Peter Diamond, Emmanuel Saez · In Janet Byrne (ed.), The Occupy Handbook, New York: Little, Brown and Company, 2012, pp. 317-329

Taxing High Earnings

7 problems found: 1 major · 1 moderate · 5 minor

What the paper claims

The top marginal income-tax rate on the top 1 percent ('roughly, earnings above $400,000') should be much higher than the 35% (or 39.6%) under political discussion. The authors 'favor a top tax rate near or in the range of 50 percent to 70 percent'. They conclude that 'a marginal income tax rate of 49 percent ... would be a plausible number, far more likely to be too low than too high in light of both fairness and efficiency concerns', and that 'the gain from a much larger increase than is discussed by politicians is pretty clear'.
The revenue-maximizing top rate, combining all taxes, is tau* = 1/(1 + a e). With Pareto parameter a = 1.5 and elasticity e = 0.25 ('a midrange estimate from the empirical literature') it is 73%, 'substantially higher than' the combined 42.5% top rate of 2011. A table maps e = 0.1-1 into combined and federal rates.
For 42.5% to be revenue-maximizing, the elasticity would need to be 0.9, 'well above the majority of the best estimates'.
Using Gruber and Saez (2002), e = 0.57 (taxable income) gives 54% and e = 0.17 (broad income, no deductions) gives 80%, i.e. 48% and 76% federal. 'The elasticity e = 0.57 is a conservative upper-bound estimate of the elasticity and so a conservative lower-bound estimate of the implied revenue-maximizing top tax rate', so 'the case that considerably higher rates at the top than at present would still raise more revenue appears robust in the context of the standard model of income taxation'.
Context: the top-1% income share rose from 9% (1970) to 23.5% (2007), the highest since 1928 and much higher than in Europe or Japan, while the top rate fell by half, from 70% to 35%. In 2007 the top 1% paid 40.4% of federal income taxes at a 22.4% average rate. Setting aside behavioral responses, raising that average rate to 29.4% or 43.5% would raise 1% or 3% of GDP, still leaving the top-1% after-tax share more than twice its 1970 level.

Every problem found

1majorlikely · previously known · overclaiming

The chapter's numbers depend heavily on one input: how much the rich cut the income they report when their tax rate goes up. The authors call their main figure 'midrange' and a higher figure a 'conservative upper bound'. But the studies they cite, including their own, allow noticeably larger responses. With those, the rate that raises the most money would be closer to 45-55% than 73%, and their 49% suggestion would be about right rather than 'far more likely too low'. A higher top rate would still raise revenue; how high it should go is much less certain than the chapter says.

Technical detail and evidence

Why it matters, in detail. tau* = 1/(1+ae) is steep in e. With a = 1.5, raising e from 0.25 to 0.50 (the PSS 2011 total elasticity) or 0.57 (Gruber-Saez) lowers the combined revenue-maximizing rate from 72.7% to 57.1% or 53.9% (federal: 68.4% to 51.2% or 47.6%), a 21-26% cut in the headline. The SSG trend-controlled top-1% estimates (0.58-0.82) give 53.5-44.8% combined (47.2-37.6% federal). The upper end of the Gruber-Saez 95% CI (1.15) gives 36.7% (28.6% federal). The 49% federal proposal (55.1% combined) is at or below the revenue maximum only for e <= 0.542 (a = 1.5) or e <= 0.479 (a = 1.7). The 70% upper end of the range requires e <= 0.232. The sign of the policy conclusion (revenue maximum above 42.5% combined, above 35% federal) holds for e < 0.90, which most long-run estimates satisfy.

