PSZ TG2b col T; adjudicator scripts/f1b_check.py: +5.0 pp (1950-2021) and +8.9 pp (1960-2021) for the top 0.1%; OLS trend +1.26 pp/decade 1950-2021 (+0.52 pp/decade 1930-2021). From 1951 to 2021, corporate+business property -28.7 pp vs income+payroll +4.8 pp.

Why this severity. This is a characterisation error that, if anything, strengthens the paper's point that mid-century progressivity came through the corporate tax. It means, though, that the corporate decline was partly (about one sixth) offset by rising individual taxes.

12minorconfirmed · newly identified here · arithmetic or transcription

Several numbers in the summary and text are rounded in a way that makes the decline look bigger. The summary's 'about 50% to 32%' suggests an 18-point fall, while the paper's own data show about 13 points from 1950. Other small text-versus-data mismatches do not change any conclusion.

Technical detail and evidence

Why it matters, in detail. The abstract-implied decline (50 -> 32) is 18 pp, vs 12.6 pp (1950-2021), 13.6 pp (1950-54 average) or 15.8 pp (1951 peak). The other discrepancies are 1-6 pp in individual years or ranges. Table 1 and Fig. 1 come from different runs (tab1 vs cbo-vs-sz).

Evidence. Workbook Data!B,C,D; scorp!B; Table1 vs cbo-vs-sz!F61,G61; adjudicator scripts/text_claims.py.

Why this severity. These are presentation slips. The body gives the correct 13 pp, and none of the mismatches changes a conclusion, but the abstract's rounding makes the decline look about 40% larger than the 1950-2021 data show.

13minorconfirmed · newly identified here · internal inconsistency

Some company shares are owned by charities and universities, and the paper's own rules say the corporate tax on those shares should be spread across everyone. The data instead charge it to private shareholders, who are mostly rich. This slightly inflates the 1950s top rate, by under one point, and so slightly exaggerates the decline.

Technical detail and evidence

Why it matters, in detail. Re-allocating the nonprofit share (s_np) by disposable income (top-1% share d1 of about 10-20%) changes the top-1% corporate share from D to D(1 - s_np) + s_np*d1, with the pre-tax income adjustment. The effect is largest when the corporate tax is large and ownership concentrated (mid-century). The 1950 nonprofit share is not observed (TB15 starts in 1962).

Evidence. build_usdina.do l.2041-2045; workbook Data!BJ = BK * TB15!K/(L+M); TB15 rows 1962 and 2019. Auditor A's scripts/nonprofit_sensitivity.py, checked by the adjudicator: top-1% rate -0.5 to -0.6 pp (1962), -0.7 to -0.9 pp (1950, assuming the 1962 nonprofit share), -0.05 to -0.08 pp (2021).

Why this severity. The mechanism is confirmed, but the effect is under 1 pp. It slightly overstates the 1950 level and therefore the decline, by about 0.6-0.8 pp.

14minorconfirmed · previously known · documentation gap

The paper's figures before 1962 are not direct measurements. They are built by projecting 1962 patterns backwards with other historical series, and one input file is not public. This is a normal way to build such series, but the paper does not explain it, and readers should know the 1950 starting point is partly modelled.

Technical detail and evidence

Why it matters, in detail. The 1950 rate inherits the 1962-63 micro anchor (whose public-file version differs by 0.8 pp; see F4), the SZ (2016) equity-wealth series, and SOI tabulations harmonised to adults and pre-tax income. Geloso et al. (2022) question the pre-1960 Piketty-Saez baseline, mainly before 1945.

Evidence. PSZ2022Programs/taxrates.do (pre-1962 imputation blocks); top400.do; PSZUpdates Sec. 3.1.3 and 3.2. The input spreadsheet is not in the public programs zip or the shared cache. Auditor A: the top-400 cap moves top-1% rates by at most 0.2 pp.

Why this severity. These are documentation gaps. The procedures are standard for this literature and are documented in PSZ's code and notes, and no bias is demonstrated. Readers should nonetheless know that the 1950 anchor is partly modelled from 1962 patterns and wealth series.

The authors' response. Fn 17 refers readers to PSZ's online methodological notes and code.

15minorconfirmed · newly identified here · selective presentation

The chart for the richest 0.1% starts in 1910, but its first three years are copies of 1913 figures rather than data. It is a small presentation issue that does not affect any trend.

Technical detail and evidence

Why it matters, in detail. The pre-1913 non-income-tax components are extrapolated flat from 1913. The 1913 total for the top 0.1% is 16.8%, above the 11.1% shown for 1910-12.

