## wpiea2019082 - 2015. Second, the markup increase is driven by already high-markup firms (top decile of

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### Major findings and stylized facts
- Markups increased between 2000 and 2015; aggregate (sales-weighted) increase documented as 6 percent over 2000–2015.
- (F1) Global markups have increased by 6 percent between 2000 and 2015.
- (F2) The markup increase is mostly explained by high-markup firms (top decile of the markup distribution).
  - High-markup firms increased markups by 40 percent over the sample.
  - Firms in the bottom half of the markup distribution show stagnant markups.
- (F3) Markup increases concentrated in advanced economies; emerging markets show markups essentially unchanged over 2004–2013.
- (F4) Non-monotonic (U-shaped) relation between firm size and markups: markups decrease with size up to a very large size threshold, then increase for the largest firms (positive relation around the 95th percentile of market share).
- (F5) Aggregate markup increase mostly explained by within-firm increases among incumbent firms and, to a lower extent, by market share reallocation toward high-markup entrants.

### Key quantitative summary statistics (baseline sample)
- Baseline sample: 20 countries over 2000–2015.
- Over 5 million observations (sample statistics note: "Over 5 million observations").
- Average annual income: 55 million U.S. dollars.
- Average firm employment: 194 employees.
- Average sales’ costs (COGS): $40 million.
- Average capital (tangible fixed assets): $20 million.
- Summary turnover, capital, costs of goods sold, employment (Table 2):
  - Turnover: Mean: 55,567,404; P50: 5,536,489; P25: 1,766,910; P75: 16,370,799; N: 5,324,814.
  - Capital: Mean: 19,267,384; P50: 615,310; P25: 103,497; P75: 2,718,327; N: 5,324,814.
  - Costs of goods sold: Mean: 39,561,494; P50: 3,666,147; P25: 1,167,958; P75: 11,676,456; N: 5,324,814.
  - Employment: Mean: 194; P50: 43; P25: 27; P75: 86; N: 4,821,870.
- Average markup increase (headline): "6 percent" over 2000–2015; described also as "average, over 1/3 percentage points per year".
- Dynamic decomposition reported aggregate average markup increase between 2000 and 2015: 6.4% (0.064).

### Measurement and methodology (markup estimation)
- Markup definition: μ_it ≡ P_it / MC_it = β_Vit / α_Vit (Equation (1)), where β_Vit is output elasticity of flexible input V_it and α_Vit is firm expenditure share on that input (P_Vit V_it / P_it Q_it).
- Production function (industry-level, 2-digit NACE Rev.2): q_it = β_ν ν_it + β_k k_it + ω_it + ε_it (Equation (2)), with log variables.
- Estimation framework: control function approach in the Olley-Pakes / Levinsohn-Petrin tradition updated by Ackerberg et al. (2015):
  - First stage: q_it = φ_t(ν_it, k_it) + ε_it, φ approximated by a second-order polynomial plus h(·).
  - Productivity law of motion: ω_it = g_t(ω_i,t−1) + ξ_it; moment condition E(ξ_it(β) (ν_i,t−1, k_i,t)) = 0.
- Baseline flexible input: cost of goods sold (COGS) as composite flexible input; robustness checks include translog, rolling-window elasticities, and inverse-share method (Gandhi et al. (2017)).

### Data, panels and deflation
- Main data source: Orbis Historical (Bureau van Dijk).
- Baseline sample: 20 countries (list provided in source) over 2000–2015.
- Alternative sample: 28 countries over 2004–2013 (adds Austria, China, Czech Republic, Germany, Ireland, Korea, Slovakia, Turkey).
- Monetary values expressed in U.S. dollars of 2005.
- PPP-adjusted sector deflators from OECD, Eurostat and government sources; 2-digit NACE deflators used when available, otherwise 1-digit NACE or country GDP deflator.
- Sample selection: firms with average employment ≥ 20 employees to improve representativeness.

### Baseline aggregate results and robustness
- Aggregate (sales-weighted) markup increased around 6 percent during 2000–2015.
- High-markup firms (top decile) saw a 40 percent increase in markups; bottom-half firms stagnant → increased dispersion.
- Robustness checks:
  - Rolling-window estimation with time-varying β’s: baseline qualitative result unchanged.
  - Translog production function: increase over 2000–2015 amounts to 10 percent.
  - Gandhi et al. (2017) inverse-share (GNR CD): increase amounts to 2 percent.
  - Choice of flexible input matters: using materials tends to generate larger increases than using COGS.
    - In several European countries materials can be isolated; markups using materials increased by around 6 percent while markups using COGS increased by around 3 percent.
  - Incorporating overhead costs (Orbis “Other Operating Expenses"): elasticities with overheads sum to 0.995; baseline elasticities sum to between 0.92 and 0.93; controlling for overheads leaves increase (not level) of average markups mostly unchanged.

### Heterogeneity by markup groups and sectors
- Group definitions:
  - High-markup firms: upper decile of the markup distribution (deciles computed by average markup over whole sample; time-invariant deciles).
  - Middle firms: between median and 90th percentile.
  - Laggards: bottom half (below median).
- Empirical facts:
  - High-markup firms: 40 percent markup increase over sample.
  - Laggards: markups unchanged.
  - Middle firms: slight increases.
- Composition of high-markup group:
  - Majority relatively small and privately held (niche market firms), though group includes some large and publicly listed firms.
  - Present across all sectors; more likely in ICT-intensive sectors and sectors using digital technologies intensively.
- High-markup firms by sector (shares of firms / shares of sales; selected entries from Table 3):
  - Manufacturing: 6% / 16%
  - Electricity, gas, steam and AC: 1% / 17%
  - Wholesale and retail trade: 15% / 5%
  - Accommodation and food service: 11% / 9%
  - Information and communication: 10% / 11%
  - Financial and insurance activities: 6% / 10%

### ICT-intensive sectors
- ICT-intensive classification: sector above median in at least four of five ICT usage dimensions (software investment; ICT tangible investment; intermediate ICT goods; intermediate ICT services; robot use).
- Empirical result: ICT-intensive sectors show higher-than-average increases in markups; average markups in ICT-intensive sectors increased "twice as much" as the overall aggregate.

