Daniel Reck, Max Risch, Gabriel Zucman · Unpublished response, October 22, 2021

Response to a Comment by Auten and Splinter on 'Tax Evasion at the Top of the Income Distribution: Theory and Evidence'

13 problems found: 1 major · 3 moderate · 9 minor

What the paper claims

Auten and Splinter's (AS) assertion of an 'inherent upward bias' in the Guyton et al. (GLRRZ, March 2021) benchmark is contradicted by principled reasoning and further data analysis; factors AS ignore suggest top-end evasion 'may actually be under-estimated on net'; the original benchmark estimates are 'reasonable and conservative'.
The uniform-multiplier DCE allocation (Johns & Slemrod 2010) is not inherently upward biased; the sign is ambiguous. AS's overall-income gradient lowers top-1% evasion, but the preferred line-by-line parameterized and two-step gradients imply 'negligible or slight downward bias' in top-1% under-reporting; the uniform method is 'a reasonable and simple means' of allocating DCE adjustments.
Pass-through evasion: the 20% under-reporting rate is 'reasonably conservative' (Johns 2009 S-corp NMPs of 12-16% use absolute-value denominators; on true net income and excluding officer-compensation corrections the rate is 19%); allocating unreported pass-through income like reported pass-through income by bin is not mechanically biased; loss-related mis-allocation is negligible; the 58% double-counting removal is 'the sole cause' of AS's finding that 99% of the net addition goes to the top 1%.
Other AS points: GLRRZ's proprietor and wage under-reporting is close to NIPA's explicit amounts (NIPA adjusts 'just two types of income'); the rest of AS's 'discrepancy' reflects definitional differences and items outside national income (NOLs), so there is 'little reason to revise our estimate of total under-reporting dramatically downwards'; AS's offshore change (95% -> 80% concealed) is 'more modest than' the existing sensitivity analysis and non-profits do not enter the offshore estimate; omitting the bottom decile from figures omits a negligible share of under-reporting.
Bigger picture: theory suggests under-reporting rises with income; in the preferred estimates accounting for under-reporting raises top-1% fiscal shares by '0.9 p.p. (with DCE) to 1.2 p.p. (without DCE)'; PSZ's top-1% share rose 'about 18 pp' (1980-2014) vs 5 pp in AS; AS's audit-based allocation lowers the top-1% share about a full point more in 2014 than in the 1980s (Fig. 5), implying implausible compliance trends.

Every problem found

1majorlikely · previously known · overclaiming

The authors said their estimate of how much hidden income raises the top 1%'s share was, if anything, too low. Their own later work cut it by about a third, from 1.5 to about 1 percentage point, and their new range runs down to zero. The main reason is that redoing the total amount of hidden income with the IRS's newer method gave about a quarter less, the kind of downward revision the reply had dismissed.

