## Annex 2.1. Data Sources and Sample

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### Data sources and country coverage
- Primary data sources:
  - IMF, World Economic Outlook database; World Bank and OECD, National Accounts databases — Gross Domestic Product, Current and Constant Prices.
  - Penn World Tables 9.0 — Gross Investment, Current Prices; Capital Stock, Current Prices.
  - United Nations and OECD, National Accounts database — Corporate Net Operating Surplus.
  - World Inequality Database — Tobin’s Q, Current Prices; Market-value National Wealth, Current Prices.
  - OECD, Main Economic Indicators database — 10-year Government Bond Rates.
  - IMF, International Financial Statistics database — National Currency per U.S. Dollar, End of Period.
  - World Bank, International Comparison Program database — Price Level Ratio of PPP Conversion Factor (GDP) to Market Exchange Rate.
  - OECD, STAN database for Industrial Analysis — Production (Gross Output), Deflators (sectoral); Value Added, Deflators (sectoral).
  - CEIC — Gross Domestic Product, Current and Constant Prices (sectoral).
  - Eurostat, Industry Trade and Services database — Domestic Producer Prices (Manufacturing); Output Price Index (Construction); Index of Turnover (Retail Trade); Index of Deflated Turnover (Retail Trade); Total Output Price Index (Industry).
  - Inklaar and Timmer (2014) — Gross Output Relative Prices for 2005 (Industry).
  - Orbis — Intangible Fixed Assets (firm); Tangible Fixed Assets (firm); Total Assets (firm); Number of Employees (firm); Costs of Goods Sold (firm); Operating Profit Loss EBIT (firm); Material Costs (firm); Costs of Employees (firm); Operating Revenue Turnover (firm).
  - PATSTAT — Patent Application Authority; Patent Application Filing Year; Patent Earliest Filing Year; Patent Publication Identification; Identification of Cited Patent Application; Patent Publication Date.
  - Federal Reserve Economic Database — Effective Federal Funds Rate (US); Real Personal Consumption Expenditures (US); Real Gross Domestic Product (US); Nonfarm Business Average Weekly Hours (US); Civilian Employment 16 Years and Over (US); GDP Implicit Price Deflator (US); Civilian Unemployment Rate (US).
  - Areawide Model Database (ECB/Eurostat) — Nominal 3-month Interest Rate, Euribor (EA); Real Consumption Expenditure (EA); Real Gross Domestic Product (EA); Harmonized Index of Consumer Prices, All Items Excluding Energy (EA); Unemployment Rate, Total (EA).
- Annex Table 2.1.1: Source: IMF staff compilation. Note: Data is aggregate unless specified otherwise.
- Country coverage for analytical exercises is presented in Annex Table 2.1.2 (grouping of countries across exercises I–IV). An asterisk (*) denotes emerging market and developing economies as classified by the IMF, World Economic Outlook.

### Orbis firm-level sample, cleaning, and representativeness
- Main firm-level dataset: Orbis (Orbis Historical product) from Bureau van Dijk.
- Sample selection:
  - Focus on countries for which firms in Orbis represent at least 40% of total output reported in official sources (United States included despite somewhat lower coverage in some years).
  - Analysis restricts to firms with average employment greater or equal to 20 employees.
  - For most countries the data span from 2000 to 2015; some countries have slightly shorter series (Austria, Czech Republic, Germany, Ireland, Korea, Romania, Russia, Slovak Republic, Turkey).
- Cleaning steps (closely following Kalemli-Özcan and others (2015), Gopinath and others (2017), Gal (2013)):
  - Correct 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; missing NACE industry code.
  - 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 by company size category.
  - Main balance sheet variables deflated and PPP-adjusted.
- Further data construction details: Díez, Fan and Villegas-Sánchez (2019).

### Sample sizes and frequency
- Sample frequency: annual, 2000 to 2015 (subject to country coverage exceptions).
- Note on United States: included despite lower coverage in some years; results consistent with other recent studies.

### Measures of market power (firm and industry)
- Markup (휇it):
  - Defined as price (P) over marginal cost (MC): 휇it = Pit/MCit.
  - Empirical estimation follows De Loecker and Warzynski (2012): markup estimated as ratio of output elasticity of a flexible input (βit^v) to the expenditure share of that input (αit^v).
  - Output elasticities obtained from industry-specific (two-digit NACE Rev. 2) Cobb-Douglas production functions estimated using Ackerberg, Caves and Frazer (2015) methodology.
- Firm-level Lerner index (lit):
  - lit = EBITit / OPERit, where EBITit = earnings before interest and tax and OPERit = operating revenue.
  - In Main Text Figure 2.2 (middle panel), only values between -1 and 1 are kept.
- Country-industry-level markup:
  - Simple average of firm-level markups within country-industry (four-digit NACE Rev. 2).
- Industry-level concentration:
  - For each country-industry-year compute ratio of sales of top 4 firms to sales of top 20 firms.
  - National concentration measures: simple country-year averages across four-digit industries.
  - Global measure (Main Text Figure 2.2 lower panel): median across countries for each year.

### Decomposition of aggregate markup changes
- Decomposition method: Melitz and Polanec (2015) — splits change in aggregate (firm-sales-weighted average) markup into:
  - Within-incumbent firm component (capturing within-firm changes in markups).
  - Reallocation effect: reallocation between incumbents, firm entry, firm exit.
- Notation summary:
  - Three firm groups: continuing (c), entrants (e), exiting (x).
  - s_Gt = ∑ s_it for i ∈ G is aggregate market share of group G.
  - Aggregate markup change between periods 1 and 2 expressed in equation (2.3) with firm-sales-weighted average markup M and covariances as defined in the source.

### Characteristics of high-markup firms (top decile)
- Definition: High-Markup dummy = 1 for firms in top 10 percent of average markup distribution (within narrowly-defined industries in each country).
- Conditional correlations (Annex Table 2.2.1; controls include firm size and country-industry-year fixed effects):
  - High Markup → log(TFP): 0.181*** (p < 0.01).
  - High Markup → Lerner: 0.028*** (p < 0.01).
  - High Markup → Intangibles (dummy): 0.025*** (p < 0.01) (expressed as 2.5 percentage points more likely).
- Additional association: Log Operating Revenue associated with:
  - 0.035*** on log(TFP),
  - 0.005*** on Lerner,
  - 0.058*** on Intangibles.
- Sample and statistics:
  - Number of Observations: 6,089,141 (column 1); 6,088,230 (column 2); 6,065,734 (column 3).
  - R-squared: 0.980 (column 1); 0.160 (column 2); 0.460 (column 3).
  - Industries defined as NACE revision 2 4-digit sectors.
  - Sample frequency: annual from 2000 to 2015.
  - Standard errors clustered at the firm level.
- Summary interpretation:
  - High-markup firms are on average 18 percent more productive, 2.8 percent more profitable, and 2.5 percentage points more likely to invest in intangible fixed assets; all correlations statistically significant at the one percent confidence level.

