Contribution Ceilings and the Incidence of Payroll Taxes

Why it matters, in detail. Mapping the published intervals through the paper's own identity (left-normalised f+/f- = A+/A-, A = 1+(1-sr)tr-se*te) gives the following. UK 1975-85: s in [0.37, 1.00] (sr >= 0.60 if se = 0). UK 1986-2007: s in [0, 0.60]. Germany: s about 0.38-0.72 across periods, with 1975-79 rejecting 0.50 at p<0.01. France: the NLS se is unidentified (intervals spanning about -4.5 to +2.7). Against this, the Dutch health threshold bounds sr >= 0.84-0.88, and France's SST rejects sr near 0 by a wide margin. The significant departures (France SST, Germany 1975-79, UK McCrary 1986-2007) are positive, i.e. towards employers bearing more than statutory. So the error lies in the claimed precision, not in the rejection of the textbook model.

Evidence. UK (Adam, Roantree & Phillips 2017, Table 2, p.193). 1975-85 estimate 0.027 [-0.044, 0.097]: admits a common employer share s in [0.37, 1.00] (statutory-equivalent 0.61) and does not reject full employer incidence (+0.079). 1986-2007 [-0.086, 0.059]: admits s in [0, 0.60]. The authors write 'a lack of statistical power means ... our results taken alone are also consistent with a wide range of less extreme incidence shares' (abstract) and 'we are wary of drawing strong conclusions' (p.195). Germany (DIW DP 1627, Tab. 1-3, p.9), with one-sided benchmarks of about -0.048/+0.066 for 1975-79 rather than the +/-0.112 (total rate drop) the paper uses. 1975-79 estimates are +0.026 (t=3.00) and +0.020 (t=2.65), with t = 2.65-3.37 in all 12 variants: s = 0.67-0.72 [95% about 0.55-0.84] against statutory 0.50. 2005-10 polynomial -0.014: s = 0.38 [0.26, 0.50]. France (Bozio, Breda & Grenet 2017, Table 4, p.160): NLS sr intervals run from [0.06, 1.92] to [0.60, 2.04]; se ranges from +0.61 to -1.83 (method 2.B interval [-3.55, -0.11], outside [0,1]); rate-drop correlation 0.95 (p.161). Evidence on the paper's side, found by the adjudicator: the Dutch health threshold is an employer-only kink with log discontinuity -0.0004 (0.0049) in 2006 and +0.0016 (0.0053) in 2011, against full-worker predictions of -0.056/-0.067 (CPB DP 311, Tables 9-10, p.29), so the employer share is at least 0.84-0.88. France's 1976 SST full-worker predictions are -0.20/-0.18, against SST means of +0.03 to +0.04 (Table 3, p.158). Computations: scripts/adj02_companion_tables.py.

Why this severity. The qualitative core survives: employer SSCs are not shifted to the individual worker at the ceilings in the short run, contrary to the textbook prediction. It is tightly estimated where the tests are most powerful (the Dutch health threshold, with employer share >=0.84-0.88, and France's early SST kinks). What fails is the precise 'coincide' reading and the 'extremely unlikely coincidence' argument. Elsewhere the intervals admit employer shares from about 0.4-0.6 up to 1, the employee side is unidentified, and Germany 1975-79 departs significantly. This overstates precision without reversing anything, so it is moderate, not major.

The authors' response. No published response found. The overview hedges ('suggesting', 'seems', 'consistent with'), and the UK paper advises interpreting its results 'in conjunction with the others in this volume' (p.195).

Why it matters, in detail. The French excess rejections are concentrated at the SST (11/64 polynomial rejections vs 3/64 at the placebo), so they are not just over-rejection by the testing procedure. They are mostly positive, implying sr>1 or se>0 locally. The German endpoint departures correspond to roughly +/-15-20pp in the employer share of the total health contribution. The UK rejection of full worker incidence is specification-dependent. Together they turn 'no discontinuity anywhere' into 'no systematic negative discontinuity of the size worker incidence implies, with scattered (mostly positive) departures'.

