Within-Firm Pay Inequality and Productivity

Layer 1: Overview

This paper investigates how within-firm pay inequality relates to firm-level labor productivity, using a novel linkage of three confidential U.S. Census Bureau datasets covering millions of workers at hundreds of thousands of firms from 2003 to 2015.

The motivating puzzle is that the dramatic rise in U.S. wage inequality since the 1970s is well documented, but the firm-side determinants of within-firm pay dispersion have been difficult to study due to the absence of comprehensive matched employer-employee data in the United States. The paper asks whether firms’ own productivity levels can explain the structure of pay inequality within firms, and whether rising aggregate productivity can account for the secular increase in the CEO-to-median-worker pay gap.

The data come from three linked sources. The Longitudinal Employer-Household Dynamics (LEHD) program provides quarterly earnings for essentially all UI-covered workers from 2003 to 2015, covering all 50 states and Washington, D.C. These earnings encompass salaries, wages, bonuses, and exercised stock options, making them comprehensive for top earners. The Longitudinal Business Database (LBD) supplies annual firm-level revenue and employment, from which the key productivity measure — real revenue per worker, deflated to 2010 dollars using the PCE deflator — is constructed. The Management and Organizational Practices Survey (MOPS), a supplement to the Annual Survey of Manufactures conducted in 2010 and 2015, provides structured management scores (scaled 0 to 1) measuring the intensity of performance monitoring, target-setting, and incentive use across manufacturing firms. The main analysis sample restricts to firms with at least 100 full-year “6-quarter sandwich” workers to ensure clean measurement of annual earnings; it covers approximately 443,000 firm-year observations and 73,000 unique firms. A supplementary Execucomp sample (4,681 firms, 2006–2016) validates results for large publicly traded firms.

Three main findings are reported. First, employees at more productive firms earn more across the entire within-firm pay distribution — from the 1st to the 99th percentile. A 10 percent increase in productivity is associated with a 0.7 percent increase in average worker pay (elasticity 0.068). Moving from the 10th to the 90th percentile of the firm productivity distribution projects an 18 percent increase in average pay.

Second, the pay-productivity relationship is steeper at higher pay ranks — it strengthens monotonically with seniority. For a given doubling of firm productivity, the top-paid employee (likely the CEO) sees approximately 15 percent more pay, while the median-paid employee sees approximately 7 percent more. Equivalently, the pay-productivity elasticity is 0.15 for the top earner and 0.07 for the median earner. At the percentile level, a 10 percent productivity increase predicts a 0.86 percent pay increase at the 90th percentile but only 0.53 percent at the 10th percentile. Consequently, more productive firms have higher within-firm inequality: a 10 percent productivity increase widens the top-earner-to-median-worker log pay gap by 0.9 percent, and moving from the 10th to the 90th percentile of productivity projects a 23.1 percent increase in this gap. These cross-sectional results survive firm fixed effects, demographic controls (sex, education, age), industry fixed effects at the 6-digit NAICS level, and 2SLS instrumentation with industry exposures to seven major currencies, oil prices, and economic policy uncertainty (Alfaro, Bloom, and Lin 2024). Within-worker, within-firm estimates confirm the pattern dynamically: when a firm’s productivity doubles, workers earning $45,000–$65,000 expect roughly a 1 percent pay increase while workers earning above $300,000 expect nearly a 2 percent increase. The pay-productivity relationship is roughly twice as strong for top earners at publicly traded firms as at private firms (coefficient of 0.22 vs. 0.13 for rank-1 earners), while workers outside the top 50 ranks show similar coefficients across ownership types.

Third, the mechanism is traced to performance-based pay. More productive firms exhibit higher within-year pay volatility (measured as the standard deviation of quarterly log earnings within a year), particularly for top earners, consistent with larger bonus payments. Firms with higher structured management scores — capturing more intensive performance monitoring, goal-setting, and incentive pay — also show higher pay levels and higher pay volatility for top earners, with the gradient across ranks matching the productivity results.