Evidence. Workbook DataF1B rows 3-5 (formulas =C4, =E4 ... chaining to 1913).

Why this severity. Three illustrative points with no effect on any trend after 1913.

16minorconfirmed · newly identified here · arithmetic or transcription

The paper says its tax increases stay worthwhile up to certain levels of taxpayer response. Calculated exactly, those cut-offs are about 5-10% lower than stated. At the paper's assumed responses the results barely change.

Technical detail and evidence

Why it matters, in detail. For a 10% rate increase the second-order term dt*dB is non-negligible at high e. The paper's 'raises revenue up to e = 3.9' corresponds to 3.76 at first order and 3.54 exactly, and the welfare thresholds fall correspondingly.

Evidence. Adjudicator scripts/table2_thresholds.py (workbook / first-order / exact): corporate revenue 3.91 / 3.76 / 3.54; corporate welfare 2.90 / 2.83 / 2.63; individual revenue 1.88 / 1.84 / 1.70; individual welfare 1.63 / 1.61 / 1.48. Exact corporate net revenue at e = 0.5 is $23.76bn vs $24.13bn.

Why this severity. Thresholds are overstated by about 1-4% (first-order) to about 10% (exact). Results at the assumed elasticities are essentially unchanged.

17minorconfirmed · previously known · methodology

When companies or people respond to a tax increase by shifting income elsewhere, some of that income is still taxed somewhere else. The paper's worked examples ignore this, although its own theory includes it. The adjustments are around 10% of the estimated revenue and can go either way, so the examples' conclusions stand.

Technical detail and evidence

Why it matters, in detail. The relevant loss is (tau - s*t)dB rather than tau*dB when a share s of the lost base is taxed at t elsewhere. The dividend/capital-gains offset to a 2.1 pp corporate-rate rise is of the order of the payout-weighted individual rate times the 2.7% fall in after-tax profits (roughly $1-3bn; adjudicator's rough order of magnitude, not estimated). Both corrections are second-order relative to the uncertainty in the elasticity itself (F8).

Evidence. Workbook Table2A!H7:H12 = 0.21*(V - T); Table2B!I = X*(W - U). Codex scripts/reproduce.py: if half of the corporate response is taxed at 30% elsewhere, net revenue is $26.79bn (vs $24.13bn) and net value $19.89bn (vs $17.23bn); a common extra 10 pp tax on responding individual income gives net revenue of $68.36bn (vs $75.08bn). Saez, Slemrod & Giertz (2012, JEL 50(1), Sec. 2.2) describe the same fiscal-externality correction. The paper's own Sec. 5.3 municipal-bond example counts destination-base revenue.

Why this severity. This is an omission in an illustrative application. Plausible magnitudes are about 10% of net revenue, with signs that differ by reform, and no verdict reverses.

18minorconfirmed · newly identified here · overclaiming

The paper says its method can show that owners of low-tax companies pay little. Its national figures, however, give every shareholder the same average corporate tax rate, so the claim describes what the method could do, not what these figures do.

Technical detail and evidence

Why it matters, in detail. Heterogeneous corporate effective tax rates across firms owned by different groups (e.g. low-tax technology firms held at the very top) are averaged away. This could bias top-group rates either way.

Evidence. build_usdina.do l.2041-2045 (corptax = ttfkcot * c_corp_equ / total_c_corp_equity); paper fn 15.

Why this severity. This describes a capability of the framework, not of the reported numbers. The direction of any bias in top-group rates is unknown.

The authors' response. Fn 15 points to Balkir, Saez, Yagan & Zucman (2025) for an implementation that links firms to owners in administrative data.

19minorconfirmed · previously known · methodology

The paper's finding that today's system is only mildly progressive depends on bookkeeping choices at the bottom of the income scale. Refundable tax credits are not counted as negative taxes, and Social Security contributions are counted as taxes but also subtracted from the income they are compared to. Other reasonable choices make the bottom half's tax rate noticeably lower; the top-1% trend is not affected.

Technical detail and evidence

Why it matters, in detail. Counting social-insurance contributions in the numerator while excluding them from pre-tax income raises measured rates for workers by about 2 pp in 2019 but only about 0.3 pp for the top 1%. Treating 2021 refundable credits and rebates as negative taxes would lower bottom-50% rates far more. Both choices flatten the measured 2021 gradient relative to CBO-style measures. The consumption-tax departures in F5 push the other way.