Evidence. France (Bozio et al. 2017). Table 2 Panel A (p.156): 16.2%, 17.1%, 9.4% and 8.9% significant at 5% for 1976-2010 (31/191, 30/175, 18/192, 17/192). The text says 'between 9 and 17% ... two to five times more often positive than negative' (p.157); only observed earnings for 1993-2010 approach 5% (10.2/9.8/7.4/5.3%). At the SST (Table 3, p.158) the rates are 25.0/28.1/17.2/17.2%, against 4.7/9.4/4.7/4.7% at the 2xSST placebo (Fisher one-sided p = 0.001-0.022). The paper also reports 'more significantly positive kinks at 1*SST' (p.157) and a McCrary time trend (p.160). Germany (DIW DP 1627, Tab. 1-3): 1975-79 is significantly positive in all 12 variants. The 'slight trend' is judged against the total rate drop (pp.9-10), twice the one-sided benchmark; re-benchmarked, the implied employer share falls from about 0.70 (1975-79) to about 0.38 (2005-10). UK (Adam et al. 2017): the overview drops 'in some cases' and the power caveat. Full worker incidence in 1975-85 is rejected in the preferred quadratic. With the current-year UEL it is not rejected at polynomial orders 3-8 against the Table-1-implied benchmark (-0.094 to -0.104), nor at orders 6 and 8 against the paper's own -0.115 (Table 3); with the previous-year UEL it is rejected at all orders (Table 6). The +/-GBP200 windows reject smoothness with opposite signs (+0.056 [0.001, 0.111], Table 5; -0.081 [-0.123, -0.038], Table 8). Annual McCrary tests are significant in 24 of 33 years (11 positive, 13 negative; Table 10), and annual polynomial estimates in 2001 and 2007 (Table 9). Computations: scripts/adj02_companion_tables.py.

Why this severity. No point estimate changes, and the exceptions do not point towards worker incidence: most significant French and German departures are positive. But the overview presents as uniformly null an evidence base that its sources call noisy, specification-sensitive and in places significantly non-zero. That is an important undisclosed caveat on the empirical synthesis the conclusions rest on.

The authors' response. None published. The overview's summaries follow each companion's own concluding sentence; Bozio et al. attribute the excess rejections to a common, non-optimal polynomial order (fn 8, p.157), and Adam et al. discount McCrary rejections as local spikes (pp.193-194).

Why it matters, in detail. A null dip identifies the realised local response under existing frictions, not the structural elasticity. With isoelastic preferences a gap of width about e*dlog(1-t) is predicted, so finding none is compatible with e = 0.2-0.3 (Adam, Phillips & Roantree 2019) and fixed adjustment costs well under 1% of the cap. In France the hours margin is shut by design, so the French evidence says nothing about hours elasticities.

Evidence. Adam et al. (2017, pp.182 and 195): no dip 'either because the underlying elasticities are very low or because optimisation frictions (whether informational, institutional or driven by adjustment costs) are significant'; footnote 11 (p.188): SERPS accrual makes the true kink smaller. Adam, Phillips & Roantree (NBER w23336, 2017; J. Public Econ. 171:29-50, 2019) estimate a compensated elasticity with respect to employee NICs of 'about 0.2-0.3, operating largely through hours of work'. Bozio et al. (2017, pp.143, 145, 154): the SST is computed on hourly wages, so hours responses cannot move workers across it. A frictionless model (scripts/adj01_identities_dip.py) with e = 0.25 at the UK employee kink (9.6% to 0) implies an empty band of 2.5% of the UEL (about GBP16/week); e = 0.05 gives about GBP3. With s1 = 0.8 and e = 0.2 the gap is 4.5% of the cap, yet a fixed cost of 0.5% of the cap suppresses all adjustment (maximum gain 0.0048 cap units). Chetty et al. (2011) provide the general friction mechanism.

Why this severity. This is a stated secondary conclusion that does not follow from the evidence and is contradicted by the same UK team's reform-based elasticity. It does not affect the incidence test, which needs only the absence of local behavioural responses.

The authors' response. The overview uses 'suggesting'. Its Sect. 5 discusses information costs and rigidities as reasons for statutory incidence, but not as an alternative explanation for the missing dip.

Why it matters, in detail. Smoothness at annually re-indexed kinks identifies short-run, individual-level non-adjustment of gross wages to marginal-rate changes. That is compatible with the standard model plus wage-setting frictions, or with near-zero local elasticities. It says nothing about firm-level pass-through (Saez, Schoefer & Seim 2019) or medium-run adjustment. If workers value the linked benefits, the standard model predicts full shifting whatever the elasticities. The French reform evidence finds pass-through of about 1 within four years of the ARRCO reform's completion, versus 6-21% for unlinked reforms. Where linked contributions dominate (French 3x, 4x and 8xSST), the kink test has no power.

