The Billionaire Tax: A (Modest) Proposal for the 21st Century

Why it matters, in detail. Post-reform all-in rate = tau_now + (m - tau_ind)(1 - e)/r, with tau_now = 22.1% of pre-tax income, tau_ind = 0.29% of wealth, e = 10% and r = pre-tax income/wealth. The increment scales with 1/r: r = 9% gives +17.1 pp (39.2%); r = 7.42% (SZ 2019, top 400 by wealth, 2016) gives +20.7 pp (42.8%); r = 5.6% (BSYZ 2025, Forbes 400, 2018-20) gives +27.5 pp (49.6%). The parity-calibrated minimum is ~1.4-1.7% of wealth, and the revenue attributable to removing under-taxation relative to parity falls to ~$121-200bn. Counter-evidence: income-ranked top groups, whose current rates enter Figure 4, have higher ratios (US 2018: 10.7%, giving 36.5%), and BSYZ use basic-price income. But the minimum applies to wealth-ranked billionaires, and 2024 valuations imply lower, not higher, ratios (the 400 richest US citizens on the Forbes global list held ~78% more wealth in 2024 than on average in 2018-20). Cross-effect: a lower ratio would also lower the 1.2%-of-wealth current rate assumed for centi-millionaires (Blueprint fn 17 uses 11%), raising that tier's revenue.

Evidence. Reproduction (scripts/parity_check.py): 22.1% + (2% - 0.29%) x 0.9 / 9% = 39.2% (Figure 4 digitised: billionaires 22.1% -> 39.3%; ordinary groups 37.0-41.3%). Evidence on the ratio: (i) Saez & Zucman (2019) appendix workbook, sheet top400hweal (top 400 ranked by wealth): pre-tax income/wealth mostly 9.0-10.6% in 2000-2012, but 7.4-8.2% in 2013-2016 and 7.42% in 2016, the latest year; the 2018 top 400 ranked by income (the group behind the US 23% input) has 10.69% (sheet full2018). (ii) Balkir, Saez, Yagan & Zucman (2025, NBER w34170, Table 1): economic income/wealth 5.6% for the Forbes 400 in 2018-20 (top 100: 5.3%); their sensitivity range (total rate 21.7-26.4%) implies at most ~6.1%. (iii) Internal consistency: the Blueprint's 7.5% return is net of business-level taxes and includes pure capital gains (Section 1.3 and fn 9); adding ~0.7-1.0% of wealth of business taxes and removing ~2% pure gains (the Blueprint's own global figure) implies a pre-tax income/wealth ratio of ~6.2-6.5%, and at most ~8.5% even with zero pure gains. With r = 7.42%, 6.14% and 5.6%, the post-reform rate is 42.8%, 47.2% and 49.6%, above every ordinary group in Figure 4 (maximum 41.3%, P90-95). The minimum that just reaches ~39% parity would be 1.71% or 1.36% of wealth, raising $160-200bn or $121-151bn rather than $193-242bn. US-only check with the author's administrative data (BSYZ 2025 Table 2, wealth-ranked Forbes 400): total taxes 1.3% of wealth, individual taxes 0.6%; a 2% individual minimum gives 2.56-2.70% of wealth = 45.7-48.2% of economic income vs 30.2% for the US population; even at r = 9% US billionaires (23.8% -> 37.8%) would exceed the US average.

Why this severity. The 'no higher'/de minimis claim is the stated justification for choosing 2% and the basis of the 'modest' framing. Under defensible ratios (5.6-7.4%) a 2% minimum would make billionaires the most heavily taxed group (43-50% vs at most 41%), so the parity claim fails rather than merely shifting. The revenue arithmetic of a 2% tax and the regressivity diagnosis are unaffected.

The authors' response. No direct response located. The Blueprint (p.29) says the results are 'illustrative of high-income countries on average', that the proposal 'does not guarantee that tax progressivity will be safeguarded in each country', and that 'some regressivity would remain at the top' (P99-$100m ~35% vs middle class ~40%). These caveats do not appear in the lecture.

