## 2.1    The firm problem under labor market power

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---

### Profit maximization and markdowns
- Firm static profit maximization (labor choice, other inputs at optimal level): max_l R(l) − w(l) l.
- First-order condition: R′(l) − w′(l) l − w(l) = 0.
- Relationship between marginal product of labor and inverse elasticity of residual labor supply (ε^{-1}_{LS}): R′(l) = (ε^{-1}_{LS} + 1) w(l).
- Definition of markdown (ν): R′(l) / w(l) ≡ ν = ε^{-1}_{LS} + 1.
- Interpretation: markdowns increase as the residual labor supply facing the firm is lower (i.e., the firm has more power on its relevant labor market).

### Estimating the markdown ν (from cost minimization dual)
- Analytical expression used to estimate ν:
  - ν = ( (ε_{X_k} α_{X_k})^{-1} · ε_l α_l ) = ε_l / ε_{X_k} · α_{X_k} / α_l
  - α_{X_k} and α_l are shares of inputs X_k and l in firm revenue.
  - ε_l and ε_{X_k} are output elasticities with respect to those inputs.
- Practical implication: estimating ν requires (i) computing cost shares from balance sheet data and (ii) estimating output elasticities for inputs.

### Estimation of the Output Elasticities
- Production function setup:
  - q_it = β_l l_it + β_m m_it + β_k k_it + ω_it + ε_it
  - q_it: real sales of firm i in year t.
  - l_it: labor costs (log).
  - m_it: material costs (log) — flexible input X_k.
  - k_it: real capital stock (log).
  - ω_it: firm productivity; ε_it: measurement error/unanticipated productivity shocks.
- Under Cobb-Douglas, β_l = ε_l and β_m = ε_{X_k}.

- Identification and estimation approach:
  - Main challenge: simultaneity bias from correlation between unobserved productivity ω_it and input choices.
  - Assumption: productivity follows a first-order Markov process and is a function of flexible inputs and capital: ω_it = h(l_it, m_it, k_it).
  - Estimation method: control function approach following De Loecker and Warzynski (2012) and literature (Olley and Pakes, 1996; Levinsohn and Petrin, 2003; Ackerberg et al., 2015).
  - Two-step estimation:
    1. Remove unanticipated productivity shocks and measurement error using a second-order approximation polynomial to obtain expected output.
    2. Use law of motion for productivity to project productivity on its lagged value and obtain estimates.
  - Moment condition for estimation: E( ξ_it(β) (x_it−1 − k_it) ) = 0, where x_it−1 represents flexible inputs (labor and materials). Firms choose flexible input x_it−1 after capital is determined at t−1 to satisfy Ackerberg et al. (2015) critique.
  - Production function estimated separately for each 2-digit NACE industry to obtain ε_l and ε_{X_k}.
  - Combined with cost shares to compute ν as in equation (4).

### Data
- Data source and cleaning:
  - Primary data: Orbis (Moody’s Bureau van Dijk) with harmonized cross-country financial information for private and public firms.
  - Cleaning follows procedures in Díez, Fan and Villegas-Sánchez (2021) and closely Kalemli-Özcan et al. (2015), Gopinath et al. (2017), Gal (2013):
    - Remove basic reporting mistakes: negative sales, total assets, employment, cost of employees, tangible fixed assets or liabilities; missing or zero values for cost of materials, operating revenue, total assets and missing NACE sectoral code.
    - Additional quality checks: firm age, ratio of short-term to long-term liabilities, ratio of employees to capital, tangible fixed assets to total assets, capital to shareholder funds, total assets to shareholder funds.
    - Filters on annual growth rates of sales, operating revenues and number of employees.
  - Deflation and PPP adjustments:
    - Revenue, wage bill, material costs, cost of goods sold deflated using value added and gross output deflators from OECD, Eurostat and government websites (use 2-digit NACE deflator when available, otherwise 1-digit).
    - PPP adjustments following Inklaar and Timmer (2011, 2014).
    - Capital deflated using WDI PPI-adjusted exchange rates.
    - All variables expressed in U.S. dollars of 2005.