Evidence. Bozio et al. (2017, p.161): kink results 'identify incidence in a very local sense ... may therefore not be extrapolated to more general and steady-state environments'; the lack of adjustment 'may also be in part explained by adjustment frictions, especially because the location of the kinks changes every year'; the findings are 'consistent with both labour demand and labour supply being very inelastic at kink points'. Adam et al. (2017, p.182): 'All we attempt to discern in this paper is how an individual's wage is affected by the tax rate applied to that individual's earnings'. Bozio, Breda & Grenet, 'Does Tax-Benefit Linkage Matter for the Incidence of Payroll Taxes?', Review of Economic Studies 93(3):1536-1573 (online 2025), abstract: 'full pass-through to workers when there is a strong and transparent link between contributions and expected benefits', but limited pass-through for unlinked employer contributions. The working-paper version (PSE WP 2019-43, July 2020, pp.5, 23-24) reports ARRCO 1996-reform pass-through 'very close to and not significantly different from 1 in the four years following the completion of the reform', and a meta-analysis averaging 103% pass-through for linked contributions vs 15% for unlinked. French kinks above the SST are dominated by such point-based pensions: in 2010, 12.0 of the 13.3pp drop at 3xSST is ARRCO and 12.6 of 12.8pp at 8xSST is AGIRC (Bozio et al. Table 1). The polynomial test at 8xSST carries no information: under smooth Pareto tails it shows a spurious -0.07 to -0.47, against a true full-worker step of -0.09 (scripts/adj03_poly_bias.py). Saez, Schoefer & Seim (2019, AER 109:1717-1763) find no individual-level shifting of a Swedish youth payroll-tax cut but firm-level rent sharing, which the kink test cannot see.

Why this severity. The long-run, all-SSC claim is a hedged closing argument rather than an estimated result, and later evidence supports the local result for unlinked contributions. But the generalisation is not supported by the kink evidence, and it is contradicted for benefit-linked contributions, which are a large share of SSCs in France and the Netherlands. It narrows the scope of C4 without overturning it.

The authors' response. The overview itself flags general-equilibrium and long-run doubts (p.138) and hedges ('may not be sufficient'). Bozio, Breda & Grenet (2025) conclude that 'in the absence of such linkage ... the individual-level incidence of payroll taxes aligns with their statutory incidence', which supports the overview for unlinked contributions.

Why it matters, in detail. At an employee-only kink, smooth g requires eS/eD = dtR/dtE = 0, which is approximately the textbook case; the test has about 7% power against eS=0.1, eD=0.5. It can only reject full employer incidence (+0.107), which it does.

Evidence. Adam et al. (2017): Table 1 (employer NICs uncapped from October 1985); p.190 ('the densities of gross earnings and employer cost will move in tandem'); p.191 (smoothness 'would imply employees bearing all of the incidence'). scripts/adj01_identities_dip.py: with tR unchanged, f+/f- = 1 and h+/h- = (1-tE-)/(1-tE+) = 0.899 at 2003-07 rates. scripts/adj02_companion_tables.py: textbook elasticities (eS=0.1, eD=0.5) predict +0.015 for 1986-2007, inside the interval [-0.086, 0.059]; the test's power against the textbook model is 0.07.

Why this severity. The general statements are wrong for the UK's dominant period (22 of 33 years), which therefore provides no evidence against the textbook model. But the case against the standard model rests on employer-rate kinks (France, Germany, the Netherlands, UK 1975-85), so the conclusions are unaffected.

Why it matters, in detail. The federal payroll marginal rate falls by 12.4pp at the OASDI base, from 15.3% to 2.9%, not from 12.4% to 0. This changes the description of the kink, not its size.

Evidence. SSA Office of the Chief Actuary tables, archived January 2024: the 2015 contribution and benefit base is $118,500; OASDI is 6.2% each for employee and employer; HI is 1.45% each, and 'After 1993, there has been no limitation on HI-taxable earnings'. Codex cites IRS Publication 15 (2015) for the same figures. The combined FICA marginal rate is 15.3% below the cap and 2.9% just above it (3.8% above $200k). Computation: scripts/adj02_companion_tables.py.

Why this severity. An illustrative example only: the OASDI cap and rate are right, and the kink exists either way.

Why it matters, in detail. The US 'no gap' evidence comes from Liebman & Saez (2006, matched SIPP-SSA earnings), not from the cited works. The proportionality of the gap to the elasticity is true (adj01: gap about e*dlog(1-t)) but is not derived in Saez (2010).

Evidence. Liebman, Luttmer & Seif (2009), J. Public Econ. 93: fn 20, p.1217 ('All earnings are topcoded at the Social Security maximum'); its records run 'up to the Social Security contribution ceiling'. Saez (2010), AEJ: Economic Policy 2(3), p.192. Liebman & Saez (2006), NBER RRC NB04-06, Sect. 4: 'There is no gap whatsoever ... The distribution is completely smooth around the kink point'.

Why this severity. A citation error; the substantive claim (no gap at the US taxable maximum) is true.

Why it matters, in detail. The (1+tR) multiplier is missing; with tR = 0.15 the printed equality is off by 15% of f(z*). No later calculation uses it.

