How Large Are Double Markups?

Because prices exceed marginal costs in many upstream and downstream industries, downstream prices often reflect a double markup. This paper estimates the size of double markups across many industries accounting for direct and indirect upstream markups. The double markups in many U

If upstream and downstream industries set their prices above marginal costs, downstream prices reflect a double markup.Market power in an upstream industry raises the price of a downstream industry that it supplies directly or indirectly by selling to other industries that provide inputs to the downstream industry.This paper systematically estimates the size of double markups across manufacturing industries, mining, and utilities accounting for direct and indirect effects.It compares estimates of the double markup based on two methods of estimating market power and demonstrates that increasing returns to scale magnify the double markups.
Many theoretical articles dating from the 1950s discuss the implications of double markups (see the literature summaries in Perry 1989, Carlton and Perloff 2005, and Riordan 2008).Some of these papers emphasize how vertical integration may eliminate double markups (Spengler 1950, Warren-Boulton 1974, and Riordan 2008).Verboven and van Dijk (2009) showed that increasing returns to scale exacerbates the downstream effects of upstream market power.
Empirical articles typically focus on the marketing channel for a single downstream industry, such as between an industry's manufacturers (or wholesalers) and retailers.For example, Bresnahan and Reiss (1985) examined the relationship between an automobile manufacturer and its dealers.Kadiyali, Chintagunta, and Vilcassim (2000) estimated the shares of retailer and manufacturer profits.Chintagunta, Bonfrer, and Song (2002) investigated how introducing a private label by one retailer affects the relative market power of the retailer and the manufacturers.J. Miguel Villas-Boas and Zhao (2005) examined the ketchup market in a single city.Sofia Berto Villas-Boas (2007) estimated double marginalization between wholesalers and retailers in yogurt supply chains.Gayle (2013) examined double marginalization when unaffiliated airlines independently determine the prices for various trip segments.Crawford et al. (2018) studied the welfare effects of vertical integration in multichannel television markets, where one potential impact is eliminating a double markup.
In contrast, this study systematically estimates the size of double markups across many industries at once.In addition, no double-markup study has explicitly analyzed the role of returns to scale. 1e use a multimarket (incomplete general equilibrium) model for two-digit manufacturing industries.We also include mining and utilities, which supply manufacturing industries.By restricting our analysis to input flows that exceed 6% of total cost, all flows go in one direction.Were we to consider smaller flows, we would see pairs of industries that supply each other.Then, we would have to use a simulation approach such as a computable general equilibrium (CGE) model.With flows going in only one direction, we derive analytic solutions that do not require specifying various ancillary parameters needed by CGE models.Appendix A shows that our approach likely produces a lower bound on the double markup.Baqaee and Farhi (2020) addressed the role of market power on productivity and misallocation across supply chains in many industries.However, they do not explicitly estimate double markups.Our paper differs from theirs because we calculate the price and consumer surplus effects of reducing double markups.Also, we use estimated, increasing returns to scale, whereas they assumed non-increasing returns to scale.
The magnitude of double markups is important for four reasons.First, failure to include double markups results in underestimating market power distortions.Virtually all empirical market power studies focus on one (typically downstream) market.By ignoring the upstream markups on the downstream firm's price, an estimate of the downstream price distortion is biased downward.Even if economists were to study distortions in upstream and downstream industries separately, these studies would underestimate the total distortions because downstream industries' markups magnify the upstream distortions.
Second, a new macroeconomic literature concludes that rising market power is harming the U.S. economy.Some (controversial) claims are that greater market power has decreased labor's share of value-added, lowered productivity growth, slowed the rate of business formation, and reduced investment (Carlton, 2020).Regardless of whether increasing market power would have these effects, the debate turns on whether market power is rising (Basu 2019).To the degree that these studies focus on downstream industries and ignore double markups, their markup estimates are biased.For example, if market power increases faster for upstream than downstream firms, these studies underestimate the rise in market power.
Third, large double markups may provide a strong justification for vertical integration or quasi-vertical integration.As many theoretical articles show, vertical integration can eliminate a double markup.Contract restrictions that otherwise might be questionable may be desirable if their quasi-vertical integration eliminates some of the double markups.
Fourth, multiple markups play a critical role in U.S. antitrust law.In its Illinois Brick decision (Landes and Posner, 1979;Shinkel, Tuistra, and Rüggeberg, 2008;Verboven and van Dijk, 2009;Basso and Ross, 2010), the U.S. Supreme Court held that only direct purchasers have standing to sue for antitrust violations.A part of the Court's reasoning was to avoid double counting.If all damages must be assessed downstream, accounting for double markups is crucial.
Because the size of the double markup depends on the estimated markup in each industry, we compare results based on the estimation methods of Diewert and Fox (2008) and Hall (2018).
To measure the size of double markups, we simulate the downstream price effects of eliminating or reducing upstream market power.Eliminating all upstream markups-that is, the double markups-would reduce downstream prices by between 10% and 73% across the 13 industries using the Diewert and Fox approach, but by only 2% to 21% with the Hall method.The difference results from using estimated increasing returns to scale in the Diewert-Fox approach and constant returns to scale in the Hall method.
The price decreases from reducing or eliminating market power would substantially increase consumer surplus.The largest annual consumer surplus rise from a one percent reduction of market power upstream is $2.2 billion in the mining-petroleum and coal pair.The paper's first section describes U.S. manufacturing supply chains.The next section develops the theory needed to calculate double markups in the presence of returns to scale.The third section covers the literature on estimating market power and returns to scale, two methods to estimate market power, the data, and our markup and production function estimates.The fourth section estimates how price and consumer surplus would change from reductions in upstream and downstream markups.The last section summarizes our results and draws conclusions.

