Bargaining and Inequality in the Labor Market: Caldwell, Haegele & Heining (2026)

What this is. The paper’s core results, the empirical framework, and the estimating equations: enough to understand what it found and how, without reading all 57 pages. To replicate or extend it, read the full source at the original.

TL;DR

The paper introduces and validates a survey measure of wage-bargaining strategies for 772 German firms, linked to German Social Security records and a worker survey of nearly 10,000 full-time workers. Most workers (78%) are in positions where firms report that individual bargaining is possible. Firm productivity proxies do not systematically predict bargaining; employee group and the difficulty of filling a position are more informative, while the evidence on market tightness is suggestive. Most outside offers are rejected; among rejected-offer events, about one-third of workers try to renegotiate with the incumbent firm. Better outside options predict more asking and successful raises, while risk tolerance is also associated with bargaining success. Women are significantly less likely to ask for and receive raises during the prior six months; estimates for asking and succeeding at the start of a job spell are negative but imprecise. Among surveyed workers, the residual gender pay gap is about 6 percentage points larger at bargaining firms than posting firms; the paper reports a 3 percentage point difference in its conclusion and attributes 44% of the residual gap at surveyed firms to bargaining. The prior-firm pay premium predicts current pay only when the worker’s current employer allows bargaining, in both the all-worker and surveyed-worker samples.