Finally, a back-of-the-envelope calculation applies the estimated pay-productivity elasticities to observed aggregate productivity growth. Aggregate U.S. labor productivity roughly doubled (96 percent compounded growth) from 1980 to 2013. The top-earner-to-median-worker pay ratio at firms with at least 100 employees rose from 7.55 in 1980 to 8.69 in 2013 (an increase of 1.14). Applying the paper’s elasticities for rank-1 (0.1534) and rank-50 (0.0657) earners to the observed productivity doubling predicts a ratio of 8.01 in 2013 — accounting for 40 percent of the actual increase. The authors interpret this as evidence that rising productivity, channeled through differential performance pay, is a quantitatively important driver of rising within-firm inequality.

Layer 2: Deep Dive

What is the primary identification strategy and what are the main threats to it?

The core cross-sectional estimates in models (1) and (2) regress percentile- or rank-specific pay on log revenue per worker, controlling for a quadratic expansion of firm-level worker demographic composition (sex, education, age and their interactions), year fixed effects, and 6-digit NAICS industry fixed effects. The main threat is omitted variable bias: unobserved firm characteristics correlated with both productivity and pay (e.g., high-skill worker sorting into high-productivity firms) could inflate estimates. The paper addresses this in three ways. First, specifications with firm fixed effects (Appendix Figure A.1) use only within-firm changes in productivity and pay, producing similar convex-across-ranks patterns. Second, the within-worker, within-firm change specification (model 4, Figure 2) holds individual workers fixed and relates earnings growth to productivity growth. Third, a 2SLS approach instruments log productivity (and its interaction with rank) using industry-level exposures to seven currency pairs, oil prices, and economic policy uncertainty constructed from rolling 10-year daily stock-return regressions by Alfaro, Bloom, and Lin (2024); the logic is that industries have idiosyncratic exposure to these aggregate shocks, so productivity movements attributable to the instruments are exogenous to individual pay-setting. The 2SLS results are broadly similar to OLS in sign and pattern, though first-stage F-statistics are approximately 3, which is weak by conventional standards. Additional tests using lagged productivity (Appendix Table A.3) show if anything stronger relationships, consistent with productivity causally passing through to pay rather than pay determining past productivity.

What are the main mechanisms proposed and how are they distinguished empirically?

The primary mechanism proposed is performance-based pay (bonuses and incentive compensation) that is disproportionately concentrated among senior managers at more productive firms. The paper cannot directly observe bonus pay in the LEHD, which reports total quarterly earnings. Instead, it uses within-year pay volatility — the standard deviation of log quarterly earnings within a calendar year — as a proxy for bonus income (most visibly fourth-quarter bonus payments). Figure 4 shows that top earners at more productive firms have significantly higher pay volatility, and this relationship is steeper at higher ranks, exactly paralleling the pay-level results. The management channel is examined separately: Figure 5 shows that firms with higher MOPS structured management scores (capturing explicit monitoring, target-setting, and incentive-pay practices) display higher pay levels and higher pay volatility for top earners, again with the gradient increasing at the top. The public-vs.-private ownership comparison is a further diagnostic: if performance-based executive compensation is the mechanism, it should be stronger at publicly traded firms, where stock grants, option awards, and formal incentive contracts are more prevalent. Panel a of Figure 3 confirms the top-earner pay-productivity coefficient is 0.22 at public firms and 0.13 at private firms, while workers outside the top 50 show similar coefficients across ownership type. This asymmetry is robust to reweighting public firms to match the employment distribution of private firms (panel b of Figure 3), ruling out pure size effects as the explanation.

What heterogeneity is documented across sectors, firm age, and ownership type?

Across sectors (Appendix Figure A.2), the positive and convex pay-productivity gradient across earnings ranks is present in nearly all 18 two-digit NAICS sectors. Shallower (less convex) patterns appear in utilities, finance and insurance, and health, which the authors attribute to heavy regulation limiting scope for differential performance pay across ranks. Across firm age groups (Appendix Figure A.3), the pattern holds across firms younger than 10 years, between 10 and 25 years, and 25 or more years. Across ownership, the pay-productivity relationship for top earners is roughly twice as large in publicly traded firms as in privately held firms, while the relationship for workers outside the top 50 is similar. Within publicly traded firms, the LEHD top-earner coefficients closely match those for named executives in the Compustat Execucomp data (Figure 3, panel a), validating both the LEHD measure of top earnings and the Execucomp-based executive pay literature.

