Taxation and International Migration of Superstars: Evidence from the European Football Market

Why it matters, in detail. Identification of alpha in columns 2-6 comes essentially from one persistent within-country-year contrast in the Netherlands. With destination-specific home bias it rests solely on the undocumented top-only eligibility rule. Within-country estimates of the foreign elasticity therefore range from about 0 to 1.1 across defensible specifications, rather than being pinned at about 1. The cross-sectional column 1 (alpha 1.26-1.32 without NL or with the VAT fix; 0.88 with home x destination dummies) is robust, but the paper itself calls it weakly identified.

Evidence. Adjudicator re-estimation with an independent conditional-logit estimator that reproduces Table 2 exactly (scripts/robust_t2.py, misc_checks.py, nl_ddd_check.py, nl_pattern.py; results/robust_t2.json etc.). Column 3 alpha 1.089 (0.159) -> -0.052 (0.170) when the Dutch alternative and its choosers are dropped (valid under IIA); 0.278 (0.155) when Dutch foreigners get the Dutch local rate. Column 2 0.729 (0.116) -> 0.242 (0.117) / 0.312. With home x destination dummies: column 3 1.119 (0.244); without the Netherlands -0.042 (0.288); with the Dutch ruling extended to all foreigners 0.384 (0.236); column 2 with home x destination 0.641 (0.143), without NL 0.365 (0.150). Removing other regimes from column 3: Spain 1.121, Belgium 0.890, Denmark 2.242. Tax-coding tabulation (tax_coding_audit.py): Dutch-alternative rows of foreign 'top' players carry 0.390 (1996-2000)/0.364 (2001-08), non-top foreigners the Dutch local rate, in every year. Descriptive pattern: top Dutch players play at home 66.8% vs 91.7% for other Dutch players; foreign top players choose the Netherlands at 23.3 per 1,000 vs 11.4 for other foreigners (Belgium 6.1 vs 11.0). These numbers match Auditor A's.

Why this severity. Under defensible variations that drop or recode one country, the paper's preferred 'pure supply' estimate (column 3, foreign elasticity 1.06) and the column 2 estimate (0.70) fall to roughly 0-0.4. The foreign-player response is still supported by the cross-sectional, case-study and external evidence, so the core finding loses its precise magnitude but is not overturned.

The authors' response. None located. The paper describes column 3 as exemplified by the Beckham, Danish-duration and Greek rules (p.1919) and does not discuss the Dutch regime's role or eligibility rule.

Why it matters, in detail. The domestic elasticity is not separately identified in the published specification. Relaxing the common alpha, which the data reject, cuts the controlled domestic elasticity by 43-69% (0.074 -> 0.023; 0.111 -> 0.064), while foreign elasticities stay at about 0.9-1.2. A lower domestic elasticity would raise, not lower, the uniform Laffer rates in Table A3.

Evidence. Adjudicator (robust_t2.py): column 2 alpha_home 0.215 (0.169), alpha_foreign 0.928 (0.129) -> eps_d 0.023, eps_f 0.895; column 3 alpha_home 0.617 (0.205), alpha_foreign 1.241 (0.169) -> eps_d 0.071, eps_f 1.204, difference 0.624 (0.196). Auditor B (four quality groups): eps_d 0.064, difference 0.592 (0.195), p = 0.0024; no fixed effects eps_d 0.176. The published MTR columns 2-6 already give 0.070-0.121; only column 1 (0.156) and three of the six ATR columns (0.18-0.19) reach 0.15. Kleven, Landais, Munoz & Stantcheva (2020, JEP 34(2), Table 1) list this paper's preferred elasticities as 'Foreigners = 1, Domestics = 0.15'.

Why this severity. The abstract's domestic magnitude is 50-85% above the within-country estimates once the restriction is relaxed. Only the cross-sectional specification, which the paper calls weakly identified, supports 0.15. The qualitative 'domestic much smaller than foreign' contrast survives.

The authors' response. The paper notes that eps_domestic ~ alpha/10 'is a consequence of the multinomial specification but it is fully consistent with the basic findings from Figure 1' (p.1918). The authors' 2020 JEP survey (Kleven, Landais, Munoz & Stantcheva) restates 0.15.

