Rethinking Capital and Wealth Taxation

Why it matters, in detail. Restricting the population to employed 25-60 year-olds removes pensioners and non-workers from the bottom deciles. Ranking by factor income and counting contributory pension and unemployment contributions as taxes then loads the roughly proportional SSC burden onto low-wage workers, which gives 46% in P0-10. On pre-tax national income for all equal-split adults, net of contributory SSCs, P10-20 pays 27.2%. The plotted series compresses the French gradient from +22.7 pp (P10-20 to P99-99.9) to about +6 pp (+5.7 pp to P99-99.9, +6.6 pp to the P95-99 peak), and turns a 1.2 pp dip at P99.9-100 into a 6.4 pp decline from P95-99 to P99.999-100. The pre-tax series is not broken down within the top 0.1%, so a steeper decline inside the top 0.01% on that concept can be neither confirmed nor excluded. Mixing this series with a US series built on all-adult pre-tax income is not the like-for-like comparison the note claims, and the bias runs in the direction of the paper's 'flat everywhere' reading.

Evidence. Independent digitization of the vector charts (scripts bozio_fig_vs_psz_france.py, digitize_psz_fig1_wp.py, bozio_workbook_2018_rates.py). PSZ Figure 1, France (WIL WP 2022/18 vector, same figure as OxREP), P0-10 to P95-99: 45.9, 47.3, 49.0, 50.2, 51.2, 51.8, 52.0, 52.4, 53.4, 53.7, 53.9; then 53.0, 50.2, 48.5, 47.5. Bozio et al. (2020) Appendix Figure 6a (PDF p.87): 46.0, 47.4, 49.0, 50.3, 51.4, 51.8, 52.1, 52.5, 53.6, 53.8, 53.9; then 53.5 (P99-99.5), 52.8 (P99.5-99.9), 50.3 (P99.9-99.99), 48.1 (P99.99-100). The maximum gap over the 11 common groups is 0.19 pp, and PSZ's four top groups are consistent with a finer split of the same series. The source's pre-tax series for all equal-split adults excludes contributive SSCs 'in line with the definition of pretax income' (fn.41). Its Figure 10.d and the data workbook (sheet DataSeries1970_2018, Figure 9 data) give: P10-20 27.2%, P20-30 28.3, P30-40 31.3, P40-50 33.5, P50-60 35.6, P60-70 38.5, P70-80 40.5, P80-90 42.5, P90-95 45.2, P95-99 47.8, P99-99.5 49.9, P99.5-99.9 49.9, P99.9-100 48.7. The source's text (pp.30-31) calls this 'an almost linear increase from 27% for P10-P20 to 50% for P99-99.9' with 'a small regressivity' at P99.9-100. On the same concept the source's US series rises from 16.8% (P10-20) to 37.6% (P99.9-100).

Why this severity. France is the paper's 'large government' example (p.576) and one of the three countries behind the cross-country claim. On the stated concept, the French bottom-to-P99 gradient is about +23 pp rather than about +6 pp, and the top-end decline is about 1 pp confined to P99.9-100 rather than about 6 pp starting after P95-99. That changes the French part of the paper's main empirical claim by far more than a quarter. The theoretical case for the triptych does not depend on it.

The authors' response. None located. Bozio et al. (2020, fn.46) describe the factor-income/working-age view as 'meaningful and complementary' to the pre-tax view; that is a possible rationale, but PSZ neither disclose the switch nor apply it to the US series.

Why it matters, in detail. Flatness below P99 is a classification result. It holds if contributory Social Security is a tax (as in OECD revenue statistics, CBO and TPC) and refundable credits are spending. Under the DINA 'pre-tax' logic, which treats contributory pensions as deferred wages, the US rate roughly doubles from the bottom half (about 16%) to P99.9-99.99 (about 33%). Pure KG (about 2% of NI, 8-9% of the top-0.1% denominator) lowers top rates by about 3 pp. Adding it is arguably more Haig-Simons-consistent, in line with the paper's own Section III logic, so its net bias is ambiguous, but it is inconsistent with the figure note. Known critiques of PSZ's denominator imputations (underreported business income and retirement income allocated toward the top; us-income-10/11, us-wealth-taxes-15) would, if accepted, raise measured top rates further. They were not quantified here.

