Bottom-Up Markup Fluctuations
What this paper finds — and why it matters
Layer 1 — Overview
Research Question
The paper asks how firm-level, sector-level, and aggregate markups comove with output at different levels of aggregation, and whether a single structural model can reconcile seemingly contradictory empirical findings about markup cyclicality that arise when researchers use different aggregation schemes.
Model
The authors build a granular macroeconomic model featuring oligopolistic competition with a nested constant-elasticity-of-substitution (CES) demand structure following Atkeson and Burstein (2008). The economy contains N sectors, each with a discrete number of firms competing under Cournot oligopoly with flexible prices. Firm-level markups are endogenously increasing in within-sector market shares: under Cournot, the sectoral markup is a simple function of the sector’s Herfindahl-Hirschman index (HHI), and the aggregate markup is a function of the expenditure-share-weighted average of sectoral HHIs. Firm-level productivity follows a discretized random growth (Gibrat’s law) process as in Carvalho and Grassi (2019), generating fat-tailed firm-size distributions and granular aggregate fluctuations. The baseline calibration features only idiosyncratic firm-level productivity shocks and abstracts from aggregate shocks, because—in the model—aggregate shocks that move all firms proportionately do not affect relative market shares and hence do not affect markups.
Data
The empirical analysis uses French administrative firm-level data from the FICUS-FARE datasets covering the universe of French firms from 1994 to 2019, yielding approximately 9.38 million firm-year observations across 26 years, 22 two-digit sectors, and 275 five-digit NAF sectors. Firm-level markups are estimated following De Loecker and Warzynski (2012) using a translog production function estimated by GMM (following De Ridder et al. 2024) on a subsample of approximately 220,733 firm-year observations where physical output quantity is available from the Enquete Annuelle de Production survey (2009-2019). Using quantity rather than revenue as the output measure avoids the measurement biases documented in Bond et al. (2021).
Main Findings and Quantitative Magnitudes
Markup-market-share relationship (firm level): Regressions of the change in the inverse firm markup on the change in firm market share yield a negative and significant coefficient of approximately -0.268 to -0.293 (depending on fixed-effect specification), consistent with the model prediction that markups rise with market share. Sector-level analogues yield a slope of the change in inverse sector markup on the change in sector HHI of approximately -0.37, which is simultaneously a calibration target (implying sigma = 1.8 given epsilon = 5) and an empirical moment the model closely matches (model counterpart: -0.36).
Within-between decomposition of sector markup changes: In the model under Cournot competition, changes in firm-level markups (the “within” term) account for exactly 50% of changes in sector-level markups, with between-firm reallocation accounting for the other 50%. In the French data, for the median sector, the within term accounts for 59% of changes in sector markups (interquartile range across sectors: 34%-81%).
Firm-level markup cyclicality with sector output (heterogeneous by size): The average firm’s markup is countercyclical with respect to own-sector output (beta_1 approximately -0.073 in levels specification), but this relationship reverses for large firms: firms with market shares roughly above 10% (top 0.1% of the market-share distribution) have procyclical markups (interaction coefficient beta_2 approximately 0.574 in levels). The model qualitatively and roughly quantitatively reproduces this heterogeneity.
Sector-level markup cyclicality with sector output (procyclical): Following Nekarda and Ramey (2013), sector markup changes comove positively and significantly with sector output changes: estimated coefficient of 0.160 (standard error 0.040) in first-differences. The calibrated model yields a median coefficient of 0.139 (std dev 0.057 across 5,000 simulated 25-year samples), close to the data. Consistently, sector concentration (HHI) is also procyclical with sector output (estimated coefficient 0.332, std error 0.067 in first-differences).
Sector-level markup cyclicality with aggregate output (acyclical to weakly countercyclical): Following Bils et al. (2018), the comovement between sector markups and aggregate output is fragile in sign and significance: the French data yields a point estimate of -0.239 (std error 0.116) in first-differences, marginally significant (t-stat 2.06) and with sign sensitive to detrending method. The model without aggregate shocks predicts positive comovement (median coefficient 0.165) that is not statistically different from zero across samples. Adding aggregate productivity shocks (calibrated to match French aggregate output volatility) brings the model-implied coefficient close to zero (median 0.008), with 20-30% of 25-year simulated samples displaying countercyclical sectoral markups relative to GDP—consistent with the ambiguity in the data.
