The Case for a Progressive Tax: From Basic Research to Policy Recommendations

Why it matters, in detail. With tau* = 1/(1+1.5e), the conclusion 'current 42.45% < tau*' holds iff e < 0.904. The paper's support for e < 0.904 is a single 2SLS coefficient of 0.567 (SE 0.298), so the break-even lies 1.13 SE above the point estimate, inside its 95% CI of [-0.02, 1.15]. tau* is 36.7% at the CI upper end and 48.4% at Saez's (2004) linear-trend top-1% estimate of 0.71. The 'upper bound' is defensible only in the conceptual sense that part of the taxable-income response is deductions or shifting with fiscal externalities. That does not address sampling error, and by SSG eq. 11 it holds only if shifted income is taxed at tau. The same threshold logic undercuts C4: with the $100k parameters unchanged, the schedule turns downward if the top elasticity exceeds 0.683, which the paper concedes on p. 174. For the broad-base proposal the inference is sturdier, since the broad-income upper 95% bound of 0.641 still gives 51.0%. Net: the qualitative direction survives at central values; the claimed robustness and the 54%/48% floor do not.

Evidence. DS p. 173 (upper-bound and robustness sentences); p. 172 ('would be optimal only if the elasticity e were extremely high, equal to 0.9'); p. 175 (long-run channels lack evidence). Gruber and Saez (2002, JPubE 84(1)) Table 9, p. 24, incomes > $100K: taxable income 0.567 (SE 0.298), N = 3,004; broad income 0.171 (SE 0.240), N = 3,076. GS p. 25: 'disappointingly imprecise ... not statistically distinguishable from each other'; p. 27: 'optimal tax rates with large standard errors'. SSG (2012, JEL 50(1)) p. 42 ('no truly convincing estimates of the long-run elasticity') and p. 43. Saez (2004, Tax Policy and the Economy 18) Table 3 panel C, p. 139: top-1% elasticities 1.83 (0.37) with no trend, 0.71 (0.22) with a linear trend, 0.50 (0.18) with a quadratic trend. Adjudicator computations (scripts/reproduce_headline.py): 95% CI for 0.567 is [-0.02, 1.15]; the break-even e for the 42.45% current rate is 0.904, which is 1.13 SE above 0.567, with about 13% of a normal sampling distribution lying above it; tau*(1.151) = 36.7%; tau*(0.71) = 48.4%; the broad-income upper 95% bound of 0.641 gives 51.0% combined (44.4% federal).

Why this severity. The paper makes robustness one of its three tests of policy relevance, and it claims robustness for Recommendation 1 on the strength of this bound. The cited evidence cannot exclude e of about 0.7-1.15 on the current base, and in that range the revenue-maximising combined rate is 37-48%, at or near the 2011 rate. So the robustness claim for the current base is unsupported, and the floor of the range falls by 6-17 pp. Not critical: central estimates still give rates above 42.5%, as does the paper's preferred broad-base reform even at the upper confidence bound of the broad-income estimate (51%).

The authors' response. No direct reply located. The paper's own defence (pp. 172-173) is that much of the taxable-income response is avoidance or shifting, which creates fiscal externalities and can be removed by base broadening, so the taxable-income elasticity overstates the efficiency-relevant distortion. This does not address sampling uncertainty.

Why it matters, in detail. d tau*/de = -a/(1+ae)^2, which is about -0.79 at the headline, so each 0.1 of elasticity moves tau* by roughly 7-8 pp. The formula needs the income-weighted top-bracket elasticity, and the paper substitutes a population-average ETI. That biases the headline upward if elasticities rise with income, as SSG, GS Table 9 and Saez (2004) all indicate. With top-specific central values, tau* = 57-64% (e = 0.50 to 0.37). Post-2011 evidence cuts both ways: about 0.25 medium-run for the 2013 reform (Saez 2017) versus 0.9-2.6 short-run (ASN 2016). The 73% is best read as the upper-middle of the static model's plausible range, not its centre. In PSS's later framework the same total elasticity (0.5) instead yields 83% if mostly bargaining, so the direction of the correction depends on how the response is interpreted.