Evidence. (1) Gruber and Saez (2002), JPubE 84, Table 9, p. 24, '$100K and above': taxable-income elasticity 0.567 (SE 0.298); broad-income elasticity 0.171 (SE 0.240). The authors call their group estimates 'disappointingly imprecise' (p. 25). The 95% CI of the taxable-income estimate is [-0.02, 1.15]; at 1.15 the revenue-maximizing rate is 36.7% combined (28.6% federal). Their group is defined on base-year broad income in 1992 dollars, which corresponds to roughly the top 2.3-3.1% of tax units in 1979-90 (Pareto interpolation between Piketty-Saez P95 and P99 thresholds). That is broader than the top 1% to which the chapter applies the estimate. (2) Saez, Slemrod and Giertz (2012), JEL 50(1), which the chapter's endnote cites as 'a recent survey': - Table 1 (p. 21), top-1% time-series elasticities: 0.60 (ERTA), 1.36 (TRA86), 0.45 and -0.39 (OBRA93), 1.71 with no trend, and 0.82/0.74/0.58 with linear, quadratic and cubic trends. - Text: with trends the estimate 'remains significant and above 0.5' (p. 22). - Footnote 72 (p. 42): 'the ETI for top earners could conceivably be higher than 0.25, especially if the top tax rate is increased while keeping the tax rate on realized capital gains constant'. - p. 42: 'no truly convincing estimates of the long-run elasticity'. (3) Piketty, Saez and Stantcheva (NBER WP 17616, Nov. 2011, pp. 4-5 and Table 3), circulated before the chapter: preferred total long-run elasticity of top incomes about 0.5, giving 57% in the standard supply-side case. (4) Auten and Joulfaian (2009), top 1%: 1.3 short run and 0.6 long run (taxable income), as tabulated in the appendix table of Mathur, Slavov and Strain (2012), Tax Notes, p. 915. (5) Wording change: the parent JEP article (Diamond and Saez 2011, p. 173) called 0.57 'a conservative upper bound estimate of the distortion'. The chapter turns this into a bound on the elasticity, and hence on the revenue-maximizing rate. Yet the charitable-giving rationale it invokes (pp. 323-324) bears on efficiency, not on revenue. (6) Recomputed federal revenue-maximizing rates (scripts/verify_ds2012.py, block A): 68.4% (e = 0.25), 56.9% (0.403), 51.2% (0.50), 47.6% (0.57), 46.2% (0.60), 37.6% (0.82).

Why this severity. The magnitude of the recommendation depends on e being about 0.25. Within the range of contemporaneous long-run top-earner estimates (about 0.4-0.6, including the authors' own), the revenue-maximizing rate falls by roughly 15-28%, from 73% to 53-62% combined (46-57% federal). The upper half of the 50-70% range would then exceed the revenue maximum, and 49% would sit at it rather than safely below. The qualitative claim (revenue maximum above the 2011 combined 42.5%) survives for e < 0.9. The issue therefore weakens the core finding but does not overturn it.

The authors' response. No direct reply to Mathur, Slavov and Strain (2012) was located. The chapter carries several qualifications: 'we have only a range of plausible answers' (p. 320); 'considerable uncertainty remains' (p. 325); base broadening and enforcement can lower the avoidance elasticity (p. 324); and pay-bargaining would raise the optimal rate (pp. 328-329). Saez's later work offers two defences. First, Piketty, Saez and Stantcheva (2014) argue that a large total elasticity (about 0.5) is mostly bargaining, which would imply a higher optimal rate (83%). Second, Saez (2017, Tax Policy and the Economy 31, Table 3) estimates a medium-run top-1% elasticity of 0.26 for the 2013 rate increase, while noting that it rests on a strong counterfactual-trend assumption. Auten, Splinter and Nelson (2016) report larger short-run responses and persistent reclassification.

2moderateplausible · previously known · speculative assumption

The formula assumes the rich respond to taxes in one simple way over a year or two. Over longer periods people may change careers, education, investment, where they live, or how they label their income. Economic models disagree a lot about what that implies: some put the best rate well below 73%, a few above. The authors mention these issues but don't put numbers on them, so the 73% is the answer of one simple model.