- Sample selection and coverage:
  - Focus on firms with average employment ≥ 20 employees (Calligaris et al., 2018).
  - Drop firms with extremely small labor- (less than 15 percent) and material-cost shares (less than 20 percent; 25 percent for goods producers).
  - Final sample: over 1 million observations, from 10 countries and 11 sectors, between 2000 and 2017.
  - Countries: Austria, Belgium, Germany, Spain, Finland, France, Italy, Norway, Portugal and Sweden.
    - Note: For Austria, Germany, Norway, Portugal and Sweden, sample starts in 2006; results robust to limiting to strongly balanced panel.
  - Sectors (11): (i) agriculture, forestry, & fishing, (ii) mining & Quarrying, (iii) manufacturing, (iv) construction, (v) transportation & storage, (vi) accommodation & food Services, (vii) information & communications, (viii) finance & insurance, (ix) real estate, (x) professionals, science, & technology, and (xi) administrative support.

- Key sample statistics (Table 1):
  - Sample size (N): 1,180,675 observations for Turnover, Capital, MaterialCost, LaborCost; Employment N = 994,934.
  - Means:
    - Turnover (mean): 30,900,000
    - Capital (mean): 7,404,013
    - MaterialCost (mean): 13,800,000
    - LaborCost (mean): 7,443,425
    - Employment (mean): 148
  - Percentiles (p25, p50, p75):
    - p25: Turnover 3,082,000; Capital 2,250,141; MaterialCost 1,133,000; LaborCost 920,099; Employment 27
    - p50: Turnover 6,134,543; Capital 781,445; MaterialCost 2,514,222; LaborCost 1,663,310; Employment 41
    - p75: Turnover 14,300,000; Capital 2,711,000; MaterialCost 6,287,914; LaborCost 3,605,000; Employment 82
  - Notes: Monetary variables are in U.S. dollars of year 2005. Turnover = operating revenue; Capital = tangible fixed assets; MaterialCost = cost of materials; LaborCost = cost of labor; Employment = number of employees.

### Labor Market Power in Europe
- Overview of markdowns (distributional snapshot):
  - Sample median markdown: 1.58.
    - Interpretation: median firm is paying around 60 (=1/1.58) percent of marginal product of labor.
  - Distributional features:
    - Large IQR and standard deviations indicate substantial heterogeneity across firms within sectors.
    - Labor market power pervasive in all industries with sizable differences across sectors.
    - Sectors: accommodation and food services have the lowest markdowns; mining has the largest markdowns.
  - Comparison with literature:
    - Yeh et al. (2022) find median 1.36 (their data back to 1970s when markdowns were smaller); estimates broadly in line though slightly higher.
    - Within range of meta-analysis by Sokolova and Sorensen (2021).

- Table 2: Summary statistics of firm-level markdowns by NACE1 (selected values)
  - Agr. For.&Fish.: Median 1.56, Mean 1.82, IQR 1.34, SD 1
  - Mining&Qua.: Median 2.23, Mean 2.43, IQR 1.48, SD 1.1
  - Manufacturing: Median 1.65, Mean 1.81, IQR 1.2, SD .88
  - Construction: Median 1.69, Mean 1.99, IQR 1.31, SD 1.08
  - Trans.&Sto.: Median 1.24, Mean 1.71, IQR 1.19, SD 1.25
  - Accom.&FoodServ.: Median 1.18, Mean 1.35, IQR .6, SD 2.68
  - Info.&Comm.: Median 1.78, Mean 2.25, IQR 1.82, SD 1.49
  - Fin.&Ins.: Median 2.27, Mean 1.81, IQR 1.2, SD 2
  - RealEstate: Median 2.04, Mean 2.39, IQR 1.97, SD 1.38
  - Prof.Sci&Tech: Median 1.8, Mean 2.17, IQR 1.78, SD 1.35
  - Admin.&SupportServ.: Median 1.64, Mean 2.06, IQR 1.54, SD 1.37
  - All: Median 1.58, Mean 1.83, IQR 1.24, SD 1.01
  - Num. Obs: 1,180,675

### Markdown dynamics across central tendency measures
- Aggregate dynamics (normalized to 2000 = 1):
  - Wage-bill weighted average markdown: small increase of 1.3 percent.
    - This result robust to alternative weights (revenue and employment).
  - Median and simple average markdowns decreased by about 10 percent.
  - Similar declines observed for other percentiles.
- Interpretation: opposing forces and compositional effects — larger firms (higher wage bills) experienced increases in labor market power while most firms saw declines. Section 5.3 formalizes this.

