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### Overview and research question
- Investigates the role of firm labor market power in the pass-through of firm output to wages.
- Motivated by empirical evidence of wage markdowns (wages below marginal product of labor) and declining labor share of output.
- Key question: Does higher firm labor market share (payroll share in sector) weaken the pass-through of firm value added growth to wage growth?

### Theoretical framework and predictions
- Framework draws from Atkeson and Burstein (2008) and Berger et al. (2022) with:
  - Finite number of firms per sector, firms use only labor, infinite number of industries.
  - Firm productivity heterogeneity generates variation in firm labor market shares.
  - Nested CES aggregation: 0 < 휖 < ∞ (elasticity across sectors) and 0 < 휃 < ∞ (elasticity across firms within sectors).
  - Workers are less mobile across sectors than within sectors (휖 < 휃).
- Key analytical results (partial equilibrium):
  - Firm labor supply elasticity: ∂ln푙𝑓𝑠𝑡 / ∂ln푤𝑓𝑠𝑡 = 휃 − (휃 − 휖) 푠𝑓𝑠𝑡, where 푠𝑓𝑠𝑡 is firm labor market share.
  - Firm production: 푦𝑓𝑠𝑡 = 푧𝑓𝑠𝑡 푙𝑓𝑠𝑡^훼 with 훼 ∈ (0,1).
  - Wage as marginal product times markdown: 푤𝑓𝑠𝑡 = 휇(푠𝑓𝑠𝑡) 훼 (푦𝑓𝑠𝑡 / 푙𝑓𝑠𝑡).
  - Markdown function: 휇(푠𝑓𝑠𝑡) = 1 / [1 + 1/휃 + (1/휖 − 1/휃) 푠𝑓𝑠𝑡].
- Predicted implication: under 휖 < 휃, ∂휇/∂푠𝑓𝑠𝑡 < 0 — firms with higher payroll share face more inelastic labor supply and suppress wages relative to marginal product, weakening the sensitivity of wages to value added.

### Data, sample, and empirical identification
- Data: ORBIS firm-level data.
- Sample: non-farm, non-financial activities with NACE codes 5–82; cross-country panel of 14 advanced European economies, 2000–2018.
- Firm “wage” measure: total “wage-bill” (total cost of employees).
- Empirical identification:
  - Tests whether pass-through of firm value added growth to wage growth varies with firm payroll share in 4-digit NACE sectors.
  - Firm fixed effects and country-sector-year fixed effects (country × 4-digit NACE sector × year) absorb time-invariant firm traits and common shocks.
  - Controls include firm productivity, innovative activities, age, export exposure; secular trends addressed via common, country-, and industry-specific trends.

### Main empirical findings (baseline and magnitudes)
- Baseline specification:
  - A 10 percentage points increase in value added growth → 3.3 percentage points higher growth in firm wage-bill within the same year (coefficient on Δ log(푌) = 0.325*** (0.003)).
  - Interaction with payroll share S: Δlog(푌) × S = -0.008*** (0.000); payroll share S coefficient = -1.786*** (0.021).
- Quantitative illustrations across payroll share distribution:
  - Atomic firm (payroll share ≈ 0): 10 percentage points higher value added growth → 3.3 percentage points wage-bill growth.
  - 99th percentile payroll share (firm wage-bill share = 7.5 percent): same 10 percentage points → 2.7 percentage points wage-bill growth — a 19 percent lower pass-through versus an atomic firm.
  - 99.5th percentile payroll share (firm payroll share = 13 percent): almost one third of pass-through erodes versus an atomic firm.
- Payroll share coefficient negative, implying convergence of wages across firms within 4-digit sectors over time.