Evidence. DS p. 171; fn 6 p. 169. SSG (2012) p. 42 and fn 72; p. 9 (uses e = 0.25 as 'the mid-range of the estimates from the literature' to obtain 72.7%, i.e. 68.4% federal). GS (2002) Table 9, p. 24. Saez (2004, TPE 18): p. 120 ('to about 0.5'), Table 3C p. 139, p. 129 (e = 0.5 'mid- to upper range'; a = 1.6 -> 55.6%). PSS NBER WP 17616 (Nov 2011): p. 4 ('around 0.5'), p. 7 (e1 = .5 -> 57%). Neisser (2021): after-deduction mean 0.403. Recomputed: tau*(0.37) = 64.3%, tau*(0.403) = 62.3%, tau*(0.50) = 57.1% (51.2% federal). Counter-evidence in the authors' favour: Saez (2017, TPE 31, Table 3) estimates a medium-run top-1% elasticity of 0.26 around the 2013 increase. Alternative counterfactual trends give -0.44 to -1.00, i.e. no detectable response, and Saez stresses the estimate is 'not as compellingly identified' as the short-run one. By contrast, Auten, Splinter & Nelson (2016, NTJ 69(4)) find short-run elasticities of 0.9-2.6 at the top.

Why this severity. Replacing 0.25 with top-income central values (0.37-0.50) lowers the headline from 72.7% to 57-64%, a fall of 9-16 pp (12-21%). That is below the rubric's roughly one-quarter threshold for major, and every value stays well above 42.5%. The paper also prints 54% and 80% beside the headline, which partly discloses the sensitivity.

The authors' response. No direct reply to Mathur, Slavov & Strain (2012) located. In Piketty, Saez & Stantcheva (NBER WP 17616, 2011; AEJ:EP 2014) Saez and co-authors adopt a total top-income elasticity of about 0.5 but attribute at least 0.3 of it to compensation bargaining, which raises the optimal rate (83%) rather than lowering it to 57%.

Why it matters, in detail. The 80% equates the post-reform top elasticity with GS's broad-income coefficient for incomes above $100k (1979-90). That implicitly assumes the entire gap between 0.57 (taxable income) and 0.17 (broad income) is removable deduction avoidance. But the 0.17 is imprecise (95% CI -0.30 to 0.64). And the authors' time-series evidence on pre-deduction top-1% income puts the elasticity near 0.5 (Saez 2004 with a quadratic trend; PSS), with PSS explicitly rejecting the avoidance scenario. Under e = 0.5 and no externality, the broad-base tau* is 57.1%. Under PSS's decomposition (e1 <= 0.2, e3 >= 0.3) it is 83%. So 80% survives only under the bargaining reading, not under the avoidance reading the paper gives.

Evidence. DS pp. 172-173, 175. GS (2002) Table 9: 0.171 (SE 0.240). Saez (2004, TPE 18): p. 120 (income 'before deductions ... market income') and Table 3C p. 139 (0.50, SE 0.18, with a quadratic trend). PSS NBER WP 17616 (Nov 2011) p. 4 and p. 34 ('Our US long-run analysis rejects this scenario'). SSG (2012) fn 69: even 0.17 may include corporate-to-individual shifting. Recomputed: tau*(0.5) = 57.1% (51.2% federal) vs 79.7% (76.1%).

Why this severity. In the paper's own no-bargaining model, a pre-deduction top elasticity of 0.5 puts the broad-base optimum at 57% (51% federal) instead of 80% (76%), a 23 pp cut to the top of the proposed range. The qualitative case is not weakened: under the authors' alternative bargaining interpretation (PSS) the same evidence gives 83%. The issue therefore affects the stated rationale and the upper end, not the direction.

The authors' response. Piketty, Saez & Stantcheva (2014) keep the large total elasticity but attribute most of it to bargaining (83%); no reconciliation with DS's avoidance-based 80% was found.