### Markdowns by country and sector
- Goods vs services:
  - Weighted averages: increase in services (blue dashed line) and a very small decrease in goods.
  - Median markdowns: decline in goods and an even larger decline in services — greater variability across service firms than goods firms.
- Country- and sector-level heterogeneity:
  - Spain, Italy, and Norway: decline in markdowns across almost all sectors.
  - Belgium, Finland, and France: increases more common.
  - Sector patterns: accommodation and food services saw declines across most countries; increases more common for transportation and storage.
- Median markdowns decreased in all countries except Belgium and Germany where there was a slight increase.

### Firms Driving Markdown Dynamics
- Markdowns and local market footprint:
  - Method: sort firms into deciles by average markdown; compute median revenue and employment shares within local market (country × NACE2 × year).
  - Findings:
    - Median revenue share increases with markdown decile — higher-markdown firms have higher median revenue share in their local market.
    - Median employment share also increases with markdown decile — higher-markdown firms have higher median employment share.
  - Implication: high-markdown firms have quantitatively relevant presence in local output and labor markets.

- High- and low-markdown firms: dynamics by percentiles:
  - Firm groups by mean markdown: below median (<50%), 50–90%, 90–99%, top 1%.
  - Median markdown evolution within groups:
    - Majority of firms experienced a decline in labor market power.
    - Bottom half (<50%): median markdown declined by approximately 10 percent.
    - 50–90%: almost the same decline (approximately 10 percent).
    - 90–99%: decline around 5 percent (about half as large).
    - Top 1%: did not decrease their markdowns.
  - Complementary sort by wage-bill percentiles:
    - Declines in all groups except the top 1% which registers an increase — larger firms increased average markdown over time.

- Table 3: Summary statistics by mean markdown percentile (mean values)
  - bottom50:
    - Turnover mean 2,000,000
    - Capital mean 0,000
    - MaterialCost mean 5,107,668
    - LaborCost mean 6,854,152
    - Employment mean 6,221,264
    - Listed (%) 129.42
  - 50-90:
    - Turnover mean 39,100,000
    - Capital mean 9,465,817
    - MaterialCost mean 18,300,000
    - LaborCost mean 8,372,503
    - Employment mean 159.53
  - 90-99:
    - Turnover mean 52,100,000
    - Capital mean 10,200,000
    - MaterialCost mean 30,300,000
    - LaborCost mean 9,608,891
    - Employment mean 184.47
  - Top1:
    - Turnover mean 91,500,000
    - Capital mean 11,900,000
    - MaterialCost mean 62,300,000
    - LaborCost mean 15,500,000
    - Employment mean 291.6
- Interpretation:
  - Top-1 percentile firms are largest across turnover, capital, and employment metrics and are more likely to be listed.
  - Top-1 percent firms are relatively more concentrated in some service sectors (Information and Communications; Professional, Scientific and Technical Activities) than in goods sectors (manufacturing) or sectors like accommodation and food services.

### Role of reallocation
- Evidence suggests reallocation toward large, high-markdown firms played a crucial role in the observed divergence:
  - Aggregate wage-bill weighted markdown rose slightly while median and average markdowns fell.
  - Top-1 percent firms did not reduce markdowns and increased their presence (wage-bill and revenue shares), driving the increase in weighted averages.
- Formal decomposition of reallocation effects is conducted in subsequent analysis.

### Melitz-Polanec Decomposition
- Decomposition approach:
  - Follows Melitz and Polanec (2015) dynamic decomposition applied to changes in the aggregate weighted average markdown.
  - Breaks the change into contributions from incumbent, entering, and exiting firms.
  - Each group’s change is further decomposed into:
    - a “within component”: change driven by the increase in average firm markdowns, keeping size fixed (unweighted simple mean change for incumbents).
    - a “reallocation component”: change driven by high-markdown firms increasing their size—wage bills—keeping markdowns fixed (change in covariance between firm markdown and size).
  - Surviving firms: present in both 2000 and 2017.
  - Entering firms: not in 2000 sample but appear in 2017 sample.
  - Exiting firms: present in 2000 but no longer in 2017.