### Markup increases in digitally-intensive industries
- Industry classification: digitally-intensive industries per Calligaris, Criscuolo and Marcolin (2018). An industry is digitally-intensive if it ranks in the upper half of cross-industry distribution in at least three of: Software investment, ICT tangible investment, Intermediate ICT goods, Intermediate ICT services, Robot use.
- Finding (Annex Figure 2.2.1):
  - Firm markups rose about twice as much in digitally-intensive industries than in the average industry over 2000–15.
  - Note: markups in that figure derived from production function where capital includes only tangible fixed assets; qualitatively similar results when intangible assets included.

### Innovation: patent-based evidence and regressions
- Patent data and measure:
  - Source: PATSTAT; link from Orbis firm identifier to patent application filings via Bureau van Dijk.
  - Patent measure: number of patents per firm-year, often citation-weighted (each patent weighted by number of citations received from outside the patent family).
  - Focus often on "triadic" patents (registered in EU, Japan, and US) as higher-quality subset.
- Regression specification (country-industry level, Poisson):
  - E[P_jct | mp_jct−1] = exp{β1 * mp_jct−1 + β2 * mp_jct−1^2 + γ_ct + γ_cj }   (equation (2.4))
  - j = industry, c = country, t = year; mp = market power measure (log markup or Lerner).
- Key sector-level coefficients (Annex Table 2.3.1; 11,735 observations):
  - 1-year Lagged Lerner: 6.373*** (1.384) in column (1); 7.977*** (1.859) in column (2).
  - 1-year Lagged Lerner Squared: -43.196*** (10.925) in column (1); -51.832*** (14.221) in column (2).
  - 1-year Lagged Log Markup: 4.016** (1.713) in column (3); 4.629** (1.890) in column (4).
  - 1-year Lagged Log Markup Squared: -3.123** (1.428) in column (3); -4.665** (1.902) in column (4).
- Interpretation:
  - Positive coefficients on market power and negative coefficients on squared terms support a hump-shaped relationship between market power and innovation across market power measures and patent samples.
- Sector-level regression results (selected coefficients from Annex Table 2.3.1; 4,723,475 observations reported in table notes):
  - 1-year Lagged Log Markup:
    - Column (1): 0.0019** (0.0006)
    - Column (2): 0.7304** (0.2340)
    - Column (3): 0.0022*** (0.0006)
    - Column (4): 0.732*** (0.199)
  - 1-year Lagged Log Markup Squared:
    - Column (1): -0.0005* (0.0003)
    - Column (2): -0.5987*** (0.1774)
    - Column (3): -0.0005* (0.0003)
    - Column (4): -0.488** (0.151)
  - 1-year Lagged Log Operating Revenue:
    - Column (1): 0.0006*** (0.0001)
    - Column (2): 0.1242*** (0.0227)
    - Column (3): 0.0007*** (0.0001)
    - Column (4): 0.120*** (0.018)
- Firm-level evidence:
  - Similar hump-shaped relationship found at the firm level with strict fixed effects and control for lagged firm size.
  - Estimators used: OLS, Poisson, and control function approach (instrument: log median markup across other firms in same country-industry-year).
  - Column (2) (Poisson with strict fixed effects) used as baseline for chapter analysis.

### Market power and investment: firm-level evidence
- Data and setup:
  - Dependent variable: net tangible investment divided by value added (I/Y), where net tangible investment = tangible assets_t – tangible assets_t-1.
  - Main explanatory variable: 1-year lagged firm markup.
  - Controls: lagged log operating revenue (firm size); some specs include lagged cash flow / total assets and lagged leverage (debt / total assets).
  - Fixed effects: firm fixed effects and alternative country-industry-year, country-year, or industry-year fixed effects.
  - Instrument: lag of median markups in a firm's country-industry-year excluding that firm.
- Selected coefficients (Annex Table 2.3.3, 2.3.4, 2.3.5, 2.3.6, 2.3.7):
  - Annex Table 2.3.3:
    - Column (1) OLS: 1-year Lagged Markup = -0.062*** (0.003); 1-year Lagged Log Operating Revenue = -0.029*** (0.001); Number of observations = 2,510,177; R2 = 0.347.
    - Column (2) OLS: 1-year Lagged Markup = -0.059*** (0.003); 1-year Lagged Log Operating Revenue = -0.027*** (0.001); Number of observations = 2,530,445; R2 = 0.310.
    - Column (3) IV: 1-year Lagged Markup = -0.093*** (0.021); 1-year Lagged Log Operating Revenue = -0.033*** (0.004); First Stage F-statistic = 101.7; Number of observations = 2,520,465; R2 = 0.002.
  - Annex Table 2.3.4 (IV first and second stages):
    - First stage: 1-year Lagged Median Markup = 0.156*** (0.015); 1-year Lagged Log Operating Revenue = -0.180*** (0.002); First Stage F-statistic = 101.7; Number of observations = 2,520,465; R2 = 0.002.
    - Second stage: 1-year Lagged Markup = -0.093*** (0.021); 1-year Lagged Log Operating Revenue = -0.033*** (0.004).
  - Annex Table 2.3.5:
    - Column (7) (OLS with firm fixed effects and country-industry-year fixed effects): 1-year Lagged Markup = -0.062*** (0.003); 1-year Lagged Log Operating Revenue = -0.029*** (0.001); Number of observations = 2,510,177; R2 = 0.347.
    - Comparison across specifications shows the coefficient on markup is several times smaller in magnitude when firm fixed effects are omitted, indicating a larger within-firm component.
  - Annex Table 2.3.6 (cash flow and leverage included):
    - Column (1) OLS: 1-year Lagged Markup = -0.060*** (0.003); 1-year Lagged Log Operating Revenue = -0.032*** (0.001); 1-year Lagged Cash Flow / Total Assets = 0.056*** (0.010); 1-year Lagged Leverage = -0.137*** (0.002); Number of observations = 2,282,040; R2 = 0.359.
    - Column (3) IV: 1-year Lagged Markup = -0.105*** (0.023); 1-year Lagged Log Operating Revenue = -0.038*** (0.004); 1-year Lagged Cash Flow / Total Assets = 0.058*** (0.012); 1-year Lagged Leverage = -0.130*** (0.004); First Stage F-statistic = 84; Number of observations = 2,293,587; R2 = 0.004.
  - Annex Table 2.3.7:
    - Using alternative dependent variable I/K (net investment in tangible assets / tangible assets in previous period) produces qualitatively similar negative coefficients on lagged markups.
- Key findings on investment:
  - Higher lagged firm markups are consistently associated with lower net investment relative to value added (negative and statistically significant coefficients across OLS and IV).
  - 1-year Lagged Cash Flow / Total Assets has a positive and statistically significant effect on investment (e.g., 0.056***).
  - 1-year Lagged Leverage has a negative and statistically significant effect on investment (e.g., -0.137***).
  - Results robust to I/K instead of I/Y and across IV and OLS; first-stage F-statistics indicate strong instruments (e.g., 101.7, 115.8).
  - Within-firm component is larger: omitting firm fixed effects yields markup coefficients several times larger in magnitude.