Core results

Magnitudes and significance as reported; */**/*** = 10%/5%/1%. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Individual bargaining is pervasive: 78% of workers at surveyed firms are in positions where the firm can differentiate pay by individual bargaining	Figure I (Panels A-B), p. 334; text pp. 318, 333, 336	95% of firms can differentiate pay for managers; 85% for experienced non-managers; the introduction reports 55% for recent entrants, while Figure I shows about 50% for new hires; 57% of firms would adjust incumbent recent entrants’ wages after an outside offer
R2	Firms expect substantial initial-offer variation: typical expected spread between highest and lowest initial offers to identically qualified candidates is 3%-10% depending on group	Figure II, p. 335; Figure III, p. 336	3% for recent entrants, 5% for experienced non-managers, 10% for managers (conditional on nonzero: 6%, 10%, 12%); final-offer gap is similar
R3	Labor market factors beat firm characteristics in explaining bargaining strategies; employee-group dummies explain as much as 500+ firm fixed effects	Table III, p. 343	Group dummies alone: R² = 0.33, adj. R² = 0.33; all firm FE: R² = 0.40, adj. R² = 0.19; firm controls without industry dummies (cols 4-7) keep adj. R² ≤ 0.35; 4-digit industry dummies (cols 8-9) reach adj. R² = 0.44
R4	Most outside offers are rejected; some workers use them to renegotiate at the incumbent firm	Table IV, p. 346	91% of workers who received outside offers stayed; 33% of workers in rejected-offer events attempted renegotiation with incumbent; 46% of renegotiation attempts succeeded
R5	Outside options drive bargaining success: workers with better outside options are 9 pp more likely to ask for a wage increase at the start of an employment spell	Table V Panel A, p. 351	Outside options (binary): +8.7 pp\*\*\* asked, +6.7 pp\* successfully negotiated upward; level: +0.056 ask, +0.487 pp negotiated; consistent effects in previous 6 months
R6	Women ask for and receive less during employment; start-of-spell differences are negative but imprecise	Table V, Panels A-B, pp. 351-352	Start of spell: -7.5 pp asked (s.e. 5.1 pp) and -6.8 pp succeeded (s.e. 4.8 pp) are both unstarred; successful negotiation’s intensive margin is -0.614 pp* (s.e. 0.325 pp). In previous 6 months: -5.8 pp*** asked (s.e. 1.8 pp), -6.4 pp*** asked for and received a raise (s.e. 1.4 pp)
R7	Among surveyed workers, the gender pay gap is about 6 pp larger at bargaining firms after occupation-establishment fixed effects; the paper’s conclusion reports a 3 pp difference overall	Table VI Panel A, p. 359; text p. 360; Online Appendix Table A13; Figure V, p. 361	Female coefficient at bargaining firms: -0.053\*\* (s.e. 0.023, occ-est FE, col. 5); at posting firms: 0.008 (s.e. 0.032, col. 2); difference is 6.1 pp (equality-test p = .063, marginal at 10% but not significant at 5%). The text reports that 44% of the residual gender gap at surveyed firms is attributed to bargaining
R8	Prior-firm pay premium predicts current pay only when the current employer bargains: 10 pp higher prior-firm AKM effect is associated with 0.5% higher current pay at bargaining employers	Table VII Panel A, p. 363	Bargaining firms: prior-firm effect = 0.049\*\*\* (s.e. 0.010); posting firms: 0.006 (s.e. 0.018); p-value of equality = 0.016
R9	Firm productivity proxies do not predict bargaining	Table II, p. 339	Total and fixed assets per employee differences have p-values .21, .25, .69, .66, .89, and .86 across employee groups
R10	Combined group and firm effects explain incidence and incumbent measures	Table III, pp. 343-344	Incidence question, Panel B: adjusted R² = .25 group, .26 firm, .59 group plus firm, .38 cols 8-9; incumbent renegotiation, Panel C: .19, .33, .58, .32, respectively
R11	Bargaining often starts before an initial offer and continues through counters	Table IV, p. 346	Salary expectations provided in 57% of rejected-offer events and 74% of accepted-offer events; worker counters in 31% and 39%; firms raise offers in 42% and 45% of counter cases, matching 21% and 28%
R12	Risk-tolerant workers ask for and receive raises more often	Table V, Panel B, p. 351	Binary risk tolerance: +0.079\*\*\* for asking and +0.085\*\*\* for asking and receiving; risk-tolerance level: +0.022\*\*\* and +0.023\*\*\*, respectively
R13	Higher AKM worker premia predict more bargaining and higher stated expectations	Table V, pp. 351-352	AKM worker effect: +0.187\*\* successful negotiation and +1.555\*\* percentage points on the intensive margin at spell start; in the hypothetical scenario +0.039\*\* for expectations at/above range midpoint and +0.050\*\*\* above range
R14	Gender gaps in salary expectations persist under a common stated salary range	Table V, Panel C, p. 352	Women are 2.2 pp\*\*\* less likely to provide expectations, 4.3 pp\*\*\* less likely to state expectations at/above range midpoint, and 5.7 pp\*\*\* less likely to state expectations above range
R15	The bargaining-firm gender gap persists with hours controls and base pay	Table VI, Panels B-C, p. 359	Female coefficient: posting vs bargaining firms is 0.020 vs -0.045\*\* with hours controls, and 0.008 vs -0.049\*\* for daily base pay
R16	Prior-firm pay premia predict starting pay, especially under current-employer bargaining	Table VII, Panel B, p. 363	All workers: 0.094\*\*\* without bargaining vs 0.234\*\*\* with bargaining, equality p = .010; surveyed workers: 0.182 vs 0.377\*\*\*, equality p = .237
R17	Bargaining differences do not shift toward nonwage amenities or special pay	Text p. 356; Online Appendix Table A9	27% report negotiating vacation days and 18% training opportunities; there is no evidence that groups that bargain less over base wages bargain more over nonwage dimensions; apart from gender, differences in special-pay bargaining are not meaningful
R18	Better outside options also predict raises during employment	Table V, Panel B, p. 351	Binary measure: +9.0 pp\*\*\* asking for a raise and +7.7 pp\*\*\* asking for and receiving one; level measure: +0.062\*\*\* and +0.054\*\*\*
R19	Risk tolerance predicts starting negotiations and higher salary expectations	Table V, pp. 351-352	At spell start, binary risk tolerance predicts +7.5 pp\* successful negotiation and level risk tolerance +0.024\*\*; in the hypothetical range, binary risk tolerance predicts +2.7 pp\*\* at/above midpoint and +2.5 pp\* above range
R20	Gender bargaining differences remain after jointly controlling worker traits	Text p. 356; Online Appendix Table G4 and Figure A2	Including outside options, risk tolerance, and gender together reduces the female coefficient by at most 15%; each dimension remains individually significant for prior-six-month outcomes
R21	Independent responses within firms support the stability of the survey measure	Text p. 332; Online Appendix Table A2	Responses from 37 firms significantly overlap across independent respondents; the main text reports no correlation coefficient
R22	Worker reports correlate with the firm survey measure	Text p. 332; Online Appendix Table A5	Worker-reported bargaining strategies are positively and significantly correlated with the corresponding firm reports; the main text reports no coefficient
R23	CBA coverage and East Germany headquarters correlate negatively with bargaining	Table II, pp. 339-340	Bargaining vs posting firms: CBA coverage .35 vs .50 for recent entrants and .39 vs .56 for experienced non-managers (p = .00 for both); East Germany HQ shares .10 vs .15, .11 vs .22, and .11 vs .32 across groups (p = .02, .00, .00)

Overall (paper’s conclusion). Individual wage bargaining is empirically pervasive in Germany and contributes to wage dispersion. Labor-market factors, especially employee group and difficulty filling positions, are associated with bargaining strategies, while firm productivity proxies are not systematically predictive. Providing workers with pay information (a common policy proposal) would not suffice to close gender gaps in bargaining behavior; residual differences persist even in hypothetical scenarios with equalized information. The prior-firm pay persistence result shows that a worker’s previous-employer pay premium predicts starting pay more strongly when the new employer allows individual bargaining.

