Inequality at Work: The Effect of Peer Salaries on Job Satisfaction

Why it matters, in detail. Under a linear-in-rank response with constant compliance (verified here by quartile: first stages 30.6/29.1/27.4, p = 0.60), b1 = -b0. Table 4 gives b0 + b1 = -4.3 (4.25), 2.3 (2.42), 4.3 (2.33): p = 0.31/0.34/0.066. II-I (p = 0.018/0.009/0.004) only rejects 'no relative-pay gradient'. Contrasts exploiting the bottom-quartile concentration give p of about 0.03-0.06 for satisfaction and the composite and 0.16-0.34 for search. The experiment identifies a relative-pay gradient but gives only borderline evidence on its curvature. Above-median effects of about +6 index points (satisfaction) or -4 pp (search), the mirror images, cannot be excluded. Concavity of v() is also confounded with relative-pay heterogeneity in prior information.

Evidence. Symmetric test from Table 4 (covariance backed out of the printed SE of II-I, computed by lincom in table4-aer-final.do): b0 + b1 = -4.3 (4.25), p = 0.31; +2.3 (2.42), p = 0.34; +4.3 (2.33), p = 0.066. Rounding ranges are 0.28-0.34, 0.28-0.40 and 0.04-0.09. Public-data approximation (adjudicator, campus dummies, HC1): p = 0.37/0.39/0.04. Average effects (Table 4 cols 1/4/7): -2.0 (2.2), p = 0.36; +1.0 (1.2), p = 0.40 (printed 0.85); +2.0 (1.1), p = 0.07. Above-median 95% CIs: satisfaction [-3.1, +7.1] contains the mirror image +6.3; search [-5.1, +1.1] contains -4.3. The 80%-power MDEs (7.3, 4.5) exceed the below-median estimates. The strongest concavity contrasts are borderline. Linear-in-rank restriction on the Table 4 quartile models (Q1 + 1.5 x upper half = 0), zero covariance assumed: p = 0.037 / 0.16 / 0.029 (public data 0.055 / 0.20 / 0.029); 2-df linear-in-rank test p = 0.053 / 0.34 / 0.082. The unreported Table 5 kink tests give p of about 0.04 / 0.12-0.20 / 0.04-0.05 in a specification that forces a zero effect at the median (F2). Job satisfaction alone is nearly symmetric (App. A4: -8.5 (4.9) vs +6.3 (4.4); sum p = 0.74). The three outcomes are not independent: the composite is a subset of 'very likely to search'; corr = 0.74. Codex's worked example (linear v, heterogeneous priors) produces the same asymmetric ITT. External evidence on the high-paid side is mixed. Perez-Truglia (2020, AER 110(4): 1019-54; quote from NBER w25622) finds Norway's income transparency caused 'a transference of well-being from poorer to richer individuals' with no significant average effect. Cullen & Perez-Truglia (2022, JPE 130(3); NBER w24841) find the same asymmetry for retention but not for effort or performance. Breza, Kaur & Shamdasani (2018, QJE; NBER w22491) find that even relatively higher-paid workers reduce attendance. Dube, Giuliano & Leonard (2019, AER 109(2): 620-63) find quits driven by comparisons with higher-paid peers. Scripts: final/scripts/01_published_number_tests.py, 02_public_data_checks.py, 04_compliance_and_outcome_dependence.py.

Why this severity. Asymmetry and nonlinearity are headline claims of the abstract and conclusion, and they underpin the policy inference. Neither the paper's own linear-vs-concave test nor the average-effect test rejects linearity, and above-median gains or losses as large as the below-median effects cannot be excluded for satisfaction and search. The strongest contrasts are borderline (p about 0.03-0.06) for two correlated outcomes and absent for search. The preference interpretation also rests on an untested equal-priors assumption. This materially weakens C3; the direction survives in the point estimates, and the below-median effect (C2) is untouched.

The authors' response. No direct response. The AER says the pattern is 'consistent with inequality aversion' (p. 2995) and lists two caveats (pp. 2997-2998): rational updating cannot be definitively rejected, and higher-paid employees may have had better prior information.