### DSGE model used to analyze macro implications of rising markups
- Framework: New Keynesian dynamic stochastic general equilibrium (DSGE) with capital adjustment costs (references: Jones and Philippon 2016; Galí 2008).
- Variables expressed in log deviations from steady-state; model comprises system of log-linear equations (equations (2.6) through (2.24)) plus flexible price economy and output growth definition.
- Endogenous variables (19): y_t, k_t, n_t, w_t, r_{k,t}, π^p_t, π^w_t, c_t, i_t, λ_t, mc_t, mrs_t, x_t, q_t, r_t, ξ_{a,t}, ξ_{d,t}, ξ_{e,t}, ξ_{q,t}, together with flexible-price equations and g_t = y_t − y_{t−1}.
- Nominal interest rate subject to zero lower bound: i_t ≥ (bound mention truncated in source).
- Selected model equations and mechanisms (equation references preserved):
  - Households:
    - E_t λ_{t+1} = γ (c_t + E_t c_{t+1}) − ξ_{d,t}. (2.6)
    - ξ_{d,t} = ρ_d ξ_{d,t−1} + σ_d ε_{d,t}. (2.7)
    - mrs_t = φ n_t + γ c_t. (2.8)
    - E_t λ_{t+1} + r_t − E_t π_{t+1} = 0. (2.9)
    - Net investment and Tobin's Q: x_t = i_k (i_t − k_t) (2.10); q_t expression in (2.11) with shock ξ_{q,t} following (2.12); x_t = (q_{φ_k}/q) q_t (2.13); x_t = k_{t+1} − k_t (2.14).
  - Resource constraint:
    - y_t = (c_y) c_t + (i_y) i_t. (2.15)
  - Firms and production:
    - y_t = α k_t + (1 − α) n_t + ξ_{a,t}. (2.16)
    - ξ_{a,t} = ρ_a ξ_{a,t−1} + σ_a ε_{a,t}. (2.17)
    - r_{k,t} = w_t + n_t − k_t. (2.18)
    - mc_t = (1 − α) w_t + α r_{k,t} − ξ_{a,t}. (2.19)
  - Phillips curves and nominal rigidities:
    - π^p_t = β E_t π^p_{t+1} + κ_p mc_t + ξ_{e,t}. (2.20) with ξ_{e,t} = ρ_e ξ_{e,t−1} + σ_e ε_{e,t}. (2.21)
    - π^w_t = β E_t π^w_{t+1} + κ_w (mrs_t − w_t). (2.22) with π^w_t = w_t − w_{t−1} + π_t. (2.23)
  - Monetary policy:
    - r_t = ρ_r r_{t−1} + (1 − ρ_r) (ρ_π π^p_t + ρ_y (y_t − y^F_t)) + ρ_g g_t + σ_i ε_{i,t}. (2.24)
- Simulation strategy:
  - Model solved subject to an unanticipated trend in the elasticity of substitution between intermediate goods-producing firms’ output to simulate a rise in markups.
  - Zero lower bound accounted for in simulations.
  - Model links rising markups to investment, Tobin’s Q, marginal costs, and the slope of the Phillips curve.

### Estimation and calibration
- Parameters of shock processes and monetary policy rule estimated on aggregate data using Bayesian likelihood methods; some parameters calibrated to standard values.
- Data used for estimation:
  - United States observables from Federal Reserve Economic Database, 1986Q1 to 2008Q4.
  - Euro area observables from ECB Areawide Model database, 1997Q2 to 2008Q4.
- All data series except nominal interest rate demeaned prior to estimation.
- Calibrated parameters (Annex Table 2.3.8):
  - β = 0.9926 (3% annual real interest rate)
  - γ = 1 (Log utility)
  - φ = 2 (Frisch labor supply elasticity of 1/2)
  - α = 1/3 (Capital share of income of 33%)
  - φ_k = 10 (Quadratic capital adjustment cost)
  - δ = 0.025 (10% annual depreciation rate)
  - μ_p = 5 (Initial price markup of 25%)
  - μ_w = 6 (Initial wage markup of 20%)
  - θ_p = 2/3 (Gali (2008). Average price duration of 3Q)
  - θ_w = 3/4 (Gali (2008). Average price duration of 4Q)
- Posterior/prior summaries (Annex Table 2.3.9 excerpts), selected posterior percentiles:
  - ρ_a: US posterior 0.921 (25% 0.905; 75% 0.936); Euro Area posterior 0.872 (25% 0.84; 75% 0.901).
  - ρ_d: US posterior 0.922 (25% 0.91; 75% 0.932); Euro Area posterior 0.787 (25% 0.752; 75% 0.819).
  - ρ_e: US posterior 0.79 (25% 0.759; 75% 0.819); Euro Area posterior 0.513 (25% 0.443; 75% 0.58).
  - ρ_q: US posterior 0.867 (25% 0.849; 75% 0.883); Euro Area posterior 0.813 (25% 0.786; 75% 0.837).
  - σ_a: US posterior 0.493 (25% 0.469; 75% 0.52); Euro Area posterior 0.485 (25% 0.451; 75% 0.523).
  - σ_q: US posterior 0.212 (25% 0.192; 75% 0.234); Euro Area posterior 0.18 (25% 0.158; 75% 0.206).
  - ρ_r: US posterior 0.801 (25% 0.783; 75% 0.817); Euro Area posterior 0.792 (25% 0.766; 75% 0.815).
  - ρ_p: US posterior 2.135 (25% 1.996; 75% 2.275); Euro Area posterior 1.809 (25% 1.618; 75% 1.994).
  - ρ_g: US posterior 0.209 (25% 0.189; 75% 0.229); Euro Area posterior 0.209 (25% 0.187; 75% 0.232).
  - ρ_y: US posterior 0.163 (25% 0.142; 75% 0.185); Euro Area posterior 0.204 (25% 0.175; 75% 0.233).

### Steady-state relationships and transition dynamics
- Steady-state markup relation:
  - 1 / markup = m c = (μ_p − 1) / μ_p.  (Equation (2.25))
- Steady-state capital-output ratio:
  - k / y = (1 / markup) * (α / r_k).  (Equation (2.26))
- Implications:
  - Lower demand elasticity of substitution → lower steady-state marginal costs → higher markup.
  - Higher steady-state markup → lower capital-output ratio and lower investment-to-output ratio (δ * (k / y)).
- Main simulation:
  - Economy faces an unanticipated and exogenous decrease in the elasticity of substitution between intermediate goods, calibrated to match average granular increase in within-incumbent firm component of markups for euro area and United States (Annex Figure 2.3.1).
  - Transition to new steady-state with lower capital features negative net investment.
- Robustness to capital adjustment costs:
  - Doubling φ_k to 20 raises estimated σ_q from around 0.2 to about 0.3 for both United States and euro area.
  - Simulated impact of trend rise in markups on investment and the natural interest rate remains qualitatively unchanged, only marginally smaller with higher φ_k.