Theory / model

The paper has no formal model of its own. It situates itself within the theoretical literature on imperfect competition in the labor market (Manning (2011)): when workers face search frictions and firms earn monopsonistic rents, wages can be set by individual bargaining rather than wage posting, and the distribution of rents varies with outside options and bargaining power.

The paper tests two classes of theoretical predictions from models of firm wage-setting strategy:

1. Productivity-based theories (Postel-Vinay and Robin (2004); Doniger (2015); Flinn and Mullins (2021)): more productive firms will be more likely to bargain with workers to capture a larger share of the surplus. The paper finds these predictions are rejected: firm age, size, and assets per employee do not predict whether a firm bargains.

2. Labor market factor theories (Ellingsen and Rosén (2003); Michelacci and Suarez (2006)): firms bargain when it is difficult to replace workers or when vacancy tightness is high. The paper finds these predictions are confirmed: market tightness (bottleneck occupations) and employee replaceability (experienced workers, managers) predict bargaining strategies, and employee-group dummies explain as much variation as all firm fixed effects combined.

For the inequality analysis, the identification logic is:

• Gender pay gap (Section VI.A): the paper extends Biasi and Sarsons (2022) to a broader multi-sector German sample, comparing conditional gender gaps within occupation-establishment cells across firms with and without bargaining.
• Prior-firm pay persistence (Section VI.B): the paper compares the relation between a worker’s prior-firm AKM wage premium (Abowd, Kramarz, and Margolis (1999); estimated from 2010-2017 population data by Bellmann et al. (2020)) and current pay at bargaining vs. posting firms. Card, Heining, and Kline (2013) documented the rise of firm heterogeneity in these AKM effects in Germany; the present paper identifies individual bargaining as a contributing mechanism.

Both exercises are descriptive comparisons conditional on observed controls; the paper does not claim causal identification.

Method

The key methodological contribution is the design and validation of a survey instrument to measure firm wage-bargaining strategies, following the management-practices survey approach of Bloom and Van Reenen (2007).

Protocol question (main measure of firm bargaining strategy). Firms were asked separately for four employee groups:

How much more could a person maximally receive compared to the fixed compensation you would have offered based on the person’s qualification/fit for the position alone?

Response options: 0% (no adjustment), 1%-10%, 11%-20%, 21%-30%, 31%-40%, more than 40%. A firm is classified as having a bargaining strategy if it reported any nonzero adjustment. For incumbent workers facing outside offers:

Suppose an employee at your company receives an external offer from another company and requests a salary increase. What is the maximum percentage by which your firm could possibly increase the fixed compensation (without changing the person’s tasks) in order to retain the person?

Incidence question (intensive margin). Firms were asked to imagine 10 candidates with identical qualifications but differing salary expectations and outside offers, and report the expected spread between the highest and lowest initial and final offers (p. 330).

Validation. The paper conducts three validation exercises:

1. Stability across respondents within the same firm (following Bloom and Van Reenen (2007)): independent responses from 37 multi-respondent firms show significant overlap, confirming firm-level determination (Online Appendix Table A2).
2. External validity with published data: answers on observable firm practices (e.g., CBA coverage) align with publicly available sources (Online Appendix C.3).
3. Correlation with worker survey: elicited firm strategies are positively and significantly correlated with worker reports at those firms (Online Appendix Table A5).

The survey-based approach builds on Hall and Krueger (2012), who provided early evidence on the incidence of wage posting vs. bargaining using worker surveys. This paper adds the firm side and links both to administrative records. The results on back-and-forth negotiation dynamics are analogous to Backus et al. (2020a), who documented sequential bargaining in eBay product markets; this paper provides the labor-market counterpart.

Worker bargaining outcomes regression (p. 350, equation 1).

$$y_i = \beta X_i + \delta \text{age}_i + \alpha \exp_i + \gamma \exp_i^2 + \zeta_{\text{educ}(i)} + \lambda_{o(i),\text{est}(i)} + \epsilon_i \tag{1}$$

where $y_i$ is a bargaining outcome (probability of asking for a raise, successfully negotiating, etc.); $X_i$ is the heterogeneity dimension of interest (outside options, risk tolerance, gender, or AKM person effect); $\lambda_{o(i),\text{est}(i)}$ are three-digit occupation-establishment fixed effects. Standard errors are clustered at the firm level.

