Micro and Macro Perspectives on Production-Based Markups

This paper reviews the scalable "production approach" to estimating markups, arguing that while it offers a model-free method for measuring market power, its results are highly sensitive to specification and measurement errors that can conflate markup variations with technological changes, necessitating greater transparency and careful interpretation of the literature's conflicting findings.

The Gist

The Big Picture: What is a "Markup"?

Imagine you run a lemonade stand.

• Cost: It costs you $0.50 to buy lemons, sugar, and cups.
• Price: You sell a cup for $1.00.
• Markup: The difference between your price and your cost. In this case, your markup is 100% (you are charging double your cost).

In economics, a markup is a measure of market power. If you are the only lemonade stand in town, you can charge $5.00. If you are in a busy street with 50 other stands, you might have to charge $0.55. Economists want to know: Are companies becoming more powerful (charging higher markups) or less powerful?

The Problem: The "Magic Residual"

This paper reviews a popular method economists use to guess markups without asking companies directly. They call it the "Production Approach."

Think of this approach like a mystery scale.

1. You put the Revenue Share (how much of the total money a company spends on a specific ingredient, like labor) on one side.
2. You put the Output Elasticity (how much extra lemonade you get if you add one more worker) on the other side.
3. The Markup is whatever is left over to make the scale balance.

The Catch: The markup is a "residual." It's the "garbage can" of the equation. If your measurement of labor costs is slightly off, or if your guess about how productive workers are is wrong, that error doesn't disappear. It gets dumped into the "Markup" bucket.

The authors say: "The markup is a residual claimant." It claims whatever the math couldn't explain elsewhere.

The "Garden of Forking Paths"

The paper argues that because the markup is a "garbage can," the results depend entirely on which path you choose to walk. The authors call this the "Garden of Forking Paths."

Imagine you are trying to measure the height of a mountain, but you have to guess the height based on how much snow is on the ground.

• Path A: You assume the snow is deep and heavy. You guess the mountain is huge.
• Path B: You assume the snow is fluffy and light. You guess the mountain is small.

In the paper, researchers make different choices, and the results change wildly:

1. Which Ingredient to Measure?

   • If you measure Labor (workers), some studies say markups are skyrocketing (companies are getting super powerful).
   • If you measure Materials (raw goods), other studies say markups are actually falling.
   • Analogy: It's like measuring a car's speed by looking at the tires (which might be slipping) vs. looking at the engine (which might be revving). You get two different speeds for the same car.

2. How Flexible is the Technology?

   • Do we assume all factories are identical (rigid)? If so, any difference in efficiency gets blamed on "market power" (markup).
   • Do we assume factories are unique and flexible? If so, the differences are blamed on "better technology," and markups stay flat.
   • Analogy: If you assume all runners are identical, and one finishes faster, you assume they cheated (high markup). If you know they have different shoes, you assume they just had better gear (technology).

The Three Big Leaks in the Bucket

The paper explains why these "residuals" are often contaminated by three main leaks:

1. The "Hidden Wedge" (Frictions)
The math assumes companies pay exactly what they should for workers and materials. But in reality, there are "wedges."

• Example: A company might have to pay a worker more to keep them from quitting (bargaining), or they might face a tax.
• Result: The math thinks the extra cost is "market power" (a high markup), but it's actually just a friction or a tax.

2. The "Bad Data" Problem
The data we have is often messy.

• Example: Companies report "Cost of Goods Sold" (COGS) and "Selling, General, and Admin" (SG&A) expenses.
• The Trap: Some researchers only count COGS. If a company spends more on marketing (SG&A) over time, and you ignore it, the math thinks their production costs went down, so their markup must have gone up.
• Analogy: It's like trying to calculate your profit by ignoring your rent. You think you're rich, but you're actually just forgetting your bills.

3. The "Circular Logic" Trap
To find the markup, you need to know how productive a worker is. But to know how productive they are, you need to know the price they charge.

• The Loop: If a company has high market power, they charge high prices. High prices make them look less productive in the data. The math gets confused and can't tell if the company is powerful or just efficient.