### Phillips curve: Calvo versus Rotemberg pricing
- Calvo pricing (baseline):
  - Linearized Phillips curve:
    - π_t^p = β E_t π_{t+1}^p + [((1−θ_p)(1−β θ_p)/θ_p) * (1/(1+μ_p) * α(1−α))] m c_t + ξ_{e t}.  (Equation (2.27))
  - Under Calvo pricing, slope of Phillips curve depends positively on a firm’s markup; higher markups → steeper Phillips curve.
- Rotemberg pricing:
  - Linearized Phillips curve:
    - π_t^p = β E_t π_{t+1}^p + ((μ_p − 1) / φ_p) m c_t + ξ_{e t}.  (Equation (2.28))
  - If φ_p chosen to match Calvo slope, aggregate dynamics are identical.
  - Under Rotemberg pricing, higher markups imply a decline in Phillips curve slope (flatter Phillips curve when markups are higher).
- Quantitative exercise:
  - Two counterfactuals:
    - Markups set at their 2000 level for entire sample.
    - Markups set at a level 8 percent above their 2000 level for entire sample.
  - Simulations under Calvo and Rotemberg show:
    - Under Calvo: Phillips curve steeper when markups are higher.
    - Under Rotemberg: Phillips curve flatter when markups are higher (Annex Figure 2.3.2).

### Labor share: regression evidence
- Dependent variable: wage bill / value added (labor income share).
- Selected regression results (Annex Table 2.3.10; sample annual 2000–2015):
  - OLS baseline (Column (1)): 1-year lagged markup = -0.032*** (0.001); Number of observations = 2,515,925; R^2 = 0.735.
  - OLS alternative fixed effects (Column (2)): 1-year lagged markup = -0.031*** (0.001); Number of observations = 2,535,858; R^2 = 0.721.
  - IV (Column (3)): 1-year lagged markup = -0.018* (0.011); Number of observations = 2,526,009; R^2 = 0.008.
  - Lagged log operating revenue coefficients: -0.033***, -0.034***, -0.031*** respectively.
- IV details:
  - Instrument: lag of median markups in a firm's country-industry 2-year, excluding that firm.
  - First stage F-statistic = 87.02.
  - First-stage coefficient on 1-year lagged median markup = 0.124*** (0.013); second-stage 1-year lagged markup = -0.018* (0.011).
- Within versus between effects:
  - Within-firm estimation (firm fixed effects) is main analysis.
  - Omitting firm fixed effects yields a negative markup coefficient up to twice as large, indicating a sizeable between-firm (reallocation) component.

### International spillovers
- Spillover channels and specification:
  - Input channel: weighted sum of each foreign supplier’s markups, weights = imports relative to total value added of importing country.
  - Demand channel: weighted sum of each foreign buyer’s markups, weights = exports relative to total value added of exporting country.
  - Controls: domestic linkages and associated markups, country-year, sector-year, and country-sector fixed effects.
  - Equation (2.28) specifies log V A_{i j t} as function of weighted foreign markups and controls.
- Empirical result for Emerging Markets (Annex Table 2.3.13; 3,424 observations):
  - Foreign import-share-weighted markup coefficient = -0.075*** (0.010).
  - Foreign export-share-weighted markup coefficient = -0.533 (0.379) (not statistically significant).
  - Number of observations = 3,424; R^2 = 0.998.
  - Interpretation example: For an industry importing 40 percent of its value added, a 10 percentage point increase in markups across all foreign suppliers is associated with a 0.3 percent decrease in value added, all else equal.
- Data sources: OECD Inter-Country Input-Output Tables; IMF staff calculations.

*Source: IMF staff compilation; Annex 2.1, Annex 2.2, and Annex 2.3 (as provided).*

### Annex 2.1. Data Sources and Sample

### Annex 2.1. Data Sources and Sample

### Data sources and country coverage
- Primary data sources (as listed):
  - IMF, World Economic Outlook database; World Bank and OECD, National Accounts databases — Gross Domestic Product, Current and Constant Prices.
  - Penn World Tables 9.0 — Gross Investment, Current Prices; Capital Stock, Current Prices.
  - United Nations and OECD, National Accounts database — Corporate Net Operating Surplus.
  - World Inequality Database — Tobin’s Q, Current Prices; Market-value National Wealth, Current Prices.
  - OECD, Main Economic Indicators database — 10-year Government Bond Rates.
  - IMF, International Financial Statistics database — National Currency per U.S. Dollar, End of Period.
  - World Bank, International Comparison Program database — Price Level Ratio of PPP Conversion Factor (GDP) to Market Exchange Rate.
  - OECD, STAN database for Industrial Analysis — Production (Gross Output), Deflators (sectoral); Value Added, Deflators (sectoral).
  - CEIC — Gross Domestic Product, Current and Constant Prices (sectoral).
  - Eurostat, Industry Trade and Services database — Domestic Producer Prices (Manufacturing); Output Price Index (Construction); Index of Turnover (Retail Trade); Index of Deflated Turnover (Retail Trade); Total Output Price Index (Industry).
  - Inklaar and Timmer (2014) — Gross Output Relative Prices for 2005 (Industry).
  - Orbis — Intangible Fixed Assets (firm); Tangible Fixed Assets (firm); Total Assets (firm); Number of Employees (firm); Costs of Goods Sold (firm); Operating Profit Loss EBIT (firm); Material Costs (firm); Costs of Employees (firm); Operating Revenue Turnover (firm).
  - PATSTAT — Patent Application Authority; Patent Application Filing Year; Patent Earliest Filing Year; Patent Publication Identification; Identification of Cited Patent Application; Patent Publication Date.
  - Federal Reserve Economic Database — Effective Federal Funds Rate (US); Real Personal Consumption Expenditures (US); Real Gross Domestic Product (US); Nonfarm Business Average Weekly Hours (US); Civilian Employment 16 Years and Over (US); GDP Implicit Price Deflator (US); Civilian Unemployment Rate (US).
  - Areawide Model Database (ECB/Eurostat) — Nominal 3-month Interest Rate, Euribor (EA); Real Consumption Expenditure (EA); Real Gross Domestic Product (EA); Harmonized Index of Consumer Prices, All Items Excluding Energy (EA); Unemployment Rate, Total (EA).
- Annex Table 2.1.1: Source: IMF staff compilation. Note: Data is aggregate unless specified otherwise.
- Country coverage for analytical exercises is presented in Annex Table 2.1.2 (grouping of countries across exercises I–IV). An asterisk (*) denotes emerging market and developing economies as classified by the IMF, World Economic Outlook.

### Orbis firm-level sample, cleaning, and representativeness
- Main firm-level dataset: Orbis (Orbis Historical product) from Bureau van Dijk.
- Sample selection:
  - Focus on countries for which firms in Orbis represent at least 40% of total output reported in official sources (United States included despite somewhat lower coverage in some years).
  - Analysis restricts to firms with average employment greater or equal to 20 employees.
  - For most countries the data span from 2000 to 2015; some countries have slightly shorter series (Austria, Czech Republic, Germany, Ireland, Korea, Romania, Russia, Slovak Republic, Turkey).
- Cleaning steps (closely following Kalemli-Özcan and others (2015), Gopinath and others (2017), Gal (2013)):
  - Correct 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; missing NACE industry code.
  - 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 by company size category.
  - Main balance sheet variables deflated and PPP-adjusted.
- Further data construction details: Díez, Fan and Villegas-Sánchez (2019).