### Robustness and heterogeneity
- Dummy-variable approach (high-payroll dummies): Δ log(푌) ~ 0.324–0.327***; interaction Δlog(푌) × high-payroll becomes more negative at higher cutoffs (e.g., country-sector-year: -0.020*** (90th) to -0.060*** (99.5th); overall sample: -0.063*** (90th) to -0.112*** (99.5th)).
- Time-varying firm controls:
  - Including lagged total assets, leverage, or lagged wage growth: Δlog(푌) coefficients 0.322***, 0.329***, 0.271***; interactions remain -0.008*** or -0.005*** as reported.
  - Lagged assets and leverage associated with lower subsequent wage growth; lagged wage growth shows mean reversion.
- Alternative measures and subsamples:
  - Replace value added growth with sales (Δ log(푌)=0.405*** (0.004)) or revenue growth (0.435*** (0.004)); replace payroll share with employment share — core pattern holds.
  - Payroll share net of sales share: interaction -0.008*** (0.001).
  - Subsamples by firm size, longevity, sector size, country subsets — results remain significant.
  - Longer windows: 3-year Δ log(푌)=0.446*** (0.004), interaction -0.011*** (0.000); 5-year Δ log(푌)=0.479*** (0.004), interaction -0.011*** (0.001).
  - Mean value of share of firm wages to value added (levels): above 0.7; 25th and 75th percentiles 0.6 and 0.9; standard deviation 0.4.
- Industry heterogeneity:
  - Service: Δ log(푌)=0.297*** (0.003); interaction -0.005*** (0.001); Eroding = 8 percent at 99th percentile (payroll share ~4.5 percent).
  - Non-service: Δ log(푌)=0.377*** (0.006); interaction -0.012*** (0.001); Eroding = 40 percent at 99th percentile (payroll share ~12.3 percent).
  - Tradable: Δ log(푌)=0.334*** (0.002); interaction -0.009*** (0.000); Eroding = 47 percent at 99th percentile (payroll share ~17.5 percent).
  - Non-tradable: Δ log(푌)=0.324*** (0.004); interaction -0.007*** (0.001); Eroding = 12 percent at 99th percentile (payroll share ~4.4 percent).
  - Manufacturing Eroding = 46 percent; Wholesale and retail trade Eroding = 11 percent; Construction Eroding = 4 percent.
- Time trends and granularity:
  - 10-year rolling windows: interaction becomes more negative over time (from -0.007*** to -0.011***); payroll share coefficient more negative (e.g., -1.876*** to -3.069***); erosion at 99th percentile increases from 18 percent to 25 percent across periods.
  - Broader industry definitions mechanically scale S down but the role of labor market power persists (2-digit NACE interaction -0.026*** (0.002); 1-digit NACE interaction -0.094*** (0.034)).
- Fixed effects and clustering: results robust to many fixed-effects schemes and clustering alternatives.

### Tests of alternative explanations
- Productivity channel:
  - Add interaction between firm TFP and value added growth: main interaction Δlog(푌) × S = -0.011*** (0.000); more productive firms show stronger pass-through (interaction significant at 10 percent) but productivity alone does not explain the main finding.
- Intangible capital / innovation:
  - Controlling for intangibility ratio and its interaction with value added: Δlog(푌) × S = -0.008*** (0.000); firms with higher intangibility have higher wage growth and stronger pass-through.
- Firm age:
  - Interaction with young-firm dummy (≤5 years): Δlog(푌) × S = -0.005*** (0.000); younger firms have higher wage growth and stronger pass-through; main result survives.
- Offshoring/globalization proxy:
  - Firm export revenue share interaction: Δlog(푌) × S = -0.024*** (0.001); pass-through weaker in firms with higher export shares but main result robust.
- Slow-moving global/country/industry trends:
  - Interacting value added growth with common, country-specific, and industry-specific year trends: main interaction remains significant; these interactions indicate pass-through has been declining on average but do not subsume the payroll-share effect.

### Decomposition of wage growth
- Δ ln W = Δ ln w (average wage per employee) + Δ ln l (employment growth).
- Average wage per employee:
  - Δ log(푌) = 0.178*** (0.002); Δlog(푌) × S = -0.005*** (0.000); S = -1.060*** (0.017).
  - Eroding = 21 percent at 99th percentile — labor market power suppresses average wages substantially.
- Employment growth:
  - Δ log(푌) = 0.135*** (0.002); Δlog(푌) × S = -0.003*** (0.000); S = -0.674*** (0.013).
  - Eroding = 16 percent at 99th percentile — labor market power also weakens pass-through to employment but to a lesser extent.

