The Hitchhiker's Guide to Markup Estimation: Assessing Estimates From Financial Data

Mon, 01 Jan 0001 00:00:00 +0000

Using matched data combining physical production records (EAP survey) and financial statements (FARE) for 147,403 firm-years across 18 two-digit manufacturing industries in France (2009–2019), the paper audits the production-approach markup estimator — μ = α × (PY/WV) — when α must be estimated from revenue rather than quantity data. The central analytical result is that revenue-based markup estimates are positively correlated with true markups whenever the estimated output elasticity falls strictly between zero and the revenue elasticity (the Bond et al. 2021 knife-edge case). For firms sharing the same production function, the correlation is exactly one — revenue markups rank firms identically to quantity markups up to an additive constant. Monte Carlo simulations in an Atkeson–Burstein (2008) oligopoly model with translog production confirm this: correlation between revenue and true markups is 0.94 (SD 0.05) across 200 simulations with 1,600 firms, 180 markets, and 40 periods. In the French matched data, within-sector Pearson correlations between quantity and revenue markup estimates are 0.61 in levels and 0.80 in first differences; rank correlations reach 0.62 and 0.83 respectively, with medians above 0.65 and 0.84 across sectors. Cross-sectional relationships between markups and profit rates, labor shares, material shares, and market shares are qualitatively robust across estimation methods (Table VI). However, average log markup levels differ sharply: 0.37 (quantity) vs 0.13 (revenue); aggregate French manufacturing markups average 1.45 (quantity) vs 1.08 (revenue). The policy implication: revenue-based financial data are adequate for studying markup dispersion, trends, and firm-level correlates; they cannot identify markup levels.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the core analytical result about when revenue data can identify true markups?

The production-approach markup estimator μ_it = α_it × (P_it Y_it / W_t V_it) recovers true markups from revenue data if and only if the estimated output elasticity α̂ equals the true quantity elasticity; when α̂ equals the revenue elasticity instead, estimated markups are identically one; in the empirically relevant intermediate case where α̂ lies strictly between these extremes, revenue markups are positively correlated with true markups. The key insight is that standard estimators (ACF, LP, OLS) applied to revenue data produce an α̂ that lies strictly between zero and the revenue elasticity (which is less than the true output elasticity for firms with market power), so revenue markup estimates are neither correct nor uninformative. For firms sharing the same production technology — the common case in Cobb-Douglas with industry-level coefficients — revenue markups equal true markups up to an additive constant, implying a within-industry correlation of exactly one. The Bond et al. (2021) result (revenue markups ≡ 1) arises only in the knife-edge case where ACF converges exactly to the revenue elasticity; under the empirically dominant case of partial revenue elasticity contamination, the correlation is high but the level is biased downward.

Q2. How does the paper relate to the Bond et al. (2021) critique, and when does that critique apply exactly?

Bond et al. (2021) showed that if the ACF procedure is applied to revenue data and converges to the revenue elasticity, then estimated markups are identically one regardless of true markups; the present paper demonstrates this is a knife-edge special case, not a generic property of revenue-based estimation. The Bond et al. result requires that the estimated α̂ equals exactly the revenue elasticity r = α/(1+α·(μ−1)/μ) × (1/price index correction) — a relationship that holds only under specific functional form and market structure assumptions. In the Atkeson–Burstein Monte Carlo (translog production, oligopolistic competition), the ACF estimator applied to revenue data produces α̂ = 0.29 against true βv = 0.32 and revenue elasticity that is strictly lower — placing the estimate in the intermediate zone. The general principle: when α̂ is strictly between zero and the revenue elasticity, revenue markups are informative; when α̂ converges to the revenue elasticity, they are not.

Q3. What do Monte Carlo simulations in the Atkeson–Burstein model show about the reliability of revenue markup estimates?

Across 200 simulations with 1,600 firms organized in 180 markets over 40 periods, using a translog production function, the correlation between revenue-based ACF markup estimates and true quantity-based markups is 0.94 (SD 0.05), and all distributional moments of the markup distribution are well-recovered from financial data. Table I reports the estimated variable input elasticity: true βv = 0.32, quantity estimate = 0.32, revenue-ACF estimate = 0.29 — the small downward bias in the elasticity generates a small downward bias in the markup level but does not destroy the cross-sectional ranking. Table II reports the markup distribution correlations: revenue vs. true = 0.94 (SD 0.05) vs. quantity vs. true = 1.00 (SD 0.01). Cross-sectional regression coefficients of revenue markups on quantity markups are 0.85 in levels and 0.99 in first differences; all moments (mean, standard deviation, median, interquartile range) are well-estimated from revenue data. The simulations thus confirm the analytical result: revenue data preserves the cross-sectional ranking of markups and their time-series variation, even though the level is biased downward.