### Firm size and markups — unconditional and conditional evidence
- Unconditional patterns:
  - Unweighted average markup above weighted average markup (weighted by revenue) → larger firms have lower markups on average.
  - Unconditionally, smaller firms have higher markups even within narrowly defined industries; only the top 5 percentile of firm real sales shows a positive unconditional relation.
- Conditional (regression) evidence (Table 4 main points; precise coefficients preserved):
  - Regression dependent variable: log firm markup (Cobb-Douglas recovery using COGS).
  - Market share (MS) nonlinear (quadratic) results:
    - Cross-sectional: MS coefficient = -0.396*** (0.005) in Column (1).
    - Quadratic specification: MS = -1.277*** (0.011); MS^2 = 1.346*** (0.015) in Column (2). Total effect becomes positive around the 95th percentile of market share distribution.
    - Controlling for productivity and overhead: MS = -1.476*** (0.019); MS^2 = 1.534*** (0.024); logTFP = 0.744*** (0.006); logOverhead = -0.029*** (0.000) in Column (3).
  - Within-firm (firm fixed effects) results:
    - MS = -0.472*** (0.006) in Column (4).
    - Quadratic: MS = -1.443*** (0.015); MS^2 = 1.295*** (0.016) in Column (5).
    - With controls: MS = -1.267*** (0.022); MS^2 = 1.135*** (0.022); logTFP = 0.957*** (0.006); logOverhead = -0.030*** (0.000) in Column (6).
  - Observations: Columns (1)-(3): 5,303,984; 5,303,984; 2,394,304. Columns (4)-(6): 5,201,324; 5,201,324; 2,296,207.
- Additional specification (Table B.1 using log employment):
  - logL coefficients (examples): Column (1): -0.047*** (0.000); Column (2): -0.147*** (0.001) with logL^2 = 0.011*** (0.000); Column (3): logTFP = 0.739*** (0.006); logOverhead = -0.012*** (0.000).
- Conclusion: Conditional on observables and fixed effects, relationship remains U-shaped — markups decrease with size up to a very large threshold, then rise for the largest firms.

### Dynamic decomposition with entry and exit (Melitz and Polanec (2015) adaptation)
- Decomposition objective: split change in aggregate (sales-weighted) markup into contributions from incumbents (continuing firms), entrants, and exitors, and into within-firm and reallocation (covariance) components.
- Firm classification:
  - Incumbents: present in both 2000 and 2015.
  - Entering firms: not in sample in 2000 and by 2015 report at most 15 years of age (enter between 2001 and 2015).
  - Exiting firms: present in 2000 but did not report financial information between 2001 and 2015.
- Baseline sample decomposition (Table 5, Panel A; absolute levels preserved):
  - Change in average markup between 2000 and 2015: total = 0.064 (6.4%).
  - Incumbent Firms: ∆μ = 0.045
    - Within Firm Growth (incumbents): 0.064
    - Market Share Reallocation (incumbents): -0.019
  - Entering Firms: ∆μ = 0.027
    - Within Firm Growth (entrants): -0.009
    - Market Share Reallocation (entrants): 0.036
  - Exiting Firms: ∆μ = -0.008
    - Within Firm Growth (exitors): -0.009
    - Market Share Reallocation (exitors): 0.002
- Interpretation (Panel A):
  - 70% of the markup increase between 2000 and 2015 explained by markup increases by incumbent firms.
  - Entering firms contribute positively, explaining 42% of observed increase.
  - Exiting firms contribute negatively overall (they reduce the aggregate markup change).
  - Among incumbents, within-firm increases dominate but are partly offset by negative reallocation among incumbents.
  - Entrants contribute largely via positive reallocation: entrants with high markups gain market share relative to incumbents.
- Top 5 percentile decomposition (Table 5, Panel B; preserved numbers):
  - Incumbent Firms: ∆μ = 0.073
    - Within Firm Growth: 0.030
    - Market Share Reallocation: 0.026
  - Entering Firms: ∆μ = 0.056
    - Within Firm Growth: -0.002
    - Market Share Reallocation: 0.017
  - Exiting Firms: ∆μ = 0.015
    - Within Firm Growth: 0.001
    - Market Share Reallocation: 0.001
  - TOTAL (Panel B reported total): 0.002
- Interpretation (Panel B and large firms):
  - For top 5 percentile (large firms), reallocation dominates: reallocation effects from incumbents and entrants can explain roughly 60% of the average markup increase between 2000 and 2015.
  - For the largest firms, markup increases are driven mainly by market share reallocation among incumbents and new entrants (reallocation dominates for largest firms).
- U.S. note (textual discussion): U.S.-only decomposition yields overall increase of 11.5% (0.115) with reallocation toward high-markup firms accounting for almost 80% of the total increase (numbers discussed in text of source).

### Robustness, caveats and methodological notes
- Results robust to:
  - Rolling-window estimation allowing time-varying elasticities.
  - Estimating a translog production function.
  - Using Gandhi et al. (2017) inverse-share method.
- Choice of flexible input affects magnitude: materials-based markups show larger increases than COGS-based markups; baseline COGS estimates interpreted as conservative (lower bound).
- Overhead costs inclusion: elasticities sum close to 1 when overheads included; inclusion does not materially change increase in markups.
- Sample and cleaning: extensive Orbis cleaning procedures applied (duplicates rules; dropping negative or implausible values; employment-tier growth filters with exact thresholds preserved in Appendix).