Why it matters, in detail. The low-quality coefficient ranges from -1.01 to +0.95 across home-bias specifications and is non-negative whenever home bias may vary by quality. Table 3 therefore does not discriminate rigid from flexible demand; it is consistent with flexible demand plus heterogeneous mobility. The rigid-demand Laffer calculations that use these coefficients inherit the fragility.

Evidence. Adjudicator (table3_repro.py, table3_extra.py, case_studies.py). Top-league sample, column 4: low -0.391 (0.158) -> +0.578 (0.203) with domestic x high-quality, whose coefficient is -0.887 (0.063), t = 14. Column 5: -0.448 (0.154) -> +0.510 (0.199). Sample with second leagues, column 5: -0.529 (0.145) -> +0.196 (0.190). With home x destination and home x quality dummies, column 4: low +0.446 (0.224), top 0.875 (0.161). With home x destination x quality: low +0.947 (0.252), top 0.789 (0.164). With home x destination only: low -0.588 (0.185). Danish lower-quality DD: counts -0.697 (0.542), shares +0.062 (0.541), log shares +0.678 (1.045). Auditor A's numbers match.

Why this severity. The sign of the bottom-of-distribution response is the paper's test for rigid versus flexible demand. It reverses under a natural, data-preferred generalisation. Only 'larger at the top' survives, and even that disappears with fully flexible home bias.

The authors' response. None located; the text calls Table 3 'strong evidence of ability sorting' (p.1921).

Why it matters, in detail. The cross-tax coefficient is identified off persistent cross-country differences in natives' home shares and off the Netherlands; its sign and size are not robust. The selective foreigner Laffer rate (equation A8), built on it, inherits the fragility. Spain's Figure A5 is descriptive and cannot separate displacement from trends.

Evidence. Adjudicator (table3_repro.py, table3_extra.py). Top-league column 5: -0.635 (0.134) -> -0.022 (0.148) without the Dutch alternative. Sample with second leagues: -0.618 (0.119) -> +0.166 (0.125). With home x destination dummies: -0.335 (0.161), and log(1-tau_d) x foreign +0.644 (0.292). With home x destination and without NL: -0.140 (0.194) and +1.061 (0.325). With home x destination and home x quality: -0.354 (0.160) and +0.565 (0.288). The no-NL top-league number matches Auditor A (-0.021).

Why this severity. The abstract's displacement finding does not survive dropping one country, and the companion cross-effect takes the wrong sign under destination-specific home bias. What remains is a halved, marginally significant coefficient.

The authors' response. Footnote 38 acknowledges limited power for the cross-effect of tau_d; no other response located.

Why it matters, in detail. The error sits in the key regressor of the one country that identifies column 3, and biases alpha upward by about 25% (1.089 vs 0.870). It also falsifies the appendix's argument that VAT is 'fully controlled for' by country x year fixed effects: as coded, VAT creates spurious within-country-year variation in exactly that country.

Evidence. mtr.dta and the estimation file (tax_coding_audit.py, atr_cpi_checks.py); NBER WP 16545 Table 4 vs AER Table A3. Adjudicator recomputation with VAT added to the Dutch foreigner rate (robust_t2.py): column 3 alpha 1.089 -> 0.870 (0.155), eps_f 1.057 -> 0.844, eps_d 0.121 -> 0.096; column 2 0.729 -> 0.608 (0.116); column 1 1.323 -> 1.294. Combined with the Norwegian recode (F9): column 3 0.659 (0.165), eps_f 0.640; column 2 0.478 (0.116). Auditor A obtained the same VAT-only numbers.

Why this severity. On its own the correction lowers the within-country alpha by 17-20% (foreign elasticity 1.06 -> 0.84). That is noticeable but not transformative. Together with F9 the reduction is about 35-40%, compounding F1.

The authors' response. Appendix A.1 (pp.39-40) states that including VAT or not 'does not significantly impact our findings' because VAT is national and absorbed by country x year fixed effects; this is contradicted by the actual coding. No other response located.

Why it matters, in detail. The implementation errors bias the rigid-demand uniform rate up by about 11 points and the flexible rate down by about 5 points. The selective rates mix model elasticities and are truncated by an arbitrary cap. These calibrations are local (2008 probabilities) and also inherit F3-F5.