What robustness checks are run?

The paper runs the following robustness checks: (1) Full demographic controls — a quadratic expansion of firm-level shares by sex, education category, and age group, plus interactions — included in all baseline regressions to account for worker sorting. (2) 6-digit NAICS industry fixed effects to net out cross-industry pay and productivity variation. (3) Firm fixed effects (Appendix Figure A.1): the convex pattern across ranks survives when only within-firm variation in productivity and pay is used. (4) Sector heterogeneity analysis (Appendix Figure A.2): the main pattern holds across nearly all 18 two-digit NAICS sectors. (5) Firm age heterogeneity (Appendix Figure A.3): results hold across all age groups. (6) Reweighting public firms to match private firms’ employment distribution (Figure 3, panel b): the stronger pay-productivity gradient for top earners at public firms is not explained by their greater average size. (7) Size controls: including log total LEHD employment does not eliminate the pattern. (8) 2SLS with macroeconomic instruments: similar signs and pattern to OLS, supporting causal interpretation despite weak first stages. (9) Lagged productivity (Appendix Table A.3): if anything, the pay-productivity relationship by rank is slightly stronger when using prior-year productivity, reducing reverse-causality concerns. (10) Comparison to Execucomp: the LEHD public-firm top-earner coefficients align with those from Execucomp named executives. (11) Analysis of sandwich-worker selection (Appendix Table A.1): workers at more productive firms are marginally more likely to remain sandwich workers the following year, with this pattern slightly stronger at lower earnings ranks; the paper discusses this selection and argues it does not drive the main results.

What exactly is the LEHD earnings measure and how does it capture bonuses?

The LEHD is based on state unemployment insurance (UI) wage records submitted by employers. It captures total quarterly earnings, including salaries, wages, bonuses, stock option exercises, and restricted stock awards when vested. Qualified (incentive) stock options are not subject to UI tax and are excluded, but these are capped and the paper judges them immaterial for top earners. The quarterly frequency of the data allows the paper to construct within-year pay volatility (the standard deviation of log quarterly earnings in a year) as a proxy for bonus income, since bonus payments typically appear as spikes in Q4. The paper uses only non-imputed demographic characteristics from ancillary LEHD sources; imputed values (e.g., education, which is imputed for 88 percent of individuals) are replaced with a constant and flagged with a missing-value indicator.

How exactly is firm productivity measured and what are its limitations?

Productivity is measured as real revenue per worker (log scale), with nominal revenue deflated to 2010 dollars using the PCE deflator. Revenue and employment come from the LBD, which covers all non-farm sectors from 1997 onward. This is a revenue-based labor productivity measure, not total factor productivity, and no industry-level price deflators are used beyond the economy-wide PCE; instead, 6-digit NAICS industry fixed effects control for cross-industry differences in revenue-per-worker levels. The LBD’s revenue coverage may be biased toward older, more stable firms, but the paper argues this has minimal impact because its sample is already restricted to large firms (at least 100 full-year workers). The paper explicitly contrasts its broad economy-wide measure with more granular TFP measures available only for manufacturing and in Economic Census years.

What is the structured management score and what does it measure?

The structured management score is derived from 16 core questions in the MOPS asking plant managers about practices in three domains: performance monitoring, target setting, and incentivization of workers. Each question is scored 0 to 1, where 0 reflects least structured (less explicit, formal, frequent, or specific) and 1 reflects most structured (more explicit, formal, frequent, or specific). The firm-level score is an employment-weighted average of establishment-level scores (requiring at least 10 non-missing responses per establishment). It ranges from 0 to 1 and follows the methodology of Bloom et al. (2019), who establish that higher scores predict higher establishment-level productivity. Because MOPS targets manufacturing establishments surveyed in the ASM, the management sample is a 2.5 percent subset of the main sample, resulting in wider standard errors for management-related estimates. The paper treats this score as an indirect proxy for the adoption of performance-based incentive systems.

How does this paper relate to and differ from Song et al. (2019) and the broader between-firm vs. within-firm inequality literature?