The Authors' Call to Action

The paper concludes that we can't just trust the numbers we see in the news or other papers. We need to be smarter. They propose three "Calls to Arms":

1. Be Transparent (The R-Squared Test):
   Researchers should report how much of the variation in costs is actually explained by technology vs. how much is just "leftover" (the markup). If the markup explains 99% of the changes, the model is probably broken.

2. Stress-Test the Results:
   Don't just trust one method. Compare the "Production Approach" (looking at costs) with the "Demand Approach" (looking at what customers buy). If they tell different stories, dig deeper. Use simulations where you know the answer to see if your method works.

3. Connect Micro to Macro:
   We need to understand why markups are rising. Is it because of bad monopolies (which hurt the economy)? Or is it because of innovation and fixed costs (which might be good)? We need to stop treating all markups as the same thing.

The Bottom Line

The "Production Approach" is a powerful tool because it lets us look at thousands of companies at once without needing a crystal ball. But it is fragile.

Because the markup is a "residual" (the leftover number), it absorbs all our mistakes, bad data, and wrong assumptions.

• The Warning: Just because a study says "Markups are rising!" doesn't mean it's true. It might just mean they chose a different ingredient to measure or ignored a specific cost.
• The Goal: We need to stop treating these numbers as absolute facts and start treating them as clues that need to be cross-checked, cleaned, and understood in context.

In short: The math is simple, but the reality is messy. Don't believe the residual until you've checked the whole bucket.

Technical Summary

1. The Problem

The paper addresses the growing empirical disagreement regarding the measurement of markups (the ratio of price to marginal cost) and their trends over time. While some studies (e.g., De Loecker et al., 2020) using the "production approach" find dramatic increases in markups, others (e.g., Foster et al., 2024; Traina, 2018) find them to be stable or even declining.

The core problem is that the production approach treats the markup as a residual. It relies on the first-order condition (FOC) of cost minimization, where the markup ($\mu$) is the ratio of an input's output elasticity ($\gamma$) to its revenue share ($s$):
$$\mu_{it} = \frac{\gamma_{it}}{s_{it}}$$
Because $\mu$ is a residual, any misspecification of the production function, measurement error in data, or unobserved frictions (wedges) in the FOC are absorbed entirely into the estimated markup. The authors argue that the stark divergence in results across studies using the same data stems from "garden of forking paths"—substantive choices in implementation that lack a single theoretically correct path, leading to different residuals.

2. Methodology and Framework

The paper reviews and critiques the production approach to markup estimation, tracing its evolution from Hall (1986, 1988, 1990) to modern firm-level microdata applications (De Loecker & Warzynski, 2012).

The Core Mechanism

The methodology rests on the assumption that firms minimize costs. For a fully flexible input $X$, the FOC implies:
$$\gamma_{it} = \mu_{it} s_{it}$$
Where:

• $\gamma_{it}$ is the output elasticity of the input.
• $s_{it}$ is the input's share of total revenue.
• $\mu_{it}$ is the markup.

To estimate $\mu$, researchers must:

1. Select a flexible input (e.g., labor, materials).
2. Measure its revenue share ($s$).
3. Estimate the output elasticity ($\gamma$) via a production function.

The "Garden of Forking Paths"

The authors demonstrate that the estimated markup is highly sensitive to three key conceptual choices:

1. Input Choice: Whether to use labor, materials, energy, or accounting aggregates (COGS vs. OPEX).
2. Functional Form Flexibility: Whether to use restrictive forms (Cobb-Douglas with constant elasticities) or flexible forms (Translog, CES with input-augmenting productivity).
3. Aggregation Level: Whether to estimate elasticities at the firm, 4-digit, or 2-digit industry level.

3. Key Contributions and Findings

A. Empirical Divergence (The "Garden")

Using direct comparisons within the same datasets, the authors show that implementation choices reverse the sign and magnitude of markup trends:

• Input Choice: In US manufacturing (1970–2010), using labor implies markups nearly doubled, while using materials implies they fell by 50%. In Spain, the conclusion on whether exporters charge higher markups flips depending on the input used.
• Accounting Definitions: Using Cost of Goods Sold (COGS) alone suggests markups rose from 1.19 to 1.45 (1950–2016). Including SG&A (Selling, General, and Administrative expenses) as a variable cost reduces the rise to just 1.15 to 1.17.
• Functional Form: Restrictive Cobb-Douglas specifications often show rising markups. Switching to Translog or allowing for labor-augmenting productivity (CES) often flattens or reverses these trends, as the model allows output elasticities to absorb variation that restrictive models force into the markup.