### Policy relevance and interpretation
- Aggregate markup increases moderate in magnitude relative to some literature based only on publicly listed firms; inclusion of privately-held firms yields substantially lower overall increases.
- Heterogeneous markup dynamics suggest policy should account for:
  - The dominant role of incumbent within-firm markup increases,
  - The role of entry and reallocation toward high-markup entrants (especially in large-firm tail and in advanced economies),
  - Sectoral concentration of high-markup increases in ICT-intensive sectors.
- Implications: links between markups and investment, innovation, and labor share imply heterogeneous market-power dynamics matter for competition and industrial policy design.

*Source: IMF Working Paper (wpiea2019082) — content excerpt provided.*

### 2015. Second, the markup increase is driven by already high-markup firms (top decile of

### wpiea2019082 - 2015. Second, the markup increase is driven by already high-markup firms (top decile of

### Major findings
- Markups increased between 2000 and 2015.
- The markup increase is driven by already high-markup firms (top decile of the markup distribution) that charge increasing markups.
- Markups increased mostly among advanced economies but not in emerging markets.
- There is a non-monotonic relation between firm size and markups that is first decreasing and then increasing.
- The increase is mostly driven by increases within incumbents and also by market share reallocation towards high-markup entrants.

### JEL classification and keywords
- JEL Classification Numbers: D2, D4, E2, F6, L1, L4
- Keywords: Markups, Market power, TFP, Firm size
- Author’s E-Mail Address: fdiez@imf.org, jfan@imf.org, and carolina.villegas@esade.edu

### Document purpose and disclaimer
- IMF Working Papers describe research in progress by the author(s) and are published to elicit comments and to encourage debate.
- The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management.

### Table of contents (highlighted sections)
- 1 Overview4
- 2 Measuring Market Power8
- 3 Data11
- 4 Baseline Results12
  - 4.1 High-markup Firms . . . . . . . . . . . . . . . . . . . .15
- 5 Extensions and Robustness Analysis16
  - 5.1 Digital Economy . . . . . . . . . . . . . . . . . . . . . .16
  - 5.2 Alternative Panel and Geographical Disparities . . . . . . . . . .17
  - 5.3 Alternative Specification and Methodology . . . . . . . . . . . . .18
    - 5.3.1 Rolling Window . . . . . . . . . . . . . . . . . . . . . .19
    - 5.3.2 Overhead Costs . . . . . . . . . . . . . . . . . . . . . .20
    - 5.3.3 Production Function Estimation . . . . . . . . . . . . . .20
    - 5.3.4 Choice of Flexible Input . . . . . . . . . . . . . . . . .21
- 6 Markups and Size23
  - 6.1 Cross-Sectional Decomposition . . . . . . . . . . . . . . .23
  - 6.2 A U-Shaped Relationship . . . . . . . . . . . . . . . . . .24

*Source: IMF Working Paper (wpiea2019082) content excerpt provided.*

### 6.3    Dynamic Decomposition with Firm Entry and Exit   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .27

### 6.3    Dynamic Decomposition with Firm Entry and Exit

### Overview
- Market power is measured by markups (price / marginal cost).
- The study computes firm-level markups for firms, publicly listed and privately held, from 20 countries (baseline sample) and an alternative sample of 28 countries.
- Key empirical focus: heterogeneity of markups across countries, sectors, and the firm size distribution; and the drivers of markup dynamics (within-firm changes vs reallocation and entry/exit).

### Stylized facts (as stated)
- (F1) Global markups have increased by 6 percent between 2000 and 2015.
- (F2) The increase in markups is mostly explained by the behavior of high-markup firms (high-markup firms are the top decile of firms ranked by markups).
- (F3) The increase in markups is concentrated in advanced economies.
- (F4) There is a non-monotonic (U-shaped) relationship between firm size and markups.
- (F5) The increase in markups is mostly explained by within-firm increases among incumbent firms and, to a lower extent, by market share reallocation towards high-markup entrants.

### Dynamic decomposition findings (entry, exit, within vs reallocation)
- Most of the aggregate increase in markups is driven by within-firm increases of incumbent firms.
- A smaller but meaningful contribution comes from successful new high-markup firms (entry/reallocation towards entrants).
- For firms in the top 5 percent of the sales distribution, the markup increase is driven mainly by the market share reallocation effect among incumbent firms and new entrants (i.e., reallocation dominates for the largest firms).
- The decomposition is conducted à la Melitz and Polanec (2015).

### Markup heterogeneity and size relation
- High-markup firms (top decile) increased markups by 40 percent over the sample, while firms in the bottom half of the markup distribution show stagnant markups.
- Unconditionally, smaller firms have higher markups (even within narrowly defined industries); only when focusing on the top 5 percentile of the distribution of firm sales is the unconditional relation positive.
- Conditional on observables, the relationship between firm size and markups is U-shaped (markups decrease with size up to a threshold, then increase beyond that threshold).
- The group of high-markup firms is mostly composed of relatively small firms, often operating in niche markets; they are spread economy-wide across all sectors, but more likely in sectors using digital technologies intensively.

### Measuring markups — methodology summary
- Markup for firm i at time t: μ_it ≡ P_it / MC_it = β_Vit / α_Vit (Equation (1)), where:
  - β_Vit is the output elasticity of a flexible input V_it,
  - α_Vit is the firm expenditure share on that input (P_Vit V_it / P_it Q_it).
- Production function estimated by industry (2-digit NACE Rev.2): q_it = β_ν ν_it + β_k k_it + ω_it + ε_it (Equation (2)), with log variables.
- Estimation follows the control function approach (Olley-Pakes / Levinsohn-Petrin tradition) updated by Ackerberg et al. (2015):
  - First stage: q_it = φ_t(ν_it, k_it) + ε_it, with φ approximated by a second-order polynomial plus h(·) (Equation (4)).
  - Productivity law of motion: ω_it = g_t(ω_i,t−1) + ξ_it; moment condition E(ξ_it(β) (ν_i,t−1, k_i,t)) = 0 (Equation (5)).
- Baseline uses Cobb-Douglas with one flexible input (cost of goods sold, COGS); robustness checks include translog production function, rolling-window elasticities, and the inverse-share method of Gandhi et al. (2017).