Song et al. (2019), also using linked LEHD-LBD data, document that the rise in U.S. earnings inequality between 1978 and 2013 was driven predominantly by increases in between-firm pay dispersion, with within-firm inequality rising more modestly. This paper takes the within-firm inequality result as a starting point and asks what firm characteristics predict cross-sectional and dynamic variation in within-firm inequality. The key addition is connecting within-firm pay dispersion to revenue labor productivity and to management practices, neither of which Song et al. (2019) directly analyze. The paper uses Song et al.’s published aggregate statistics on top-earner and median-earner pay (from their Figure VI) as the benchmark for the back-of-the-envelope calculation linking rising productivity to rising inequality. More broadly, the paper contributes to a cross-country literature (Barth et al. (2016), Card, Heining, and Kline (2013), Faggio, Salvanes, and Van Reenen (2010), Mueller, Ouimet, and Simintzi (2017)) that documents firms as the locus of increasing wage dispersion, by providing a specific firm-level mechanism — productivity and performance-pay practices.

How does this paper relate to and differ from the CEO pay literature?

The CEO pay literature (Gabaix and Landier (2008), Frydman and Jenter (2010), Kaplan (2013), Edmans and Gabaix (2016)) debates whether rising CEO pay reflects performance, firm size, or rent extraction, but typically studies only the named top executives at large publicly traded firms covered by Execucomp. This paper’s key innovation is extending the analysis to all workers across the full within-firm pay distribution, for millions of U.S. workers at firms of all sizes and ownership types. It finds that the pay-productivity gradient is present across all earnings ranks, not only at the CEO level, though it is steeper at the top. The paper validates its LEHD-based top-earner results against Execucomp, finding close agreement for publicly traded firms, and interprets the public-vs.-private differential as consistent with formal performance-based executive contracts being more prevalent at public firms — a finding consistent with Gao and Li (2015), who show CEO pay-performance sensitivity is greater at public firms.

What are the aggregate inequality implications and how robust is the 40 percent estimate?

The 40 percent figure comes from a back-of-the-envelope calculation in Table 4. Using Song et al.’s (2019) data, the top-earner-to-median-worker pay ratio rose from 7.55 in 1980 to 8.69 in 2013 (a change of 1.14). Aggregate U.S. labor productivity grew 96 percent compounded over this period (sourced from FRED series PRS85006092). The paper applies the pay-productivity elasticities for rank-1 (0.1534) and rank-50 (0.0657) earners from Figure 1 to this productivity growth to predict earnings levels in 2013. The predicted top-earner mean earnings is $224,357 (versus actual $301,614) and predicted median mean is $28,013 (versus actual $34,702), yielding a predicted ratio of 8.01 and an explained change of 0.46, which is 40.13 percent of the actual change of 1.14. The authors label this a ‘simple back-of-the-envelope’ calculation and do not claim it as a structural decomposition. Key caveats: (i) the cross-sectional elasticities from 2003–2015 are applied to a 1980–2013 trend, assuming stability of these relationships over time; (ii) aggregate productivity growth may also shift the productivity distribution of firms, which the calculation does not fully model; (iii) the calculation attributes none of the remaining 60 percent, which could include technology, globalization, changing labor market institutions, or other forces.

What is the role of firm size in explaining the results?

Publicly traded firms in the sample are substantially larger than private firms on average (mean 7,763 versus 491.7 full-year employees). To ensure the stronger pay-productivity gradient at public firms is not simply a size artifact, the paper reweights public firms to match the employment distribution of private firms (using ventile-based inverse-probability weights) and finds the differential persists (panel b of Figure 3). The paper also includes log total LEHD employment as a control in additional specifications and reports similar results. The large-firm pay premium literature (Brown and Medoff (1989), Oi and Idson (1999)) posits that large firms pay more due to compensating differentials, monitoring difficulties, or rent-sharing. The paper’s finding that pay is higher at more productive firms across the entire earnings distribution is interpreted as more supportive of the rent-sharing explanation, since compensation-based and monitoring-based explanations would not apply uniformly to all workers.

What are the policy implications and their scope conditions?