Technical detail and evidence

Why it matters, in detail. Defended: +1.5 pp (20.3% -> 21.8%, 2006-13), top-1% misreporting ~21%. Later: 21.4% (+1.1 pp, Dec 2023) and 21.3% (+1.0 pp, Dec 2025; DCE-inclusive range 20.3-22.4%); top-1% misreporting 16-17%. The change sits in the DCE column (20.9% -> 20.5%) while the no-DCE + sophisticated column is unchanged (21.0%). DCE-adjusted under-reporting fell from $1,304bn (14.0%) to $975bn (10.7%) at an unchanged ~$300bn tax gap, while the top-1% share of unreported income held at 31.0% -> 30.9%; a static calculation with that share fixed reproduces the decline (21.75% -> 21.40%). The reply's argument that tax-gap consistency rules out a large downward revision of income under-reporting was therefore wrong. A further ~-0.3 pp (static) would follow from using S-corp audit concentration (51% vs 79%) for the pass-through addition.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response: abstract p.1, pp.2-3, pp.21-22 ('on 1 through 5 we take ... a rather conservative stance'), p.20 ('little reason to revise our estimate of total under-reporting dramatically downwards. Doing so would bring our estimates in conflict with official estimates of the individual income tax gap'). GLRRZ NBER WP 28542 (March 2021): Table 3 (PDF p.41) 20.3/19.8/20.9/21.0/21.8; '21% in the top 1%' (PDF p.4); Tables A2/A5/A6: DCE-adjusted under-reported income $1,304bn (14.0% of true income), tax gap $282bn; Table 2 (PDF p.38) top-1% share of unreported income 24.6% (DCE) / 31.0% (benchmark). GLRRZ NBER WP 28542 revised Dec 2023: Table 2 (PDF p.44) 20.3/19.8/20.5/21.0/21.4 (only the DCE column changes); PDF p.36: replicating IRS (2019), '$975 billion of income was under-reported and $300 billion ... unpaid' (10.7% of true income); Table 1 (PDF p.42) top-1% share of unreported income 23.8% (MA-DCE) / 30.9% (benchmark); PDF p.5: top-1% rate 16%. GLRRZ revision Dec 22, 2025 (danreck.com): PDF p.41 'the top 1% income share ranges from 20.3% to 22.4% (21.3% under the benchmark ...)'; PDF p.38 top-1% misreporting 12.4% (DCE) / 17.1% (benchmark); PDF p.42 disputed share of recommended additional tax rises from 10-20% (bottom 90%) to >50% (top 0.01%). Guyton, Langetieg, Reck, Risch & Zucman, 'The Distribution of Undetected Under-Reported Income Identified by DCE Methods' (Nov 21, 2023): PDF p.10 newer DCE methods lower under-reporting 'from about 14% to 11% of true income'; Table 4b (PDF p.42): at common (DCE2019) aggregates the uniform-multiplier (DCE2001) allocation gives a top-1% share of 19.7% vs 20.6% for MA-DCE. Static check (scripts/static_checks.py, sec. 8): holding the top-1% share of unreported income at 31% and lowering the aggregate as in Dec 2023 reproduces the benchmark fall 21.75% -> 21.40% (actual 21.4%). Pass-through: GLRRZ NBER WP 28542 revised Dec 2023 PDF p.26: 51% of S-corp under-reporting vs 79% of reported S-corp income in the top 1%; GLRRZ revision Dec 22, 2025 (danreck.com) PDF pp.29-30 treats the S-corp distribution as the low end; Iselin & Reck (Dec 2025, PDF p.5): relative misreporting rate of 1 'is on the high end of the range of possibilities'; static effect of the S-corp concentration on the 2021 benchmark -0.32 pp.

Why this severity. The reply's bottom-line claim is about the size of the benchmark: that it is conservative. The authors' own later central estimate is about a third lower (+1.0 vs +1.5 pp), beyond the rubric's quarter threshold, and their range runs from 0 to +2.1 pp. The direction (accounting for evasion raises the top-1% share) and the rejection of a demonstrated inherent upward bias survive, so this is major rather than critical.

The authors' response. No erratum to the reply. Later versions concede the DCE criticism 'rightly identifies an important gap' (GLRRZ revision Dec 22, 2025 (danreck.com) PDF p.87), adopt IRS-2019-replicated aggregates and MA-DCE, report ranges, and maintain that 'a decrease is difficult to rationalize' (GLRRZ NBER WP 28542 revised Dec 2023 PDF p.43).

2moderateconfirmed · previously known · documentation gap

When an auditor simply moves income from one line of a tax form to another, nothing was really hidden. The method multiplies the increase but leaves the matching decrease alone, which can create extra 'hidden' income. The critics raised this, the reply did not answer, and the authors never documented how they handled it, so its size is unknown.

Technical detail and evidence

Why it matters, in detail. If offsetting corrections are not netted, DCE totals are inflated by roughly 2.3-2.4x the uncleaned offsets: about $35-110bn a year in aggregate on this back-of-envelope (some of which may be genuine over-reporting rather than switches). Because DCE income re-ranks heavy under-reporters upward, the top-1% share could also be affected; the direction and size are unknown.