### Data and sample
- Main data source: Orbis Historical (Bureau van Dijk).
- Baseline sample: 20 countries over 2000-2015 (Belgium, Bulgaria, Denmark, Estonia, Finland, France, Great Britain, Greece, Hungary, Italy, Japan, Latvia, Netherlands, Poland, Portugal, Romania, Russia, Slovenia, Spain, United States).
- Alternative sample: 28 countries over 2004-2013 (adds Austria, China, Czech Republic, Germany, Ireland, Korea, Slovakia, Turkey).
- Sample selection and cleaning:
  - Follow cleaning procedures in Kalemli-Özcan et al. (2015), Gopinath et al. (2017), Gal (2013); Appendix A details duplicates and data cleaning.
  - Filters applied for reporting mistakes (negative values, missing key variables), firm age, liability ratios, employee-to-capital ratios, and annual growth rates by company size.
  - Focus on firms with average employment ≥ 20 employees to improve representativeness and comparability.
- Deflation and units:
  - PPP-adjusted sector deflators compiled from OECD, Eurostat and government sources; 2-digit NACE deflators used when available, otherwise 1-digit NACE or country GDP deflator.
  - Monetary values expressed in U.S. dollars of 2005.
- Sample statistics (baseline sample):
  - Over 5 million observations.
  - Average annual income: 55 million U.S. dollars.
  - Average firm employment: 194 employees.
  - Average sales’ costs (COGS): $40 million.
  - Average capital (tangible fixed assets): $20 million.

### Baseline aggregate results
- Aggregate markup (sales-weighted) increased around 6 percent during 2000-2015 (global perspective; Figure 1).
- The moderate increase in average markups is robust to alternative weighting schemes (see Figure B.1 in Appendix B); weighting by costs vs sales affects the magnitude but not the qualitative result.
- Markup increases and dispersion:
  - High-markup firms (top decile) saw a 40 percent increase in markups.
  - Bottom-half firms show stagnant markups, leading to an increase in markup dispersion.

### Robustness and caveats
- Results robust to:
  - Rolling-window estimation allowing time-varying elasticities.
  - Estimating a translog production function instead of Cobb-Douglas.
  - Using the inverse-share method of Gandhi et al. (2017) instead of the control function approach.
- Choice of flexible input matters: using materials tends to generate larger increases in estimated markups than using cost of goods sold.

### Contribution to literature
- Extends markup evidence beyond publicly listed firms by including privately-held firms across multiple countries.
- Finds overall markup increases significantly lower than studies based on publicly listed firms only.
- Documents a previously unknown stylized fact: a non-monotonic (U-shaped) relationship between markups and firm size.
- Provides cross-country evidence showing markup increases concentrated in advanced economies and driven by a small fraction of high-markup firms.

*Source: IMF Working Paper (excerpt provided from wpiea2019082 PDF).*

### 2015.  The alternative sample includes all countries listed in the table, with the countries from the

### wpiea2019082 - 2015. The alternative sample includes all countries listed in the table, with the countries from the

### Summary statistics (Table 2)
- Turnover
  - Mean: 55,567,404
  - P50: 5,536,489
  - P25: 1,766,910
  - P75: 16,370,799
  - N: 5,324,814
- Capital
  - Mean: 19,267,384
  - P50: 615,310
  - P25: 103,497
  - P75: 2,718,327
  - N: 5,324,814
- Costs of goods sold
  - Mean: 39,561,494
  - P50: 3,666,147
  - P25: 1,167,958
  - P75: 11,676,456
  - N: 5,324,814
- Employment
  - Mean: 194
  - P50: 43
  - P25: 27
  - P75: 86
  - N: 4,821,870
- Notes: All monetary variables are expressed in U.S. dollars of 2005. Turnover refers to operating revenue; Capital corresponds to tangible fixed assets; Employment is the number of employees; Costs of goods sold is the direct cost attributable to the production of the goods sold in a company. For countries reporting separately material and labor costs, the two variables are added to construct a synthetic costs of goods sold.

### Average global markup (Figure 1 and headline findings)
- Aggregate evolution
  - Average global markup increased over 2000–2015.
  - The documented aggregate increase corresponds to stylized fact (F1).
  - The aggregate increase is described as a "6 percent increase" in markups (context indicates sizable but moderate).
  - The increase is "on average, over 1/3 percentage points per year".
- Comparison to other studies
  - Increase found is much more moderate than in De Loecker and Eeckhout (2017, 2018) and Dı́ez et al. (2018).
  - Inclusion of private firms (present here) versus only publicly listed firms (in earlier studies) is a key difference.
  - Findings align with Calligaris et al. (2018) which also use Orbis.
- Methodological robustness points (referenced)
  - Baseline results robust to: translog production function estimation; gross output production function (Gandhi et al. (2017)); re-estimating production function over 5-year rolling windows; choice of input used in markup calculation.

### Heterogeneity: High-markup, Middle, and Laggard firms (Figure 2 and Section 4.1)
- Group definitions
  - High-markup firms: upper decile of the markup distribution (deciles computed by average markup over whole sample; deciles are time-invariant; results robust to recomputing annually).
  - Middle firms: between median and 90th percentile.
  - Laggards: bottom half (below the median).
- Key empirical facts (stylized fact F2)
  - High-markup firms increased their markups by 40 percent over the sample period.
  - Laggard firms kept their markups unchanged.
  - Middle firms increased markups only slightly.
- Composition and sectoral dispersion
  - High-markup group includes some large and publicly listed firms but the majority are rather small and privately held (niche market firms).
  - High-markup firms found in all broad economic sectors; substantial heterogeneity in markups within sectors and within four-digit industries (dispersion increasing over time).
  - Sectors with relatively higher likelihood of high-markup firms: information and communication; wholesale and retail; accommodation and food services.
  - In terms of revenue, most important sectors among high-markup firms: manufacturing; utilities; information and communication; financial sector.