- Key quantitative findings (2000–2017):
  - The weighted average markdown increased by 1.26 percent between 2000 and 2017 (black ‘1.  Total change’ bar).
  - Incumbent firms (dark blue ‘2.  Incumbent’ bar) contributed a total change of -8.2 percent.
    - Incumbent - Within (light blue “2a.  Incumbent - Within”): -12.2 percent (the drop is entirely driven by this within-firm component, measured as the unweighted simple mean change in markdown of incumbents between 2000 and 2017).
    - Incumbent - Realloc: 4 percent (positive change in covariance between markdown and size; high-markdown firms tend to become larger among incumbents).
  - Entry and exit (extensive margin) contributed positively:
    - Entering firms (pink “3a.  Entering”): 5.62 percent (entering firms had a higher than average markdown).
    - Exiting firms (pink “3b.  Exiting”): 3.89 percent (exiting firms had a lower than average markdown).

- Interpretation and implications from the decomposition:
  - The weighted mean increase in markdown between 2000 and 2017 is explained by:
    - Reallocation across firms toward higher-markdown firms gaining higher wage-bill shares (Incumbent - Realloc = 4 percent).
    - Entry-exit dynamics where entrants have higher markdowns and exits have lower markdowns (Entering 5.62 percent; Exiting 3.89 percent).
    - These positive reallocation and extensive-margin effects offset the decline from the within-firm component (-12.2 percent) to yield the net increase of 1.26 percent.
  - Suggests divergent markdown paths: the vast majority of firms saw markdown declines (within-firm), while a few high-markdown firms expanded their wage-bill shares and drove the aggregate increase.

- Related summary findings from the paper (contextual):
  - The paper finds evidence of firm monopsony power in labor markets using firm-level data from 10 European countries.
  - Weighted average markdowns increased 1.3% over 2000-2017.
  - Substantial cross-firm heterogeneity:
    - The median markdown decreased around 10% over the same period.
    - High-markdown firms are large and have a sizable footprint in local product and labor markets.
    - Decomposition shows within-firm markdowns decreased but were offset by strong reallocation effects toward high-markdown firms.

*Source: wpiea2022247-print-pdf - 2.1 The firm problem under labor market power (IMF Working Paper content provided).*

### 2.1    The firm problem under labor market power

### 2.1    The firm problem under labor market power

### Profit maximization and markdowns
- Firm static profit maximization (labor choice, other inputs at optimal level): max_l R(l) − w(l) l.
- First-order condition: R′(l) − w′(l) l − w(l) = 0.
- Relationship between marginal product of labor and inverse elasticity of residual labor supply (ε^{-1}_{LS}): R′(l) = (ε^{-1}_{LS} + 1) w(l).
- Definition of markdown (ν): R′(l) / w(l) ≡ ν = ε^{-1}_{LS} + 1.
- Interpretation: markdowns increase as the residual labor supply facing the firm is lower (i.e., the firm has more power on its relevant labor market).

### Estimating the markdown ν (from cost minimization dual)
- Analytical expression used to estimate ν:
  - ν = ( (ε_{X_k} α_{X_k})^{-1} · ε_l α_l ) = ε_l / ε_{X_k} · α_{X_k} / α_l
  - α_{X_k} and α_l are shares of inputs X_k and l in firm revenue.
  - ε_l and ε_{X_k} are output elasticities with respect to those inputs.
- Practical implication: estimating ν requires (i) computing cost shares from balance sheet data and (ii) estimating output elasticities for inputs.

---

### 2.2    Estimation of the Output Elasticities

### Production function setup
- Industry-specific Cobb-Douglas production function (logs):
  - q_it = β_l l_it + β_m m_it + β_k k_it + ω_it + ε_it
  - q_it: real sales of firm i in year t.
  - l_it: labor costs (log).
  - m_it: material costs (log) — flexible input X_k.
  - k_it: real capital stock (log).
  - ω_it: firm productivity; ε_it: measurement error/unanticipated productivity shocks.
- Under Cobb-Douglas, β_l = ε_l and β_m = ε_{X_k}.