### Sample sizes and notes
- Sample frequency: annual, 2000 to 2015 (subject to country coverage exceptions).
- Note on United States: included despite lower coverage in some years; results consistent with other recent studies.

### Measures of market power (firm and industry)
- Markup (휇it):
  - Defined as price (P) over marginal cost (MC): 휇it = Pit/MCit.
  - Empirical estimation follows De Loecker and Warzynski (2012): markup estimated as ratio of output elasticity of a flexible input (βit^v) to the expenditure share of that input (αit^v).
  - Output elasticities obtained from industry-specific (two-digit NACE Rev. 2) Cobb-Douglas production functions estimated using Ackerberg, Caves and Frazer (2015) methodology.
- Firm-level Lerner index (lit):
  - lit = EBITit / OPERit, where EBITit = earnings before interest and tax and OPERit = operating revenue.
  - In Main Text Figure 2.2 (middle panel), only values between -1 and 1 are kept.
- Country-industry-level markup:
  - Simple average of firm-level markups within country-industry (four-digit NACE Rev. 2).
- Industry-level concentration:
  - For each country-industry-year compute ratio of sales of top 4 firms to sales of top 20 firms.
  - National concentration measures: simple country-year averages across four-digit industries.
  - Global measure (Main Text Figure 2.2 lower panel): median across countries for each year.

### Decomposition of aggregate markup changes
- Decomposition method: Melitz and Polanec (2015) — splits change in aggregate (firm-sales-weighted average) markup into:
  - Within-incumbent firm component (capturing within-firm changes in markups).
  - Reallocation effect: reallocation between incumbents, firm entry, firm exit.
- Notation summary (as in text):
  - Three firm groups: continuing (c), entrants (e), exiting (x).
  - s_Gt = ∑ s_it for i ∈ G is aggregate market share of group G.
  - Aggregate markup change between periods 1 and 2 expressed in equation (2.3) with firm-sales-weighted average markup M and covariances as defined in the source.

### Characteristics of high-markup firms (top decile)
- Econometric results (within narrowly-defined industries in each country; controls for firm size and country-industry-year fixed effects):
  - High-Markup dummy = 1 for firms in top 10 percent of average markup distribution.
  - Conditional correlations (Annex Table 2.2.1):
    - High Markup → log(TFP): 0.181*** (p < 0.01).
    - High Markup → Lerner: 0.028*** (p < 0.01).
    - High Markup → Intangibles (dummy): 0.025*** (p < 0.01) (expressed as 2.5 percentage points more likely).
  - Additional coefficient: Log Operating Revenue associated with:
    - 0.035*** on log(TFP),
    - 0.005*** on Lerner,
    - 0.058*** on Intangibles.
  - Sample and statistics:
    - Number of Observations: 6,089,141 (column 1); 6,088,230 (column 2); 6,065,734 (column 3).
    - R-squared: 0.980 (column 1); 0.160 (column 2); 0.460 (column 3).
    - Industries defined as NACE revision 2 4-digit sectors.
    - Sample frequency: annual from 2000 to 2015.
    - Standard errors clustered at the firm level.
  - Summary interpretation:
    - High-markup firms are on average 18 percent more productive, 2.8 percent more profitable, and 2.5 percentage points more likely to invest in intangible fixed assets; all correlations statistically significant at the one percent confidence level.

### Markup increases in digitally-intensive industries
- Industry classification: digitally-intensive industries identified per Calligaris, Criscuolo and Marcolin (2018). An industry is digitally-intensive if it ranks in the upper half of cross-industry distribution in at least three of: Software investment, ICT tangible investment, Intermediate ICT goods, Intermediate ICT services, Robot use.
- Finding (Annex Figure 2.2.1):
  - Firm markups rose about twice as much in digitally-intensive industries than in the average industry over 2000–15.
  - Note: markups in that figure derived from production function where capital includes only tangible fixed assets; qualitatively similar results when intangible assets included.

### Innovation: patent-based evidence and regressions
- Patent data:
  - Source: PATSTAT; link from Orbis firm identifier to patent application filings via Bureau van Dijk.
  - Patent measure: number of patents per firm-year, often citation-weighted (each patent weighted by number of citations received from outside the patent family).
  - Focus often on "triadic" patents (registered in EU, Japan, and US) as higher-quality subset.
- Regression approach:
  - Country-industry level: regress average citation-weighted patents on 1-year lagged market power measure and its square, with country-year and country-industry fixed effects.
  - Functional form: Poisson regression following Aghion and others (2005):
    - E[P_jct | mp_jct−1] = exp{β1 * mp_jct−1 + β2 * mp_jct−1^2 + γ_ct + γ_cj }   (equation (2.4))
    - j = industry, c = country, t = year; mp = market power measure (log markup or Lerner).
- Key regression results (Annex Table 2.3.1; country-industry regressions):
  - Columns (1)–(2): full sample of patents; Columns (3)–(4): triadic patents.
  - Coefficients shown (standard errors in parentheses):
    - 1-year Lagged Lerner: 6.373*** (1.384) in column (1); 7.977*** (1.859) in column (2).
    - 1-year Lagged Lerner Squared: -43.196*** (10.925) in column (1); -51.832*** (14.221) in column (2).
    - 1-year Lagged Log Markup: 4.016** (1.713) in column (3); 4.629** (1.890) in column (4).
    - 1-year Lagged Log Markup Squared: -3.123** (1.428) in column (3); -4.665** (1.902) in column (4).
  - Fixed effects: Country-Year and Country-Industry fixed effects included in all reported specifications.
  - Number of Observations in table: 11,735 (for each column).
  - Interpretation: coefficients on market power and its square are positive and negative respectively and statistically significant, supporting a hump-shaped relationship between market power and innovation for both market power measures and patent samples.
- Firm-level analysis:
  - Similar findings at firm level with stricter fixed effects (including firm fixed effects and country-industry-year fixed effects in some specifications).
  - Firm specifications include lagged firm size (log real operating revenue) as control.
  - Estimation approaches reported: OLS, Poisson, and a control function approach to address endogeneity (instrument: log median markup across other firms in same country-industry-year).
  - Column (2) (Poisson with strict fixed effects) used as baseline for chapter analysis.