Evidence. Auten & Splinter comment, May 5, 2021 version (the one answered) Sec. IV.3 (PDF p.13); Auten & Splinter comment, revised (cover 'August 15, 2021'; PDF created Nov 8, 2021) pp.5, 8, 15. Johns & Slemrod (2010) manuscript p.3 fn 3 and p.3 (about 45,000 sampled, 36,699 used, exclusions 'primarily due to data anomalies'). Reck, Risch & Zucman (Oct 22, 2021) response p.4 ('exactly like'). No mention of line switching in GLRRZ NBER WP 28542 (March 2021); GLRRZ NBER WP 28542 revised Dec 2023 PDF p.25 fn 36 and GLRRZ revision Dec 22, 2025 (danreck.com) mention it only for Form 1120-S line 19. Aggregate DCE ratio 3.91-3.95 vs 3.358 for most under-reporting; using GLRRZ fn 8 (under-reporters 4.5%, over-reporters 0.5% of true income), the blended multiplier needed is 3.59, implying ~$15-50bn of within-return offsets whose one-sided scaling adds ~$35-110bn (3-8%) to the $1,304bn DCE total (scripts/static_checks.py, sec. 3).

Why this severity. The mechanism is real and the critique went unanswered, but its size and incidence by income cannot be measured without the microdata. The back-of-envelope bound is a few percent of the DCE total, not enough on its own to overturn the benchmark.

3moderateconfirmed · newly identified here · selective presentation

The reply says it answers every point the critics made, but it skips several. One skipped point, that the IRS correction factors were out of date, turned out to matter most: when the authors later used the IRS's newer method, their estimate came down.

Technical detail and evidence

Why it matters, in detail. Replicating the official IRS (2019) DCE cut aggregate under-reported income by 25% and accounts for most of the later -0.4/-0.5 pp in the top-1% effect. If, as IRS (2008a) suggests, S-corps need no additional adjustment beyond NRP-DCE, much of the ~0.41 pp pass-through component (static) would go, since S-corps earn about two-thirds of pass-through income. The FY2010 choice did not drive the operational-audit result.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response p.1, p.21. Auten & Splinter comment, May 5, 2021 version (the one answered): pp.6-7 (IRS 2008a; outdated multipliers; fn 8 citing Bloomquist et al. 2012), p.11 fn 21 (pre-DCE sensitivity), p.12 (FY2010; tax vs income; 'unconvincing'), p.13 (Nordic 'only ten observations'; PSZ), p.14 (non-filers), p.9 (volatility). GLRRZ NBER WP 28542 (March 2021) PDF p.13 (FY2010 'the year with the highest total assessed tax'). Later: GLRRZ NBER WP 28542 revised Dec 2023 PDF p.11 uses a FY2007-13 average ($967m/yr; top 0.01% evaded >= 1.2% vs < 0.05% in NRP); Guyton, Langetieg, Reck, Risch & Zucman, 'The Distribution of Undetected Under-Reported Income Identified by DCE Methods' (Nov 21, 2023) PDF p.10 (newer DCE methods lower under-reporting from ~14% to ~11% of true income).

Why this severity. The reply's claim to have answered the critique in full is inaccurate. One unanswered point (outdated multipliers) later drove most of the authors' downward revision (F1), and another (IRS 2008a) directly undercuts the reply's conservatism argument. The operational-audit point was later accommodated with no change in conclusion, and the rest are small.

The authors' response. Operational-audit comparison later revised to a FY2007-13 average (Dec 2023 PDF p.11); other points not addressed.

4moderateplausible · previously known · methodology

To answer the critics, the authors re-ran their correction for hidden income several ways and said their original method was, if anything, slightly too low for the top 1%. One version pointed the other way, the test could not catch some ways the totals themselves might be inflated, and nobody outside the IRS can re-run it. The safer conclusion is that the direction of any error is unknown, as the authors themselves later wrote.