Evidence. TOI Oct-2019 DINA micro-file, 2018: equal-split adults with pre-tax income of at least half the minimum wage, PSZ denominator (scripts fig1_us_conventions.py, fig1_us_refundable_credits.py). Bottom 50% / middle 40% / top 10% / top 1%: PSZ convention 23.4/27.4/29.4/30.8%; excluding contributory SSCs (the convention of Bozio et al. 2020, the paper's own French source) 15.7/20.0/26.8/30.1%; keeping contributions as taxes but adding them back to income (internally consistent, CBO-like) 21.7/25.5/28.7/30.6%. Refundable credits as negative taxes: bottom 50% 18.7%, D1-D3 15.0-16.5%. Both changes together: 11.1/19.8/26.8%. Bozio et al.'s published US 2018 profile on their convention is 16.5/20.7/28.6%, rising from 16.8% (P10-20) to 37.6% (P99.9-100). Capital-gains denominator (Sept-2020 workbook, sheet TG3, 127 g-percentiles aggregated; script fig1_us_tg3_groups.py), with KG vs without: P99.9-99.99 34.2 vs 37.1; P99.99-99.999 34.9 vs 38.2; P99.999-100 29.4 vs 32.2; P80-90 29.1 vs 29.4.

Why this severity. Under the convention of the paper's own French source, bottom-half and middle rates fall by 7-8 pp (about a third) and the US becomes clearly progressive up to the top 0.1%. But the internally consistent variant that keeps payroll contributions as taxes, which is mainstream incidence practice, remains only modestly progressive (about 22% rising to 29%). The double treatment itself is worth only about 1-2 pp, so 'modest progressivity' is defensible under PSZ's all-taxes approach. Without capital gains in the denominator, regressivity within the top 0.01% survives (38.2% falling to 32.2%), but the top 0.001% then pays more than every group below P99.9. The issue qualifies the US claim rather than overturning it.

The authors' response. Saez & Zucman treat transfers, including refundable credits, as spending rather than negative taxes and assign current taxes following national-accounts concepts ('Clarifying Distributional Tax Incidence', Oct 2019 draft; Zucman as reported by Gleckman, TPC, 11 Oct 2019; per corpus entry us-wealth-taxes-12). No response on the contributory-SSC or capital-gains-denominator choices in this paper was located.

Why it matters, in detail. The corporate tax was about 4.5% of NI in 1962 and about 1.25% in 2018. Assigning it to equity, which was far more concentrated than other capital, loads the historically large tax onto the top 0.01%. CBO-based federal progressivity indices rise after 1979 (Splinter 2020) partly because of different incidence and credit conventions. Both pictures can be true at once: top-end rates fell under SZ's conventions while whole-distribution progressivity rose.

Evidence. TOI Oct-2019 micro-files, equal-split adults, denominator peinc (script corptax_incidence_1962_2018.py). 1962 top-0.01% rate: 46.2% with the file's allocation in proportion to wealth excluding housing; 59.0% in proportion to equity (dividends capitalized); 70.2% in proportion to equity (dividends plus KG capitalized). The Sept-2020 published value (sheet TG3) is 56.8%, close to the equity-based variants. Top 0.1%: 45.4% vs 59.2-63.4% (published 52.3%). Top 1%: 40.3% vs 48.6-48.9%. In 2018 the incidence variants change the top-0.01% rate by at most about 1 pp (36.4-37.5% on peinc), because the corporate tax is 1.25% of NI against 4.5% in 1962. The 1962-2018 fall in the top-0.01% rate is therefore about 9-10 pp under PSZ-2018 incidence vs about 20-33 pp under shareholder incidence. Bottom 50%: 19.6% (1962) and 23.9% (2018) under either convention.

Why this severity. The direction (high mid-century top rates, lower today) survives under every allocation tried. But the size of the decline at the very top, a central element of the 'decline of progressivity' narrative in Section V(ii), varies by a factor of 2-3 with a contested convention that the paper presents as settled.