Why it matters, in detail. Below the median, rank and level deviations are highly collinear, and the combined models give rank t-statistics of 1.83/1.55/2.00 with level terms near zero. No non-nested or joint test is reported. 'Significant ... for all three outcomes' holds at 5% only for the composite. Measurement error in levels would mechanically favour the bounded rank regressor (plausible, untested).

Evidence. Table 5 cols 3/6/9, below-median rank terms: 3.3 (1.8), t = 1.83, p = 0.067; -1.7 (1.1), t = 1.55, p = 0.12; -2.0 (1.0), t = 2.0, p = 0.046. Rounding ranges are [0.056, 0.079], [0.096, 0.152] and [0.031, 0.064]. The level terms are near zero. AER p. 2997: 'for the intended search the two alternatives are very similar'. 2011 draft p. 24: 'rank wins ... for these two outcomes ... For the job search variable we do not have the precision to be able to distinguish between the two.' AEA/Crossref abstract: 'Differences in pay rank matter more than differences in pay levels.'

Why this severity. C5 is in the official abstract. The evidence for it is suggestive (one coefficient significant at 5%, one at 10%, one not at 10%), and the wording was strengthened between versions without new data. The lean toward rank survives.

The authors' response. The conclusion hedges ('The evidence further suggests', p. 3001), and fn 29 reports that models with a treatment main effect also favour rank.

Why it matters, in detail. Disclosure's net effect is not distinguishable from zero for satisfaction (-0.03 SD) or search. Under the 2011 draft's own model, a negative average effect is the signature of concavity, and none is detected. An employer's incentive depends on quits, effort and wage bargaining, none of which is shown to move. Equilibrium evidence suggests transparency can raise employer rents through lower wages.

Evidence. Table 4 cols 1/4/7: -2.0 (2.2), about -0.03 SD, p = 0.36; +1.0 (1.2), p of about 0.40; +2.0 (1.1), p of about 0.07. F1 symmetric tests p = 0.31/0.34/0.066. Cullen & Pakzad-Hurson (2023), 'Equilibrium Effects of Pay Transparency', Econometrica 91(3): 765-802, as summarised in Cullen (2024), 'Is Pay Transparency Good?', JEP 38(1): 153-180 (doi:10.1257/jep.38.1.153): transparency policies 'caused employers to bargain more aggressively, lowering average wages'. AER p. 3002 notes possible longer-run endogenous wage-setting.

Why this severity. This is a policy inference highlighted in the introduction and conclusion but not in the abstract. It rests on the unestablished asymmetry (F1) and on self-reported satisfaction as a proxy for employer costs. It is a qualitative overreach rather than an error in any estimate.

The authors' response. AER p. 3002: in the longer run, disclosure 'may lead to endogenous changes in wage-setting policies and employee composition'.

Why it matters, in detail. Dropping the fairness item moves the below-median index effect from -5.9 (2.6) to -5.1 (2.8) (p 0.025 to 0.073). The item-level ordered probits for pay and job satisfaction have p of about 0.16 and 0.08. The index became the primary outcome only after the first draft's item-level results were marginal, which raises a researcher-degrees-of-freedom concern. The bottom-quartile satisfaction result holds for every item.

Evidence. AER App. A4 (ordered probit, below median): fairness -10.1 (4.9), p of about 0.04; pay satisfaction -6.3 (4.5), p of about 0.16; job satisfaction -8.5 (4.9), p of about 0.08. Adjudicator public-data OLS (campus dummies, HC1): pay satisfaction -4.5 (3.6), p = 0.21; job satisfaction -5.6 (3.2), p = 0.08; fairness -7.6 (3.3), p = 0.02. The two-item index without fairness is -5.1 (2.8), p = 0.073, against -5.9 (2.6), p = 0.025 with it. In the bottom quartile every item is significant: -13.5 (5.1), -15.0 (4.5), -14.1 (4.7), p <= 0.008. September-2010 draft: Table 5 cols 3/7 (-7.8 (4.6), -8.9 (5.0)) and p. 26; Table 9 and pp. 31-32. April-2011 draft pp. 20-21 (index introduced; fn 30). Script: final/scripts/02_public_data_checks.py, section B.

Why this severity. Without the perception item, the below-median satisfaction effect falls by about 14% and loses 5% significance, and item-level pay and job satisfaction effects are only marginal. The search outcome and the bottom-quartile effects are unaffected. The index's composition is disclosed.