Aggregate output volatility: The baseline calibration with only granular firm-level shocks generates a standard deviation of detrended aggregate output of 0.83%, equal to 26% of the 3.16% observed in the French data. (The comparable granular ratio from Carvalho and Grassi 2019 for a perfectly competitive US model is 30%.) Variable markups dampen granular aggregate volatility: the standard deviation of aggregate output under variable markups is 0.87 times that under heterogeneous-but-constant markups (95% CI: 0.82-0.97), because incomplete pass-through reduces the effective weight of large firms in the price index.
Aggregate markup volatility: In the data, the relative standard deviation of aggregate markup to aggregate output is 0.40-0.50 (depending on detrending). The model generates a relative volatility of 0.36 (median across samples). The correlation between aggregate markup and output in the data is at most 0.06; the model without aggregate shocks implies a counterfactually large median correlation of 0.91, which falls to 0.27 when aggregate TFP shocks are superimposed (with 16% of 25-year samples displaying countercyclical aggregate markups).
Scope Conditions
Results pertain to French private-sector firms (including formerly government-owned firms, most of which privatized during the sample period) across manufacturing and some non-manufacturing sectors at the national-market level. The analysis abstracts from import competition (market shares are computed relative to all French firms in the sector), local geographic markets (relevant for non-tradeable goods where national-level shares understate local concentration), and multi-product firm structure. Findings are for a flexible-price model driven by idiosyncratic productivity shocks; the paper explicitly discusses how nominal rigidities would further strengthen procyclicality at the sector level.
Layer 2 — Q&A
Q1: What is the central mechanism by which granular firm-level shocks generate markup cyclicality?
A: Because markups are endogenously increasing in within-sector market shares under oligopolistic competition, a firm that receives a positive productivity shock gains market share and therefore raises its markup, while its competitors lose market share and lower their markups. The net effect on the sectoral markup depends on the shocked firm’s initial size: a positive shock to a sufficiently large firm (above a threshold market share) raises the sectoral markup, while a positive shock to a small firm lowers it. Since sectoral expansions in a granular economy are disproportionately driven by large firms, sector output and sector markup tend to comove positively in the medium run.
Q2: Why does the sign of markup cyclicality differ depending on the level of aggregation?
A: Sector-level markups react only to within-sector idiosyncratic shocks, so sectors that happen to be driven by large-firm booms display positive comovement between sector markup and sector output. However, a given sector’s markup is uncorrelated with aggregate output movements coming from other sectors. In small samples (such as 25-year windows), whether a sector’s markup comoves positively or negatively with aggregate output depends on whether the sector happens to lead or lag the aggregate cycle. Over sufficiently long samples, the model implies positive comovement of sector markups with aggregate output, but in finite samples the relationship is indeterminate. This asymmetry across aggregation levels explains why researchers using different reduced-form specifications in the same dataset can reach opposing conclusions about procyclicality versus countercyclicality.
Q3: What is the within-between decomposition of sectoral markup changes and what does it imply quantitatively?
A: Changes in the inverse sectoral markup can be decomposed into (i) a within term—changes in firm-level markups holding market shares fixed—and (ii) a between term—changes in market shares holding firm-level markups fixed. Under Cournot competition, the within and between terms are analytically equal in every period, so each accounts for exactly 50% of the change in sectoral markups; this 50-50 split holds globally (not only to first order). In the French data, for the median sector, within-firm markup changes account for 59% of sector markup changes (interquartile range across sectors: 34%-81%), close to but slightly above the model’s 50% prediction.
Q4: How do variable markups affect granular aggregate output volatility relative to a model with constant markups?
A: Variable markups (endogenous pass-through that is decreasing in firm size) reduce granular aggregate output volatility relative to a model where markups are heterogeneous but fixed. The intuition is that larger firms have lower pass-through rates, so their productivity shocks translate into smaller price changes and therefore smaller output responses than they would under constant markups—effectively reducing the weight of large firms in the aggregate price index in a way similar to a decline in market concentration. Quantitatively, using first-order approximations around equilibrium distributions from the calibrated model, the standard deviation of aggregate output under variable markups is 0.87 times that under heterogeneous-but-constant markups (95% confidence interval: 0.82-0.97). The overall standard deviation under variable and heterogeneous markups is only 1.02 times that under homogeneous and constant markups (95% CI: 0.99-1.14), meaning markup heterogeneity and variability together have limited net effects on aggregate output volatility.
Q5: What does the model predict for firm-level markup cyclicality, and how heterogeneous is this across firm size?