The authors' response. Saez & Zucman defend current-burden statutory incidence ('Clarifying Distributional Tax Incidence', Oct 2019 draft; 'Distributional Tax Analysis in Theory and Practice: Harberger Meets Diamond-Mirrlees', NBER w31912, 2023), arguing that general-equilibrium effects belong in reform analysis; they report a top-1% effective rate falling from about 50% in the early 1950s to 32% in 2021 (per corpus entry us-wealth-taxes-13).

Why it matters, in detail. Under the inverse-elasticity logic tau* = 1/(1+e). Replacing mechanical or bunching-based responses with the difference-in-differences estimates from the same literature cuts tau* by a factor of roughly 2-5 in Blanchet's own model. SZ's 6.25% is an upper bound with respect to avoidance, evasion and saving responses. The counter-argument, that enforcement design (comprehensive base, third-party reporting, exit taxes) lowers the relevant elasticity, is plausible but has not been tested at US scale.

Evidence. Blanchet (WIL WP 2023/02, 23 Nov 2022), p.46: the baseline uses 'a limited tax avoidance response (epsilon = 1), which is around the values found by Seim (2017), Londono-Velez and Avila-Mahecha (2021) and Jakobsen et al. (2020)' and 'a medium savings response (eta = 1)'. p.45: Jakobsen et al.'s 8-year elasticity of about 18 implies 'a yearly behavioral elasticity of 1.4'; Zoutman (2018) finds 'almost 14'; Brulhart et al. find 23-34. Figure 10a (p.47): the medium-response Laffer curve peaks near 12% with revenue of about 1.15% of NI; the high-response curve (epsilon = eta = 3) peaks near 5% with about 0.7% of NI. Figure 10b: revenue-maximizing rates of 10-20% at low elasticities fall to 2-3% at eta of about 6-8. Static check: 1.5% of NI at a 1% rate becomes 1.39/1.30/1.24% with base semi-elasticities of 7.5/13/17 (SZ / PWBM / upper end of Advani-Tarrant) and 0.86% with 43 (Brulhart et al. 2022).

Why this severity. The qualitative claim that a billionaire wealth tax can raise substantial revenue survives: even with high elasticities, revenue at a 1% rate stays at about 0.9-1.4% of NI. But the size of the 'high' revenue-maximizing rate (6-12%) holds only at the low end of the elasticity range, and that bears on the 6-8% policy targets in Section V(iv).

The authors' response. Saez & Zucman (BPEA 2019; 'How would a progressive wealth tax work?', Feb 2019) argue that avoidance is a policy choice that can be limited through base breadth, third-party reporting, audits and exit taxes (per corpus entries optimal-tax-behavior-16, us-wealth-taxes-18).

Why it matters, in detail. Dropping near-zero-income adults avoids meaningless ratios; including them would put D1 at about 50% and make the US profile U-shaped. The choice should be disclosed. The year and group mismatches impair replication but not the qualitative reading.

Evidence. TOI micro-file 2018: the truncation drops 9.56% of adults; untruncated, D1 pays 49.6% under PSZ's convention. With the truncation, D1-D9 reproduce the figure within about 0.2-1.2 pp (24.6/23.7/23.7/22.6/23.2/24.9/26.0/27.3/29.3 vs 25.8/24.4/24.6/23.6/24.4/25.4/26.4/27.8/29.5). Sept-2020 TG3 aggregated to the figure's groups: P40-50 25.7 vs 24.4, P50-60 26.9 vs 25.4, P99.999-100 29.4 vs 29.5. CPB DP 436 p.2: 'distributional national accounts for the Netherlands for the year 2016'. The WP vector chart has 12 Dutch markers starting at P20-30, with 39.4% repeated for P90-95 and P95-99.

Why this severity. Labelling and documentation slips that change the shape of no series. The truncation makes the US look less regressive at the bottom, not more, and the Dutch year and group mismatches do not alter the Dutch pattern.

Why it matters, in detail. The inverse-elasticity rule needs the elasticity evaluated at the optimum, with counterfactual wealth weights. Plugging in an unweighted mean hides heterogeneity, and heterogeneity raises tau*. Calling the censored 36-year e_T 'long-run' ignores that e_T rises with T, which lowers tau*. The two errors partly offset. The number is best read as an illustration within a range of roughly 5-10% in the mechanical model, before any behavioural response (F4).