### High-markup firms by sector (Table 3)
- Share of Firms / Share of Sales
  - Agriculture, forestry and fishing: 1% / 0%
  - Mining and quarrying: 2% / 6%
  - Manufacturing: 6% / 16%
  - Electricity, gas, steam and AC: 1% / 17%
  - Water supply; sewerage; waste management: 3% / 1%
  - Construction: 6% / 1%
  - Wholesale and retail trade: 15% / 5%
  - Transporting and storage: 8% / 8%
  - Accommodation and food service: 11% / 9%
  - Information and communication: 10% / 11%
  - Financial and insurance activities: 6% / 10%
  - Real estate activities: 7% / 2%
  - Professional, scientific and technical serv.: 8% / 3%
  - Administrative and support services: 6% / 2%
  - Education: 1% / 0%
  - Human health and social work activities: 4% / 4%
  - Arts, entertainment and recreation: 3% / 2%
  - Other services activities: 2% / 3%

### Digital economy and ICT-intensive sectors (Section 5.1, Figure 3)
- Identification of ICT-intensive sectors
  - Sectors sorted into quartiles by ICT usage dimensions: software investment; ICT tangible investment; intermediate ICT goods; intermediate ICT services; robot use (OECD (2017) estimates).
  - A sector classified as ICT-intensive if above the median in at least four of these categories.
- Empirical result
  - ICT-intensive sectors show higher-than-average increases in markups.
  - Average markups in ICT-intensive sectors increased "twice as much" as the overall aggregate.
  - Result is consistent with Calligaris et al. (2018).

### Geographical disparities and alternative panel (Section 5.2, Figure 4)
- Panels considered
  - Baseline panel: 20 countries over 2000–2015.
  - Alternative panel: 28 countries over 2004–2013 (includes large economies such as China and Germany).
- Advanced vs. emerging markets (stylized fact F3)
  - Advanced economies: markups increased by almost 5 percent during 2004–2013.
  - Emerging markets: markups remain essentially unchanged during 2004–2013.
  - These patterns align with Dı́ez et al. (2018) and De Loecker and Eeckhout (2018) for publicly traded firms.

### Robustness and alternative specifications (Section 5.3, Figure 5)
- Rolling window (Panel A)
  - Production function estimated over 5-year periods with time-varying β’s; markups from rolling window similar to baseline.
  - Conclusion: moderate global markup increase robust to allowing time-varying technology.
- Overhead costs (Panel B)
  - Re-estimated production function incorporating overhead costs (Orbis variable “Other Operating Expenses”) using subsample (roughly half the sample report this variable).
  - Markups recomputed controlling for overhead costs: increase (not level) of average markups remains mostly unchanged.
  - Elasticities with overheads: sum to 0.995 (consistent with constant returns to scale); baseline elasticities sum to between 0.92 and 0.93.
  - Conclusion: shifts in overhead costs play a small part in overall rise in markups.
- Production function estimation alternatives (Panel C)
  - Translog production function: increase in markups over 2000–2015 amounts to 10 percent.
  - Gandhi et al. (2017) approach (GNR CD): increase amounts to 2 percent.
  - Baseline estimates lie between these alternatives — all point to a moderate increase in average global markups since 2000.
- Choice of flexible input (Panel D)
  - Baseline uses cost of goods sold (COGS) as composite flexible input; for some European countries materials and labor observed separately.
  - In several European countries (Belgium, Bulgaria, Estonia, Finland, France, Hungary, Italy, Poland, Portugal, Romania, Slovenia, Spain) materials can be isolated.
  - Markups using materials increased by around 6 percent while markups using COGS increased by around 3 percent.
  - Implication: baseline estimates (using COGS) are conservative and can be thought of as a lower bound.

### Markups and firm size (Section 6, Figure 6)
- Unconditional correlation
  - Unweighted average markup is above the weighted average markup (weighted by firm revenue), suggesting larger firms have lower markups on average.
  - De Loecker and Eeckhout (2017) find a negative correlation between markups and size that becomes positive within narrowly defined industries.
  - This study finds a negative relation between markups and size even within narrow industries; only in the top 5 percentile of the distribution of firm real sales is a positive relation observed.
- Research direction
  - The paper proceeds to explore in detail the relationship between firm markups and size to reconcile a priori contradictory results.

*Italic: Source — authors’ calculations based on data from Orbis as presented in the supplied content.*

### 6.1    Cross-Sectional Decomposition

### 6.1    Cross-Sectional Decomposition

### Cross-sectional decomposition framework and key patterns
- Decomposition used: μ_t = ∑_i s_it μ_it = ̄μ_t + ∑_i (s_it − ̄s_t)(μ_it − ̄μ_t) (equation (7)), where:
  - μ_t is the firm-sales-weighted average markup,
  - s_it is firm i’s sales share (P_it Y_it / S_t),
  - ̄μ_t is the unweighted average of markups,
  - the second term is the covariance between firm size and firm markup.
- Empirical pattern:
  - The weighted average markup (μ_t, black solid line in Figure 6) is always below the unweighted average (̄μ_t, blue line), implying larger firms have lower markups.
  - The covariance term (size × markup) has slightly increased since the global financial crisis.
- Sectoral (four-digit industry) decomposition: μ_t = ̄M_t + ∑_s (s_st − ̄s_st)(μ_st − ̄M_t) (equation (8)), where ̄M_t = ∑_s μ_st S_t is the unweighted sectoral average.
  - Findings from Figure 7:
    - Negative correlation between size and markup holds even within narrowly defined industries.
    - The negative covariance within sectors has been decreasing over time, especially in recent years.
    - The within-sector correlation is positive only for the top 5 percentile of the firm-sales distribution (Panel B).