The authors' response. AER fn 21: estimates are 'not sensitive' to other index constructions such as the first principal component. Item-level ordered probits are reported in App. Table A4.

Why it matters, in detail. With about 14-16% excess non-response among treated workers at UCSD and UCLA, Lee bounds on b0 are [-22.7, +9.0] for satisfaction, [-0.2, +15.8] for search and [+2.6, +17.9] for the composite. Point identification needs ignorability, which the placebo supports only if the two e-mails induce the same selection. Because the response effects are equal across pay halves, b1 - b0 is robust to selection that is homogeneous across halves.

Evidence. Table 1 col 1: -3.81 (0.54); col 4: -3.60 / -4.04. Campus response rates from the 2010 draft, fn 29 (controls vs treated): UCSC 0.163/0.171, UCSD 0.229/0.197, UCLA 0.201/0.169, giving control trimming shares of 0 / 14.0% / 15.9%. Adjudicator bounds (trimming within campus x pay half, OLS with campus dummies) for the below-median effects: satisfaction [-22.7, +9.0] around -5.9; search [-0.2, +15.8] around 3.9; composite [+2.6, +17.9] around 5.0. Auditor A got [-22.4, 7.4], [0.3, 15.1], [3.0, 17.9]; Auditor B (15% trim) got [-24.7, 9.6], [-0.4, 17.2], [2.6, 20.0]. When the same trimming applies in both halves, II-I stays at 9.2/7.7, -4.5/-4.8 and -8.9/-5.2. The 2010 draft (Table 7) reported trimmed bounds 'relatively close to our baseline' for its ordered-probit kink models. Trimming the same numbers of controls (349 UCSD, 296 UCLA) in the closest public analogue (ordered probit by pay half) moves the below-median coefficients by about 14-40 points (x100), so that robustness was not reproduced; the exact model needs withheld wages. The 2011 draft (p. 22) judged its selection-correction models 'not generally robust'. AER fn 26 refers readers to Card et al. (2010). Scripts: final/scripts/02_public_data_checks.py section H; 03_trimming_ordered_probit.py.

Why this severity. This is a robustness concern with limited demonstrated impact. Actual selection bias is not shown, and the placebo evidence is informative. The composite and the relative-pay contrast survive. But the below-median satisfaction level effect, part of C2, is not identified under worst-case selection, and the AER's 'show ... not an artifact' overstates what the placebo can establish.

The authors' response. AER pp. 2988-2990 and Sec. III.C: the response effect does not depend on the content of the e-mail (placebo), and observables are balanced among respondents (Table 2). fn 26 refers to selection-correction models in Card et al. (2010).

Why it matters, in detail. Across the draft and the AER there are at least six turnover specifications on two snapshots. The best is t = 1.74 (Q1, FE). Below-median effects in the draft were -0.4 (1.4), and the Q1-minus-upper contrast is t <= 0.9. The evidence for any turnover effect is weak, and for a rank-specific one absent. The Table 7 note mixes March-2011 descriptive statistics with an August-2011 outcome.

Evidence. 2011 draft Table 10 (March 2011): treated 0.0 (1.1) full sample; below median -0.40 (1.4); above 0.31 (1.1); mean 0.27; found-rates 49/76/74.5%. AER Table 7 (August 2011): Q1 2.61 (1.78), t = 1.47, and 2.30 (1.32) with department FE, t = 1.74, p of about 0.08. Q2 -0.39 / -0.71. Above median 1.42 (1.29) / 0.84 (0.93). Q1 minus above median is 1.19 (2.20) and 1.46 (1.61), t <= 0.9. Rank slope below the median -0.74 (0.51) / -0.63 (0.36). The note gives mean 0.31 and the same found-rates. Weighted by the A1 matched counts, those found-rates imply 0.269 not found (final/scripts/01_published_number_tests.py, section 9). In app-table9-aer-final.do, gen around=(gross10!=.) is placed inside the loop 'foreach var in around overtime_ind ...', with the note '* I could not find anything stable for other variables'. That this payroll measure gave a null is an inference (unverified).