### Cyclical amplification
- Theoretical expectation: markdowns increase when labor mobility weakens (θ→0 and/or ε→0) — thus labor market power effects should be larger in downturns.
- Empirical triple-interaction specification (Δlog(푌) × S × cycle measure):
  - Column 1 (unemployment rate ΔQ):
    - Δlog(푌) = 0.325*** (0.003); Δlog(푌) × S = -0.008*** (0.000); Δlog(푌) × S × ΔQ = -0.062*** (0.022).
    - Example: if unemployment rate increases by 3 percentage points (ΔQ = 0.03), the role of labor market power becomes 25 percent higher compared to a year with no increase.
  - Column 2 (labor market slack ΔQ):
    - Δlog(푌) = 0.309*** (0.005); Δlog(푌) × S = -0.011*** (0.001); triple interaction -0.151*** (0.029).
    - Example: a 3 percentage points increase in labor market slack increases the role of payroll share by 40 percent.
  - Column 3 (real GDP ΔQ):
    - Δlog(푌) = 0.325*** (0.004); Δlog(푌) × S = -0.009*** (0.000); triple interaction 0.036*** (0.011).
    - Example: a 3 percentage points lower economic growth inflates the role of firm labor market power in eroding pass-through by about 12 percent.
- Overall: weakening of pass-through by firms with higher payroll share is amplified in years with worsening labor market conditions or lower GDP growth.

### Policy implications and recommendations
- Policies that enhance competition and labor mobility can strengthen output-to-wage pass-through and improve welfare by enabling workers to benefit more from economic growth.
- Suggested measures (as discussed in the paper):
  - Effective implementation of merger controls and stronger antitrust enforcement.
  - Curtailing lobbying activities by larger firms and reducing entry barriers.
  - Improving restrictions and enforcement against non-compete agreements, no-poaching agreements, and wage-fixing arrangements among employers.
  - Regulatory interventions and case-by-case assessment for measures like merger controls.
  - Cross-border coordination among competition authorities to address global market challenges.
  - Supply-side measures to increase labor mobility: reskilling and upskilling, improving internet accessibility to reduce job search costs, and supporting flexible work arrangements (e.g., work from home).
- Policy emphasis: supporting smaller firms and enhancing labor mobility is especially important during economic downturns to increase labor market resilience and limit erosion of wage pass-through.

### Contributions, implications, and avenues for future research
- Contributions:
  - Provides systematic cross-country firm-level evidence that higher firm labor market share weakens the pass-through of firm value added to wages.
  - Connects to literature on declining labor share, monopsony/oligopsony wage effects, and the rise of superstar firms.
- Implications:
  - The weakened pass-through to average wages in high-market-share firms has implications for consumption, wealth, and inequality; effects may be concentrated among low-earners or less skilled workers.
  - Macroeconomic consequences require worker-level data to assess heterogeneity across earnings groups.
- Suggested future research:
  - Explore the role of specific policies to buttress the link between wages and output.
  - Investigate heterogeneity across labor market segments (low-earners vs high-earners) using worker-level data.
  - Examine whether findings generalize to emerging market and developing economies.

*Source: wpiea2024136-print-pdf*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Overview and research question
- Investigates the role of firm labor market power in the pass-through of firm output to wages.
- Motivated by empirical evidence of wage markdowns (wages below marginal product of labor) and declining labor share of output.
- Key question: Does higher firm labor market share (payroll share in sector) weaken the pass-through of firm value added growth to wage growth?

### Theoretical framework
- Adopts a framework drawing from Atkeson and Burstein (2008) and Berger et al. (2022).
- Assumptions:
  - Finite number of firms use only labor in production; infinite number of industries.
  - Firms are ex-ante heterogeneous in productivity, creating variation in labor market shares (payroll shares).
  - Imperfect labor mobility across firms and sectors yields upward-sloping labor supply curves and wage markdowns.
  - Nested constant elasticity of substitution (CES) functions generate a double-stage labor allocation with higher mobility across firms within industries than across industries.
  - Firms with higher labor market share face flatter (more inelastic) labor supply curves.
- The model produces a closed-form expression showing wage markdowns as a function of firms’ labor market share and predicts a weaker sensitivity of wages to value added for firms with higher payroll share.

### Data and sample
- Empirical tests use ORBIS firm-level data.
- Main sample covers non-farm, non-financial activities with NACE codes ranging between 5-82.
- Cross-country panel: 14 advanced European economies over the period of 2000-2018.
- Firm “wage” is defined as the total “wage-bill” (total cost of employees).