Technical detail and evidence

Why it matters, in detail. Whether the uniform multiplier over- or under-allocates to the top depends on the benchmark used. In the authors' later comparisons at common aggregates its top-1% share of under-reporting matches MA-DCE (24.4% vs 24.9%) but is far above the IRS's own DCE2019 simulation (15.3%), which shifts the DCE-step top-1% income share from about 19.1% to 18.1% (2008-13). The reply's sensitivity design cannot detect inflation of line totals: the Line-21 channel alone is worth up to about 0.5 pp on the DCE-only share (static upper bound).

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response pp.7-13, eqs. (1)-(5), fn 10. GLRRZ NBER WP 28542 (March 2021) Tables A1/A2/A5 (notes: Line-21 corrections 'typically disallowed loss carryforwards or carrybacks'): Line 21 total $39bn -> $179bn (x4.6); top 1% $3.1bn -> $76bn (x24), top-1% share of Line-21 under-reporting 8% -> 42%; top-1% under-reporting overall $37bn -> $321-341bn (x9) against multipliers <= 3.36. Static upper bound: dropping the whole Line-21 DCE increment lowers the DCE-only top-1% share 20.90% -> 20.43% (scripts/static_checks.py). Auten & Splinter comment, revised (cover 'August 15, 2021'; PDF created Nov 8, 2021) Sec. IV.5 (PDF p.15): line-by-line assumes separate auditor-skill distributions by income type. GLRRZ revision Dec 22, 2025 (danreck.com) PDF p.102 ('plainly unrealistic ... the extent and direction of the bias ... is ambiguous'); Guyton, Langetieg, Reck, Risch & Zucman, 'The Distribution of Undetected Under-Reported Income Identified by DCE Methods' (Nov 21, 2023) PDF p.32 ('we do not recommend using DCE2001'); PDF p.30 (2008-13): top-1% share of under-reporting 24.4% (DCE2001) vs 24.9% (MA-DCE) vs 15.3% (IRS DCE2019 micro-simulation).

Why this severity. It weakens the evidence for C2's strong claim (slight downward bias) but not its weak claim (no inherent upward bias). The weak claim is supported by theory and by the authors' later like-for-like comparisons. No quantified effect on the headline is demonstrated.

The authors' response. Later concessions: GLRRZ revision Dec 22, 2025 (danreck.com) PDF pp.87, 102; Guyton, Langetieg, Reck, Risch & Zucman, 'The Distribution of Undetected Under-Reported Income Identified by DCE Methods' (Nov 21, 2023) PDF p.32. No direct reply to the design points.

5minorconfirmed · newly identified here · methodology

The reply argued intuitively that the original method would, if anything, understate evasion at the top. Simple examples show the error can go either way, which fits the reply's broader point that the direction is unknown.

Technical detail and evidence

Why it matters, in detail. The sufficient-condition claim is false in general; the first counterexample relies on an unrealistically compressed income distribution. It undermines the reply's hint that downward bias is more likely, not its ambiguity conclusion.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response pp.5-6. Codex constructions, re-run in scripts/static_checks.py sec. 6 (multiplier 25/7). With incomes compressed (100-101) and uniform 20% evasion, the estimated top 1% is all thorough-audit cases, giving an estimated evasion rate of 47.2% vs 20% true (upward). With a true top 1% evading 90% and a compliant bottom 99%, the estimated rate is 26.1% vs 90% true (downward).

Why this severity. An intuition offered in an illustrative example, which the reply immediately hedges (p.6). The counterexamples reinforce its main conclusion that the sign is ambiguous.

6minorconfirmed · newly identified here · internal inconsistency

In one sentence the reply gives its own paper's main number as 0.9-1.2 points instead of 1.5. The figures it quotes are real but measure something narrower; nothing else in the reply rests on that sentence.