*Source: IMF staff compilation; Annex 2.1, Annex 2.2, and Annex 2.3 (as provided).*

### Annex Table 2.3.1. Market Power and Innovation: Sector-Level Analysis

### Annex Table 2.3.1. Market Power and Innovation: Sector-Level Analysis

### Data, sample, and estimation methods
- Sample frequency: annual from 2000 to 2015.
- Industries: NACE revision 2 4-digit sectors.
- Estimation: Poisson estimation reported; some columns use OLS and some use Poisson/CF (control function).
- Dependent variables:
  - Columns (1) and (2): the average number of citation-weighted patents in the country-industry-year (log(Citation Weighted+1) and Citation Weighted).
  - Columns (3) and (4): the average number of citation-weighted patents jointly filed in the European Union, Japan, and the United States in the country-industry-year (log(Citation Weighted+1) and Citation Weighted).
- Key controls and design:
  - Lerner is the average EBIT-to-turnover ratio in the country-industry-year.
  - Firm fixed effects included in all reported specifications.
  - Instrument for lagged markups: the lag of median markups in a firm's country-sector-year, excluding that firm.
  - Number of observations: 4,723,475 (columns reported).
- Significance notation preserved: * p < 0.10; ** p < 0.05; *** p < 0.01.

### Sector-level regression results (selected coefficients from Annex Table 2.3.1)
- 1-year Lagged Log Markup:
  - Column (1): 0.0019** (standard error (0.0006))
  - Column (2): 0.7304** (standard error (0.2340))
  - Column (3): 0.0022*** (standard error (0.0006))
  - Column (4): 0.732*** (standard error (0.199))
- 1-year Lagged Log Markup Squared:
  - Column (1): -0.0005* (standard error (0.0003))
  - Column (2): -0.5987*** (standard error (0.1774))
  - Column (3): -0.0005* (standard error (0.0003))
  - Column (4): -0.488** (standard error (0.151))
- 1-year Lagged Log Operating Revenue:
  - Column (1): 0.0006*** (standard error (0.0001))
  - Column (2): 0.1242*** (standard error (0.0227))
  - Column (3): 0.0007*** (standard error (0.0001))
  - Column (4): 0.120*** (standard error (0.018))
- Additional notes:
  - Specification choices include country-industry-year, country-year, and industry-year fixed effects depending on column.
  - First-stage F-statistics reported as above 10 where IV used.

### Interpretation from sector-level analysis
- The reported coefficients imply a non-linear (hump-shaped) relationship between markups and innovation at the sector level: positive linear term and negative squared term for lagged log markup across specifications.
- Results are robust across OLS, Poisson, and control-function procedures according to the table notes and accompanying text.

*Source: IMF staff calculations.*

### Annex Table 2.3.2–2.3.7. Market Power and Investment: Firm-Level Analysis

### Data, sample, and estimation methods for investment regressions
- Sample frequency: annual from 2000 to 2015.
- Dependent variable for investment regressions: net tangible investment divided by value added (I/Y), where net tangible investment = tangible assets_t – tangible assets_t-1.
- Main explanatory variable: 1-year lagged firm markup (same measure as innovation analysis).
- Controls: lagged log operating revenue (firm size); some specifications include lagged cash flow / total assets and lagged leverage (debt / total assets).
- Fixed effects: firm fixed effects and alternative country-industry-year, country-year, or industry-year fixed effects depending on specification.
- Instrumental variable: lag of median markups in a firm's country-industry-year excluding that firm (first-stage F-statistics reported, e.g., 101.7 and 115.8 in different tables).
- Robust standard errors clustered at the firm level in firm-level analysis and reported in tables.

### Firm-level regression results (selected coefficients)
- Annex Table 2.3.3 (Markups and the Ratio of Investment to Value Added):
  - Column (1) OLS: 1-year Lagged Markup = -0.062*** (standard error (0.003)); 1-year Lagged Log Operating Revenue = -0.029*** (standard error (0.001)); Number of observations = 2,510,177; R2 = 0.347.
  - Column (2) OLS: 1-year Lagged Markup = -0.059*** (standard error (0.003)); 1-year Lagged Log Operating Revenue = -0.027*** (standard error (0.001)); Number of observations = 2,530,445; R2 = 0.310.
  - Column (3) IV: 1-year Lagged Markup = -0.093*** (standard error (0.021)); 1-year Lagged Log Operating Revenue = -0.033*** (standard error (0.004)); First Stage F-statistic = 101.7; Number of observations = 2,520,465; R2 = 0.002.
- Annex Table 2.3.4 (IV first and second stages):
  - First stage: 1-year Lagged Median Markup = 0.156*** (standard error (0.015)); 1-year Lagged Log Operating Revenue = -0.180*** (standard error (0.002)); First Stage F-statistic = 101.7; Number of observations = 2,520,465; R2 = 0.002.
  - Second stage: 1-year Lagged Markup = -0.093*** (standard error (0.021)); 1-year Lagged Log Operating Revenue = -0.033*** (standard error (0.004)).
- Annex Table 2.3.5 (Fixed effects decomposition, selected columns):
  - Column (7) (OLS with firm fixed effects and country-industry-year fixed effects): 1-year Lagged Markup = -0.062*** (standard error (0.003)); 1-year Lagged Log Operating Revenue = -0.029*** (standard error (0.001)); Number of observations = 2,510,177; R2 = 0.347.
  - Comparison across specifications shows the coefficient on the markup variable is several times smaller in magnitude when firm fixed effects are omitted, indicating a larger within-firm component.
- Annex Table 2.3.6 (Extra control variables: cash flow and leverage included):
  - Column (1) OLS: 1-year Lagged Markup = -0.060*** (standard error (0.003)); 1-year Lagged Log Operating Revenue = -0.032*** (standard error (0.001)); 1-year Lagged Cash Flow / Total Assets = 0.056*** (standard error (0.010)); 1-year Lagged Leverage = -0.137*** (standard error (0.002)); Number of observations = 2,282,040; R2 = 0.359.
  - Column (3) IV: 1-year Lagged Markup = -0.105*** (standard error (0.023)); 1-year Lagged Log Operating Revenue = -0.038*** (standard error (0.004)); 1-year Lagged Cash Flow / Total Assets = 0.058*** (standard error (0.012)); 1-year Lagged Leverage = -0.130*** (standard error (0.004)); First Stage F-statistic = 84; Number of observations = 2,293,587; R2 = 0.004.
- Annex Table 2.3.7:
  - Alternative dependent variable (net investment in tangible assets / tangible assets in previous period, I/K) produces qualitatively similar results to I/Y (tables report comparable negative coefficients on lagged markups; specific coefficients preserved where reported).

### Key findings on investment
- Higher lagged firm markups are consistently associated with lower net investment relative to value added (negative and statistically significant coefficients across OLS and IV specifications).
- Inclusion of cash flow and leverage:
  - 1-year Lagged Cash Flow / Total Assets has a positive and statistically significant effect on investment (e.g., 0.056***).
  - 1-year Lagged Leverage has a negative and statistically significant effect on investment (e.g., -0.137***).
- Robustness:
  - Results are robust when using I/K instead of I/Y.
  - IV and OLS estimates are statistically and quantitatively comparable in the main specifications; first-stage F-statistics indicate strong instruments (e.g., 101.7, 115.8).
- Within versus between effects:
  - Regression comparisons imply the within-firm component plays a larger role in the negative relationship between markups and investment; omitting firm fixed effects yields markup coefficients several times smaller in magnitude.