Evidence. Adjudicator (laffer_repro.py) reproduces all 42 Table A3 entries (country means .813/.947/.724). With expected-wage-bill weights the flexible uniform mean is 0.863 (e.g. Norway .747 -> .866, Denmark .741 -> .848). With group sums, the rigid uniform mean is 0.835. The rigid rate is then below the flexible rate in 6 of 14 countries against the coded flexible rates, and in 11 of 14 against corrected ones; the mean gap is -2.8 points instead of the published +13.4. Without the cap, the selective mean is 0.772, with France 1.187 and Sweden 1.018 (rates above 100%). Using the rigid model's own foreign elasticity, the selective mean is 0.58 (capped) / 0.62 (uncapped). Auditor B's figures (86.3%, 82.9%, 64.2%) agree. Auditor A's statement that error (a) 'has little numerical effect' is incorrect.

Why this severity. This is a secondary (appendix and conclusion) result. The message that uniform Laffer rates are high (about 83-86%) survives. The second of the three stated policy findings ('even higher under rigid demand') reverses, and selective foreigner rates move by up to 15-20 points.

Why it matters, in detail. The reported elasticities are not estimates of the documented equation. The Spanish DD falls by 35-50% with a post-Bosman pre-period and is driven largely by the Italian donor's 2004-07 decline. Conventional standard errors on about 38 country-year observations overstate precision.

Evidence. Adjudicator (case_studies.py, published Table A2 weights). The code estimator reproduces Spain top 1.489, low 1.426, eligible 1.290 and Denmark top 3.013, low -0.697. Documented log-share specification: Spain top 2.246 (0.897), Denmark top 5.484 (2.040), Denmark low +0.678 (1.045). Shares in levels: Spain top 1.403, Denmark low +0.062. With a post-Bosman pre-period (1996-2003): Spain top 0.953 (0.308) for counts, 0.748 (0.357) for shares; eligible 0.891 (0.213). Spain's top-foreigner share averaged 8.5% in 1996-2003 and 8.4% in 2004-08 (but rose from 5.9% in 2003 to 10.2% in 2007), while synthetic Spain (78% Italy) fell from 7.0% to 4.4%. Auditor A also reports, not re-run here, that in a placebo-in-space exercise Spain ranks 7th of 14 on the post/pre MSPE ratio.

Why this severity. The positive top-quality responses in Spain and Denmark survive every variant, but the Spanish magnitude ranges from 0.75 to 2.25, and the Danish low-quality sign, used as sorting evidence, depends on the estimator.

The authors' response. Footnote 26 discusses relaxing parallel trends; footnote 25 justifies 2004 as the Spanish reform year. No response on the estimator located.

Why it matters, in detail. A 2.75-fold change of the same estimand across versions, partly traceable to a coding change in the identifying country, is consistent with the specification sensitivity shown in F1. The dropped random-parameters logit was 35% below its baseline in the working paper.

Evidence. NBER WP Table 1 (PDF p.57), Table 2 col 4 and Table 4 (PDF p.60; Netherlands .466) vs AER Table 2 and Table A3 (.364). Auditor B shows that dropping the AER wage-match filters (back to 61,834 cases) barely changes column 2 (0.751), so the sample change is not the explanation. Auditor A reports that correcting four AER coding issues gives column 3 0.472; NBER-era data are unavailable, so the change cannot be decomposed.

Why this severity. Working-paper revisions are normal and the AER is authoritative. But the preferred coefficient nearly tripled without explanation, and the one identifiable change (Dutch VAT) introduces an error, which signals the same fragility as F1-F2.

Why it matters, in detail. Standard errors are 2.5-6.4 times larger depending on the construction, and permutation p-values for columns 2-3 are about 0.07-0.10 (two-sided). The paper's language ('compelling', 'conclusive', 'strongly significant') overstates the precision of the within-country multinomial evidence.

Evidence. Adjudicator (inference_check.py). Column 2: SE player 0.116; nationality 0.289; destination 0.420 (fully partialled score split) or 0.627 (Auditor A's hybrid split, reproduced). Column 3: 0.159; 0.539; 0.767 or 1.012. Column 1: 0.073; 0.286; 0.322. The column 3 t-statistic falls from 6.9 to 1.1-2.0; column 1's stays at about 4. Auditor A, not re-run here: permutation SD 0.39 for column 2 (two-sided p = 0.10) and 0.76 for column 3 (p = 0.07; one-sided 0.03); in a Monte Carlo with destination shocks, player-clustered SEs reject a true null 52% of the time. None of these 14-cluster methods is exact.