Technical detail and evidence

Why it matters, in detail. It understates the defended effect by 0.6 pp (40%) and reverses the paper's ordering (DCE raises the top share: +1.5 with vs +0.7 without). That obscures the DCE step to which AS attribute two-thirds of the effect.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response p.23. GLRRZ NBER WP 28542 (March 2021) PDF p.4 ('In our preferred estimates, the top 1% income share rises from 20.3% before audit to 21.8%'), PDF p.40 ('1.5 points more'; '0.6 percentage point' DCE only; '20.3% pre-audit to 21.0%' without DCE), Table 3: 21.8-20.9 = 0.9; 21.0-19.8 = 1.2. Auten & Splinter comment, May 5, 2021 version (the one answered) p.2 targets +1.5 pp.

Why this severity. A labelling error; the numbers are correct as increments and no analysis in the reply depends on the sentence.

7minorconfirmed · newly identified here · misrepresentation of source

The reply roughly doubles how much another study's top-1% income share rose since 1980. The mistake doesn't help the authors; the correct number makes their point slightly stronger.

Technical detail and evidence

Why it matters, in detail. The PSZ-AS trend gap is about 4.5-4.7 pp, not 13. The ~1 pp trend effect of AS's under-reporting allocation (Fig. 5) is then a larger share (about a fifth) of the divergence.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response p.24. PSZ2018MainData.xlsx (Dataverse and replication copies), sheet Data, col. BP 'Top 1% pre-tax share equal-split': 10.67% (1980) -> 20.20% (2014) = +9.53 pp; fiscal incl. KG +11.84; post-tax +7.10 (scripts/psz2018_trend_check.py). AS (2019) report 9.0 (PSZ) vs 4.8 (AS) pp for 1979-2014.

Why this severity. A supporting literature comparison; correcting it does not weaken, and slightly strengthens, the reply's point.

8minorconfirmed · newly identified here · misrepresentation of source

The reply says the national accounts adjust only two kinds of income for under-reporting. Corporate profits, including S corporations, are adjusted too, as the authors' own paper notes. The slip doesn't change the argument.

Technical detail and evidence

Why it matters, in detail. It weakens the reply's general claim that NIPA totals for non-proprietor income may not include misreporting, but the component that matters (S-corps) matches, so the NOL/definitional explanation of AS's excess stands.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response p.19, fn 16. BEA NIPA Handbook ch.13 (Dec 2024): Table 13.1 (corporate profits include 'S corporations'), Table 13.3 / NIPA Table 7.16 line 2 'Adjustment for misreporting on income tax returns' ($411.5bn in 2017), 'based on IRS audit data'. GLRRZ NBER WP 28542 (March 2021) PDF p.30 ('National Income and Product Accounts use a 20% income misreporting rate for C- and S-corporations combined'). Auten & Splinter comment, May 5, 2021 version (the one answered) p.6 ('$561 billion ... when averaging 2006-2013 (at 2012 dollars)').

Why this severity. The conclusion is unaffected: GLRRZ's S-corp under-reporting (~$81bn) roughly equals AS's NIPA comparator ($80bn), and the excess lies in Line 21, rental and 'other'.

9minorconfirmed · newly identified here · arithmetic or transcription

A back-of-envelope calculation in the reply is off by about a factor of two (5% should be about 8-10%). The amount involved is still small.

Technical detail and evidence

Why it matters, in detail. The illustrative upper bound on under-reporting misplaced at the bottom rises from 5% to 8-10% of pass-through under-reporting, or more in recession years; it is still modest relative to the benchmark.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response p.17; benchmark rate p.15. scripts/static_checks.py sec. 5 (2%/20% = 10%; 2%/25% = 8%; 1.67%/20% = 8% if the overstatement is relative to reported losses). Claude's SOI Table 1.4 check: no-AGI pass-through losses 11.7% of net income in non-recession years, 15.3% over 2006-13.