Why this severity. This affects a secondary and heavily hedged result: the only behavioural, non-survey evidence. Re-measuring and re-specifying after a null, without disclosure, makes 'suggestive' too strong. The low-rank-specific effect is not shown at all.

The authors' response. AER p. 3001: the estimates are 'too imprecise to reach a definite conclusion' and 'at best only suggestive'. The authors cite diffusion of information and the recession as confounders.

Why it matters, in detail. Through-the-origin slopes are biased by -/+3a when the response at the median is a. With a = +6.7 for the composite, a linear response (-5.2 vs -4.6) is turned into a kink (-7.3 vs -2.5). With a = +10.3 for satisfaction, an inverted V (7.0 vs -3.9: gains near the median, losses at the top, as in Fehr-Schmidt) is turned into 'flat above the median' (3.8 vs -0.8). Only the search kink (-4.4 vs -1.4) does not depend on the restriction, and it is imprecise. The AER's restricted OLS pattern mirrors the draft's restricted probit pattern, so the same mechanism very likely applies.

Evidence. 2011 draft App. A5 (unrestricted; main x100, rank slopes x10): satisfaction 10.3 (5.7), slopes 7.0 (2.1) below and -3.9 (2.2) above. Search 0.6 (6.8), -4.4 (2.7) and -1.4 (2.7). Composite 6.7 (8.7), -5.2 (3.3) and -4.6 (4.2). Predicted restricted slopes are 3.9/-0.8, -4.6/-1.2 and -7.2/-2.6, against printed 2011 Table 6 values of 3.8/-0.8, -4.6/-1.3 and -7.3/-2.5 (final/scripts/05_restricted_vs_unrestricted_kink.py). For the composite, the restricted kink (-7.3 vs -2.5) is therefore produced by the restriction. For satisfaction, the 'flat' above-median segment (-0.8) masks an unrestricted slope of -3.9 (2.2): top earners lose relative to the median. AER eq. (4), p. 2997; Table 5; fn 29; 2011 draft fn 35 and p. 45.

Why this severity. This undercuts the paper's most direct evidence on the shape of the response (C3) and the basis for the 'flat above the median' statement. The unrestricted estimates are imprecise and come from the draft's ordered probits, so the size of the effect in the AER's OLS specification is not known. The change is noticeable but not transformative on its own; F1 carries the main weight.

The authors' response. AER fn 29: models with a treatment main effect (not reported) 'also show that the rank variable appears to be more significant'. 2011 draft p. 45: 'Some precision is lost in the estimates but the results remain generally consistent with those presented in Table 6'.

Why it matters, in detail. Below-median search effects range from 2.8 to 5.6 pp, with p from 0.026 to 0.24 across variants. Campus heterogeneity is insignificant, and the pooled median-split effect is driven by UCLA and UCSC. Q1 effects are robust everywhere.

Evidence. Adjudicator public-data approximation (HC1), below-median search: baseline 3.9 (1.8), p = 0.033; excluding placebo recipients 3.5 (1.9), p = 0.061; excluding UCSC 3.2 (1.9), p = 0.09; excluding UCLA 3.1 (2.5), p = 0.20; excluding UCSD 5.6 (2.5), p = 0.026; within treated departments only 2.8 (2.4), p = 0.24; 'likely or very likely' 3.5 (2.0), p = 0.075. Q1 search p <= 0.045 throughout. UCSD (n = 3,182; first stage 27.8 pp) below-median effects: -1.2 (3.9), 1.6 (2.7), 0.9 (2.3); Q1 -12.1 (5.4), 6.8 (3.9), 4.2 (3.2). UCSC Q1 search +24.7 (8.6). Auditor A's campus heterogeneity tests give p = 0.10/0.42/0.14. Codex's campus estimates agree (its R17). Script: final/scripts/02_public_data_checks.py, sections D-E.

Why this severity. The published estimate (t = 2.4; Holm-adjusted p = 0.034) stands, and point estimates are stable. The p-value changes mostly reflect smaller samples. This is a caution that C4, not the median split, is the robust result.

Why it matters, in detail. For faculty with a campus reference group, b0 + b1 is about 0 (p = 0.98): a linear relative-pay response, with significant gains above the median. The department-level reference group is the maintained definition, and faculty search effects remain asymmetric but insignificant.