Evidence. Paper Table 1 notes and fn 18; CBO (2024) Table C-2; build_usdina.do globals (plinc = flinc + plcon + plbel) and l.2195-2202 (tax includes govcontrib). Adjudicator scripts/micro_payroll_denominator.py: adding own government social-insurance contributions back to the denominator lowers 2019 rates by 1.7 pp (bottom 50%), 2.0 pp (middle 40%) and 0.26 pp (top 1%); 1962: 0.9 / 1.0 / 0.17 pp. Splinter (2020, NTJ online appendix Sec. 6, step 1) makes the same point for SZ (2019).

Why this severity. These conventions are mostly disclosed and leave the top-1% trend unchanged (within 0.1 pp). They make the bottom-group levels in Table 1, and hence the 'mildly progressive' characterisation, convention-dependent by a few points.

The authors' response. The Table 1 notes disclose that refundable credits are treated as transfers, following national accounts. Fn 18 defines pre-tax income as after the operation of the pension and UI systems.

20minorconfirmed · newly identified here · arithmetic or transcription

There are a few typos in the appendix maths and one slightly misquoted study. None affects the results.

Technical detail and evidence

Why it matters, in detail. The p.45 identity is mis-stated (even the printed equality is wrong: rK + (r* - r̄)K = (r* + τ_K r)K). The p.50 slip inverts the policy advice in one sentence. The FPS figure understates the wage share the paper cites in support of its incidence discussion.

Evidence. Appendix pp.45, 50 and fn 72; FPS (2018) AER 108(2) abstract (OpenAlex record for doi:10.1257/aer.20130570).

Why this severity. These are typographical and citation slips. The intended derivations are clear from context and no result changes.

21minorlikely · newly identified here · overclaiming

The paper says a known inefficiency of the corporate tax had not been noticed before. Economists have measured this inefficiency since at least the 1970s. This affects only how new the paper's point is.

Technical detail and evidence

Why it matters, in detail. The efficiency cost of differential capital taxation across corporate and non-corporate sectors is the subject of the cited computable-GE literature. What is arguably new is presenting it as an infinite household supply elasticity of corporate capital within a sufficient-statistics reform test.

Evidence. Shoven (1976) 'The Incidence and Efficiency Effects of Taxes on Income from Capital', JPE 84:1261-1283, with the Harberger & Bruce reply, JPE 84:1285-1292; Gravelle & Kotlikoff (1989) JPE 97:749-780 (all verified via Crossref).

Why this severity. This concerns attribution only, not the validity of any result.

Claims examined and rejected

Problems one auditor raised that did not survive checking.

The shareholder-only convention accounts for 'roughly one third to one half' of the 1950-2021 decline (the upper end based on a fiscal-income CBO base giving 6.5 pp). — Upper bound rejected. The fiscal-income CBO series (Data!R) is discontinuous at 1962 (26.7% -> 33.2%, as Auditor A notes). The denominator-consistent DINA-based computations give 8.3-9.0 pp (CBO) and about 10.1 pp (TPC-style), i.e. about one fifth to one third of the decline (retained as F1).
Correcting the Berkshire 'realized gains' add-back would put Buffett's rate at about 16% rather than 18.4%. — The $22,455m add-back is the net investment/derivative loss. It nearly equals the unrealized equity loss ($22,729m), and GAAP gains on equities sold were only $291m, so the add-back mostly removes unrealized losses as intended. Including tax-basis realized gains (about $3.3bn) and correcting the PP&E and ownership errors gives about 18.9-21.1%, not 16% (retained as F10).
2019 (32.6%) is 'the last actual-data year' and close to the projected 2021 endpoint. — Under the PSZ procedure 2017-2019 are themselves projections: 2017 is the aged 2012 PUF inflated to SOI aggregates, and 2018+ is grown with GDP. The last year matched to internal tabulations is 2016 (34.9%). The substance of the projection issue is retained in F3.
Table 1's top-1% income share (23.69%) and the Figure 3 input share (cbo-vs-sz!B61 = 20.36%) are an unreconciled inconsistency in income concepts. — This is explained by the inclusion of pure realized capital gains. In 2021 realized gains were 10.25% of national income (pure gains 7.25%, about 70% of them to the top 1%). The Fig. 3 input share excludes them, while Table 1 and the rates include them. The same pattern holds on the 2019 public file (19.65% incl. vs 18.76% excl.). The share is not used in any published post-1962 rate. Only the small 2021 rate difference (32.80% vs 32.67%) remains, in F12.
Attribution of the paper's '7 points' to the denominator-mixing arithmetic is only 'likely' because no final formula cell exists. — Confidence upgraded. The workbook's 1950-2021 change cells (C121, K121, L121) reproduce 6.90 pp exactly with the hybrid formula. The same hybrid is shown to under-predict the micro-based CBO-method rate by 1.2-2.6 pp in 1962-80, so the attribution is confirmed (F2).
Under the Appendix A.2 transfer rule the bottom-50% rate falls by about 2.0-2.2 pp (2014-2019). — Magnitude not reproduced. Defining transfer-financed consumption as cash transfers excluding SNAP (consistent with the PSZ consumption proxy), the adjudicator obtains about -1.0 pp in 2014 and 2019 (-0.4 pp in 1962). Auditor A's larger figure reflects a broader transfer definition. The direction is retained in F5.
'Raises net revenue up to an elasticity of 3.9' is 'false' because the exact finite reform loses $2.7bn at e = 3.9. — Wording too strong. The paper uses a small-reform first-order framework, under which the threshold is 3.76 rather than 3.9, and the exact finite-reform threshold is 3.54. The overstatement (about 4-10%) is retained as a minor issue (F16), not as a false claim.