Evidence. scripts/adj01_identities_dip.py: with tR = 0.15, g(y*)- = (1+tR)g(y*)+ = 0.7673 while f(z*) = 0.6672 and (1+tR)f(z*) = 0.7673. Both auditors' scripts give the same result.

Why this severity. Typographical: Eq. (2) and the stated jump factor are correct.

Why it matters, in detail. These are inversions in the prose only; no reported significance decision is reversed.

Evidence. McCrary (2006 working paper, p.1): 'Wald test of the null hypothesis that the discontinuity is zero'. Bozio et al. (2017, p.155) and Adam et al. (2017, pp.191-193) regress density on the polynomial and test for a non-zero dummy. The inverted McCrary wording recurs verbatim in Adam et al. (p.191). UK bandwidths: Tables 2 and 10.

Why this severity. Wording slips: the companion papers use the correct null and regression direction.

Why it matters, in detail. Bibliographic and typographical errors only.

Evidence. Crossref metadata for doi:10.1007/s10645-017-9298-3 (authors Kai-Uwe Mueller and Michael Neumann); overview pp.130-139.

Why this severity. Copy-editing only; no effect on content.

Why it matters, in detail. Classical multiplicative error of SD sigma relative to the base smears a step over roughly +/-2 sigma around y*, attenuating polynomial-dummy estimates. If a share p of observations faces another year's threshold, the step is scaled by (1-p). Both biases push towards 0, i.e. towards statutory incidence. At 8xSST, misspecification biases the step negatively and swamps the signal (Table 3 Panel B: SD 0.26-0.47). So the high French kinks, where the benefit-linked pension contributions sit, are uninformative.

Evidence. France: gross earnings before 1993 are calculated from net taxable earnings using TAXIPP; after 1993 the observed variable is the CSG base, 'close but not exactly the same' as the SSC base (Bozio et al. fn 3, p.149; p.151). UK: pay periods straddle the 6 April change, so 'we cannot be certain which fiscal year's NICs schedule applies' (pp.187-188), and some benefits in kind are missing (fn 9). Netherlands (CPB DP 311, 2015): 'even minor measurement errors can mask any discontinuity' (p.44), for labour costs whose thresholds vary across workers. scripts/adj03_poly_bias.py: under a smooth Pareto tail, the cubic step fit over [4.1, 11.9]xSST shows a spurious -0.07 to -0.47 (alpha = 1.5-3), against a true full-worker step of -0.09; the bias at SST, 2x, 3x and 4xSST is <= 0.02. Mitigating evidence: in France, calculated and observed earnings give similar results for 1993-2010 (p.157). In the UK, previous-year-UEL estimates are similar (Tables 6-8), and the 1975-85 rejection of full worker incidence survives misassignment of up to about 57% of observations (adj02). Germany's SIAB earnings are the administrative SSC base. Dutch gross earnings are the employer-reported base (published notes), and observed partial labour costs do jump (+0.039, +0.114; CPB DP 311 Table 14).

Why this severity. The concern is valid in principle and biases towards the paper's preferred conclusion. But the companions' robustness checks and the exact administrative bases in Germany and the Netherlands leave the decisive tests unaffected. Its main effect is to weaken 'cannot reject smoothness' at small or high kinks, which F1 already covers.

The authors' response. The companion papers report the robustness checks listed in the evidence.

Why it matters, in detail. If the overview's local statutory-incidence result held in aggregate, employer payroll taxes would partly fall on profits rather than labour in DINA post-tax series. A reconciliation is plausible: linked contributions are fully shifted (Bozio, Breda & Grenet 2025), and sharing happens at firm level (Saez, Schoefer & Seim 2019). But the authors do not state it.

Evidence. Piketty, Saez & Zucman (2018) Data Appendix B.4.1; NBER w22945, p.14. Overview p.130 ('as we expect labour demand to be substantially more elastic than labour supply (Hamermesh 1993), the incidence of these taxes should be borne primarily by workers') and pp.136-139. CORPUS us-wealth-taxes-13 (Kopczuk 2019 BPEA comment and others) criticises Saez-Zucman for treating the corporate tax by statutory incidence but payroll taxes as borne entirely by workers.

Why this severity. No bearing on this paper's results. The two conventions can be reconciled: aggregate factor incidence differs from the individual employer/employee split, US OASDI contributions are benefit-linked, and costs can be passed through at firm level. The tension is simply never discussed.

The authors' response. Saez and Zucman defend assigning current taxes to the factor taxed without behavioural responses (Oct 2019 draft 'Clarifying Distributional Tax Incidence'; NBER w31912), as summarised in corpus entry us-wealth-taxes-13. Nothing specific to this paper.