Gender pay gap regression (p. 358, equation 2).

$$\log w_i = \beta \, \text{Female}_i + \delta \, \text{age}_i + \alpha \exp_i + \gamma \exp_i^2 + \zeta_{\text{educ}(i)} + \lambda_{o(i),\text{est}(i)} + \epsilon_i \tag{2}$$

where $\log w_i$ is log daily pay. Estimated separately for workers exposed to individual bargaining and those whose wages are set by posting (based on the firm’s reported strategy for the worker’s group). Standard errors are clustered at the firm level.

Prior-firm pay persistence regression (p. 362).

$$\log w_i = \beta \, \psi_{i,j^{\text{prev}(i)}} + \delta \, \text{age}_i + \alpha \exp_i + \gamma \exp_i^2 + \zeta_{\text{educ}(i)} + \lambda_{o(i),\text{est}(i)} + \epsilon_i \tag{3}$$

where $\psi_{i,j^{\text{prev}(i)}}$ is the AKM wage premium of individual $i$‘s previous employer (from population regressions using log daily pay 2010-2017; Bellmann et al. (2020)). Estimated separately by bargaining exposure.

Empirical specifications

Table II (Section IV.B): firm characteristics. The paper compares means for posting and bargaining firms separately by employee group and reports p-values from equality tests; no regression equation or standard-error treatment is reported for this table. It compares firm assets per employee, size, age, CBA coverage, East Germany headquarters, and legal form. The posting/bargaining firm counts are 341/399 for recent entrants, 112/627 for experienced non-managers, and 39/691 for managers. Total and fixed assets per employee differences are not statistically significant (Table II, pp. 339-340). CBA coverage and East Germany HQ correlate with the strategy reported for several employee groups.

Table III (Section IV.B): variance decomposition of firm bargaining strategies. The dependent variable is the continuous firm-group measure: the midpoint of the firm’s protocol response for new hires (Panel A), expected variation in final offers (Panel B), or amount of possible incumbent adjustment (Panel C). The authors compare explanatory sets as follows (Table III, pp. 343-344). The following is an unnumbered reconstruction of the decomposition reported in Table III; it is not an equation printed in the paper:

$$b_{ig} = \alpha_g + \varepsilon_{ig}, \qquad b_{ig} = \eta_i + \varepsilon_{ig}, \qquad b_{ig} = \alpha_g + \eta_i + \varepsilon_{ig},$$

where $b_{ig}$ is the bargaining measure for firm $i$ and employee group $g$, $\alpha_g$ are group effects, and $\eta_i$ are firm effects. Other columns add firm size, total assets (productivity), norms including CBA coverage, East Germany HQ and legal form, industry dummies, and group interactions. The table reports R-squared and adjusted R-squared, not coefficient estimates or standard errors. Up to four observations per firm enter the regression. Group effects alone produce adjusted R² of .33 in Panel A, .25 in Panel B, and .19 in Panel C; firm effects alone produce .19, .26, and .33, respectively. The combined specification’s adjusted R² is .63, .59, and .58. In columns 8-9, which include four-digit industry effects, adjusted R² is .44, .38, and .32. The authors do not state a standard-error treatment for this fit decomposition.

Table V (Section V): worker bargaining behavior. Equation (1), shown in Method, is estimated by OLS for the four worker heterogeneity measures: outside options, risk tolerance, gender, and AKM person effects. Outcomes are bargaining actions at the start of a job spell, during the prior six months, and responses to a hypothetical pay-range question. Specifications include age, experience and its square, education dummies, and three-digit occupation-establishment fixed effects; standard errors are clustered by firm. Panel A uses workers who started their job in the previous three years; Panel B uses workers with a bargaining event in the prior six months; Panel C uses workers answering the hypothetical scenario. Table V reports row-specific observation counts (pp. 351-352).