The main policy-relevant implication is that rising productivity — itself associated with technology adoption and innovation — contributes substantially (estimated 40 percent) to the CEO-to-median-worker pay gap that the Dodd-Frank Act requires publicly traded firms to disclose annually from 2018. This implies that policies targeting within-firm pay inequality may need to grapple with the fact that a significant share of observed inequality is tied to real productivity differences and performance-pay practices, not purely to governance failures or rent extraction. However, several scope conditions limit this implication: the 40 percent figure is an economy-wide back-of-the-envelope estimate with caveats about stability of elasticities over time; the paper does not assess whether performance pay practices are optimally structured or reflect rent-seeking; the mechanism analysis uses pay volatility and management scores as proxies rather than direct observation of bonus contracts; and the remaining 60 percent of the inequality increase is left unaccounted for, potentially reflecting factors outside the paper’s framework.

What are the key data limitations and potential measurement concerns?

Several limitations are acknowledged or implicit. (1) Revenue labor productivity is used rather than TFP; the measure conflates product demand and productivity shocks and does not adjust for industry-specific output price variation. (2) LEHD earnings exclude qualified (incentive) stock options not subject to UI tax; the paper argues these are capped and immaterial for top earners, but this may understate total compensation for senior executives, especially at technology firms. (3) Within-year pay volatility is used as a proxy for bonus income rather than direct bonus data. (4) The management sample is confined to firms with at least one manufacturing establishment in the MOPS, covering only 2.5 percent of main-sample firm-year observations, limiting precision. (5) Education is imputed for 88 percent of individuals in the LEHD; the paper uses only non-imputed values and controls for missingness, but this reduces demographic control precision. (6) The IV first-stage F-statistics are approximately 3, suggesting weak instruments, so 2SLS standard errors are wide and the causal interpretation should be taken cautiously. (7) The sample is restricted to firms with at least 100 full-year workers, so results do not speak to smaller firms, which employ a large share of the U.S. workforce.

Key Concepts

Revenue labor productivity: Real revenue per worker at the firm level, computed from LBD annual revenue deflated to 2010 dollars using the PCE deflator and divided by total firm employment; the paper’s primary measure of firm performance, entered in log form in all regressions.

Pay-productivity elasticity (by rank): The regression coefficient on log firm productivity in a regression of mean log annual earnings for a given within-firm earnings rank or percentile; the paper documents that this elasticity rises monotonically from approximately 0.07 for the median earner to 0.15 for the top earner (rank 1), producing a convex schedule across ranks.

Within-firm earnings inequality: Dispersion in annual earnings among full-year workers within a single firm in a given year; measured variously as the 90th-10th percentile log earnings gap, the 99th-10th gap, the top-earner-to-50th-percentile gap, and the top-earner-to-10th-percentile gap.

Within-year pay volatility: The standard deviation of log quarterly earnings within a calendar year for a given worker rank; used as a proxy for variable (bonus) compensation since it captures deviations from a constant salary path, particularly fourth-quarter bonus payments.

Structured management score (MOPS): A continuous index bounded between 0 and 1 derived from 16 MOPS survey questions on performance monitoring, target-setting, and worker incentivization practices; higher values indicate more explicit, formal, frequent, and specific management practices, following the scoring methodology of Bloom et al. (2019).

6-quarter sandwich worker: An individual who is employed at and earns above the minimum wage at the same firm in all four quarters of the current year, the fourth quarter of the prior year, and the first quarter of the following year; the restriction ensures that measured annual earnings reflect genuine full-year employment rather than partial-year spells or job transitions.

DHS (Davis-Haltiwanger-Schuh) growth rate: A symmetric growth rate measure defined as (x_t - x_{t-1}) / (0.5 * (x_t + x_{t-1})), bounded between -2 and 2; used in the within-worker, within-firm change analysis to measure both earnings growth and productivity growth while accommodating entry and exit.

Top-earner-to-median-worker pay ratio: The ratio of mean annual earnings of the highest-paid worker to mean annual earnings of the median-paid worker within firms, aggregated across firms of different sizes using employment weights; the Dodd-Frank Act metric that publicly traded firms have been required to disclose annually since 2018, and the paper’s primary metric for the aggregate inequality calculation.