### Empirical strategy (overview)
- Tests whether pass-through of firm value added growth to wage growth varies with firm payroll share in narrowly-defined 4-digit NACE sectors.
- Identification features:
  - Firm fixed effects to control for time-invariant firm-level factors.
  - Country-sector-year fixed effects to absorb trends, developments, or shocks common within each country × 4-digit NACE sector × year cell.
- Controls and robustness:
  - Controls for firm-level characteristics potentially affecting pass-through: productivity, innovative activities, age, export exposure.
  - Accounts for secular trends: globalization, demography and education, technological change via common, country-, and industry-specific trends.

### Main empirical findings
- Positive association between firm value added growth and wage growth, but the relationship weakens for firms with higher payroll share in their sector.
- Quantitative illustrations:
  - For an atomic firm with payroll share of around zero, a 10 percentage points higher growth in value added translates into a 3.3 percentage points boost in wage-bill growth within the same year.
  - At the 99th percentile of the payroll share distribution (corresponding to a 7.5 percent payroll share in a 4-digit sector), almost one fifth of this pass-through disappears.

### Cyclical variation
- Extends specification with triple interactions: firm value added × labor market share × change in unemployment rate.
- Finds that the weakening of pass-through associated with higher firm labor market power becomes more pronounced during periods of increasing unemployment rates and economic downturns.
- Results remain similar when using an extended definition of labor market slack or real GDP growth as an alternative cycle measure.

### Robustness to alternative explanations
- Results persist after controlling for:
  - Firm-level heterogeneity (productivity, innovation, age, export exposure).
  - Secular trends and country-/industry-specific trends.
- Authors note limits on causal claims but argue firm-level panel and fixed effects mitigate omitted variable concerns.

### Policy implications
- Policies that enhance competition and labor mobility can strengthen output-to-wage pass-through and improve welfare by enabling workers to benefit more from economic growth.
- Suggested measures include:
  - Effective implementation of merger controls and stronger antitrust enforcement.
  - Curtailing lobbying activities by larger firms and reducing entry barriers.
  - Improving restrictions and enforcement against non-compete agreements, no-poaching agreements, and wage-fixing arrangements among employers.
  - Regulatory interventions and case-by-case assessment for measures like merger controls.
  - Cross-border coordination among competition authorities to address global market challenges.
  - Supply-side measures to increase labor mobility: reskilling and upskilling, improving internet accessibility to reduce job search costs, and supporting flexible work arrangements (e.g., work from home).
- Policy benefits are especially pronounced during economic downturns; supporting smaller firms can increase labor market resilience.

### Contributions to the literature
- First paper to provide systematic cross-country firm-level evidence that higher firm labor market share weakens the pass-through of firm value added to wages.
- Connects to literature on declining labor share, monopsony/oligopsony wage effects, and the rise of superstar firms, while addressing a broad set of alternative mechanisms using granular firm-level data.

### Paper organization
- Section 2: Theoretical model.
- Section 3: Data.
- Section 4: Empirical methodology.
- Section 5: Results.
- Section 6: Conclusions and implications.

*Source: wpiea2024136-print-pdf - 1. Introduction*

### 2. Theoretical Underpinnings

### 2. Theoretical Underpinnings

### Environment
- Economy: continuum of sectors s ∈ [0,1]. Each sector contains a finite number of firms f ∈ {1,2,...,푁} heterogeneous in productivity.
- Assumptions:
  - Product markets are perfectly competitive.
  - Firms use only labor for production.
  - Representative household allocates homogeneous workers across firms and sectors with imperfect labor mobility within and across sectors.
  - Firm heterogeneity and finite number of firms allow differing firm labor market shares.
- Empirical motivation: model delivers partial equilibrium results to motivate testing the role of firm labor market share in the relationship between wages and value added.