Audit notes

What reproduced. Reproduced exactly from the authors' workbook (both auditors and the adjudicator): the headline series (top 1%: 45.30% in 1950, 48.52% in 1951, 32.67% in 2021, -12.63 pp; 32.2% in 1932; reform-episode values); the 1950 rate as the sum of PSZ TG2b components; Table 1, Table A1 and Table 2A/2B (net revenue $24.13bn / $75.08bn; net value $17.23bn / $64.07bn; equal-weights $7.19bn; MVPF 1.16). Published PSZ Feb-2022 TG1 values match the workbook within about 0.2 pp. The 2021 federal corporate tax in the workbook ($278.6bn) matches the Oct-2023 BEA vintage ($279.9bn); the Oct-2026 vintage is 20% higher ($335.5bn). Recomputed with consistent denominators: the CBO-method decline is 8.30 pp (8.3-9.0 pp with bias and component uncertainty), not 6.90 ('7'); TPC-style about 10.1 pp. Break-even elasticities are 3.76/3.54 (corporate revenue) and 2.83/2.63 (corporate welfare) rather than 3.9/2.9. Buffett's illustrative rate is 21.1% after fixing PP&E and ownership; the health-funding effect for the bottom 50% is -0.04 pp rather than -0.93 pp after returning employee premiums. Micro re-implementation of PSZ code on public files matches macro rates and corporate components but not published top-1% rates: 1962 43.55 vs 42.73; 1979 41.76 vs 39.43; 1980 42.31 vs 39.80; 2014 34.33 vs 33.95; 2019 33.07 vs 32.59 (32.64 ranking by peinc). Sensitivities on the same files: removing the 30% factor slice of consumption taxes changes top-1% rates by -1.37 pp (1962) and -0.97 pp (2014/2019); the A.2 transfer rule changes bottom-50% rates by -0.4 to -1.0 pp; adding social-insurance contributions to the denominator changes top-1% rates by -0.17/-0.26 pp and bottom-50% rates by -0.9/-1.7 pp (1962/2019). Not reproduced (inputs not public): the pre-1962 series from raw SOI tabulations (taxratespre62.xls), the 2020-21 micro-files and tabulation code, the 39% foreign share, and the published 1979-80 values from public files.

Limits of this audit. The adjudicator could not rebuild the pre-1962 series (raw SOI input not public) or the 2020-21 micro-files and paper-specific tabulation code ('data available on request'); the authors were not contacted. Micro checks used public February 2022 files for 1962, 1979, 1980, 2014 and 2019 with a Python translation of PSZ's Stata code (tie-breaking and minor details may differ). The sales-tax and payroll-denominator sensitivities omit PSZ's top-400 fix. That fix lowers 2019 top-1% levels by about 0.3 pp (it does not bind in 1962), but these sensitivities are reported as differences, which it barely affects. The trend effect of contested income imputations (F6) could not be quantified because rival estimates use confidential IRS data. The 39% foreign share and the cross-border offset assumption could not be tested. Some figures are taken from the auditors or the corpus without full re-derivation: Auditor A's NIPA 1929-2019 comparison and fed+state 2021 corporate share; Auditor A's nonprofit sensitivity (formula checked); Codex's cross-base and Buffett tax-basis sensitivities; Auten-Splinter magnitudes from the corpus. No dedicated published critique of this specific paper's empirical series was found (OpenAlex/web search of citing works). The theoretical critique (F7) rests on established literature rather than a paper-specific rebuttal. Health-illustration corrections assume a uniform employee premium share across income groups.