B. Conceptual Rationales for Disagreement

The paper identifies two main theoretical reasons for the divergence:

1. Misspecified First-Order Conditions (Wedges): The standard FOC assumes frictionless input markets. However, adjustment costs (dynamic inputs), monopsony power (input markdowns), and bargaining frictions create a wedge ($\tau$) between observed prices and allocative shadow costs. If ignored, these wedges contaminate the markup estimate: $\hat{\mu} = \mu(1+\tau)$.
2. Restrictive Production Technology: If the assumed production function is too rigid (e.g., Cobb-Douglas), genuine technological heterogeneity (variation in $\gamma$) cannot be captured. This variation is mechanically forced into the residual, inflating the estimated dispersion and trend of markups.

C. Data and Econometric Challenges

• Measurement Error: Missing inputs (intangibles, business services) and misclassification of costs (COGS vs. SG&A) distort revenue shares. Capital measurement (book values vs. economic value) is particularly problematic.
• Endogeneity (Two Layers):
  • Layer 1: Unobserved productivity shocks correlate with input choices (transmission bias).
  • Layer 2 (Crucial): Unobserved output prices correlate with input choices under imperfect competition. Firms with market power charge higher prices and use fewer inputs.
  • Result: If researchers use revenue data without correcting for output prices, standard estimators (like OLS or Control Functions) may recover a revenue elasticity ($\gamma/\mu$) rather than physical elasticity. Plugging this into the markup formula yields a tautology where $\hat{\mu} = 1$, rendering the estimate uninformative.

D. Gross Output vs. Value Added

The authors argue against using value-added production functions for markup estimation. Value added is a construct that nets out intermediates; under imperfect competition, it leads to biased elasticity estimates. Furthermore, converting gross-output markups to value-added markups for macro models requires strong assumptions (e.g., fixed intermediate proportions) that often fail empirically.

4. Recommendations and "Call to Arms"

The authors propose three specific methodological shifts to improve the field:

1. Transparency (The $R^2$ Diagnostic):
   Researchers should report an $R^2$ decomposition of revenue share variation. They should regress $\ln(s_{it})$ on $\ln(\hat{\gamma}_{it})$. If the $R^2$ is near zero, it means the estimated elasticities explain almost none of the variation in revenue shares, implying that all variation is being mechanically attributed to markups due to restrictive functional forms. This is a warning sign of misspecification.

2. Stress-Testing:
   Production-based estimates should be validated against:

   • Demand-based estimates from Industrial Organization (IO) literature.
   • Simulations where the true markup is known (Monte Carlo).
   • Natural experiments (e.g., mergers, policy shocks) to see if estimates detect real shifts in market power.

3. Aggregation and Macro Mapping:
   Macro models need to distinguish between "good" markups (returns to innovation/fixed costs) and "bad" markups (entry barriers/inefficiency). Aggregating firm-level heterogeneity into representative firm models requires careful handling of network effects (upstream vs. downstream markups) and the distinction between gross-output and value-added measures.

5. Significance

• Theoretical: The paper reframes the markup debate, moving it from a dispute over "who is right" to a structural analysis of why estimates diverge. It highlights that the production approach is a measurement tool, not a structural model of competition.
• Empirical: It provides a rigorous diagnostic toolkit (the $R^2$ check, input sensitivity analysis) to assess the robustness of any markup study.
• Policy: It cautions against interpreting rising markups solely as evidence of anti-competitive behavior without ruling out measurement artifacts, technological shifts, or fixed-cost recovery. It emphasizes that understanding the source of markups is essential for welfare and antitrust policy.

In conclusion, the paper argues that while the production approach is uniquely scalable, its results are fragile. The "residual" nature of the markup means it captures everything the model fails to explain. Therefore, greater transparency, rigorous stress-testing, and better data on prices and inputs are required to reliably measure market power.