### Identification and estimation approach
- Main challenge: simultaneity bias from correlation between unobserved productivity ω_it and input choices.
- Assumption: productivity follows a first-order Markov process and is a function of flexible inputs and capital: ω_it = h(l_it, m_it, k_it).
- Estimation method: control function approach following De Loecker and Warzynski (2012) and literature (Olley and Pakes, 1996; Levinsohn and Petrin, 2003; Ackerberg et al., 2015).
- Two-step estimation:
  1. Remove unanticipated productivity shocks and measurement error using a second-order approximation polynomial to obtain expected output.
  2. Use law of motion for productivity to project productivity on its lagged value and obtain estimates.
- Moment condition for estimation: E( ξ_it(β) (x_it−1 − k_it) ) = 0, where x_it−1 represents flexible inputs (labor and materials). Firms choose flexible input x_it−1 after capital is determined at t−1 to satisfy Ackerberg et al. (2015) critique.
- Production function estimated separately for each 2-digit NACE industry to obtain ε_l and ε_{X_k}.
- Combined with cost shares to compute ν as in equation (4).

---

### 3    Data

### Data source and cleaning
- Primary data: Orbis (Moody’s Bureau van Dijk) with harmonized cross-country financial information for private and public firms.
- Cleaning follows procedures in Díez, Fan and Villegas-Sánchez (2021) and closely Kalemli-Özcan et al. (2015), Gopinath et al. (2017), Gal (2013):
  - Remove basic reporting mistakes: negative sales, total assets, employment, cost of employees, tangible fixed assets or liabilities; missing or zero values for cost of materials, operating revenue, total assets and missing NACE sectoral code.
  - Additional quality checks: firm age, ratio of short-term to long-term liabilities, ratio of employees to capital, tangible fixed assets to total assets, capital to shareholder funds, total assets to shareholder funds.
  - Filters on annual growth rates of sales, operating revenues and number of employees.
- Deflation and PPP adjustments:
  - Revenue, wage bill, material costs, cost of goods sold deflated using value added and gross output deflators from OECD, Eurostat and government websites (use 2-digit NACE deflator when available, otherwise 1-digit).
  - PPP adjustments following Inklaar and Timmer (2011, 2014).
  - Capital deflated using WDI PPI-adjusted exchange rates.
  - All variables expressed in U.S. dollars of 2005.

### Sample selection and coverage
- Focus on firms with average employment ≥ 20 employees (Calligaris et al., 2018).
- Drop firms with extremely small labor- (less than 15 percent) and material-cost shares (less than 20 percent; 25 percent for goods producers).
- Final sample: over 1 million observations, from 10 countries and 11 sectors, between 2000 and 2017.
- Countries: Austria, Belgium, Germany, Spain, Finland, France, Italy, Norway, Portugal and Sweden.
  - Note: For Austria, Germany, Norway, Portugal and Sweden, sample starts in 2006; results robust to limiting to strongly balanced panel.
- Sectors (11): (i) agriculture, forestry, & fishing, (ii) mining & Quarrying, (iii) manufacturing, (iv) construction, (v) transportation & storage, (vi) accommodation & food Services, (vii) information & communications, (viii) finance & insurance, (ix) real estate, (x) professionals, science, & technology, and (xi) administrative support.

### Key sample statistics (Table 1)
- Sample size (N): 1,180,675 observations for Turnover, Capital, MaterialCost, LaborCost; Employment N = 994,934.
- Means:
  - Turnover (mean): 30,900,000
  - Capital (mean): 7,404,013
  - MaterialCost (mean): 13,800,000
  - LaborCost (mean): 7,443,425
  - Employment (mean): 148
- Percentiles (p25, p50, p75) for variables (exact formatting preserved from the source):
  - p25: Turnover 3,082,000; Capital 2,250,141; MaterialCost 1,133,000; LaborCost 920,099; Employment 27
  - p50: Turnover 6,134,543; Capital 781,445; MaterialCost 2,514,222; LaborCost 1,663,310; Employment 41
  - p75: Turnover 14,300,000; Capital 2,711,000; MaterialCost 6,287,914; LaborCost 3,605,000; Employment 82
- Notes: Monetary variables are in U.S. dollars of year 2005. Turnover = operating revenue; Capital = tangible fixed assets; MaterialCost = cost of materials; LaborCost = cost of labor; Employment = number of employees.