Q4. What does the matched French production-and-financial-statement data show about within-sector correlations?

In the French manufacturing data (EAP physical production records matched to FARE financial statements, 2009–2019, 147,403 observations, 18 two-digit industries), within-sector Pearson correlations between quantity and revenue markup estimates are 0.61 in levels and 0.80 in first differences; rank correlations reach 0.62 (levels) and 0.83 (first differences), with medians above 0.65 and 0.84 respectively across sectors. Table III documents the divergence in average output elasticities: 0.54 (quantity) vs. 0.40 (revenue), with quantity exceeding revenue in 16 of 18 industries and an average gap of 38%. Table IV shows the implied log markup averages: 0.37 (quantity, SD 0.23) vs. 0.13 (revenue, SD 0.16) — a large level gap but smaller dispersion gap. Table V reports within-sector correlations: Pearson 0.61 (levels) and 0.80 (first differences); rank 0.62 and 0.83. Binned scatter regressions confirm: slope 0.89 (levels) and 0.92 (first differences). These within-sector correlations are what matter for studying which firms have relatively higher or lower markups, and they are high enough to support revenue-based research on markup dispersion, cyclicality, and firm-level correlates.

Q5. Are the relationships between revenue markup estimates and other firm characteristics reliable?

Table VI shows that the associations of markup estimates with profit rate, labor share, material share, and market share are qualitatively robust across revenue and quantity estimation methods — the sign and relative magnitude of correlations are preserved, even though the level of markups differs. This result validates using financial data for the dominant research application of production-approach markup estimation: studying the firm-level determinants and correlates of markups. The positive correlation between markups and profit rates, the negative correlation with labor shares, and the positive correlation with market shares all survive the switch from quantity to revenue-based estimation. The key caveat is that the magnitudes of these correlations are attenuated under revenue estimation due to the downward bias in markup levels, but the qualitative patterns are preserved with statistical significance.

Q6. What do aggregate French manufacturing markup trends show, and what is the paper’s policy conclusion?

Aggregate French manufacturing markup trends are qualitatively well-captured by revenue-based estimates (Figure 5), but the average level differs substantially: 1.08 (revenue) vs. 1.45 (quantity) — a gap of 37 log points. The time-series evolution of the markup distribution (aggregate mean, trends, cyclical variation) is reliably estimated from financial statements. This implies that the empirical literature documenting rising markups over the past decades — primarily using revenue-based financial data — has correctly identified the direction and approximate magnitude of markup trends, even if the levels are underestimated. The paper’s policy conclusion is precise: revenue data are adequate for studying markup dispersion across firms, trends over time, and correlates with other firm characteristics; they are not adequate for measuring the absolute level of markups or for calibrating models that require accurate markup levels (e.g., models of aggregate price-setting or optimal tax policy).

Key concepts

production-approach markup estimator : the method pioneered by Hall (1986, 1988) and formalized by De Loecker and Warzynski (2012) that estimates firm-level markups as μ = α × (PY/WV), where α is the output elasticity of the variable input V, P is output price, Y is output, and W is input price; requires physical quantity data in principle but is widely applied to revenue (PY) data from financial statements.

revenue elasticity : the elasticity of firm revenue with respect to variable input, which equals the true output elasticity divided by a markup adjustment term; equals the output elasticity only for perfectly competitive firms; lies strictly below the output elasticity for firms with market power; when the estimated α̂ converges to the revenue elasticity, the production-approach estimator returns markups identically equal to one (the Bond et al. 2021 result).

Bond et al. (2021) knife-edge : the special case in which the ACF production function estimator applied to revenue data converges to the revenue elasticity — causing estimated markups to be identically one and uninformative about true markups; the present paper shows this is not a generic property but a specific functional-form restriction.

within-sector cross-sectional rank : the ordering of firms within an industry by their estimated markups; the statistic most reliably preserved when using revenue rather than quantity data, because within-industry production function homogeneity causes revenue markups to equal true markups up to an additive constant, so ranks are identical analytically.

level vs. dispersion distinction : the paper’s central empirical finding that revenue markup estimates reliably measure within-industry dispersion, trends, and rankings (the first moment of changes and cross-sectional variation) but cannot recover the absolute level of markups (the mean log markup is 0.13 from revenue vs. 0.37 from quantity in French manufacturing, and aggregate average is 1.08 vs. 1.45).

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