Evidence. AER App. A7 col 1: -16.9 (6.6) vs +16.7 (5.3); II-I 33.5 (8.6); b0 + b1 = -0.2 (8.3), p = 0.98 (adjudicator). Faculty search effects 3.4 (3.7) vs -0.8 (3.2). 2011 draft p. 25 (its Table 7, ordered probit: satisfaction -24.7 (10.4) vs +25.2 (8.9); search 10.2 (11.1) vs -10.9 (11.2), also symmetric there). Faculty are 1,015 of 6,411 respondents (A5).

Why this severity. The result is disclosed in the AER text and appendix and concerns about 16% of the sample under an alternative reference group. It is nonetheless direct evidence against a universal 'above-median unaffected' claim.

The authors' response. AER p. 2996: 'for faculty a broader comparison group may be relevant'.

Why it matters, in detail. A3 provides experimental evidence against rational updating: no upward revision of raise expectations among below-median treated workers, and a positive treated x wage gradient. Reporting it would have strengthened C6. C3(b) could have shown whether high earners' priors were already accurate, which is the confounder of preference curvature in F1.

Evidence. Sept 2010 draft pp. 26-27 and Appendix Table 3 (UCLA, N = 2,819, mean 0.29): treated below-median -0.8 (2.9), above +2.3 (2.6); treated x wage +0.9 (0.4), t of about 2.1, 'contrary to the prediction' of the learning model. A3 is absent from the April-2011 draft and the AER. Survey on web appendix pp. 31-34. No other version or do-file uses C3(b), A1(b-c), B1 or C4-C5 (text search of all three versions and the 17 do-files).

Why this severity. There is no sign of adverse selective reporting: the dropped expected-raise evidence favoured the authors' interpretation. C3(b) is endogenous (asked only of users) but would have informed F1's identification concern. The interpretive tests are weaker than the instrument allowed.

Why it matters, in detail. With hundreds of tests, one result with p of about 0.03 is expected by chance. The undisclosed sensitivity to department fixed effects makes it more likely to be a false positive.

Evidence. app-table9-aer-final.do: commented-out loop over 9 variables (around, overtime_ind, extra_ind, gross, lngross, base, lnbase, growbase, growgross) x 6 years x 8 specifications, plus 2007 randomisation checks. Notes: '* notes: results are weaker with dept fixed effects, placebo using earlier years do not deliver significant results;' and '* I could not find anything stable for other variables ...'. A9: -1.64 (0.73) all, -2.14 (0.74) non-responders, -0.13 (1.29) responders. The A9 note says only that department fixed effects are not included.

Why this severity. This is a footnote result outside the core findings. Fn 32 does say that 'in general, our models failed to uncover significant differences'.

The authors' response. fn 32: 'In general, our models failed to uncover significant differences ... with one exception.'

Why it matters, in detail. Fehr-Schmidt implies an inverted-V v(d) with slope -beta above the reference point, not an increasing concave v. That shape matches the unrestricted satisfaction estimates in F2 better than the AER's framework, but the distinction cannot be resolved with these data.

Evidence. Fehr & Schmidt (1999), QJE 114(3): 817-868, eq. (1) and the text that follows (local copy /mnt/zdata/downloads/cmms2012-lit/fs1999.txt): 'player i's utility function obtains a maximum at xj = xi. The utility loss from disadvantageous inequality ... is larger than the utility loss if player i is better off'. AER p. 2984.

Why this severity. Interpretive only. A null above-median effect is equally consistent with Fehr-Schmidt with a small beta, so no estimate is affected.

Why it matters, in detail. The gender contrast is not significant (t of about 0.8). Tenure patterns differ by outcome: satisfaction moves for high-tenure workers, search for low-tenure workers.

Evidence. AER App. A5: women's below-median search effect 5.5 (2.2) vs men's 2.2 (3.3), a difference of about 3.3 (4.0), t of about 0.8. Satisfaction below median: low tenure -3.0 (3.8), high tenure -9.5 (4.2); low-tenure II-I 0.3 (5.6). AER p. 2996; 2011 draft pp. 44-45.

Why this severity. These are secondary subgroup interpretations, presented with hedges. The underlying table is fully reported.