Evidence. Gomez (2023) Forbes 400 panel, 2017 members (script forbes400_revenue_max.py; claude's forbes400_exposure_elasticity.py agrees). Years on the list: unweighted mean 14.7 (person) and 18.3 (family-linked); wealth-weighted 19.3 and 22.6. Directly maximizing R(tau) = tau * sum_i W_i (1-tau)^T(i) gives 9.85% (person) and 6.95% (family). A 6.25% rate yields 96% and 99.7% of the maximum revenue. Censoring: 72 families (18% of members, 29% of wealth) are on the list in all 36 years, so their exposure is truncated at 1982. SZ's own DataFig6 note calls the 10% 'radical' tax 'the rate that approximately maximizes tax revenue'.

Why this severity. Within SZ's mechanical model, the correct calculation on the same data gives a higher rate (7-10%) than 6.25%, while censoring biases the true long-run rate the other way. The qualitative statement that mechanical revenue-maximizing rates are high is unaffected; the problems are the 'long-run' label and the false precision.

Why it matters, in detail. With delta = 1/50 and alpha of about 1.5-1.65, a 100% estate tax caps the Pareto coefficient at alpha1 of about 1.65, which an annual tax of about 1.2% already achieves; higher annual rates go further, so the asymmetry between the two instruments is larger than stated. The mapping is sensitive to generation length: 1.92%/1.48%/1.21%/1.02% for H = 30/40/50/60 (codex).

Evidence. Blanchet pp.48-49: alpha1 = 1/2 [alpha0 + sqrt(alpha0^2 + 8 delta/sigma^2)] = 1.6514. Matching it with an annual tax requires tau = delta/alpha1 = 0.012111. Adjudicator re-derivation: alpha0 = 1 - 2(mu - tau)/sigma^2 = 1.5; (1.5 + sqrt(2.25 + 1.0))/2 = 1.6514; tau = (1.6514 - 1) sigma^2/2 - 0.04 = 0.01211. Both auditors obtained 1.2111%, codex also by numerical root-finding.

Why this severity. The error overstates the annual-tax equivalent of a confiscatory bequest tax about 2.5-fold. Correcting it strengthens PSZ's point that annual wealth taxes are more powerful than bequest taxes. The 10% vs 12% wording is immaterial.

Why it matters, in detail. In the simplified R = 1 model, tau_B = 1 - b_bar at e_B = 0, so b_bar of 0.65 rather than 0.5 lowers the zero-elasticity optimum by 15 pp. PS13 obtain 50-60% because nu < 1 and R/G = 1.82 shrink the effective b_bar. The paper's number is right for partly offsetting reasons. Moving e_B from 0.1-0.2 to 0.3-0.4 lowers tau_B by about 3-6 pp.

Evidence. PS13 p.1876 and Table I. Plugging b_bar = 0.6-0.7 into eq. (2) gives 30-40% at e_B = 0 and 25-33% at e_B = 0.2; with PSZ's own nu of about 0.5, 65-70% and 54-58%. PS13's full formula gives 50-60% (Table I panel 0: US 70%/59% at e_B = 0/0.2; panel 2 with R/G = 1: 46-56% at e_B = 0). GLI (JPubE 2018), p.22: 0.23 (long term), 0.36 (medium term), 0.29 (balances), 'upper bound'; p.32: 'around 0.32 for contributions and 0.38 for account balances'. US federal estate-tax top rate: 77% (1941-76), 70% (1977-81), 55% (1984-2001).

Why this severity. The ~50% headline lies inside PS13's own calibrated range for linear rates (Table I: about 46-82% at e_B = 0 and 38-68% at e_B = 0.2 across specifications), and the paper's nu adjustment more than offsets the b_bar correction. The bottom line, substantial meritocratic inheritance taxation, survives; what fails is the stated empirical basis of the stand-alone illustration.

The authors' response. PSZ (p.582) acknowledge that other welfare weights can make optimal rates negative; PS13 (p.1876) state that 'there remains considerable uncertainty about e_B'.