Why this severity. The bound roughly doubles but remains a small share of pass-through under-reporting.

10minorconfirmed · newly identified here · arithmetic or transcription

There are several small copying and wording mistakes, two of which say the opposite of what the authors meant. Readers can work out the intended meaning from context.

Technical detail and evidence

Why it matters, in detail. No effect on any estimate; two slips reverse the literal meaning of key summary sentences.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response pp.4, 9, 10, 13, 14, 18. Johns & Slemrod (2010) manuscript p.6 (4.158; 'Schedule C or Schedule F'; TPI >= $100,000). GLRRZ NBER WP 28542 (March 2021) PDF p.27 ('About 60%'; 'detected via an audit of an affiliated pass-through business in only 3.8% of cases').

Why this severity. Editing errors whose intended meaning is recoverable from context; no evidence that the code used the wrong values.

11minorlikely · newly identified here · overclaiming

The reply's discussion of economic theory lists only reasons the rich might evade more. It skips the obvious reason they might evade less: they were audited much more often during the period studied. This is argument, not calculation, so no number depends on it.

Technical detail and evidence

Why it matters, in detail. The section supports a prior, not an estimate. In the authors' own model high top audit rates push evasion toward undetected forms, so the omission is a matter of balance rather than a logical error.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response pp.22-23 ('at least recently, audit rates at the top ... are very low'). GLRRZ NBER WP 28542 (March 2021) abstract and PDF p.5 ('overall audit rates and scrutiny of tax returns are substantially higher at the top'); GLRRZ NBER WP 28542 revised Dec 2023 PDF p.11 (17% of the top 0.01% audited on average, FY2007-13).

Why this severity. Qualitative argument; no estimate depends on it.

12minorplausible · previously known · speculative assumption

The 19% figure the authors calculated from IRS audit data holds up. Calling 20% 'conservative' leans on hunches, such as conversations with practitioners. Still, even the critics' lower number would barely move the final result.

Technical detail and evidence

Why it matters, in detail. The rate is well grounded as a central value, not as a lower bound. Its leverage on the post-DCE benchmark is a net addition that falls ~70% (from $50bn to ~$15bn) at 15%, but only -0.18 pp on the top-1% share.

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response pp.15-16, fns 13-14. Johns (2009) slides: NMP = NMA / sum of absolute values; officer compensation NMA -$11bn (2003), -$12bn (2004), 'typically offset at shareholder level'. Auten & Splinter comment, revised (cover 'August 15, 2021'; PDF created Nov 8, 2021) fn 20: IRS (2008b) $40.9bn on $271.3bn = 15%; adding back ~$11.5bn gives 18.5-19.3% (reply: 18.5/19.4%). GLRRZ NBER WP 28542 revised Dec 2023 PDF p.26: 19.5%. Static (scripts/static_checks.py sec. 4): 15% -> -0.18 pp (exact u/(1-u) scaling; -0.15 linear), 12% -> -0.28 pp.

Why this severity. Even the critics' 15% moves the benchmark by under 0.2 pp, and the central 19-20% rate is later supported.

The authors' response. Later S-corp analysis estimates 19.5% (Dec 2023 PDF p.26); Dec 2025 keeps 20% as benchmark, 26% high end, 19.5% low end.

13minorplausible · previously known · overclaiming

The reply dismisses two critics' points about money hidden offshore more firmly than the evidence allows. Even if the critics are right, offshore money is a small part of the total effect.

Technical detail and evidence

Why it matters, in detail. Over-allocation of the global gap to US households via corporate or non-profit Cayman deposits, or a less concentrated distribution than the Nordic leaks, would lower the offshore component. Low-end offshore assumptions roughly halve it (Dec 2025 Table A10: +0.2 vs +0.4 pp without DCE).