Why it matters, in detail. BHL's steady-state formula, tau* = (1 - a2*e2 - a3*e3)/(1 + a1*e1), adds revenue effects on taxes paid below the threshold and on other bases. In their model these terms cut the peak from 65% to 49%; the remaining gap to 73% comes from a1 = 1.70 rather than 1.5 (see F7) and e1 = 0.317. Scheuer-Werning show the formula survives superstar effects, but the relevant elasticity is larger (0.25 -> 0.4 for beta = 1) if estimates hold job assignment fixed. Jones separates the revenue maximum from worker welfare when top incomes reflect non-rival ideas. Kindermann-Krueger obtain 79-87% through insurance and wealth-accumulation channels. The sign and size of the correction to 73% are therefore model-dependent. What is overstated is the static formula's precision; its direction is not refuted.

Evidence. DS p. 175. Badel, Huggett & Luo (EJ 130(629), 2020; accepted ms. Aug 2019): abstract ('approximately 49 percent' vs the 'established' 73%), eq. (*) with a1 = 1.70 and e1 = .317, and 65% if e2 = e3 = 0. Scheuer & Werning (QJE 132(1), 2017; ms.): introduction and fn 30, 'the adjusted earnings elasticity is .4 and the revenue-maximizing top tax rate is 62%'. Jones (JPE 130(9), 2022), introduction: 91% vs 9% (range -26% to 50%), and 'the point of this paper is not to estimate the optimal top income tax rate'. Kindermann & Krueger (AEJ:Macro 14(2), 2022) pp. 319-321: 79% (87% revenue-maximising). Guner, Lopez-Daneri & Ventura (JME 80, 2016): 36.6%/42% effective federal rates on the top 5% (not like-for-like). Mathur, Slavov & Strain (Tax Notes, 19 Nov 2012): DS 'have effectively assumed that the long-run effects are zero'.

Why this severity. If the dynamic models with negative spillovers are right, the revenue maximum falls by 11-24 pp (to 49-62%), which would be a major change. But other well-calibrated models push it up (79-87%), and none of the alternatives is empirically identified. What is demonstrated is model uncertainty in both directions, not a measured bias, and the paper flags the omission.

The authors' response. DS (p. 175) acknowledge the long-run channels but argue that the evidence on them is lacking; no reply by the authors to the later model-based critiques was located.

Why it matters, in detail. With heterogeneous elasticities, the a to use is the one at the optimum, a(tau*), which data generated at tau = 35% cannot identify. Descriptively, a(P99) rises with the top rate and the slope survives a linear trend (b of about 0.39-0.86). Solving tau = 1/(1 + 0.25*[a0 + b(tau - 0.35)]) lowers tau* by 1.9-3.4 pp. Using the 1960-80 levels gives 58-66%, but that would imply large top-end responses inconsistent with e = 0.25, so it overlaps F2 rather than adding to it. The association is trend-confounded and not causal. The zero-top-rate conclusion (C3) is unaffected because a stays finite.

Evidence. DS p. 170 and fn 8. Adjudicator computations on Piketty-Saez TabFig2007 (rev. Aug 2009), a(P99) = mean/(mean - threshold), against TPC top statutory rates for 1960-2007 (scripts/pareto_checks.py). For income incl. KG / excl. KG / wages: mean a 1960-80 = 2.06 / 2.40 / 2.89 (average top rate 75%) vs 2003-07 = 1.48 / 1.63 / 1.78 (35%); correlation with the top rate 0.82 / 0.93 / 0.94; coefficient on the top rate controlling for a linear trend 0.39 / 0.83 / 0.86. tau*(e = .25) at the 1960-80 mean a = 66.1% / 62.5% / 58.0%; the fixed point using the detrended slopes changes tau* by -1.9 / -3.4 / -3.2 pp. Counterpoint: 1988-92 had a 28-31% top rate but a(incl. KG) = 1.66, higher than in 2003-07. Reynolds (2019, Cato Journal), section 'A Pareto Parameter Cannot Be Assumed Constant, or Independent of Top Tax Rates'.

Why this severity. If the tail thins as rates rise, the headline is overstated by about 2-3.5 pp on detrended descriptive slopes. Attributing the whole 1960-80 vs 2003-07 difference to taxes gives 7-15 pp, but that reading is speculative, conflicts with e = 0.25 and largely double-counts F2. It is a real robustness gap with limited demonstrated impact, and it is disclosed in fn 8.