### Household Labor Supply
- Aggregate labor 퐿푡 has a CES aggregation from sectoral labor supply:
  - 퐿푡 = [∫0 1 푙𝑠𝑡^(휖+1)/휖 d s]^(휖/(휖+1))
  - 0 < 휖 < ∞ is elasticity of substitution across sectors.
- Optimal sectoral labor allocation (taking sectoral wages as given):
  - 푙𝑠𝑡 = (푤𝑠𝑡/푊𝑡)^휖 퐿𝑡
  - 푤𝑠𝑡 and 푊𝑡 are sectoral and aggregate wage levels, respectively.
- Within-sector (firm-level) CES aggregation:
  - 푙𝑠𝑡 = [∑_{N} 푙𝑓𝑠𝑡^(휃+1)/휃]^(휃/(휃+1))
  - 0 < 휃 < ∞ is elasticity of substitution across firms within sector s.
- Firm-level labor allocation solution:
  - 푙𝑓𝑠𝑡 = (푤𝑓𝑠𝑡/푤𝑠𝑡)^휃 푙𝑠𝑡
- Combined firm- and sector-level expressions:
  - 푙𝑓𝑠𝑡 = (푤𝑓𝑠𝑡/푤𝑠𝑡)^휃 (푤𝑠𝑡/푊𝑡)^휖 퐿𝑡
  - 푤𝑓𝑠𝑡 = (푙𝑓𝑠𝑡/푙𝑠𝑡)^{1/휃} (푙𝑠𝑡/퐿𝑡)^{1/휖} 푊𝑡
- Labor supply elasticity that firms face:
  - ∂ln푙𝑓𝑠𝑡 / ∂ln푤𝑓𝑠𝑡 = 휃 − (휃 − 휖) 푠𝑓𝑠𝑡
  - Firm labor market share defined as 푠𝑓𝑠𝑡 = (푤𝑓𝑠𝑡 푙𝑓𝑠𝑡) / ∑_{N} (푤𝑓𝑠𝑡 푙𝑓𝑠𝑡)
- Implication: labor supply elasticity varies across firms depending on 휃, 휖 and firm labor market share 푠𝑓𝑠𝑡.

### Firms
- Technology (per firm):
  - 푦𝑓𝑠𝑡 = 푧𝑓𝑠𝑡 푙𝑓𝑠𝑡^훼
  - 훼 ∈ (0,1) is labor share; 푧 is exogenous firm productivity.
- Productivity heterogeneity generates differences in firm labor market shares (more productive firms have greater market shares).
- Perfect competition in product markets implies common prices: 푝𝑓𝑠𝑡 = 푝𝑠𝑡 = 푝𝑡, and for simplicity 푝𝑡 = 1.
- Firms maximize profits:
  - max_{푙𝑓𝑠𝑡} [푧𝑓𝑠𝑡 푙𝑓𝑠𝑡^훼 − 푤𝑓𝑠𝑡 푙𝑓𝑠𝑡]
  - subject to 푤𝑓𝑠𝑡 = (푙𝑓𝑠𝑡/푙𝑠𝑡)^{1/휃} (푙𝑠𝑡/퐿𝑡)^{1/휖} 푊𝑡
- First-order conditions yield wages as marginal product times a markdown:
  - 푤𝑓𝑠𝑡 = 휇(푠𝑓𝑠𝑡) 훼 (푦𝑓𝑠𝑡 / 푙𝑓𝑠𝑡)
  - Markdown 휇(푠𝑓𝑠𝑡) is a function of firm labor market share 푠𝑓𝑠𝑡 and elasticities 휃 and 휖.

### Partial Equilibrium and Markdown Formula
- Rearranged expression linking firm labor cost and value added:
  - 푤𝑓𝑠𝑡 푙𝑓𝑠𝑡 = 휇(푠𝑓𝑠𝑡) 훼 푦𝑓𝑠𝑡
- Firm markdown function:
  - 휇(푠𝑓𝑠𝑡) = 1 / [1 + 1/휃 + (1/휖 − 1/휃) 푠𝑓𝑠𝑡]
- Interpretation of elasticities and labor mobility:
  - As labor mobility costs increase (휃 → 0 or 휖 → 0), labor markets exhibit greater firm labor market power (larger markdowns).
  - As 휃 → ∞ or 휖 → ∞, labor markets approach perfect competition and firm labor market power is eliminated.
- Assumption: workers are less mobile across sectors than within sectors → 휖 < 휃.
  - Under 휖 < 휃, (1/휖 − 1/휃) > 0 and markdowns decrease with firm labor market share:
    - ∂휇(푠𝑓𝑠𝑡)/∂푠𝑓𝑠𝑡 < 0
  - Implication: firms with higher labor market share face more inelastic labor supply curves and suppress wages below marginal product of labor, generating a stronger disconnect between value added and labor costs.
- Empirical strategy: test equation (2) across 14 European countries using firm-level ORBIS data.