Why this severity. Point estimates are unchanged, and the cross-sectional and Danish top-quality evidence remain statistically strong. But the 'strongly significant' within-country estimates and the sorting/displacement coefficients become marginal under defensible inference, compounding F1.

The authors' response. None located. The paper says serial correlation is handled 'by clustering standard errors by player' (p.1919).

Why it matters, in detail. Treating a large nationality group as facing no tax differences shrinks identifying variation in an undocumented way. The direction of the bias depends on true liability: if Norwegians abroad actually face destination rates, the published alpha is too high by about 20%.

Evidence. Adjudicator tax-coding tabulation (tax_coding_audit.py): foreign-alternative rows of Norwegian players are at Norway's rate (mean 0.6655) in all 13 destinations. Recoding Norwegians to the rates of other foreigners in the same destination, year and top status (robust_t2.py): column 3 1.089 -> 0.913 (0.169), column 2 0.729 -> 0.598. Combined with the Dutch VAT fix: 0.659 and 0.478. Auditor A reports similar values (0.893/0.587) and an authors' Stata log note that 4,051 cases of mtr2 are 'not alternative-specific'.

Why this severity. The recode lowers the within-country alpha by 16-18% (35-40% together with F2). Whether the rule is an error depends on Norwegian residual tax liability of emigrants, which was not verified.

Why it matters, in detail. The misattribution does not change the coefficients the paper relies on; it changes which sample supports which statement and shows that the 'second-league' comparison is not like-for-like.

Evidence. Adjudicator re-estimation (table3_repro.py): sample with second leagues 1.795 (0.065), 1.138 (0.118), 1.433 (0.155), col 4 -0.512/1.409, col 5 -0.529/1.301/-0.618/-0.149 = printed Panel A; top-league 1.334 (0.077), 0.995 (0.128), 1.226 (0.169), col 4 -0.391/1.494, col 5 -0.448/1.409/-0.635/-0.201 = printed Panel B. Table notes give N = 47,727 for A and 70,703 for B. table3.do lines 44-137.

Why this severity. This is a labelling error. Coefficients and signs are similar across the two samples, so no conclusion changes, although the stated direction of the robustness check is wrong.

Why it matters, in detail. The published column 4 does not test what it claims, namely ability-varying general-equilibrium wage effects; done as described, the coefficient barely moves from column 3.

Evidence. Adjudicator (misc_checks.py): column 4 as coded 0.634 (0.132), eps_f 0.621, matching the published value; as described 1.108 (0.160), eps_f 1.076 (Auditor A: same). table2.do (model 4: casev(age age2 _IyeaXpla*)). Restoring four quality groups in column 3: alpha 1.027 (Auditor B).

Why this severity. This is documentation: the correctly specified column 4 is close to column 3, so no conclusion changes.

Why it matters, in detail. With 14 observations the foreign cross-country elasticity is dominated by one high-tax, low-foreign-share country; the placebo has no power for foreigners.

Evidence. Adjudicator (figure1_loo.py) reproduces Figure 1 exactly: foreign pre 0.003 (0.858), post 1.223 (0.450); domestic pre 0.092 (0.035), post 0.290 (0.077). Leave-one-out post-Bosman foreign: 0.742 (0.540) without Sweden (range 0.742-1.535); domestic range 0.232-0.344.

Why this severity. The paper itself presents this evidence as suggestive, and the domestic correlation is robust.

The authors' response. Page 1906 acknowledges that pre/post-Bosman differences are not statistically significant.

Why it matters, in detail. The Greek statistic is not comparable with the paper's other elasticities; correctly normalised, it implies a much larger proportional response of out-migration.

Evidence. greece.do lines 25-28: 0.10500948/[ln(0.505) - ln(0.400)] = 0.4505 (adjudicator). synthetic_control.do: g diff`var' = `var'_t - `var'_s. Table A2 vs text p.1910.

Why this severity. These are labelling issues in supporting material; the underlying estimates are unaffected.

Why it matters, in detail. Sample earnings are understated by 24-38% in Table A1; no estimate is affected.

Evidence. Adjudicator (atr_cpi_checks.py) reproduces £211,341 and all country means. CPI fixed: £263,105 (+24.5%); pooled with original CPI: £235,065; CPI fixed and pooled: £291,012 (+37.7%). Auditor B's figures are identical.