The authors' response. Footnote 8 acknowledges the dependence and states that tau* = 1/(1+ae) remains valid with a evaluated appropriately; no quantification is offered.

Why it matters, in detail. In the participation model, tau1/(1-tau1) = (1-g1)/e1. A negative participation tax requires g1 > 1, and the revenue-saving 'win-win' logic of Figure A3 requires e1 > 0. If e1 is near zero for EITC-eligible groups (Kleven), that logic disappears. The optimal bottom schedule is then governed mainly by the relative welfare weights on non-workers and low-wage workers, and with any intensive response it moves toward the high-phase-out Mirrlees benchmark (A2: 80% at g0 = 3, e0 = 0.5). Kleven attributes the 1993 rise in single mothers' employment to welfare reform, which is itself a change in transfer design. Participation responses to transfers in general are therefore not refuted; the premise is weakened for the EITC, not overturned.

Evidence. DS pp. 166, 176-177; online appendix (A3). Meyer, 'The Effects of the EITC and Recent Reforms' (NBER TPE conference version, 1 Sept 2009, of the 2010 chapter): 'the credit has sharply increased the fraction of single mothers that work', and the absence of an hours effect is 'robust' - so DS cite it accurately. Kleven, 'The EITC and the Extensive Margin: A Reappraisal', NBER WP 26405 (rev. May 2024), abstract; Journal of Public Economics 236 (2024) 105135 (Crossref-verified). Schanzenbach & Strain, 'Employment Effects of the Earned Income Tax Credit: Taking the Long View', NBER WP 28041 (Oct 2020).

Why this severity. Recommendation 2 is one of the paper's three core recommendations, and its efficiency rationale (A3) needs extensive responses that are large relative to intensive ones. If EITC participation responses are near zero, the efficiency case for negative participation tax rates weakens, and the recommendation rests mainly on social preferences for low-income workers (which the paper also invokes). The evidence is contested rather than settled, and no one has re-derived the optimal schedule, so the demonstrated impact is limited.

Why it matters, in detail. The sufficient statistic a must describe the base to which tau applies. With preferential rates on gains and qualified dividends, that base is ordinary income, whose tail is thinner: a of about 1.58-1.70, or 1.72-1.85 for wages. Holding e = 0.25, tau* falls to 68-72%. The mismatch also implies an omitted cross-base response (shifting into preferentially taxed gains), which belongs in the elasticity and fiscal-externality terms (F1, F3, F9) rather than in a.

Evidence. DS p. 168 fn 4 ('ordinary labor income'), p. 170 (AGI definition), Figure 2. BHL (2020; accepted ms.) section 5.3: 'a1 = 1.70 when income excludes qualified dividends and capital gains and ... a1 = 1.50 using AGI as an income measure' (2010), with a wage-and-salary statistic of 1.85 (2010). Codex's IRS 2010 reconstruction: 1.5026 vs 1.7003. PS TabFig2007 a(P99, 2007): 1.413 incl. KG, 1.575 excl. KG, 1.718 wages (adjudicator). tau*(e = .25) = 72.7% at a = 1.5, vs 71.7% (1.575), 70.2% (1.70), 70.0% (1.718) and 68.4% (1.85).

Why this severity. Moving to the ordinary-income or wage tail lowers the headline by 1-4.3 pp (2.5 pp at BHL's 1.70), about 1-6%, which affects no conclusion. AGI is in any case the appropriate base for the paper's own broadened-base proposal, which would tax capital income more fully.

Why it matters, in detail. The shortcut zm/z* = 3 => a = 1.5 mixes years. Same-year IRS or PS pairs give a = 1.41-1.44, which raises tau*(e = .25) by 0.9-1.3 pp; the error works against the authors' conclusion, not for it.

Evidence. IRS SOI Table 5 (July 2009), via scripts/pareto_checks.py: 2005 floor $364,657 and mean $1,200,280 -> a = 1.436; 2007 floor $410,096 and mean $1,423,580 -> a = 1.405. Piketty-Saez TabFig2007, 2007: $398,909 / $1,364,494 -> a = 1.413. DS p. 169 uses $1,364,000.