---

### 4    Labor Market Power in Europe

### 4.1 Overview of markdowns (distributional snapshot)
- Sample median markdown: 1.58.
  - Interpretation: median firm is paying around 60 (=1/1.58) percent of marginal product of labor.
- Distributional features:
  - Large IQR and standard deviations indicate substantial heterogeneity across firms within sectors.
  - Labor market power pervasive in all industries with sizable differences across sectors.
  - Sectors: accommodation and food services have the lowest markdowns; mining has the largest markdowns.
- Comparison with literature:
  - Yeh et al. (2022) find median 1.36 (their data back to 1970s when markdowns were smaller); estimates broadly in line though slightly higher.
  - Within range of meta-analysis by Sokolova and Sorensen (2021).
- Table 2: Summary statistics of firm-level markdowns by NACE1 (selected values preserved)
  - Agr. For.&Fish.: Median 1.56, Mean 1.82, IQR 1.34, SD 1
  - Mining&Qua.: Median 2.23, Mean 2.43, IQR 1.48, SD 1.1
  - Manufacturing: Median 1.65, Mean 1.81, IQR 1.2, SD .88
  - Construction: Median 1.69, Mean 1.99, IQR 1.31, SD 1.08
  - Trans.&Sto.: Median 1.24, Mean 1.71, IQR 1.19, SD 1.25
  - Accom.&FoodServ.: Median 1.18, Mean 1.35, IQR .6, SD 2.68
  - Info.&Comm.: Median 1.78, Mean 2.25, IQR 1.82, SD 1.49
  - Fin.&Ins.: Median 2.27, Mean 1.81, IQR 1.2, SD 2
  - RealEstate: Median 2.04, Mean 2.39, IQR 1.97, SD 1.38
  - Prof.Sci&Tech: Median 1.8, Mean 2.17, IQR 1.78, SD 1.35
  - Admin.&SupportServ.: Median 1.64, Mean 2.06, IQR 1.54, SD 1.37
  - All: Median 1.58, Mean 1.83, IQR 1.24, SD 1.01
  - Num. Obs: 1,180,675

### 4.2 Markdown dynamics across central tendency measures
- Aggregate dynamics (normalized to 2000 = 1):
  - Wage-bill weighted average markdown: small increase of 1.3 percent.
    - This result robust to alternative weights (revenue and employment).
  - Median and simple average markdowns decreased by about 10 percent.
  - Similar declines observed for other percentiles.
- Interpretation: opposing forces and compositional effects — larger firms (higher wage bills) experienced increases in labor market power while most firms saw declines. Section 5.3 formalizes this.

### 4.3 Markdowns by country and sector
- Goods vs services:
  - Weighted averages: increase in services (blue dashed line) and a very small decrease in goods.
  - Median markdowns: decline in goods and an even larger decline in services — greater variability across service firms than goods firms.
- Country- and sector-level heterogeneity (sector-by-country heatmap):
  - Spain, Italy, and Norway: decline in markdowns across almost all sectors.
  - Belgium, Finland, and France: increases more common.
  - Sector patterns: accommodation and food services saw declines across most countries; increases more common for transportation and storage.
- Median markdowns decreased in all countries except Belgium and Germany where there was a slight increase.

---

### 5    Firms Driving Markdown Dynamics

### 5.1 Markdowns and local market footprint
- Method: sort firms into deciles by average markdown; compute median revenue and employment shares within local market (country × NACE2 × year).
- Findings:
  - Median revenue share increases with markdown decile — higher-markdown firms have higher median revenue share in their local market.
  - Median employment share also increases with markdown decile — higher-markdown firms have higher median employment share.
- Implication: high-markdown firms have quantitatively relevant presence in local output and labor markets.

### 5.2 High- and low-markdown firms: dynamics by percentiles
- Firm groups by mean markdown: below median (<50%), 50–90%, 90–99%, top 1%.
- Median markdown evolution within groups:
  - Majority of firms experienced a decline in labor market power.
  - Bottom half (<50%): median markdown declined by approximately 10 percent.
  - 50–90%: almost the same decline (approximately 10 percent).
  - 90–99%: decline around 5 percent (about half as large).
  - Top 1%: did not decrease their markdowns.
- Complementary sort by wage-bill percentiles:
  - Declines in all groups except the top 1% which registers an increase — larger firms increased average markdown over time.
- Table 3: Summary statistics by mean markdown percentile (mean values)
  - bottom50:
    - Turnover mean 2,000,000
    - Capital mean 0,000 (source formatting preserved)
    - MaterialCost mean 5,107,668
    - LaborCost mean 6,854,152
    - Employment mean 6,221,264
    - Listed (%) 129.42
  - 50-90:
    - Turnover mean 39,100,000
    - Capital mean 9,465,817
    - MaterialCost mean 18,300,000
    - LaborCost mean 8,372,503
    - Employment mean 159.53
  - 90-99:
    - Turnover mean 52,100,000
    - Capital mean 10,200,000
    - MaterialCost mean 30,300,000
    - LaborCost mean 9,608,891
    - Employment mean 184.47
  - Top1:
    - Turnover mean 91,500,000
    - Capital mean 11,900,000
    - MaterialCost mean 62,300,000
    - LaborCost mean 15,500,000
    - Employment mean 291.6
- Interpretation:
  - Top-1 percentile firms are largest across turnover, capital, and employment metrics and are more likely to be listed.
  - Top-1 percent firms are relatively more concentrated in some service sectors (Information and Communications; Professional, Scientific and Technical Activities) than in goods sectors (manufacturing) or sectors like accommodation and food services.