*Source: IMF staff calculations.*

### C. DSGE model used to analyze macro implications of rising markups

### Model architecture and calibration inputs
- Framework: New Keynesian dynamic stochastic general equilibrium (DSGE) with capital adjustment costs.
- References: Jones and Philippon 2016, and Galí 2008 (model structure and derivations referenced in text).
- Variables are expressed in log deviations from steady-state; terms without time subscript are steady-state values.
- The system of log-linear equations (equations (2.6) through (2.24)) together with the flexible price economy and definition of output growth constitutes the model.
- The model includes 19 endogenous variables: y_t, k_t, n_t, w_t, r_{k,t}, π^p_t, π^w_t, c_t, i_t, λ_t, mc_t, mrs_t, x_t, q_t, r_t, ξ_{a,t}, ξ_{d,t}, ξ_{e,t}, ξ_{q,t}, together with flexible-price equations and g_t = y_t − y_{t−1}.
- Nominal interest rate subject to zero lower bound: i_t ≥ (text truncates at bound mention in source).

### Selected key model equations and mechanisms (equation references preserved)
- Households:
  - Euler/consumption relationship: E_t λ_{t+1} = γ (c_t + E_t c_{t+1}) − ξ_{d,t}. (2.6)
  - Discount-factor shock process: ξ_{d,t} = ρ_d ξ_{d,t−1} + σ_d ε_{d,t}. (2.7)
  - Marginal rate of substitution: mrs_t = φ n_t + γ c_t. (2.8)
  - Bond Euler equation: E_t λ_{t+1} + r_t − E_t π_{t+1} = 0. (2.9)
  - Net investment definition and Tobin's Q: x_t = i_k (i_t − k_t) (2.10); q_t expression given in (2.11) with shock ξ_{q,t} following (2.12); net investment in log-linear terms x_t = (q_{φ_k}/q) q_t (2.13); x_t = k_{t+1} − k_t (2.14).
- Resource constraint:
  - y_t = (c_y) c_t + (i_y) i_t. (2.15)
- Firms and production:
  - Cobb-Douglas production: y_t = α k_t + (1 − α) n_t + ξ_{a,t}. (2.16)
  - Productivity shock AR(1): ξ_{a,t} = ρ_a ξ_{a,t−1} + σ_a ε_{a,t}. (2.17)
  - Return and wage relations: r_{k,t} = w_t + n_t − k_t. (2.18)
  - Marginal cost: mc_t = (1 − α) w_t + α r_{k,t} − ξ_{a,t}. (2.19)
- Nominal rigidities and Phillips curves:
  - Price Phillips curve: π^p_t = β E_t π^p_{t+1} + κ_p mc_t + ξ_{e,t}. (2.20) with ξ_{e,t} = ρ_e ξ_{e,t−1} + σ_e ε_{e,t}. (2.21)
  - Wage Phillips curve: π^w_t = β E_t π^w_{t+1} + κ_w (mrs_t − w_t). (2.22) with π^w_t defined as π^w_t = w_t − w_{t−1} + π_t. (2.23)
  - κ_p depends on Calvo probability of price adjustment (1 − θ_p); κ_w depends on labor supply elasticity, elasticity of substitution between labor varieties μ_w, the Calvo wage adjustment probability (1 − θ_w), and discount factor β.
- Monetary policy:
  - Standard Taylor rule with interest rate smoothing, inflation and output gap responses, and policy shock: r_t = ρ_r r_{t−1} + (1 − ρ_r) (ρ_π π^p_t + ρ_y (y_t − y^F_t)) + ρ_g g_t + σ_i ε_{i,t}. (2.24)
  - Flexible-price economy used to form y^F_t.

### Simulation strategy and uses
- The model is solved/approximated subject to an unanticipated trend in the elasticity of substitution between intermediate goods-producing firms’ output to simulate the economy under a rise in markups.
- The model accounts for the zero lower bound on the nominal interest rate in simulations (i_t ≥ ... as constrained).
- The model links rising markups to implications for investment, Tobin’s Q, marginal costs, and the slope of the Phillips curve through the nominal rigidities and firm pricing decision structure.

*Source: IMF staff calculations.*

### 0. The solution methodology is described in Jones and Philippon (2016).

### 0. The solution methodology is described in Jones and Philippon (2016).

### Estimation and Calibration
- A number of parameters are calibrated to standard values used in the literature.
- The parameters of the shock processes and the parameters of the monetary policy rule are estimated on aggregate data using Bayesian likelihood methods.
- Calibrated parameters are presented in Annex Table 2.3.8 and are set to standard values.
- Wide priors are used; moments of the prior and posterior distributions of the parameters of the shock processes and the monetary policy rule are given in Annex Table 2.3.9.
- Data used for estimation:
  - United States observables drawn from the Federal Reserve Economic Database, over the time period 1986Q1 to 2008Q4.
  - Euro area observables drawn from the European Central Bank’s Area-wide Model database, over the time period 1997Q2 to 2008Q4.
- All data series, except the nominal interest rate, are demeaned prior to estimation.

### Calibrated Parameters (Annex Table 2.3.8)
- β = 0.9926 (3% annual real interest rate)
- γ = 1 (Log utility)
- φ = 2 (Frisch labor supply elasticity of 1/2)
- α = 1/3 (Capital share of income of 33%)
- φ_k = 10 (Quadratic capital adjustment cost)
- δ = 0.025 (10% annual depreciation rate)
- μ_p = 5 (Initial price markup of 25%)
- μ_w = 6 (Initial wage markup of 20%)
- θ_p = 2/3 (Gali (2008). Average price duration of 3Q)
- θ_w = 3/4 (Gali (2008). Average price duration of 4Q)

### Posterior/Prior Parameter Summaries (Annex Table 2.3.9 excerpts)
- Prior distributions: B (beta), IG (inverse-gamma), N (normal).
- Selected prior values and posterior percentiles (25%, 50%, 75%) for some parameters:
  - ρ_a prior median 0.5; US posterior 0.921 (25% 0.905; 75% 0.936); Euro Area posterior 0.872 (25% 0.84; 75% 0.901).
  - ρ_d prior median 0.5; US posterior 0.922 (25% 0.91; 75% 0.932); Euro Area posterior 0.787 (25% 0.752; 75% 0.819).
  - ρ_e prior median 0.5; US posterior 0.79 (25% 0.759; 75% 0.819); Euro Area posterior 0.513 (25% 0.443; 75% 0.58).
  - ρ_q prior median 0.5; US posterior 0.867 (25% 0.849; 75% 0.883); Euro Area posterior 0.813 (25% 0.786; 75% 0.837).
  - σ_a prior 0.6 (IG); US posterior 0.493 (25% 0.469; 75% 0.52); Euro Area posterior 0.485 (25% 0.451; 75% 0.523).
  - σ_q prior 0.6 (IG); US posterior 0.212 (25% 0.192; 75% 0.234); Euro Area posterior 0.18 (25% 0.158; 75% 0.206).
  - ρ_r prior median 0.75; US posterior 0.801 (25% 0.783; 75% 0.817); Euro Area posterior 0.792 (25% 0.766; 75% 0.815).
  - ρ_p prior 2 (N); US posterior 2.135 (25% 1.996; 75% 2.275); Euro Area posterior 1.809 (25% 1.618; 75% 1.994).
  - ρ_g prior 0.13 (N); US posterior 0.209 (25% 0.189; 75% 0.229); Euro Area posterior 0.209 (25% 0.187; 75% 0.232).
  - ρ_y prior 0.13 (N); US posterior 0.163 (25% 0.142; 75% 0.185); Euro Area posterior 0.204 (25% 0.175; 75% 0.233).