Why it matters, in detail. Real per-household growth of top-0.0001% wealth is ~5.3-5.4% with the World Bank deflator (4.6-5.1% with US deflators), not 7.1%. Against average wealth per adult (3.2% under the lecture's assumption; ~2.85% with WID private wealth 306% -> 524%), the excess is ~2.1-2.5 pp rather than 3.9 pp. The growth-accounting return becomes ~5.7-5.8% (~6.3-6.4% if charitable giving of ~0.6% of wealth, BSYZ 2025, is added as an outflow). That is below the 6-7% global average pre-tax return the Blueprint uses to argue that billionaires earn excess returns, and the Blueprint's net return under a 2% minimum falls from 5.5% to ~3.8-4.4%. Concentration still accounts for ~53% (author's wealth/income path) to ~63% (WID private wealth) of the rise in top wealth/GDP, so 'most' survives.

Evidence. Arithmetic identity: average top wealth growth = growth of (top wealth/GDP) + growth of income per adult (+ drift in adults per household). With 7.1% and 1.3%, top wealth/GDP would have to rise x7.85 (to ~24-25% of GDP); the plotted series rises x4.19 (3.19% -> 13.39%, adjudicator digitisation of the PDF vector path; Claude: 3.15% -> 13.32%). World Bank data (scripts/fig3_growth.py): real GDP per adult aged 15+ grows 1.33%/yr, matching the 1.3%. With the same World Bank deflator (current/constant USD GDP), the group's TOTAL real wealth grows 7.07-7.17%/yr, matching 7.1%; per adult it grows 5.33-5.42%/yr. With the US GDP deflator per-adult growth is 5.0-5.1%; with US CPI, 4.6-4.7%. Reconciling 7.1% as an average would require adults per household to rise ~80-85% over 1987-2024. The arithmetic mean of annual per-adult growth is ~6.6% (Codex), still not 7.1%.

Why this severity. A confirmed error in a prominent secondary statistic: growth is overstated by ~1.7 pp (~25%), the excess over average wealth growth by ~45%, and the derived return (7.5% -> ~5.8%). The qualitative conclusions survive (top wealth outpaced average wealth; 2% is below the return), and the revenue and tax-rate findings do not depend on it.

Why it matters, in detail. Static score R = (m - mean tau) W (1 - lambda), with W = $14.21T, mean tau = 0.3% and lambda in {0, 0.2}. The lambda = 0.2 low end is equivalent to a one-off base response with semi-elasticity ~13. Long-run difference-in-differences estimates (Jakobsen et al. ~20.8; Brülhart et al. >= 43, partly cantonal mobility) imply $116-170bn. Upside factors partly offset this: taxpayer-level heterogeneity in current rates (which makes the average-rate calculation conservative), the larger 2025 Forbes base (~$16T), and possible under-coverage of 'Southern billionaires'. Net: the static potential is robust, but the expected recurring yield under realistic enforcement and participation is plausibly 10-40% below the $200-250bn headline, and lower still with incomplete participation.

Evidence. Reproduction: $14.2096T (2,781 entries) x 1.7% = $241.6bn; x 0.8 = $193.3bn (scripts/revenue_check.py). Mitigating: the 20% loss equals a taxable-wealth semi-elasticity of ~13 for the 1.7 pp increase (-ln 0.8 / 0.017), the Penn Wharton weighted literature average (optimal-tax-behavior-17). Sensitivity with W' = W exp(-e x 1.7pp): e = 7 -> $214bn; e = 17 (Advani & Tarrant 2021 upper end) -> $181bn; e = 20.8 (Jakobsen et al., 8-year response) -> $170bn; e = 43 (Brülhart et al. 2022, includes inter-cantonal mobility) -> $116bn. Participation: US citizens hold 40.1% of the Forbes 2024 base, so without US participation revenue is ~$116-145bn. Valuation: BSYZ (2025) report that for single Forbes-400 decedents the gross estate is 39% of the Forbes estimate, and estate taxes paid equal 6.8% of Forbes wealth against a 40% statutory rate. This shows how far assessed values can fall below rich-list values under current practice; it is an upper bound on pure valuation error, since it includes legal planning. Skar et al. (2025) find a median statutory-value/sale-price ratio of 61% for Norwegian unlisted firms, but a mean of 109%.