Evidence. Reck, Risch & Zucman (Oct 22, 2021) response p.20, fn 18. GLRRZ NBER WP 28542 (March 2021) PDF pp.20-22 and Table 1 (equal weight on FBAR and Nordic distributions; lower-bound scenario already 85% concealed). Alstadsaeter, Johannesen & Zucman (2018) NBER w23805 pp.11-12: 'U.S. corporations may own the bulk of the bank deposits in the Cayman Islands ... we cannot quantify the size of the potential bias'; the US owns 33% of assets held outside Switzerland. Auten & Splinter comment, May 5, 2021 version (the one answered) p.12 fn 26 and p.13.

Why this severity. The offshore component adds only about +0.44 pp to the benchmark (static), and the reply's main offshore point (AS's concealment change is small, -0.07 pp at 80%) holds.

Claims examined and rejected

Problems one auditor raised that did not survive checking.

The authors' later fall in the benchmark top-1% effect (+1.5 -> +1.1/+1.0 pp) 'comes almost entirely from replacing the DCE allocation the response defended' (the uniform multiplier). — Not supported by the authors' own figures. Between versions the aggregate DCE-adjusted under-reported income fell 25% ($1,304bn -> $975bn, IRS-2019 replication) while the top 1%'s share of unreported income was essentially unchanged (benchmark 31.0% -> 30.9%; DCE-only 24.6% -> 23.8%). Holding that share fixed and lowering the aggregate reproduces the benchmark fall statically (21.75% -> 21.40% vs 21.4% actual). At common aggregates the uniform-multiplier (DCE2001) allocation gives a lower top-1% share than MA-DCE (19.7% vs 20.6%, DCE companion Table 4b). The overclaiming finding itself is upheld as F1, with the mechanism corrected.
Figure 5's increasingly negative correction need not imply changing compliance (a fixed-compliance two-group example with rising reported concentration yields a 0.81 pp decline), so the reply's inference is invalid (codex I4). — The counterexample does not fit the data. AS's series is positive from 1968-87 (1980s mean +0.13 pp) and negative from 1988 (2006-13 mean -0.84 pp) (scripts/as2019_fig5_check.py). In codex's own formula the sign of S-R equals the sign of uT-uB for any reported share, so a sign reversal cannot arise with fixed compliance and no re-ranking. The reply's inference is informal but matches later analysis showing AS's method implies a falling relative misreporting rate (Iselin & Reck 2025, co-authored by Reck and therefore not independent).
The reply mischaracterizes AS as not disputing the paper's first two findings (NRP random audits under-measure top-end evasion; pass-through and offshore evasion are missed). — AS's May-2021 abstract credits GLRRZ with 'an important contribution by bringing attention to limitations of NRP audits in discovering evasion from passthrough businesses and income from offshore assets' and calls such evasion 'a serious issue'. Their Sec. III.C disputes one supporting comparison (operational audits) while granting that 'there likely is unidentified passthrough business evasion'. The reply's characterization is fair; the unanswered operational-audit point is recorded under F4.
The 95% offshore concealment rate is inconsistent with Zucman's own 2015 figures (10% of offshore wealth declared in 2008, 20% in 2014). — Zucman (2015) refers to global offshore wealth. The 95% is justified by US Senate (2008, 2014) findings that 90-95% of US clients' Swiss-bank wealth was undeclared before FATCA (GLRRZ PDF p.20), and the lower-bound scenario already uses 85%. Moving to 90% or 80% changes the benchmark by only -0.02 to -0.07 pp, so the reply's point that AS's change is within the sensitivity range holds.
The heavy DCE re-ranking visible in the paper's tables (top-1% under-reporting x9; Line 21 x24) shows that the uniform multiplier over-allocated evasion to the top. — Partly rejected. The figures are correct and show how sensitive the top-1% estimates are, but re-ranking is inherent in any allocation that assigns undetected evasion to detected evaders and is not by itself a bias. At common aggregates the uniform multiplier's top-1% share of unreported income (25.1%) is essentially the authors' later benchmark (24.8%) (DCE companion Table 4b). The Line-21 channel is kept only as an example of what the reply's sensitivity design cannot test (F2).
Because the available critic PDF was created after the reply (Nov/Dec 2021), it cannot be established that the line-switching critique predated the reply. — The May 5, 2021 AS comment (Wayback capture 2021-05-14), the version the reply answers, already contains Sec. IV.3 'Line Switches and Income Shifting Across Years' (PDF p.13), so the omission is attributable to the reply (F3).
The response's low-p results with negative DCE adjustments are 'the ones behind downward bias'. — Overstated. The reply's 'downward bias' conclusion also rests on the two-step method (Fig. 3), whose handling of negative exam-corrected income is documented (fn 10), and the reply explicitly warns against relying on very low p. The eq.(5) concern is kept, in narrower form, under F2.