Technical detail and evidence

Why it matters, in detail. The sufficient-statistic formula omits dynamic and cross-base terms. Adding them gives: - 47.5-47.6% (formula) or 49% (simulated) in BHL, against 65% without the cross-base terms; - 62.5% with Scheuer-Werning's superstar correction at the chapter's own a and e; - 36.6-42% (effective federal rate on the top 5%) in Guner et al.'s general-equilibrium model; - 9% (worker welfare) with Jones's innovation spillovers; - 79% optimal or 87% revenue-maximizing in Kindermann-Krueger. The capital-gains conversion margin has an ambiguous sign: the fiscal externality t a e2 raises tau*, while unmeasured extra shifting lowers it. The direction of the net bias against the 73% is therefore model-dependent, but its spread is large compared with the gap between 73% and the 2011 combined rate of 42.5%.

Evidence. - Badel, Huggett and Luo (2020, EJ; 2019 draft, Table 5, p. 21): tau* = (1 - a2e2 - a3e3)/(1 + a1e1) = (1 - 0.180 - 0.089)/(1 + 0.539) = 0.475 (simulated Laffer peak 49%), against 65% with e2 = e3 = 0. The dominant term is taxes paid below the threshold (human-capital investment by future top earners), not capital-gains conversion. - Scheuer and Werning (2017, QJE; 2016 draft, eq. 43 and fn 30): the superstar adjustment raises e from 0.25 to 0.25/(1 - 1.5 x 0.25) = 0.40, giving 62.5%. - Guner, Lopez-Daneri and Ventura (2016, JME; pp. 69-70 and Table 4): federal income-tax revenue peaks when the richest 5% face an effective marginal rate of about 36.6% (42.6% for the top 1%) if the whole schedule is tilted, or about 42% if only the top 5% is taxed more heavily. The revenue gains are small (6.4-8.4%). These are effective federal rates, not directly comparable with the chapter's combined statutory rate. - Jones (2022, JPE, pp. 2227-2228): 91% revenue-maximizing if innovation is ignored; 9% maximizes worker welfare once innovation is included. - Kindermann and Krueger (2022, AEJ: Macro, pp. 319-320): 79% optimal and 87% revenue-maximizing in a life-cycle model. - Mertens and Montiel Olea (2018, QJE): short-run ETI about 1.2 overall and about 1.5 for the top 1%, with real output effects. This is later evidence. - Diamond and Saez (2011), fn 8: a may depend on tau. - SSG (2012), fn 72: holding the capital-gains rate constant could raise the top-earner ETI. - Gruber and Saez (2002, p. 6): capital gains excluded from both income measures.

Why this severity. A robustness concern that the authors acknowledge qualitatively. The demonstrated effects are model-specific and run in both directions (about 9% to 87%), with most published alternatives below 73%. This adds material uncertainty to the headline but establishes no alternative number.

The authors' response. Within the chapter, the authors acknowledge the long-run evidence gap (p. 327) and the capital-income conversion argument (pp. 326-327), and qualify robustness as 'in the context of the standard model' (p. 325). No reply to the later model-based critiques was located.

3minorconfirmed · previously known · methodology

The calculation measures how top-heavy incomes are using an income measure that includes investment gains. Those gains are taxed separately at lower rates and are far more concentrated than pay. Using the income that would actually face the higher rate trims the answer by about 1-3 percentage points, a small change.

Technical detail and evidence

Why it matters, in detail. a = zm/(zm - z*) on AGI including capital gains is about 1.4-1.5 (TabFig2007: 1.413; IRS 2007 bracket data: 1.39 at $0.5m-$1m thresholds). The base the ordinary top rate applies to gives 1.575 (income excluding capital gains) to 1.72 (wages), or 1.70 in BHL. tau*(e = 0.25) falls by 1.0-2.7 points (72.7% to 70.0-71.7%) and tau*(e = 0.5) by 1.2-3.3 points.

Evidence. - Piketty-Saez TabFig2007, 2007, P99 threshold and P99-100 mean: including capital gains $398,909 and $1,364,494 (a = 1.413); excluding capital gains $347,564 and $952,388 (a = 1.575); wages $298,295 and $713,994 (a = 1.718). - IRS SOI Table 1.4 (2007): wages are 31.5% of AGI for returns at $500k or more and 16.1% at $10m or more. - IRS top 400 (2007): net capital gains are 66.3% of AGI, wages 6.5%. - Badel-Huggett-Luo (2019 draft, section 5.3): a1 = 1.70 for 2010 income excluding capital gains and qualified dividends, against 1.50 for AGI. - tau* at e = 0.25: 72.7% (a = 1.5), 71.7% (1.575), 70.2% (1.70), 70.0% (1.718). At e = 0.5: 57.1% to 53.8%.