Why this severity. The arithmetic is exact and the conditions (2024, 0-20% loss, 'globally') are partly visible, so the headline is not wrong as a static potential. Presenting it as recurring annual revenue, however, overstates its reliability. Under central literature elasticities realised revenue sits near or below the $193bn low end (10-30% below $242bn), and partial participation or Swiss-type responses would cut it by 40-50% or more.

The authors' response. The Blueprint (p.27) states the first-year limitation and argues that in the short run non-avoidance responses can be neglected because wealth is a stock. It notes (p.25) that the 20% loss exceeds the 15% used by Saez & Zucman (2019a); proposes valuing private firms by listed-company multiples and transactions (Section 4.1); and proposes stronger exit taxes and 'tax collector of last resort' rules for incomplete participation (Section 4.3). The lecture (p.22) calls for rules effective 'even with less than full participation'.

Why it matters, in detail. The comparator is total compulsory levies divided by net national income (~52%). It includes contributory pension contributions (~11 pp) and VAT (~9 pp), which are negligible for billionaires. Because DINA pre-tax income is defined after the operation of the pension system, contributions are also netted from workers' income while counted in their taxes (Bruil et al. 2025 acknowledge this). The ~25 pp gap (52 vs 27) shrinks to ~14 pp (41 vs 27) or ~5 pp (32 vs 27) under the author's own alternative numbers. The Figure 1 splice exaggerates the cliff at P99.99 by roughly 5-7 pp (51.9% under DINA vs ~45-46% under Bach et al.'s concept at the top-0.1% threshold). The billionaire endpoint itself is little affected, since VAT and contributions are negligible for that group.

Evidence. The author's own reply (Le Grand Continent, 2 Jul 2025): excluding pension contributions 'le taux d'imposition du Français moyen tombe à 41 % environ'; excluding VAT as well, '32 %'. IPP excludes 'La TVA, les cotisations retraite, la taxe d'habitation et la taxe foncière'. Within one consistent study the rate falls from 46% at the top 0.1% to 26% for the top 0.0002% (IPP Note 92, 2023), or from ~45% to ~25% (Bach et al. 2025). Adjudicator digitisation of the Figure 1 France line, P0-10 to billionaires: 45.6, 47.3, 49.1, 50.1, 51.3, 51.5, 52.0, 52.1, 53.0, 53.4, 53.8, 53.8, 51.9, 37.6, 28.6, 27.2. GTER 2024 4-progressivity.xlsx (sheet datafig4.1, column 'Bozio et al. (2020)'): 46.0, 47.4, 49.0, 50.3, 51.4, 51.8, 52.1, 52.5, 53.6, 53.8, 53.9, 53.2, 50.3, 48.6 (P99.99-99.999), billionaires 26. The GTER 2024 source note reads: France 'for P0-10 to P99.9-99.99, ... Bozio ... (data is for 2018); for billionaires: Laurent Bach ... (data is for 2016)'. Bruil et al. (2025, fn 24) describe the same Bozio/Bach splice for France. Bach et al. (2025) also show that the DINA dividend-imputation method behind Bozio et al. gives flat 39-41% rates at the top.

Why this severity. The direction (billionaires pay less than other groups) survives every convention, but the size does not. Billionaires pay ~52% of the comparator under the author's convention, ~66% excluding pension contributions and ~84% also excluding VAT. Within one consistent study the drop from the top 0.1% is ~20 pp, not the ~25 pp implied.