The authors' response. AER p. 2996: 'without additional data our findings are only suggestive'.

Why it matters, in detail. None alters an estimate. Item (a) only mislabels the significance of an insignificant pooled effect. Items (b) and (d) show descriptive numbers carried over from the 2010 sample.

Evidence. (a) Table 4 col 4 prints p = 0.85 for a coefficient of 1.0 (1.2); the implied p is about 0.40 (rounding range 0.36-0.45), confirmed on the page image. (b) App. A1 col 6 totals 6,437 (425/3,193/2,819, the 2010-draft sample) against the 6,411 analysed (423/3,182/2,806 in the public file and A2 note). (c) App. A3: treated N printed as '776' and '1766' (actual 1,776); the index category '9' should be '3'; control 'not at all likely' 47.2% should be 47.4% (2,198/4,635). (d) p. 2991 gives control site use as 19.1%; the Table 3 note and the data give 19.2%. (e) The text says SEs are clustered by department x occupation (p. 2986). The notes say campus/department, and Table 1 uses 1,078 clusters, the number of departments in A0. (f) The Table 3 col 3 command omits female although gender is listed among the controls. Table 3's bottom-row p-values are joint tests against col 3, as the row label says, but the prose reads them as tests of identical treatment effects. p. 2992 says 'cannot reject heterogeneous' where it means homogeneous. (g) The Table 5 col 3 exclusion test omits t_relwagep (table5-aer-final.do line 158). (h) The introduction says 'four-fifths' of new users looked at their own department; Sec. III.A says 87%. High-profile lookups are 9.5/27.8 = 34%, not 'about a quarter'. (i) Column headings say 'likely looking' while the definition uses 'very likely'. p. 2997 calls c1 'negative' for all outcomes, though for satisfaction it is positive, as expected. A9's columns are numbered 2, 3, 3. (j) The 'one-third of US companies' statistic (p. 2983) is uncited. (k) 'There is no evidence of such [peer] interactions' (p. 2986) rests on spillover tests of survey response and site use only (2010/2011 drafts, Tables 2 and 4a). Outcome spillovers were never tested; an adjudicator pooled check finds none (section F of final/scripts/02_public_data_checks.py).

Why this severity. These are presentation and transcription errors that do not affect any estimate or conclusion.

Why it matters, in detail. Without wages or rank, the shape tests (Table 5), the turnover analysis and design-based inference cannot be audited. The undocumented pooling of small units affects what 'department reference group' means for about 17% of individuals (43% at UCSC).

Evidence. readme.pdf/readme.txt in 20110453_data.zip: 'the public dataset does not contain several variables used in the analysis ... the do-files cannot be run on the public use dataset'. The do-files load combo, combo_turnover, combo_names, campus directory CSVs and ucpay files (e.g. table4-aer-final.do line 12; table7-aer-final.do line 184). table5-aer-final.do line 38: replace rank=(rank-0.5)/usize. Sept 2010 draft fn 19, p. 17. Approximate re-estimation reproduces Tables 3, 4 and 6 within about 1.2 points (see reproduction summary).

Why this severity. Confidentiality is a legitimate reason, the authors offer mediated replication, and the approximate re-estimates match the headline numbers closely. The gap limits verification of C5, C7 and the clustered inference rather than undermining any result.

The authors' response. readme: 'Researchers interested in replicating the estimates in this paper should contact the authors and we will arrange for a process to do so.'

Why it matters, in detail. A significant mobility gradient among above-median workers, who on average show no search response, would undercut the argument that search responses are truthful because they appear only among mobile workers. The arithmetic shows the printed value is almost certainly not the estimate.

Evidence. AER App. A6 Panel B: col 1 -1.8 (1.6); col 2 -2.0 (3.1) + 0.5 (0.2) x predicted probability. At the above-median control 'very likely' share of 18.9% (public file) the implied average effect is -2.0 + 0.5 x 18.9 = +7.5 pp, against -1.8. Panel A: -8.6 + 0.5 x 25 = 3.9 against 4.0. 2011 draft App. A7 Panel B: 0.6 (0.6); draft p. 45.

Why this severity. This is an appendix table. If the printed number were correct, it would weaken the fn 27 'truthful reporting' check, but the check rests on Panel A, which is consistent.