### 5.3 Role of reallocation
- Evidence suggests reallocation toward large, high-markdown firms played a crucial role in the observed divergence:
  - Aggregate wage-bill weighted markdown rose slightly while median and average markdowns fell.
  - Top-1 percent firms did not reduce markdowns and increased their presence (wage-bill and revenue shares), driving the increase in weighted averages.
- Formal decomposition of reallocation effects is conducted in subsequent analysis (section referenced in source).

*Source: wpiea2022247-print-pdf - 2.1 The firm problem under labor market power (IMF Working Paper content provided).*

### 5.3    Melitz-Polanec Decomposition

### 5.3    Melitz-Polanec Decomposition

### Decomposition approach
- Follows Melitz and Polanec (2015) dynamic decomposition applied to changes in the aggregate weighted average markdown.
- Breaks the change into contributions from incumbent, entering, and exiting firms.
- Each group’s change is further decomposed into:
  - a “within component”: change driven by the increase in average firm markdowns, keeping size fixed (unweighted simple mean change for incumbents).
  - a “reallocation component”: change driven by high-markdown firms increasing their size—wage bills—keeping markdowns fixed (change in covariance between firm markdown and size).
- Surviving firms: present in both 2000 and 2017.
- Entering firms: not in 2000 sample but appear in 2017 sample.
- Exiting firms: present in 2000 but no longer in 2017.

### Key quantitative findings (2000–2017)
- The weighted average markdown increased by 1.26 percent between 2000 and 2017 (black ‘1.  Total change’ bar).
- Incumbent firms (dark blue ‘2.  Incumbent’ bar) contributed a total change of -8.2 percent.
  - Incumbent - Within (light blue “2a.  Incumbent - Within”): -12.2 percent (the drop is entirely driven by this within-firm component, measured as the unweighted simple mean change in markdown of incumbents between 2000 and 2017).
  - Incumbent - Realloc: 4 percent (positive change in covariance between markdown and size; high-markdown firms tend to become larger among incumbents).
- Entry and exit (extensive margin) contributed positively:
  - Entering firms (pink “3a.  Entering”): 5.62 percent (entering firms had a higher than average markdown).
  - Exiting firms (pink “3b.  Exiting”): 3.89 percent (exiting firms had a lower than average markdown).

### Interpretation and implications from the decomposition
- The weighted mean increase in markdown between 2000 and 2017 is explained by:
  - Reallocation across firms toward higher-markdown firms gaining higher wage-bill shares (Incumbent - Realloc = 4 percent).
  - Entry-exit dynamics where entrants have higher markdowns and exits have lower markdowns (Entering 5.62 percent; Exiting 3.89 percent).
  - These positive reallocation and extensive-margin effects offset the decline from the within-firm component (-12.2 percent) to yield the net increase of 1.26 percent.
- Suggests divergent markdown paths: the vast majority of firms saw markdown declines (within-firm), while a few high-markdown firms expanded their wage-bill shares and drove the aggregate increase.

### Related summary findings from the paper (contextual)
- The paper finds evidence of firm monopsony power in labor markets using firm-level data from 10 European countries.
- Weighted average markdowns increased 1.3% over 2000-2017.
- Substantial cross-firm heterogeneity:
  - The median markdown decreased around 10% over the same period.
  - High-markdown firms are large and have a sizable footprint in local product and labor markets.
  - Decomposition shows within-firm markdowns decreased but were offset by strong reallocation effects toward high-markdown firms.

*Source: wpiea2022247-print-pdf - 5.3    Melitz-Polanec Decomposition*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022247-print-pdf.pdf_