*Source: IMF Working Paper — Section 2. Theoretical Underpinnings*

### 5. Results

### 5. Results

### 5.1. Main Results
- Baseline (specification (4)): A 10 percentage points increase in value added growth is associated with a 3.3 percentage points higher growth in firm wage-bill (coefficient on Δ log(푌) = 0.325*** (0.003)).
- Interaction with firm payroll share (푆): Δlog(푌) × 푆 = -0.008*** (0.000); payroll share 푆 coefficient = -1.786*** (0.021). Interpretation: the link between changes in firm value added and wages is weaker for firms with relatively higher payroll share in their 4-digit NACE sector (statistically significant at the 1 percent level).
- Economic magnitudes across payroll share distribution (jointly estimated 훽1 + 훽2푆):
  - At the 99th percentile of payroll share distribution (firm wage-bill share = 7.5 percent), a 10 percentage points increase in value added growth is associated with a 2.7 percentage points higher growth in firm wage-bill — a 19 percent lower pass-through compared to an atomic firm.
  - At the 99.5th percentile (firm payroll share = 13 percent), almost one third of the pass-through erodes compared to an atomic firm.
- Additional baseline observation: the payroll share coefficient is negative, suggesting convergence of wages across firms within 4-digit sectors over time.

### 5.2. Robustness Checks
- Dummy-variable approach (Table 3): defining high payroll share by top percentiles within country-sector-year cells or overall sample:
  - Coefficients on Δ log(푌) remain ~0.324–0.327***.
  - Interaction Δlog(푌) × high-payroll dummy becomes larger with higher cutoff:
    - Country-sector-year cells: -0.020*** (90th), -0.029*** (95th), -0.051*** (99th), -0.060*** (99.5th).
    - Overall sample: -0.063*** (90th), -0.077*** (95th), -0.102*** (99th), -0.112*** (99.5th).
  - Payroll share coefficients also become more negative at higher cutoffs.
  - Example interpretation: ~6 percent erosion at 90th percentile; ~19 percent erosion at 99.5th percentile (relative to peers).
- Time-varying firm controls (Table 4, specification (5)):
  - Including lagged total assets (log) or leverage or lagged wage growth: main interaction remains significant.
  - Δ log(푌) coefficients: 0.322*** (col 1), 0.329*** (col 2), 0.271*** (col 3).
  - Δlog(푌) × 푆: -0.008***, -0.008***, -0.005*** respectively.
  - Lagged assets and leverage are associated with lower subsequent wage growth; lagged wage growth shows mean reversion.
- Alternative dependent/explanatory variables and subsamples (Table 5):
  - Replace value added growth with sales (col 1: Δ log(푌) = 0.405***(0.004)) or revenue growth (col 2: 0.435***(0.004)); replace payroll share with employment share (col 3) — main pattern holds.
  - Payroll share net of sales share (col 4): interaction -0.008*** (0.001).
  - Subsamples: firms with ≥10 employees yearly (col 5), firms with ≥10 years observations (col 6), 4-digit sectors with ≥100 firms/year (col 7), five countries with largest observations (col 8) — results remain significant.
  - Longer windows: 3-year (col 9: Δ log(푌)=0.446***(0.004), interaction -0.011*** (0.000)); 5-year (col 10: Δ log(푌)=0.479***(0.004), interaction -0.011*** (0.001)). Note: longer windows raise the Δ log(푌) coefficient toward ~0.5 from ~0.3; mean value of share of firm wages to value added (levels) is above 0.7 in the sample (25th and 75th percentiles 0.6 and 0.9; standard deviation 0.4).
- Industry heterogeneity (Table 6):
  - Service (col 1): Δ log(푌)=0.297*** (0.003); interaction -0.005*** (0.001); Eroding = 8 percent (99th percentile payroll share ~4.5 percent).
  - Non-service (col 2): Δ log(푌)=0.377*** (0.006); interaction -0.012*** (0.001); Eroding = 40 percent (99th percentile payroll share ~12.3 percent).
  - Tradable (col 3): Δ log(푌)=0.334*** (0.002); interaction -0.009*** (0.000); Eroding = 47 percent (99th percentile payroll share ~17.5 percent).
  - Non-tradable (col 4): Δ log(푌)=0.324*** (0.004); interaction -0.007*** (0.001); Eroding = 12 percent (99th percentile payroll share ~4.4 percent).
  - Manufacturing (col 5): Eroding = 46 percent; Wholesale and retail trade (col 6): Eroding = 11 percent; Construction (col 7): Eroding = 4 percent.
- Time variation (10-year rolling windows, Table 7):
  - Interaction Δlog(푌) × 푆 becomes more negative over time across windows ending 2010–2018 (from -0.007*** to -0.011***).
  - Payroll share coefficient becomes more negative over time (e.g., -1.876*** to -3.069***).
  - Economic importance: erosion at 99th percentile increases from 18 percent in earliest period to 25 percent in most recent period (see footnote).
- Industry granularity (Table 8):
  - Using payroll share in broader industries:
    - 2-digit NACE: Δlog(푌) × 푆 = -0.026*** (0.002); 푆 = -4.659*** (0.246).
    - 1-digit NACE: Δlog(푌) × 푆 = -0.094*** (0.034); 푆 = -13.341*** (3.105).
  - Conclusion: role of labor market power robust to industry definition; mechanical scale effects explained by S decreasing with broader industry definitions.
- Fixed effects and clustering checks: results robust to dropping/altering firm F.E., country-sector-year F.E., alternative fixed-effects schemes, and many clustering schemes (one-way, two-way, three-way, no clustering but robust).