The authors' response. Zucman (Le Grand Continent, 2 Jul 2025) argues that excluding any compulsory levy 'n'a guère de justification', that all statistical agencies include them, and that once the other levies are reintegrated the average returns to ~52% 'sans que celui des milliardaires n'augmente significativement pour autant'.

Why it matters, in detail. R = g + tau + c identifies an average total return only for a closed, unranked cohort. With re-ranking, the between term (~2.5 pp/yr for the Forbes 400) and population growth (~1.7 pp/yr, F2) inflate g. Even a correctly measured R includes pure price effects, whereas the minimum must be paid from distributions, sales, borrowing or in kind; for the Forbes 400, cash income other than realised gains is ~1% of wealth. Liquidity pressure is therefore concentrated on high-valuation, low-payout founders, and handling it requires design features (deferral, payment in shares) whose fiscal cost is not scored.

Evidence. Blueprint Section 1.3 (p.18) derivation. Gomez (2023): the 3.9%/yr growth of the Forbes-400 wealth share (1983-2017) = within 3.0% + between (displacement) 2.5% + demography -1.5%. BSYZ (2025) Table 1 (Forbes 400, 2018-20): economic income 5.6% of wealth; fiscal income $188.7m per tax unit = 2.35% of wealth, of which 61% is realised capital gains; dividends, interest, rents/other and wages together ~1.0% of wealth; listed firms distribute 19% and private C-corporations 7.4% of pre-tax profits. A 2% charge is thus ~85% of reported fiscal income and ~2x non-capital-gains cash income on average. Codex counterexample: two fortunes of 100 and 90, where the second adds 60 of saved labour income; the top-ranked fortune grows 50% with zero return on any initial asset.

Why this severity. The inference from average fractile growth to limited liquidity strain is invalid as stated, but the conclusion may still hold for most billionaires (borrowing, higher payouts, asset sales, payment in shares), and the revenue and tax-rate findings do not depend on it. How common and how costly genuine liquidity cases would be is unmeasured.

The authors' response. Lecture p.16 and Blueprint Section 1.2: billionaires can borrow against their shares, and their income is 'neither virtual nor trapped'. In the Aghion-Zucman debate (Challenges, September 2025) Zucman proposed allowing the 2% minimum to be paid 'en nature, c'est-à-dire avec des actions de son entreprise' and acknowledged 'des cas limites qu'il faut étudier'.

Why it matters, in detail. One of four countries' billionaire endpoints is an anecdote, and group definitions (income- vs wealth-ranked), years (2015-2020) and tax concepts differ across countries, so 'same methodology' overstates comparability. Ranking by income selects high-income years and high income/wealth ratios, which matters when converting wealth-based minima into income shares (F1).

Evidence. Blueprint fn 2 (p.10), fn 21 and Appendix A (p.47). Bruil et al. (2025, fn 24): the Berlusconi estimate 'is purely illustrative'. BSYZ (2025, fn 3): Bach et al. (2023) and Bruil et al. (2025) rank by economic income, not wealth. SZ (2019) sheet full2018: the US top 400 by income have average wealth of $4.27bn. Figure 1 (adjudicator digitisation): Italy's solid line ends at 37.8% (P99.9-99.99), with a dashed segment down to ~18% for billionaires. BSYZ Table 2: for the US top 400, individual income and payroll taxes are 11.0% of economic income vs 8.9% for corporate taxes.

Why this severity. A transparency problem with little effect on conclusions. Italy's top-0.1% rate (~38% vs ~55-58% for middle groups) already shows a decline at the top without the single billionaire point, and Italy is not used in the revenue calculation.

The authors' response. Blueprint fn 2 argues that Berlusconi's case 'is likely to be representative of other Italian (and more broadly European) billionaires', because the same tax-minimising structures are available to all of them; the lecture states that it summarizes the Blueprint.

Why it matters, in detail. Post-reform all-in rate_i = (CIT_i + max(2% W_i, T_ind,i) + other_i)/Y_i. With CIT_i/Y_i varying across fortunes (e.g. 0-15 pp), post-reform rates spread around the 39% average by a similar amount, so high-CIT fortunes exceed parity even when the average meets it.