Why it matters, in detail. The earned/unearned differential existed only in the 1970s and was larger than stated; its use as evidence that comprehensive income taxes taxed capital at least as heavily as labour is unaffected. The buyback description overstates what changed in 1982, which was regulatory certainty rather than the lifting of a ban.

Evidence. TS14.1 (script ts14_checks.py): US 1960 91.0 vs earned 91.0; 1971 70 vs 60; 1972-81 70 vs 50. UK 1960-70 identical; 1971 88.8 vs 82.9; 1974-78 98 vs 83. US 2012 35.0 (2013: 39.6); TS14.2 US 2012 35. SEC Release 34-48766 (68 FR 64952, 17 Nov 2003), section II.A and fn.4 (codex). Published p.584 rendered at 110 dpi (adjudicator).

Why this severity. Narrative and figure details only. The statutory-rate series match the source within about 0.5 pp in every other country-year, so no conclusion changes.

Why it matters, in detail. The statement was accurate for the November-2022 working paper but not, as worded, for the end of 2022.

Evidence. Official English text of the Act (Addenda Art. 1), cached by codex; Ministry of Economy and Finance release of 9 November 2023.

Why this severity. A chronological slip in a passing remark. Implementation was still prospective, and the paper's substantive points about the agreement's design are unaffected.

Why it matters, in detail. Fractile growth includes turnover and re-ranking, so it is not Delta k_i/k_i; for the deconcentration argument in Section V(iv), however, fractile growth is the relevant statistic. The window matters: endpoints of 1987 and 2013 give about 6.5%, 1990-2010 about 4%.

Evidence. TS12.3 rows 35-40: 6.42% (top 1/20M) and 6.77% (top 1/100M) for 1987-2013; 3.79% and 4.10% for 1990-2010. Mean wealth of all listed billionaires: $2.11bn (1987) and $3.79bn (2013), nominal. Claude's within-person Forbes-400 growth, including drop-outs, was 6.2% a year over 1987-2013, which supports the order of magnitude for the largest fortunes. The 2013 Forbes mean was about $3.8bn.

Why this severity. The point being illustrated, that wealth gains dwarf consumption for billionaires, holds even at 3-4% growth ($90-120m a year on $3bn, against a hypothetical $10m of consumption), and within-person growth of the largest US fortunes is close to 6%.

The authors' response. Piketty (AER P&P 2015, p.52) cites Forbes-type rankings as showing top wealth growing at 6-7% a year in real terms (per corpus entry capital21-14).

Why it matters, in detail. The statements hold for regions and for the US, not country by country; most exceptions are small (bottom-50% shares of 5-7%), and many WIR country distributions are imputed.

Evidence. WIR 2022 country appendix A1T1 (2021): the bottom-50% share is 5% or more in 13 of 27 countries (e.g. Italy 10.0, Spain 6.7, China 6.4, Australia 6.1, Japan 5.8, Sweden 5.8). In the Chapter-1 workbook (data-F1.14abc), 97 of 174 country rows are 5% or more; it gives Spain 17.25%, inconsistent with A1T1's 6.7%. The top-10% share is below 60% in 10 of 11 non-US advanced economies (47.7-59.6%). The top-1% share is below 25% in the UK (21.3), Italy (18.0), Australia (23.7), Spain (24.2), Japan (24.5) and Korea (24.9). Regional bottom-50% shares are all below 5% (Europe 4.4%, US 1.5%, Latin America 0.6%), which supports the regional figures on p.589.

Why this severity. Framing only: wealth is far more concentrated than income under any of these figures.

Why it matters, in detail. The bottom half's post-reform share depends on assumptions about private bequests and how they are distributed. Claude's flow calculation gives 17-24%, which overlaps PSZ's 20-30% but not Piketty's 36%.

Evidence. Piketty (2022), official figures-and-tables PDF: interpretation note to Figure 30; note to Table 2.

Why this severity. Illustrative policy numbers. PSZ's post-reform share is more conservative than the source's, and the ~5%-of-NI cost is consistent (about 4.6-6.5% under plausible demographic ratios).

Why it matters, in detail. Bibliographic accuracy only.