### 5.3. Alternative Explanations
- Productivity channel (Table 9, col 1, specification (6)):
  - Add interaction between firm TFP and value added growth. Main interaction Δlog(푌) × 푆 remains negative and significant: -0.011*** (0.000). Conclusion: empirically rules out firm productivity being the sole driver of the main finding; more productive firms tend to have higher wage growth and somewhat stronger pass-through (interaction significant at 10 percent).
- Intangible capital / innovation (col 2):
  - Control for intangibility ratio and its interaction with value added: Δlog(푌) × 푆 remains -0.008*** (0.000). Firms with higher intangibility have higher wage growth and stronger pass-through.
- Firm age (col 3):
  - Interaction with young-firm dummy (≤5 years): Δlog(푌) × 푆 = -0.005*** (0.000). Younger firms have higher wage growth and stronger pass-through; labor market power result remains after controlling for age.
- Offshoring/globalization proxy (col 4):
  - Use firm export revenue share and its interaction: Δlog(푌) × 푆 = -0.024*** (0.001). Pass-through weaker in firms with higher export revenue shares; main result robust.
- Slow-moving global/country/industry trends:
  - Interact value added growth with a common year trend (col 5): main interaction remains significant and the new interaction implies pass-through has been declining on average.
  - Interact value added growth with country-specific year trends (col 6): role of firm payroll share remains significant; coefficients of these interactions shown in Appendix.
  - Interact with industry-specific year trends (1-digit) (col 7): main result remains robust; industry-specific trends shown in Appendix.

### 5.4. Decomposing wage growth
- Decomposition: Δln푊 = Δln푤 (average wage per employee) + Δln푙 (employment growth).
- Results (Table 10):
  - Average wage per employee (col 1): Δ log(푌) = 0.178*** (0.002); Δlog(푌) × 푆 = -0.005*** (0.000); 푆 = -1.060*** (0.017). Eroding = 21 percent at 99th percentile.
    - Interpretation: firms use labor market power to suppress average wages; about 21 percent of pass-through to average wage per employee is eroded for firms at 99th percentile payroll share versus atomic firm.
  - Employment growth (col 2): Δ log(푌) = 0.135*** (0.002); Δlog(푌) × 푆 = -0.003*** (0.000); 푆 = -0.674*** (0.013). Eroding = 16 percent at 99th percentile.
    - Interpretation: firm labor market power also weakens pass-through to employment, though economically smaller than for average wages; possible mechanisms include unpaid overtime or suppressed new hires.