### Steady-State Relationships
- Steady-state markup relation (as presented):
  - 1 / markup = m c = (μ_p − 1) / μ_p.  (Equation (2.25) in source)
- Interpretation:
  - Lower demand elasticity of substitution → lower steady-state marginal costs → higher markup.
  - As demand becomes more inelastic, firms cut production and charge higher markups; labor and capital hired fall.
- Steady-state capital-output ratio:
  - k / y = (1 / markup) * (α / r_k).  (Equation (2.26) in source)
  - Higher steady-state markup → lower capital-output ratio, given steady-state r_k (function of household discount factor).
- Investment-to-output ratio in steady state is δ * (k / y); this ratio declines when steady-state markups are higher.

### Transition Dynamics and Main Simulation
- Main simulation: each period the model economy faces an unanticipated and exogenous decrease in the elasticity of substitution between intermediate goods, chosen to match the average granular increase in the within-incumbent firm component of markups for the euro area and the United States (Annex Figure 2.3.1).
- In the transition to the steady-state with lower capital, net investment is negative.
- Other key simulation results are discussed in the chapter (not reproduced here).
- Note: Annex Figure 2.3.1 shows the calibrated rise in markups (Index, 2000=100), capturing only the within-firm component of markups.

### Robustness: Capital Adjustment Costs
- Sensitivity check: capital adjustment cost parameter doubled relative to baseline value (calibrated to φ_k = 20 in robustness exercise).
- Effect on estimated standard deviation of investment shocks σ_q:
  - σ_q increases from around 0.2 to about 0.3 for both the United States and the euro area.
- Simulated impact of the trend rise in markups on investment and the natural interest rate:
  - Remains qualitatively unchanged, only marginally smaller under higher capital adjustment costs, as higher φ_k makes investment more sluggish in response to shocks.

### Phillips Curve: Baseline Calvo versus Rotemberg Pricing
- Baseline Calvo pricing (Calvo (1983)):
  - Linearized Phillips curve:
    - π_t^p = β E_t π_{t+1}^p + [((1−θ_p)(1−β θ_p)/θ_p) * (1/(1+μ_p) * α(1−α))] m c_t + ξ_{e t}.  (Equation (2.27) in source)
  - Under Calvo pricing, the slope of the Phillips curve depends positively on a firm’s markup; higher markups → steeper Phillips curve.
  - Intuition: decreasing returns to scale imply marginal costs rise more with output; with lower μ_p (higher markup), firms cut output reducing marginal costs and dampening marginal-cost responses to relative price changes, affecting slope.
- Rotemberg pricing (Rotemberg (1982)):
  - Linearized Phillips curve:
    - π_t^p = β E_t π_{t+1}^p + ((μ_p − 1) / φ_p) m c_t + ξ_{e t}.  (Equation (2.28) in source)
  - φ_p parameterizes quadratic price adjustment cost.
  - If φ_p is chosen to imply same Phillips curve slope as Calvo baseline, aggregate dynamics are identical.
  - Under Rotemberg pricing, higher markups imply a decline in the slope of the Phillips curve (i.e., flatter Phillips curve when markups are higher).
  - Intuition: less elastic demand (lower μ_p) makes firm revenue less sensitive to shocks, lowering willingness to incur resource cost to change price; prices and inflation become less responsive to shocks.
- Quantitative exercise:
  - Estimated shocks generating US aggregate data are extracted.
  - Two counterfactuals simulated:
    - Markups set at their 2000 level for entire sample.
    - Markups set at a level 8 percent above their 2000 level for entire sample.
  - Simulations performed under Calvo and Rotemberg pricing.
  - Annex Figure 2.3.2 shows simulated Phillips curves: under Calvo pricing the Phillips curve is steeper when markups are higher; under Rotemberg pricing it is flatter when markups are higher.

### Labor Share: Regression Analysis
- Dependent variable: wage bill / value added (labor income share).
- Regression specifications mirror those used for markups on investment rate (OLS and IV, see Equation 2.5 referenced).
- Sample: annual frequency from 2000 to 2015.
- Key regression results (Annex Table 2.3.10):
  - OLS baseline (Column (1)): 1-year lagged markup coefficient = -0.032*** (standard error 0.001).
  - OLS with alternative fixed effects (Column (2)): coefficient = -0.031*** (0.001).
  - IV specification (Column (3)): coefficient = -0.018* (0.011).
  - 1-year lagged log operating revenue coefficients: -0.033***, -0.034***, -0.031*** respectively.
  - Number of observations: 2,515,925; 2,535,858; 2,526,009 respectively.
  - R^2: 0.735, 0.721, 0.008 respectively.
- IV details:
  - Instrument for lagged markups is the lag of median markups in a firm's country-industry 2-year, excluding that firm.
  - First stage F-statistic = 87.02.
  - Annex Table 2.3.11 presents first and second stages: first-stage coefficient on 1-year lagged median markup = 0.124*** (0.013); second-stage 1-year lagged markup = -0.018* (0.011).
- Within versus between effects:
  - Main analysis relies on within-firm estimation (firm fixed effects).
  - Regressions without firm fixed effects yield a negative markup coefficient up to twice as large in magnitude as with firm fixed effects, indicating a sizeable between-firm component (reallocation from high-labor-share to low-labor-share firms) in the overall relationship.

### International Spillovers
- Spillovers operate through input and demand channels.
- Specification includes:
  - Input channel: weighted sum of each foreign supplier’s markups, weights = imports relative to total value added of importing country.
  - Demand channel: weighted sum of each foreign buyer’s markups, weights = exports relative to total value added of exporting country.
  - Controls: domestic linkages and associated markups, country-year, sector-year, and country-sector fixed effects.
- Equation (2.28) in source specifies log V A_{i j t} as function of weighted foreign markups and controls (full equation in source).
- Empirical result for Emerging Markets (Annex Table 2.3.13):
  - Foreign import-share-weighted markup coefficient = -0.075*** (0.010).
  - Foreign export-share-weighted markup coefficient = -0.533 (0.379) (not statistically significant at conventional levels).
  - Number of observations = 3,424; R^2 = 0.998.
  - Interpretation example: For a hypothetical industry in an emerging market country that imports 40 percent of its value added from abroad, a hypothetical 10 percentage point increase in markups across all foreign suppliers is associated with a 0.3 percent decrease in value added, all else equal.
- Data sources: OECD Inter-Country Input-Output Tables; IMF staff calculations.

*Source: IMF staff calculations, Annex material from the chapter.*

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_Source: https://www.imf.org/-/media/files/publications/weo/2019/april/english/ch2annex.pdf_