Evidence. Crossref records: 10.1016/0047-2727(76)90041-4; 10.1093/restud/rds001; 10.3386/w31080 (issued 2023-03).

Why this severity. The works remain identifiable; no result is affected.

Why it matters, in detail. The share of profits labelled 'shifted' depends on the counterfactual: local-firm profitability (TWZ) or regression on real activity (CbC studies). Revenue-loss estimates converge more than profit shares do.

Evidence. Corpus entries offshore-havens-09, -10, -12. TWZ's own robustness range (REStud 2023, Table 2) runs down to a $369bn lower bound, against a $616bn baseline.

Why this severity. A passing contextual statistic in the tax-competition discussion; no conclusion of the paper depends on the share being 40% rather than 15-25%.

The authors' response. TWZ (REStud 2023, Sec. 2.1) argue that firm-level micro data miss most haven profits (only 17% of consolidated global profits traceable to subsidiaries in Orbis), and they acknowledge that taking haven data at face value would lower their estimate by 18% (per corpus entries offshore-havens-09, -10).

Why it matters, in detail. In SZ's mechanical simulation even the 2-3% schedule offsets more than half of the rise in Forbes-400 concentration; only about 10% restores the 1982 level. Behavioural responses would shrink all of these effects.

Evidence. SZ (2019a) DataFig6 (mechanical, zero evasion): actual Forbes-400 wealth share 0.93% (1982) and 3.26% (2018). With taxes in place since 1982 the 2018 share would be 1.96% with Warren, 1.34% with Sanders (up to 8%) and 1.03% with the 10% 'radical' tax. Warren therefore removes 40% of the 2018 level and 56% of the 1982-2018 rise; Sanders removes 83% of the rise and the radical tax 96%.

Why this severity. A hedged ('might') policy remark, which may refer to returning to earlier concentration or to the bottom half's share. The ranking (higher rates deconcentrate more) is correct, but the dichotomy is overstated relative to the authors' own simulation.

Why it matters, in detail. The sufficient statistic is conditional on the welfare-weighted group. Without that restriction, tau_B is not identified by an aggregate nu; for a given aggregate share, the stylized example's admissible range runs from about 40% to 85%.

Evidence. Codex counterexample: zero-receivers are half the population and leave half the mean bequest; the aggregate motive share is 0.5 and e_B = 0.2. The optimum is 83.3% if none of their bequests is motive-driven and 41.7% if all are, against 62.5% from the shortcut. PS13 p.1866 define nu as 'the population average of nu_ti (weighted by g_ti b_t+1i)'. PS13 themselves use nu = 0.7 and PSZ use nu = 0.5, both citing Kopczuk & Lupton.

Why this severity. A correct qualification of an illustrative extension. No evidence was found that zero-receivers' motive shares differ from the population's in a particular direction, so no impact is demonstrated.

Why it matters, in detail. Valuation and Forbes measurement error affect both the tax base and the elasticity calibrations. Payment in kind solves liquidity, not valuation, for a progressive tax with thresholds.

Evidence. 2013 draft (17 Sept 2013), p.6. Corpus: estate-tax values of Forbes decedents are about 50% (Raub et al. 2010, as cited by Kopczuk) or about 30% (Balkir et al. 2025) of Forbes estimates (us-wealth-taxes-11); Norwegian wealth-tax valuations are a median 61% of sale prices (Skar et al. 2025; offshore-havens-23).

Why this severity. These are caveats on feasibility and data quality. They do not refute the theoretical rationale but temper the word 'easily'.

The authors' response. SZ (2020 JEP, p.9) concede that Forbes is 'far from an ideal data source'; SZ (2022b) check billionaire equity against SEC ownership filings; SZ (2022c, cited in fn.11) propose a tax on corporations' stock that avoids valuation (per corpus entry us-wealth-taxes-11).

Why it matters, in detail. Sequential (Markov) equilibria without commitment typically feature positive recurrent capital taxes, so the footnote's inference is a non sequitur. It does not bear on the paper's own rationales.

Evidence. Comparison of WIL WP 2022/18 fn.2 with OxREP fn.4.

Why this severity. It concerns a rationale the paper explicitly sets aside; no core finding depends on it.