Audit notes

What reproduced. Reproduced from public documents: (i) the parent's Table 3 (20.3/19.8/20.9/21.0/21.8): the reply's 0.9 and 1.2 pp are increments from sophisticated evasion; total effects are +1.5 pp with DCE and +0.7 pp without. (ii) A static rebuild of the benchmark from Tables A2/A3/A5/A6 gives 21.75%: offshore +0.44 pp, pass-through +0.41 pp (AS said +0.3/+0.6). AS's 15% pass-through rate moves it -0.18 pp (exact u/(1-u) scaling; -0.15 linear), 80% concealment -0.07 pp, both together -0.25 pp (effect still +1.20 pp); the S-corp audit concentration -0.32 pp. (iii) AS's '99% to the top 1%' is a net figure: 70% of a $119bn gross addition minus 49% of a $70bn removal. (iv) Response Figure 5 from AS's 2020 workbook (C1-Incomes DM/DJ - DE/DB): 1980s mean +0.13 pp, sign change in 1988, 2006-13 mean -0.84 pp; the rendered figure matches. (v) PSZ (2018) top-1% pre-tax share +9.53 pp 1980-2014, not 18. (vi) S-corp rate 18.5-19.3% from IRS (2008b) aggregates quoted by AS plus Johns (2009) officer-compensation corrections, vs the reply's 18.5/19.4%. (vii) Loss bound 8-10%, not 5%. (viii) Codex's counterexamples (47.2% vs 20%; 26.1% vs 90%). (ix) Johns & Slemrod multipliers (4.158); NIPA's corporate misreporting adjustment; Johannesen et al. ~$100bn of ~$1,000bn (~10%). (x) Later-version figures, plus a static calculation showing that a 25% smaller aggregate, with the top-1% share of unreported income held fixed, reproduces the benchmark's fall to 21.4%. Not reproducible: the reply's Figs. 1-4, the 14%/1.2% sole-proprietor loss shares, the exact 19%, and '>65%' (confidential NRP/S-corp microdata; no code released).

Limits of this audit. The reply's new analyses use confidential IRS microdata and could not be re-run. All quantifications here are static re-aggregations of published tables that ignore further re-ranking. Comparisons with later versions mix new data (IRS-2019 simulations, S-corp audit microdata) and new methods (MA-DCE), so the decomposition of the later decline is approximate. The DCE companion paper does not say explicitly how its DCE2001 column is scaled, and the DCE2001 column of the Dec-2023 appendix Table A13 appears mis-populated (it repeats under-reporting shares), so it was not used. The March-2021 Tables 2 and A2 disagree by about $20bn on top-1% DCE under-reporting. AS's revised comment cites a July 21, 2021 version of this reply that could not be located (Wayback captures start in Feb 2022 and redirect to the Oct 22 file), so the audited version may differ from the one AS rebutted. IRS (2008a,b), Auten & Langetieg (2020) and Auten et al. (2020) are not public and are known only through AS's quotations. Iselin & Reck (2025), cited as corroboration, is co-authored by one of the reply's authors and is not independent.