Table VI and Figure V (Section VI.A): gender wage gaps. Equation (2), shown in Method, is estimated separately for workers exposed and not exposed to bargaining. The covariates are female, age, experience and its square, education dummies, and the fixed effects listed below; standard errors are clustered by firm. Table VI columns 1/4 have no fixed effects, columns 2/5 include occupation-establishment fixed effects, and columns 3/6 include finer level-occupation-establishment fixed effects. Panel A uses daily pay, Panel B adds log hours, and Panel C uses daily base pay. In the occupation-establishment FE columns, the sample is 1,226 posting-firm workers and 3,381 bargaining-firm workers for daily pay; it is 1,225 and 3,376 for daily base pay (Table VI, p. 359). Figure V estimates the fully interacted form below, with demographic covariates and fixed effects interacted with firm bargaining exposure; its outcome variants include daily pay, daily base pay, and hourly wages, and its samples include surveyed workers and all workers at surveyed firms. Standard errors are clustered by firm (Figure V, p. 361):

$$\log w_i = \beta_0 + \beta_1 \text{Female}_i + \beta_2 B_i + \beta_3 (\text{Female}_i \times B_i) + X_i'\delta + B_i X_i'\theta + \lambda_{o(i),est(i)} + B_i\lambda_{o(i),est(i)} + \epsilon_i.$$

The target coefficient in Figure V is $\beta_3$, and $B_i$ indicates that pay is set via individual bargaining. The main surveyed-worker sample is drawn from workers in firms with survey responses; the table reports the sample size for each specification.

Table VII (Section VI.B): prior-firm pay persistence. The prior-firm specification displayed as equation (3) in Method is estimated separately for workers with and without bargaining exposure and for the full set of workers at surveyed firms (columns 1-2) and surveyed workers (columns 3-4). Panel A uses current log daily pay; Panel B uses starting log daily pay. Regressors include the prior-firm AKM effect, age, experience and its square, education dummies, and occupation-establishment fixed effects. Standard errors are clustered by firm. Each panel has 36,117 and 118,233 observations in the no-bargaining and bargaining columns for all workers, and 1,030 and 2,879 for surveyed workers. Bargaining exposure refers to the worker’s current employer. The paper reports p-values for equality of prior-firm coefficients between bargaining regimes; for current pay among all workers this p-value is .016, and for starting pay it is .010 (Table VII, p. 363).

Datasets used

Dataset	Role in paper	Wiki page
IAB Integrated Employment Biographies (IEB)	Administrative employer-employee records; daily pay, demographics, occupation codes, employer IDs; linked to firm survey (553/772 firms consented); 416,821 full-time employees at matched firms in 2020; AKM firm and worker effects from 2010-2017 population data	IEB Germany (confidential)
ifo HR Survey Panel (firm survey)	Novel survey of 772 German private-sector firms on wage-bargaining strategies; elicited for four employee groups and two bargaining contexts (new hires, incumbents with outside offers); fielded 2021-2022	No page yet (new data, introduced by this paper)
IAB Worker Survey (HOPP, worker survey)	Novel survey of 9,756 full-time German workers on bargaining behavior, outside options, and risk tolerance; linked to IEB; fielded 2022-2024 to a sample drawn from Social Security records	No page yet (new data, introduced by this paper)
Orbis (Bureau van Dijk)	Balance sheet characteristics for surveyed firms (firm age, total assets, fixed assets, stock corporation status); matched to 99% of surveyed firms	Orbis BvD (licensed)

Sample: 772 firms, workers ages 25-50 employed in 2020, IEB data from 1975 onward (main analysis uses 2010-2020), AKM effects estimated on 2010-2017 population.

When to read the full paper

Read the original if you are:

• Building or calibrating a model of individual wage bargaining in the labor market (the survey statistics on firm willingness to differentiate pay and the share of workers exposed to bargaining are key inputs);
• Studying the sources of the gender wage gap (the paper provides unusually direct evidence that bargaining, not productivity, drives residual gaps);
• Using AKM firm effects to interpret wage dispersion (the prior employer’s AKM premium predicts current pay under current-employer bargaining, with implications for how firm effects should be interpreted);
• Interested in survey-based measurement of firm practices (the validation exercises in the Online Appendix provide a detailed template).

The locators above point to the exact tables and figures in the source.

Attribution and rights

Source: peer-reviewed, The Quarterly Journal of Economics (2026), pp. 315-371. Published by Oxford University Press on behalf of Harvard University. All rights reserved; no CC licence. This distillation was extracted by an LLM on 2026-06-28 and is not human-verified or independently reproduced.

Caldwell, Sydnee, Ingrid Haegele, and Jörg Heining. “Bargaining and Inequality in the Labor Market.” The Quarterly Journal of Economics (2026): 315-371. DOI: 10.1093/qje/qjaf049. © The Author(s) 2025. Published by Oxford University Press on behalf of President and Fellows of Harvard College. All rights reserved. Extracted under fair-use / extract-only policy; no verbatim reproduction of substantial portions.