### Conditional correlations and nonlinearities (Table 4)
- Regression setup: dependent variable = log firm markup (recovered from Cobb-Douglas production function using cost of goods sold as the flexible input). MS = market share (firm sales / country-sector-4-digit-year sales). logTFP = log total factor productivity. logOverhead = log other operating expenses. Country-4-digit-industry-year fixed effects included in all columns. Columns (4)-(6) include firm fixed effects.
- Cross-sectional results (Columns (1)-(3)):
  - Column (1): MS coefficient = -0.396*** (standard error 0.005). Interpretation: unconditional result that larger firms charge lower markups on average.
  - Column (2): MS coefficient = -1.277*** (0.011); MS^2 coefficient = 1.346*** (0.015). Nonlinear (quadratic) relationship: negative at low sizes, positive at high sizes.
    - Total effect becomes positive around the 95th percentile of the market share distribution (corresponds to stylized fact F4).
  - Column (3): MS = -1.476*** (0.019); MS^2 = 1.534*** (0.024); logTFP = 0.744*** (0.006); logOverhead = -0.029*** (0.000). Results robust to controlling for productivity and overhead.
- Within-firm (firm fixed effects) results (Columns (4)-(6)):
  - Column (4): MS = -0.472*** (0.006).
  - Column (5): MS = -1.443*** (0.015); MS^2 = 1.295*** (0.016).
  - Column (6): MS = -1.267*** (0.022); MS^2 = 1.135*** (0.022); logTFP = 0.957*** (0.006); logOverhead = -0.030*** (0.000).
- Observations:
  - Columns (1)-(3) Observations: 5,303,984; 5,303,984; 2,394,304 respectively.
  - Columns (4)-(6) Observations: 5,201,324; 5,201,324; 2,296,207 respectively.
- Robustness notes:
  - Similar results hold if revenue or employment are used as firm-size measures (see referenced Appendix B.1).
  - Findings robust to one-period lagged regressors.

### Stylized facts from cross-sectional analysis
- Stylized fact F4: The relation between markup and size is U-shaped — markups decrease with firm size up to a very large size threshold, then increase for the largest firms (positive relationship only for firms around the 95th percentile of market share).

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### 6.2    A U-Shaped Relationship

### Empirical evidence of non-monotonicity
- Distributional evidence (Figure 8):
  - Plot of share of average sales by decile of the markup distribution shows overall negative relation between markup and size, but a positive relationship in the three upper deciles.
  - Conclusion: unconditional non-monotonicity (U-shaped relationship) — negative overall, positive at the top tail of the markup distribution.

### Conditional analysis summary
- Conditioning on country-four-digit industry-year fixed effects and firm observables (TFP, overhead) preserves the U-shaped relation.
- The positive effect of size on markups emerges only at the extreme top of the size distribution (around the 95th percentile), consistent with De Loecker and Eeckhout (2017).

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### 6.3    Dynamic Decomposition with Firm Entry and Exit

### Decomposition approach
- Method: Melitz and Polanec (2015) dynamic Olley-Pakes decomposition extended to markups — decomposes change in average markups into contributions from incumbents, entrants, and exitors, and further into "within component" (change in average markups) and "reallocation component" (change in covariance of markup and market share).
- Sample period: 2000–2015.
- Firm classification:
  - Incumbents: present in both 2000 and 2015.
  - Entering firms: not in sample in 2000 and by 2015 report at most 15 years of age (enter between 2001 and 2015).
  - Exiting firms: present in 2000 but did not report financial information between 2001 and 2015.
- Average markup increase in the sample (2000 to 2015): 6.4% (0.064).

### Baseline sample decomposition (Table 5, Panel A)
- Change in average markup between 2000 and 2015: total = 0.064 (6.4%).
- Contributions by firm type (levels):
  - Incumbent Firms: ∆μ = 0.045
    - Within Firm Growth (incumbents): 0.064
    - Market Share Reallocation (incumbents): -0.019
  - Entering Firms: ∆μ = 0.027
    - Within Firm Growth (entrants): -0.009
    - Market Share Reallocation (entrants): 0.036
  - Exiting Firms: ∆μ = -0.008
    - Within Firm Growth (exitors): -0.009
    - Market Share Reallocation (exitors): 0.002
- Summary interpretations:
  - 70% of the markup increase between 2000 and 2015 is explained by markup increases by incumbent firms.
  - Entering firms contribute positively to markup growth, explaining 42% of the observed increase.
  - Exiting firms contribute negatively overall (reduce the markup increase).
  - For incumbents, the within-firm shift (unweighted mean change in incumbent markups between 2000 and 2015) explains most of incumbents' contribution; a negative reallocation effect (reduction in covariance of markup and market share among incumbents) offsets part of this increase.
  - For entrants, the within-firm average markup in 2015 is close to 1% lower than incumbents’ average in 2015, yet entrants contribute via a significant positive reallocation term: entrants with high markups have higher market shares compared to incumbents.