A: Proposition 4 states that, in the asymptotic limit, firm-level markups comove positively with own-sector output for firms with market shares above a threshold, and negatively for firms below it. This occurs because large firms have a disproportionate impact on sector-level price and output (when the product of market share and pass-through rate is increasing in size), so large-firm shocks simultaneously drive sector expansions and raise large-firm markups while compressing small-firm markups. In the French data, the average firm’s markup is countercyclical with respect to sector output (beta_1 approximately -0.073 in log-levels with firm and year fixed effects), but firms with market shares above roughly 10% (top 0.1% of the distribution, since the average market share is only 0.07%) display procyclical markups (interaction coefficient beta_2 approximately 0.574). The model reproduces this qualitative pattern and the order of magnitude of these estimates.
Q6: How does the paper calibrate the key demand elasticities, and what are the resulting pass-through implications?
A: The within-sector substitution elasticity is set to epsilon = 5, a standard value. The cross-sector substitution elasticity sigma is calibrated to match the slope of the inverse sector markup on sector HHI in first-differences. The empirical slope is -0.37; under the model, the slope equals -(epsilon/sigma - 1)/(epsilon - 1), and given epsilon = 5, sigma = 1.8 delivers a model counterpart of -0.36. These parameter values imply own-cost pass-through rates that are decreasing in firm size; for large firms (with market share >= 57%, approximately the top 0.004% of the distribution), the implied pass-through rate is 0.63, within the confidence intervals reported in Amiti, Itskhoki, and Konings (2019) for large Belgian firms.
Q7: Why do aggregate productivity shocks not affect markups in the model, and what are the implications for aggregate markup cyclicality?
A: In the model, firm-level markups are functions of within-sector market shares, not the level of productivity. An aggregate shock that shifts all firms’ productivity proportionately leaves relative market shares unchanged and therefore leaves all markups unchanged. This means aggregate shocks increase aggregate output volatility but leave markup volatility unchanged, reducing the correlation between aggregate markup and aggregate output. When aggregate TFP shocks are added to match French aggregate output volatility, the model-implied median correlation between aggregate markup and output falls from 0.91 (without aggregate shocks) to 0.27 (with aggregate shocks), while 16% of 25-year simulated samples display countercyclical aggregate markups—more consistent with the weak and fragile empirical relationship.
Q8: How does the paper address the potential measurement-error bias in the negative correlation between markups and marginal costs?
A: Since marginal cost is computed as price divided by estimated markup, regressing market shares or markups on marginal costs risks spurious correlation via measurement error in the markup (which appears in both sides). The authors address this concern by constructing an instrumental variable for marginal cost based on firm-specific energy intensity interacted with energy price changes, following Ganapati, Shapiro, and Walker (2020). Table A10 confirms that instrumenting for marginal cost yields negative effects on both markup and market share with larger point estimates than the OLS specifications in Table 4, validating the baseline findings.
Q9: Is the 50-50 within-between decomposition of sectoral markup changes robust to the choice of competition mode?
A: No. The exact 50-50 split of within and between terms in sectoral markup changes is a specific property of Cournot competition and holds globally (not just as a first-order approximation). Under Bertrand competition, the within and between terms are generally not equal to each other. The paper derives analytic results under both competition modes and focuses on Cournot for quantitative work because it generates more markup variation and better matches the estimated pass-through rates and markup-size relationship.
Q10: What do model simulations imply for the magnitude and cyclicality of aggregate markups versus the data, and what is the role of variable versus constant markups?
A: In the data (detrended), the standard deviation of aggregate markup is 1.27% with a relative volatility (to output) of 0.40 and a correlation with output of 0.03. The baseline model with only granular shocks yields a median markup standard deviation of 0.30%, relative volatility of 0.36, and correlation with output of 0.91. The model with aggregate shocks added yields median markup standard deviation of 0.30%, relative volatility of 0.09, and correlation of 0.27. Counterfactually fixing markups at their initial heterogeneous levels while keeping the same market shares and shock variance yields aggregate markup standard deviation approximately 0.93 times the variable-markup value (standard deviation of markups under variable markups is 1.08 times that under constant markups, with a 95% CI of 1.00-1.18), and a correlation with output of 0.92 versus 0.87 under variable markups. Overall, the magnitude and cyclicality of aggregate markups are not substantially different between variable and constant-markup specifications.
Q11: How does the paper reconcile its findings with prior literature on markup cyclicality (Bils et al. 2018 vs. Nekarda and Ramey 2013)?