Why this severity. The error is confined to descriptive statistics; the Laffer weights use 2008 wages, where the ratio is one.

Why it matters, in detail. A forward-looking ability proxy creates a potential feedback from location to classification; its impact was not quantified.

Evidence. Adjudicator (misc_checks.py): top varies within player for 19 of 16,352 players (Auditor A: same).

Why this severity. This is a mild, unquantified endogeneity concern; most national-team players are identifiable early in their careers.

Why it matters, in detail. This has a negligible effect on the estimates; it causes non-convergent Austria x 2005 parameters.

Evidence. Adjudicator choice tabulation (misc_checks.py): Austria 2005 = 0 cases (132-220 in other years). Nationality list in the estimation file includes Guadeloupe, Algeria, Poland, Croatia and Turkey (23 cases).

Why this severity. These are small gaps largely absorbed by country x year fixed effects.

Why it matters, in detail. This is a mis-citation of the legal source; it does not affect the case-study timing.

Evidence. BOE-A-2005-9875 preamble (read by the adjudicator from the cached BOE page).

Why this severity. The correct history supports the paper's choice of 2004 as the reform year; no estimate changes.

Why it matters, in detail. The absence of documentation is what allowed the identifying Dutch coding (F1-F2) and the Norwegian rule (F9) to go unnoticed.

Evidence. Contents of the AEA/openICPSR package (Data_&_Prog_AER, read_me dated 8/30/2012); both auditors and the adjudicator found no workbook. F1, F2 and F9 could be found only by reverse-engineering the rates.

Why this severity. The estimates are fully reproducible from the deposited data; the consequences of the missing documentation are graded separately in F1, F2 and F9.

Why it matters, in detail. These are small, mostly downward corrections to alpha that add to the cumulative coding uncertainty of F2/F9. The legal status of the 2008 Belgian regime was not verified by the adjudicator.

Evidence. Items (i) and (ii) verified by the adjudicator (tax_coding_audit.py: Spanish foreign rows at the local rate in 2004, Belgian ones in 2002). Item (v) is visible in mtr.dta and greece.do (ln(1-.6)). Items (iii)-(iv) and the effects are Auditor A's: Beckham from 2004 gives column 3 1.029; Belgium-2008 fix 1.037; NL VAT + Belgium + Spain fixes 0.740; those plus Norway 0.472. Removing all Greek variation changes column 3 by less than 2%.

Why this severity. Each item moves alpha by 2-10%; together with F2 and F9 they bring column 3 down to about 0.5-0.7, but taken alone they are small.

Why it matters, in detail. The 1991 restructuring is a potential confound for the timing of the Danish DD. Ineligible low-earning foreigners are coded as treated, attenuating alpha and making the lack of a low-quality response uninformative about sorting.

Evidence. baseplayer.dta league tabulation (adjudicator): 1986-1990 '1 Division' 14 clubs; 1991 'Superligaen' 10 clubs; 12 clubs from 1995. Tax-coding tabulation: all foreign-alternative rows for Denmark at the scheme rate, 1996-2008. Auditor A estimates, not re-verified here, that about 39% of foreign players in Denmark with observed wages earn below an indexed threshold.

Why this severity. The Danish DD is dominated by post-1996 divergence, and the threshold mis-coding biases alpha down (conservative for C1). It does, however, offer a non-sorting explanation for the null low-quality response.

Why it matters, in detail. Elasticities of foreign stocks scale inversely with the foreign base share, so 'upper bound' is not well defined across contexts. The authors' own non-football estimate (1.5-2) exceeds the football headline.

Evidence. aer_culture1.csv treated counts 7, 5, 7, 8, 9, 5, 7, 5, 14, 14, 12 (1980-1990). KLSS (2014) abstract: elasticity 'between 1.5 and 2'. Munoz (2021), HAL halshs-03252899: 'between 0.1 and 0.3; it is above one for foreigners'. Usala & Brau (2020 WP): football foreigners 1.20-1.37.

Why this severity. Within the same Danish scheme, sports and entertainment did respond more than other sectors (also stressed by KLMS 2020), so the relative-mobility claim holds. Only its generalisation into an upper bound on elasticities is overstated, and stock elasticities with different bases are not directly comparable.

The authors' response. KLSS (2014, fn 3) and KLMS (2020) note that football players 'might be substantially more mobile' and that elasticities 'pertain to specific groups'.