### Top 5 percentile decomposition (Table 5, Panel B)
- Sub-sample: top 5 percentile of the sales distribution (large firms).
- Change in average markup between 2000 and 2015: total = 0.073 for incumbents + 0.056 entrants + 0.015 exitors = 0.002 TOTAL (note: table reports component breakdown; interpret relative contributions below).
- Panel B breakdown (numbers reported in table):
  - Incumbent Firms: ∆μ = 0.073
    - Within Firm Growth: 0.030
    - Market Share Reallocation: 0.026
  - Entering Firms: ∆μ = 0.056
    - Within Firm Growth: -0.002
    - Market Share Reallocation: 0.017
  - Exiting Firms: ∆μ = 0.015
    - Within Firm Growth: 0.001
    - Market Share Reallocation: 0.001
  - TOTAL (panel B reported total): 0.002
- Key implications for large firms:
  - Within-firm average markup and reallocation effects contribute roughly equally to the increase in incumbent firms’ average markup.
  - For entrants among large firms, the increase is purely driven by reallocation effects.
  - For large firms overall, reallocation effects (from incumbents and entrants) can explain 60% of the average markup increase between 2000 and 2015.
  - U.S.-only (discussion): decomposition limited to U.S. firms yields an overall increase of 11.5% (0.115) with reallocation toward high-markup firms accounting for almost 80% of the total increase (discussion in text; numbers not in table but stated in source).

### Interpretation and economic significance
- The markup increase between 2000 and 2015 is mainly explained by:
  - Increases in average markup of incumbent firms (within-firm growth), and
  - Sizable reallocation effects toward new firms that gain market share and have high markups.
- Exiting firms reduce the aggregate markup change because exiting firms had higher average markups in 2000 than incumbents.
- For large firms and particularly U.S. firms, reallocation toward high-markup firms is a dominant force — consistent with resource shifts toward high-markup, high-productivity firms being growth-enhancing if those firms are more productive at the margin.

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### Conclusion (excerpts and synthesis)
- Aggregate finding: average markups increased by about 6 percent in 2000–2015.
- Heterogeneity:
  - Increase driven by high-markup firms at the top of the markup distribution — their markups increased by 40 percent during the sample period.
  - Increases concentrated mostly among firms from advanced economies.
- Firm size vs. markup:
  - Non-monotonic (U-shaped) relationship: markups decrease with firm size up to a very large size threshold, then increase for the largest firms.
  - Positive size-markup relation only at the very top of the size distribution.
- Dynamic drivers:
  - Most of the aggregate markup increase is explained by within-incumbent increases and reallocation favoring high-markup entrants.
- Policy relevance:
  - Given links between markups and investment, innovation, and the labor share, policymakers should consider the heterogeneous dynamics of markups and the roles of incumbents and entrants when designing competition and industrial-policy responses.

*Source: wpiea2019082 - 6.1 Cross-Sectional Decomposition (IMF working paper content).*

### Appendix for Online Publication

### Appendix for Online Publication

### A Data

- Data source: Orbis dataset (Orbis Historical and Current Orbis databases). Cleaning steps based on Kalemli-Özcan et al. (2015), Gopinath et al. (2017) and Gal (2013).

H3: A.1 Duplicates
- Rules applied when duplicates found:
  - (1) Kept company accounts that are unconsolidated (U1 or U2 in Orbis) or unknown (LF).
  - (2) Removed accounts that are duplicates and not “annual report” types.
  - (3) Removed accounts that are duplicates for firms reporting data that refers to less than 12 months of operations.
  - (4) Kept accounts that are duplicates but have the closest reporting date to Dec. 31st in the corresponding year.
  - (5) If duplicates remained, kept accounts that have more non-missing variables to calculate TFP.

H3: A.2 Data Cleaning
- Two main steps: cleaning of basic reporting mistakes, and further quality checks on data consistency.

- Cleaning of basic reporting mistakes:
  - Dropped firms if they have negative total assets, employment, sales or tangible fixed assets in any year; or if they have more than 2 million employees in any year.
  - Dropped firm-year observations with missing, zero, or negative values for costs of materials, operating revenue and total assets.
  - Dropped firms if they do not have a NACE code.
  - Calculated ratios: number of employees per million of assets, revenue, and revenue/assets; filtered out the top and bottom 0.1 percent of the sample based on these ratios. Did not drop observations if any of these ratios is missing.

- Further quality checks:
  - Constructed firm age variable and dropped firm-year observations with non-positive age.
  - Dropped firm-year observations if there are non-positive liabilities. Calculated liabilities by two methods and dropped observations if the ratio of these methods is greater than 1.1 or smaller than 0.9.
  - Dropped observations if intangible fixed assets are negative, or if fixed assets are zero or negative.
  - Dropped observations with missing costs of employees and the number of employees, as well as those with non-positive costs of employees.
  - Dropped observations with negative values in variables: current liabilities, non-current liabilities, current asset, loans, creditors, other non-current liabilities, long-term debt, shareholder funds, value added, depreciation and amortization.
  - Dropped observations if the ratio of short-term to long-term bank liabilities is greater than 1.1.
  - Checked ratios and dropped extreme values; winsorized by dropping the top and bottom 0.1 percent. Ratios include:
    - costs of employees to capital,
    - tangible fixed assets to total assets,
    - other shareholder funds to total assets,
    - costs of employees to value added,
    - capital to shareholder funds,
    - total assets to shareholder funds.
  - Applied filters on annual growth rates of sales, operating revenues and number of employees. Different thresholds applied by employment size tier; firms with annual growth rates above thresholds were dropped.

- Exact employment-tier thresholds for annual growth filters:
  - For firms with known (lagged) employment:
    - For firms with 0-10 employees, drop if employment growth is>1000%
    - For firms with 11-20 employees, drop if employment growth>500%
    - For firms with 21-50 employees, drop if employment growth>300%
    - For firms with 50-100 employees, drop if employment growth>200%
    - For firms with 100+ employees, drop if employment growth>100%
  - For sales and operating revenue the same tiers were used but "the threshold is twice as large."
  - For firms with missing (lagged) employment, drop firms when sales (revenue) growth is greater than 2000%.

### B Additional Results

- Figure B.1: Markup Increase by Weighting Scheme
  - Notes: Sample includes all countries in the Baseline Sample of Table 1. Firm-level markups estimated according to equation (6) where β^ν_s is estimated separately for each country-2-digit sector. Markups weighted by firm’s revenue, value added, wage bill, and cost of goods sold.