Why this severity. Lowers the headline by about 1-3 points, in the same direction as F1. Small next to the elasticity uncertainty.

4minorconfirmed · newly identified here · selective presentation

The chapter says a 70% top rate was in force from 1965 to 1981, which suggests high earnings were once taxed that heavily for 17 years. In fact, from 1972 wages and salaries were capped at 50%, the same as the Reagan rate, so the 70% applied mainly to investment and other unearned income. This makes the historical precedent sound stronger than it was, but it does not change the chapter's calculation.

Technical detail and evidence

Why it matters, in detail. The statutory 70% applied to unearned income. Under IRC section 1348, earned (later personal-service) income was capped at 60% in 1971 and 50% in 1972-81. Top-1% wage earners' average marginal federal rate was 47.9% in 1972-81 against 43.1% in 1982-86, so there was no 70-to-50 drop on earnings in 1982. The tau* calculations are unaffected.

Evidence. - IRS SOI Bulletin, 'Personal Exemptions and Individual Income Tax Rates, 1913-2002', notes 23-24: 1971 'earned net income' subject to a 'maximum tax' of 60%; 1972-1981 a 'maximum tax' of 50%. - Saez (2004), Tax Policy and the Economy 18, pp. 160-161: the maximum tax 'reduced the top rate for earned income from 70 percent ... to 60 percent in 1971 and then 50 percent starting in 1972'. - Saez (2004) data, TPE04.xls sheet data-Fig9B: average marginal federal income-tax rate of top-1% wage earners 43.8% (1966-71), 47.9% (1972-81), 43.1% (1982-86). - Tax Policy Center top-rate table: 75.25% (1968), 77% (1969) and 71.75% (1970) including the surcharge; 69.125% (1981).

Why this severity. Wrong historical framing, but no number in the formula-based case depends on it. Downgraded from auditor A's 'moderate' because the core finding does not rest on the historical precedent.

The authors' response. None located. Saez (2004, pp. 160-161) documents the maximum tax; Slemrod (1994), cited there, notes that the interaction with tax preferences could push some earners' marginal rates above the cap.

5minorconfirmed · newly identified here · internal inconsistency

The chapter gives two different figures for the same group's average income, $1.2 million and $1.364 million. It is a small slip. Using the right figure would slightly strengthen, not weaken, the authors' numbers.

Technical detail and evidence

Why it matters, in detail. With the 2007 values (a = 1.413) tau*(e = 0.25) is 73.9% rather than 72.7%. The a = 1.5 used is a reasonable multi-year AGI value (1.39-1.55 at $0.5m-$10m thresholds in IRS 2007 and 2011 data; 1.67 at the 2007 top-400 cutoff).

Evidence. - TabFig2007 (the August 2009 vintage cited for the top-1% share), 2007: P99 $398,909 and mean $1,364,494, so a = 1.413 and tau*(e = 0.25) = 73.9%. - TabFig2008 (the July 2010 vintage cited for the $1,364,000): 2007 mean $1,416,885 in 2008 dollars, which is $1.364m in 2007 dollars. For 2008: P99 $368,238, mean $1,137,684 (a = 1.48). - The '$1.2 million' therefore fits 2005 ($1,195,621 in 2007 dollars, with a $372,262 threshold) or 2008 better than 2007. - The JEP article (pp. 168-169) has the same juxtaposition.

Why this severity. Negligible. Consistent 2007 figures would raise tau* by about 1 point, against the authors' interest.

6minorconfirmed · newly identified here · arithmetic or transcription

Two numbers in the conversion from 'all taxes combined' to 'federal income tax only' are off by one percentage point. These are typo-level slips that do not change anything.