Evidence. Lecture p.13 (27% = 1.7% individual + ~25% corporate) and p.15 (taxes excluded from the minimum). BSYZ (2025) Table 2: corporate tax is 8.9% of economic income for the US top 400 (10.1% for the top 100). Boadway & Keen (Intertax 2026, abstract) point to 'anomalies' of the hybrid design.

Why this severity. A disclosed, deliberate design choice. It affects how post-reform rates are distributed across billionaires, not the average calibration or the revenue.

The authors' response. This is a deliberate design: only individual taxes count, because the minimum is meant to remedy the failure of the individual income tax (lecture pp.15-16; Blueprint Section 2.1).

Why it matters, in detail. A consistent private-wealth path implies 1.0133 x (5.24/3.06)^(1/36) - 1 ~ 2.85%/yr; concentration then explains ~63% (vs ~53%) of the rise in top wealth/GDP.

Evidence. WID bulk data, world aggregate (WO): wwealpi999 (private) 3.06 in 1987 and 5.24 in 2023; wwealni999 (national) 4.23 in 1995, 6.46 in 2020, 6.17 in 2023; wwealhi999 (household) 3.38 in 1995 and 5.02 in 2023. WIR 2022 Figure 3.1: global wealth 600% and private wealth 525% of global income in 2020.

Why this severity. It overstates average wealth growth (~2.85% vs 3.2%), which works against the author's concentration claim; no conclusion changes.

Why it matters, in detail. The largest numerical slips are the US income-tax rate (8% vs 9.2%, ~1 pp) and the Forbes total ($14.4T vs $14.2T, 1.3%); neither enters Table 1.

Evidence. Adjudicator digitisation of Figure 2: US billionaires 9.25%, US peak 22.2%, France 1.84%, Netherlands 0.13%. scripts/revenue_check.py ($14.2096T). World Bank NY.GDP.MKTP.CD 2024: $111.67T. Lecture pp.3, 5, 11-13, 23.

Why this severity. Small inconsistencies that affect no conclusion and do not enter the revenue calculation.

Why it matters, in detail. The undisclosed parameters (r = 9%, current tau = 0.3%, a loss of at most 20%, the household normalisation of Figure 3) are exactly those to which the lecture's headline claims are most sensitive.

Evidence. Lecture p.17 (Table 1 note); Blueprint pp.24-27 and Appendix B; WIR 2022 Table 7.1 (p.139). WID simulator file sample3.dta (world, 2021): >$100m n = 65,127, w = $28.14T; >$1bn w = $12.85T, so (28.14/12.85 - 1) x 14.21 = $16.92T. Using WIR Table 7.1 instead would give ~$17.9T and ~$143bn at 2% (vs $135bn).

Why this severity. Everything can be traced through the parent report and public data, and the attribution slip is immaterial (~$8bn). But the lecture is not self-contained, and it hides precisely the assumptions that drive F1 and F2.

Why it matters, in detail. In random-growth models a lower tau thickens the Pareto tail and, if tau falls with wealth, can make the distribution non-stationary (Blueprint Section 1.3). But a top share rising over 37 years is also consistent with slow transition dynamics (Gabaix, Lasry, Lions & Moll 2016) and with return heterogeneity. The author's own accounting attributes only a minority to about half of the excess growth to taxes.

Evidence. Blueprint fn 10: the 0.8 pp lower individual capital tax rate explains 36-66% of the net-return gap, and 'a smaller fraction' if business-level taxes are counted as taxes. With the corrected growth rate (F2: ~5.4% vs 2.85-3.2% for average wealth), a 0.8 pp tax differential accounts for at most ~30-40% of the excess. Gomez (2023): about half of the rise in the Forbes-400 wealth share comes from displacement by new fortunes.

Why this severity. An interpretive overstatement of a motivating claim. It does not affect the revenue, effective-rate or calibration results, and the parent report gives the partial attribution.