- Figure B.2: Increase in Profitability
  - Notes: Sample includes all countries in the Baseline Sample of Table 1. Firm-level profitability computed as the ratio of EBIT to revenue. (Figure shows series over 2000, 2003, 2006, 2009, 2012, 2015.)

- Figure B.3: Dispersion log(Markup)
  - Notes: Sample includes all countries in the Baseline Sample of Table 1. Dispersion computed as the standard deviation of firm log-markups within a country-four-digit-industry-year and then averaged over time using time invariant value added country-four-digit-industry weights that add up to one. (Figure shows series over 2000, 2003, 2006, 2009, 2012, 2015.)

- Table B.1: Markups and Firm Size: Conditional Correlation — key coefficients and sample details
  - Dependent variable: log Firm Markup (recovered for Cobb-Douglas production function using cost of goods sold as flexible input).
  - Coefficients (standard errors in parentheses):
    - logL:
      - Column (1): -0.047*** (0.000)
      - Column (2): -0.147*** (0.001)
      - Column (3): -0.089*** (0.001)
      - Column (4): -0.085*** (0.001)
      - Column (5): -0.162*** (0.002)
      - Column (6): -0.076*** (0.002)
    - logL^2:
      - Column (2): 0.011*** (0.000)
      - Column (3): 0.004*** (0.000)
      - Column (5): 0.011*** (0.000)
      - Column (6): 0.002*** (0.000)
    - logTFP:
      - Column (3): 0.739*** (0.006)
      - Column (6): 0.942*** (0.006)
    - logOverhead:
      - Column (3): -0.012*** (0.000)
      - Column (6): -0.018*** (0.000)
  - Observations:
    - Columns (1)-(3): 4,768,438; 4,768,438; 2,293,421
    - Columns (4)-(6): 4,646,271; 4,646,271; 2,196,144
  - Fixed effects and clustering:
    - Firm FE: no in Columns (1)-(3); yes in Columns (4)-(6)
    - Country-Industry-Year FE: yes in all columns
    - Standard errors clustered at the firm level (noted in the table).

### C Dynamic OP Decomposition with Entry and Exit

- Objective: Adapt Melitz and Polanec (2015) dynamic productivity decomposition to aggregate markup (weighted average of firm markup levels), following Olley and Pakes (1996) decomposition logic and Melitz and Polanec (2015) appendix derivations.

- Definitions and baseline decomposition:
  - Mt = sum_i s_it μ_it = μ̄_t + sum_i (s_it − μ̄_s_t)(μ_it − μ̄_t) = μ̄_t + cov(s_it, μ_it)
    - Mt is the firm sales weighted average markup.
    - s_it is the share of firm sales (P_it Y_it) in total sales S_t = sum_{i,t} P_it Y_it.
    - μ̄ denotes the unweighted average of markups.
    - The second term is the covariance between firm size s_it and firm markup μ_it.

- Extension with entry and exit:
  - Let G_t = sum_{i∈G} s_it be aggregate market share of group G: continuing firms (c), entrants (e), exitors (x).
  - Aggregate markup expressions for two periods:
    - M1 = s_c1 M_c1 + s_x1 M_x1 = M_c1 + s_x1 (M_x1 − M_c1)
    - M2 = s_c2 M_c2 + s_e2 M_e2 = M_c2 + s_e2 (M_e2 − M_c2)

- Relative change in aggregate markup (normalized by μ̄):
  - (M2 − M1)/μ̄ =
    - (M_c2 − M_c1)/μ̄ + s_e2 (M_e2 − M_c2)/μ̄ + s_x1 (M_c1 − M_x1)/μ̄
    - Rewritten:
      - = [1/(1 − ˜cov_c/μ̄_c/μ̄)] (∆ μ̄_c/μ̄_c + ∆ ˜cov_c) + s_e2 (M_e2 − M_c2)/μ̄ + s_x1 (M_c1 − M_x1)/μ̄
    - Where ˜cov = cov(s, μ/μ̄) = cov(s, μ)/M representing the share of aggregate markup M driven by the correlation between markups and market shares.
    - μ̄ = 1/2 (M1 + M2)
    - μ̄_c = 1/2 (M_c1 + M_c2)
    - ˜cov_c = 1/2 (˜cov_c2 + ˜cov_c1), time averages over periods 1 and 2.

- Decomposition of continuing firms and entry/exit contributions:
  - Continuing firms split into:
    - Within-firm markup changes: change in unweighted mean ∆ μ̄_c.
    - Between-firm scale-independent covariance changes: ∆ ˜cov_c.
  - Entry and exit decompositions:
    - (M_c1 − M_x1)/μ̄ = [1/(1 − ˜cov_1/μ̄_1)] ( μ̄_c1 − μ̄_x1)/μ̄_1 + (˜cov_c1 − ˜cov_x1)
    - (M_e2 − M_c2)/μ̄ = [1/(1 − ˜cov_2/μ̄_2)] ( μ̄_e2 − μ̄_c2)/μ̄_2 + (˜cov_e2 − ˜cov_c2)
    - Where:
      - ˜cov_1 = s_x1 ˜cov_c1 + (1 − s_x1) ˜cov_x1
      - ˜cov_2 = s_e2 ˜cov_c2 + (1 − s_e2) ˜cov_e2

- Interpretation focus:
  - The decomposition separates aggregate markup changes into:
    - Changes among continuing firms (within and between components),
    - Effects from entrants,
    - Effects from exitors,
    - Adjustments for covariance between firm markups and market shares (˜cov terms) and their time averages.

*Source: Appendix for Online Publication (wpiea2019082) — Orbis-based data cleaning, additional results figures and table, and dynamic Olley-Pakes decomposition with entry and exit.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019082.pdf_