Technical detail and evidence

Why it matters, in detail. Federal = 1 - [(1 - tau_c)(1.0145)(1.0232) + 0.0145]/0.9414. Applied to tau_c = 0.4706 this gives 0.4008, and to 0.7059 it gives 0.6603. Both printed values overstate the federal equivalent by 1 point.

Evidence. scripts/verify_ds2012.py, block A. The other conversions reproduce: 84.08, 68.39, 51.20, 32.30, 47.64 (printed 48), 76.06 (printed 76) and 63.27 (printed 63). The printed '0.75 47% 41%' row appears identically in two Internet Archive scans and in the Google Books ebook text. A simple proportional conversion (using the note's .575/.65 factor) yields 66.75%, which would round to 67%, but it gives 69.2% for the 68% table entry, so the table was not computed that way. The table and the g = 0.1/0.2 examples are new in the chapter; they are not in the JEP article.

Why this severity. One percentage point in two illustrative numbers; no effect on any conclusion.

7minorconfirmed · newly identified here · misrepresentation of source

A figure described as the typical family's income is actually the typical household's income, which is lower. It is only used as an illustration and does not affect the results.

Technical detail and evidence

Why it matters, in detail. Mislabelled comparator: household (ACS) vs family (CPS) median, $52.7k vs $61.4k. It enters only the 3.9% welfare-weight illustration (it would be 4.5%) and leaves tau* = (1 - g)/(1 - g + ae) essentially unchanged at small g.

Evidence. ACSBR/08-2 table: United States 2007 median household income $52,673 (in 2008 dollars). Census CPS ASEC historical Table F-7: 2007 median income of all families $61,360. The log-utility weight ratio would be 4.5% instead of the printed 3.9% (52,700/1,364,000 = 3.86%).

Why this severity. Labelling error in an illustration; no effect on any calculation.

Claims examined and rejected

Problems one auditor raised that did not survive checking.

I3: the Gruber-Saez elasticities were estimated 'under small or zero rate gaps' between ordinary income and capital gains. The omitted capital-gains margin therefore unambiguously lowers the revenue-maximizing rate, by as much as about 16 points according to Badel-Huggett-Luo's decomposition. — Partly incorrect, for three reasons. - Rate gaps: the Gruber-Saez sample (1979-1990) includes 1979-86, when the top ordinary rate (70%, then 50%) exceeded the maximum effective capital-gains rate (28%, then 20%; 40% inclusion) by 30-42 points. Only 1987-90 had small or zero gaps (Gruber-Saez 2002, p. 6). - Direction: the net direction is not unambiguous. If conversion is already in the measured elasticity, the formula ignores revenue recouped at the capital-gains rate and so understates tau*, as the chapter itself says (p. 324). Only conversion beyond what e captures lowers tau*. - BHL magnitude: BHL's 65% to 47.6/49% drop is driven mainly by taxes paid below the threshold (a2e2 = 0.180, human-capital investment by future top earners) and by lower consumption and capital-income taxes of top earners (a3e3 = 0.089). It does not come from reclassifying labor income as capital gains. The valid residue is kept within F1 and F2: SSG (2012) fn 72's warning, and the chapter's own unquantified concession on p. 327.
I1 (sub-claim): the 50-70% range holds only for e of roughly 0.17-0.5. — Small arithmetic slip in the audit. With the chapter's conversion, 70% federal (74.2% combined) is revenue-maximizing at e = 0.232 and 50% federal (56.1% combined) at e = 0.523 (a = 1.5); e = 0.17 gives 76% federal. F1 uses the corrected range of 0.23-0.52.
I4 (sub-claim): Mertens and Montiel Olea (2018) contradict the chapter's statement that 'no compelling study to date has shown substantial responses along the real economic responses margin among top earners'. — Not an error of the chapter. The statement accurately summarized the 2011-12 literature: SSG (2012, p. 42) says 'there is no compelling evidence to date of real economic responses to tax rates ... at the top of the income distribution'. MMO's short-run SVAR estimates appeared later and are kept only as later evidence under F2.
Badel-Huggett-Luo's printed expression (1 - 4.508 x 0.040 - 0.120 x 0.739)/(1 + 1.7 x 0.317) evaluates to 47.5%, not the printed 'approximately 49%', an unexplained discrepancy in the critic's draft. — Explained in BHL's own Table 5 (2019 draft, p. 21). The formula value is .476 and the simulated Laffer-curve peak is .49; the elasticities are difference quotients between tau = .422 and the peak, and the introduction's '= 0.49' reports the simulated peak. This is not an arithmetic error, and in any case it is not a claim about the chapter.
No validated work-specific issues (0 critical, 0 major, 0 moderate, 0 minor). The table cell '0.75 / 47% / 41%' might reflect an unseen conversion convention or a text-index error. — Superseded. Auditor A recovered the full running text of pp. 317-329 from Internet Archive OCR fragments. The adjudicator re-verified every quotation used here against the raw fragments (two independent scans) and Google Books ebook snippets. The 41% appears identically in all three sources, and no tested conversion rule reproduces all printed federal values, so it is a one-point slip (F6). Codex's zero count reflected lack of access, as Codex itself stated, not a finding that the chapter is sound.