Why this severity. The pairing is purely illustrative, and the error is conservative: consistent pairs give tau* = 73.6-74.0% vs 72.7%. Figure 2 ('slightly below 1.5') supports the rounded value.

Why it matters, in detail. With a shifting share s going to a base taxed at t, the revenue cost per unit of behavioural response is (tau - s*t), not tau. Shifting therefore lowers tau* relative to 1/(1 + a(1-s)e) unless t = tau; in SSG's example, 76.8% < 84.2%. The main US channel is shifting into preferentially taxed capital gains (t of about 15-20% in 2011), so the qualification is not negligible for the current base.

Evidence. DS p. 173. SSG (2012) section 2.2, eqs. (8)-(11), and its own example: s = 0.5, t = 0.3 gives 76.8%. Adjudicator: treating the shifted half as harmless would give 84.2%; a pure real response gives 72.7% (scripts/reproduce_headline.py).

Why this severity. No number in the paper relies on the sentence, and the paper refers readers to SSG for the exact formulas. The overstatement (about 7 pp in SSG's example) matters only for how much avoidance can be discounted.

Why it matters, in detail. A thinner extreme tail (a of about 1.7-2.2 above $22-139m) implies a somewhat lower revenue-maximising rate for a hypothetical bracket at that level (65-70% vs 73%). It does not affect the irrelevance of the Sadka-Seade zero rate, which requires a to go to infinity.

Evidence. IRS, 'The 400 Individual Income Tax Returns Reporting the Highest Adjusted Gross Incomes Each Year, 1992-2007', Table 1, cols (3) and (7); Piketty-Saez TabFig2007 Table A6 (P99 threshold and mean, incl. KG). scripts/pareto_checks.py: a(top-400) = 2.09, 1.95, 2.07, 2.16, 2.02, 1.99, 2.08, 2.01, 2.00, 1.80, 1.84, 1.72, 1.76, 1.88, 1.72, 1.67 for 1992-2007.

Why this severity. The argument only needs a to stay finite far below the single top earner, which holds in every year (tau*(e = .25) at the top-400 level is 65-70%), so the zero-top-rate conclusion is unaffected. Using 2007, the latest year then available and the paper's reference year, is natural rather than deliberate selection.

Why it matters, in detail. MWY mention the Saez (2002a) participation result only in a footnote and immediately note that the in-work incentives are 'taxed away as income rises'. The accurate characterisation would be 'do not incorporate', not 'do not discuss'.

Evidence. DS p. 189; MWY (2009) p. 158 and fn 7 (text of the published article).

Why this severity. This is a mischaracterisation in an appendix comparison. MWY do not let the point change their Lesson 3, so DS's substantive disagreement stands and no result is affected.

Why it matters, in detail. The unit and price-year mismatch changes the log-utility weight from 3.86% to 3.72%, which is irrelevant for tau* (g = 0.04 already moves tau* by only 0.8 pp). Mixing universes overstates the 2007 after-tax top share by 0.6 pp (20.9% vs 20.3%).

Evidence. Census ACSBR/08-2 (Sept 2009), table p. 3: United States 2007 = $52,673 (2008 inflation-adjusted dollars). IRS SOI Table 5 (July 2009), 2007: top-1% AGI share 22.825%, tax $450,926m, AGI $2,008,259m; totals $1,115,760m tax and $8,798,500m AGI. Adjudicator: the ratio in 2007 dollars is 3.72% vs 3.86%; the IRS-consistent after-tax share is 20.27% vs 20.9%; the hypothetical 43.5% case gives 15.6% vs 16.1% (ratio to 1970 of 2.05 vs 2.11). PS (2007, JEP 21(1)) Table 3a: 25.83%.

Why this severity. Each discrepancy moves the reported statistic by under one percentage point and leaves every conclusion intact: the top-1% after-tax share stays 'more than twice' its 1970 level, and the log-utility weight stays about 4%.

Why it matters, in detail. Navigation and date inconsistencies only; every cited argument is present in the article.

Evidence. JEP pp. 181-183, 186-187, 190; Crossref record 10.3386/w16619 (December 2010).

Why this severity. These are copy-editing residue from footnote renumbering between the working paper and the JEP; no result depends on them.