A: Nekarda and Ramey (2013) find procyclical sector markups with respect to sector output in US data—a result replicated in French data (beta approximately 0.160). Bils, Klenow, and Malin (2018) find countercyclical sector markups with respect to aggregate output in US data. Both results can be generated simultaneously in the model: sector markups are positively correlated with own-sector output because granular booms in a sector are driven by large-firm expansions that raise sector markups; however, a given sector’s markup is weakly and ambiguously correlated with aggregate output because aggregate fluctuations reflect shocks across many sectors, only some of which are in the same sector. The model can therefore simultaneously predict procyclicality with respect to sector output and an acyclical-to-weakly-countercyclical relationship with aggregate output—explaining why both empirical findings can be correct.
Q12: What are the data limitations and how do they affect the interpretation of results?
A: Three limitations are noted. First, market shares are computed relative to total revenue of all French firms in the sector without accounting for imports, so foreign competition is ignored and domestic concentration may be overestimated. Second, revenues are reported at the national level, so for non-tradeable goods (whose relevant market is local) the paper underestimates true local market concentration, attenuating the markup-concentration relationship in those sectors. Third, the model abstracts from entry and exit (the number of firms per sector is held fixed at sector-year averages), though Appendix D demonstrates robustness of main empirical results to restricting the sample to continuing firms.
Key Concepts
Granular macroeconomic model: A model in which the economy consists of a finite (large but discrete) number of firms, so that idiosyncratic firm-level shocks to large firms do not average out and instead generate aggregate fluctuations. In the paper’s usage, granularity means that sectoral and aggregate business-cycle fluctuations are driven primarily by shocks to the largest firms, which also have the highest markups and market shares.
Nested CES demand structure (Atkeson-Burstein): A two-level constant-elasticity-of-substitution aggregation where the final good aggregates N sectors with cross-sector elasticity sigma, and each sector aggregates the output of its Nk firms with within-sector elasticity epsilon > sigma. This structure generates firm-level markups that are endogenously increasing in within-sector market shares (under both Cournot and Bertrand competition) and yields closed-form expressions for sector-level markups as a function of sector HHI and aggregate markups as a function of the expenditure-weighted average of sector HHIs.
Markup elasticity with respect to market share (Gamma_ki): Under Cournot competition, the semi-elasticity of firm i’s log markup with respect to its log market share, equal to (epsilon/sigma - 1)s_ki / (epsilon/(epsilon-1) - (epsilon/sigma - 1)s_ki). This is strictly positive for epsilon > sigma and increasing in market share, implying that larger firms have markups that are more responsive to changes in their competitive position.
Pass-through rate (alpha_ki): The fraction of an idiosyncratic cost shock that is passed into the firm’s price relative to the sectoral price index, given by 1/(1 + (epsilon-1)Gamma_ki). Pass-through is decreasing in market share (larger firms have lower pass-through), which dampens their price response to own shocks and mutes the impact of large-firm shocks on aggregate price volatility—acting like a reduction in market concentration.
Within-between decomposition of sector markup changes: The change in inverse sector markup decomposed into (i) a within term measuring changes in firm-level markups holding market shares fixed, and (ii) a between term measuring reallocation of market shares across firms with heterogeneous markups. Under Cournot competition, these two terms are exactly equal (each 50%) for any firm-level shocks—a result that holds globally (not merely as a first-order approximation)—because the forces that increase the within term (higher markup sensitivity) also raise heterogeneity between firms (increasing the between term).
Sectoral markup (mu_kt): Defined as the ratio of sectoral revenues to total wage payments in the sector, equal to the harmonic mean of firm-level markups weighted by market shares. Under Cournot competition, this is a simple increasing function of the sector’s HHI: mu_kt = (epsilon/(epsilon-1))[1 - (epsilon/sigma - 1)/(epsilon-1) x HHI_kt]^(-1). This mapping between concentration and the markup price-cost wedge gives the central empirical prediction tested at the sector level.
Markup cyclicality (at different aggregation levels): The comovement between markups and output, which the paper distinguishes sharply across three levels: (i) firm markup vs. own-sector output—countercyclical for small firms, procyclical for large firms; (ii) sector markup vs. own-sector output—procyclical (positive covariance) under conditions proven in Proposition 3; (iii) sector markup vs. aggregate output—theoretically positive over long samples but ambiguous and close to zero in short samples, because aggregate output also reflects shocks to other sectors whose markups are uncorrelated with the focal sector’s markups. The paper’s central insight is that the same underlying model generates all three empirical patterns simultaneously.