Audit notes

What reproduced. Reproduced independently (scripts/verify_ds2012.py; scripts/aps_check.py): - every formula output and the table's total-rate column; - the combined 42.45% top rate and the 0.902 break-even elasticity; - the Gruber-Saez values and implied rates (53.9/79.7% combined; 47.6/76.1% federal); - the welfare-weight rates (70.6/68.1%); - the top-1% shares (9.03% in 1970, 23.50% in 2007; 1928 23.94%) and the international comparison; - the IRS 2007 figures (22.45%, 40.42%, $450.9bn) and the static revenue and after-tax-share arithmetic (0.999% and 3.00% of GDP; 7.64/20.89/16.13%); - the AGI Pareto parameters (1.39-1.55; top-400 1.674) and the log-utility ratio (3.86%). Not reproduced: - two federal conversions (41% printed vs 40.08%; 67% printed vs 66.03%); - the 'roughly $1.2 million' top-1% mean for 2007 (data: $1,364,494; $1.2m fits 2005 in 2007 dollars, or 2008); - 'median family' $52,700 (it is median household income; family median $61,360). Not rebuilt: the 5.86% state and 2.32% sales-tax inputs (auditor A's partial rebuild gives 5.4-5.8% state, about 0.3 pp effect on tau); the 2005 IRS public-use-file Pareto graph (licensed data); and 'the U.S. government collects most of its revenue from taxes on earnings'. Both auditors' reproductions agree with the adjudicator's to the stated precision.

Limits of this audit. - Text access: no PDF or scan of the chapter was available (copyrighted; Internet Archive copies restricted). The text was rebuilt from OCR search fragments by auditor A and spot-verified here against raw fragments from two scans and the Google ebook. Short seams were bridged from single fragments, so minor OCR wording errors cannot be excluded, though every number and quotation used was matched in at least one raw fragment. - Endnotes were read only partly (42.5% decomposition, Pareto, $1,364,000, Census, Gruber-Saez, after-tax shares, sources). Their quantitative content duplicates the JEP footnotes, which were read in full. - Not estimated or replicated: no elasticity was re-estimated, and no structural model (BHL, Jones, Guner et al., Kindermann-Krueger) was replicated. F1 and F2 rest on published estimates and their standard errors. - The dynamic revenue figure is a simple illustration: the chapter's constant-elasticity response applied to top-1% AGI above the $410k floor, with an assumed 28% federal rate on the income that disappears. - The 'top 2.3-3.1%' location of the Gruber-Saez income group uses Pareto interpolation between Piketty-Saez thresholds and the Gruber-Saez income index; it is approximate. - Critiques of the Piketty-Saez top-share series (corpus us-income-01, -08, -09, -17) bear on the size of the inequality rise used as context (C5), not on the tax-rate calculation. They were not adjudicated here. - Author responses were searched only through the corpus and the critics' texts; no direct reply to Mathur-Slavov-Strain was found.