### 5.5. The Role of Economic Cycles
- Theoretical expectation: wage markdowns increase (greater disconnect between wages and marginal product) when labor mobility decreases or when it becomes costlier for workers to move (θ→0 and/or ε→0); thus firm labor market power should be more pronounced during labor market downturns.
- Empirical tests (specification (7), Table 11):
  - Column 1 (unemployment rate ΔQ):
    - Δlog(푌) = 0.325*** (0.003); Δlog(푌) × 푆 = -0.008*** (0.000); Δlog(푌) × 푆 × ΔQ = -0.062*** (0.022).
    - Interpretation example: if unemployment rate increases by 3 percentage points (ΔQ = 0.03), the role of labor market power becomes 25 percent higher compared to a year with no increase (compare 0.008 vs 0.008 + 0.062 × 0.003).
  - Column 2 (labor market slack ΔQ):
    - Δlog(푌) = 0.309*** (0.005); Δlog(푌) × 푆 = -0.011*** (0.001); triple interaction -0.151*** (0.029).
    - Interpretation: a 3 percentage points increase in labor market slack increases the role of firm payroll share by 40 percent.
  - Column 3 (real GDP ΔQ):
    - Δlog(푌) = 0.325*** (0.004); Δlog(푌) × 푆 = -0.009*** (0.000); triple interaction 0.036*** (0.011).
    - Interpretation: a 3 percentage points lower economic growth inflates the role of firm labor market power in eroding pass-through by about 12 percent (sign and magnitude reported in text).
- Overall: weakening of pass-through from value added to wages by firms with higher payroll share is amplified in years with worsening labor market conditions or lower GDP growth.

*IMF Working Paper — Section 5 (Results) from the supplied PDF content.*

### 6. Conclusions and Implications

### 6. Conclusions and Implications

### Main findings
- The paper identifies a disconnect between wages and output with potential consequences on consumption, wealth and inequality.
- Firm labor market power is proposed and analyzed as a factor affecting this disconnect.
- Empirical evidence uses firm-level data from 14 advanced European economies since the 2000s.
- Key empirical result: against the same amount of value added growth, wage growth is lower in firms with higher labor market power.
- The estimated role of firm labor market power in this disconnect becomes large in firms with substantially high payroll share in their sectors.
- The significant role of labor market power in weakening the pass-through from value added to wages remains similar across different subsamples and is robust when different firm-level explanations and the roles of slow-moving trends are accounted for.

### Cyclicality and downturns
- The channel from firm labor market power to a weaker wage–output pass-through is escalated during downturns (i.e., when unemployment rate or labor market slack increases, or economic growth is lower).
- This escalation is possibly due to a weakening in worker bargaining power during turbulent times.
- The role of policies to address labor market power becomes even more crucial during downturns.

### Policy implications and recommendations
- Policies to improve competitiveness in labor markets can strengthen the pass-through of output to wages.
- Considered measures include:
  - Pro-competition reforms.
  - Enforcements of prohibitions against non-compete agreements.
  - Merger controls.
  - Labor market regulations to prevent labor markets from being controlled by fewer firms.
  - Regulatory intervention when needed.
- Cross-border coordination and cooperation of national competition authorities are important given the interconnectedness of global markets.
- Policies aimed at reskilling and upskilling the labor force would enhance labor mobility across firms and sectors, potentially addressing rising firm labor market power by a few firms.
- Reskilling/upskilling policies are emphasized as especially important in downturns.
- The findings are noted as particularly relevant in the post-Covid-19 period, given that the pandemic had adverse effects on SMEs (e.g., Juergensen et al. 2020).

### Implications for inequality and measurement
- The paper shows that the pass-through of value added to average wages is weakened in firms with greater labor market power.
- This average-wage result has distinct implications for inequality and policy design if firms with high market share suppress wages particularly for low-earners or less skilled workers.
- Assessing macroeconomic consequences (e.g., on wage inequality and overall income inequality) requires going beyond average wage dynamics.

### Suggested avenues for future research
- Explore the role of specific policies to buttress the link between wages and output to better inform policy design.
- Investigate heterogeneity in the wage–output pass-through across different segments of the labor market (for example, low-earners versus high-earners), ideally using worker-level data where available.
- Examine whether the role of firm labor market power in the wage–output disconnect is similar in emerging market and developing economies.

*Source: 6. Conclusions and Implications (wpiea2024136-print-pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024136-print-pdf.pdf_