Supply Chains in Manufacturing
We want to measure how upstream markups affect downstream prices in manufacturing industries.To do so, we investigate the channels by which inputs flow from mining, utilities, and upstream manufacturing industries into downstream manufacturing industries.We assume that the other factors of production, such as food and labor, are supplied by competitive markets.
To examine how upstream markups affect downstream prices in manufacturing industries, we need to know the downstream input share of each upstream manufacturing industry, mining, and utilities. 2We calculate input flows using data from the 2000 Bureau of Economic Analysis (BEA) input-output tables and BEA and Bureau of Labor Statistics (BLS) total cost information.
We examine only flows between industries that exceed 6% of total cost. 3This restriction simplifies our analysis greatly.Smaller flows are relatively unimportant.Were we to examine smaller flows, we would see pairs of industries that supply each other.However, all the flows that exceed 6% go in one direction: If Industry 1 supplies Industry 2, Industry 2 does not supply Industry 1.
As a result of this restriction, we have two non-overlapping vertical supply chains.One supply chain "starts" with the mining industry, while the other "starts" with the chemical industry.
Figure 1 shows the vertical supply chain that starts with mining (though mining does not supply the computer and electronics industry in this figure).The percentage next to each directional arrow is the value of the upstream input divided by the downstream industry's total cost.For example, mining's input is 78.08% of petroleum and coal's total cost.
The figure illustrates how an upstream industry may supply a downstream industry directly or indirectly.For instance, mining inputs flow directly to the primary metal industry.In addition, mining supplies utilities, which in turn supply primary metal.Thus, mining provides inputs to primary metals directly and indirectly through utilities.
2 Total cost includes manufactured inputs, energy, non-energy materials, labor, capital services, and purchased business services. 3The largest feedback flow is 5.47% from utilities to mining.The next largest feedback is about 3% between Chemical and Plastic & Rubber Products.The remaining feedback flows are smaller than about 3%, and most are 2% or less.In Appendix A, we show that restricting our analysis to only flows above 6% may provide a lower bound on the price distortion from a double markup.
Figure 2 shows the vertical supply chain that starts with chemicals (or wood).We use the relationships and input shares in Figures 1 and 2 to calculate the direct and indirect effects of upstream markups on downstream prices.

Theory
Although the theory behind the double markup is well-known, the role of returns to scale and the downstream price effects with complicated supply chains have rarely, if ever, been examined.We start with the simplest possible case to illustrate the role of returns to scale in determining a double markup.A downstream monopoly buys its only input from a single upstream industry.
We then generalize our model for a downstream monopoly that buys a variety of inputs from many upstream monopolies and competitive industries along a complex supply chain.This model allows for indirect and direct flows from upstream industries to those downstream.
Throughout, we assume that the manufacturing industries, mining, and utilities face constant elasticity demand functions, have Cobb-Douglas production functions, and are monopolies.We make the monopoly assumption for three reasons.First, it simplifies our analysis.Second, this assumption underlies the Diewert and Fox (2008) method of estimating market power, which is one of the two approaches we use.
Third, we can approximate the empirical outcome of other market structures using a monopoly model.For example, suppose the market consists of n identical Cournot firms.The Cournot-Nash equilibrium outcome is the same as the monopoly outcome with an elasticity of n times the market elasticity.If these firms cooperate, the cartel outcome is the same as that of a monopoly with the market demand elasticity.

One Upstream and One Downstream Industry
Initially, suppose a downstream monopoly buys its sole input from a single upstream industry.We first derive the double markup equation with constant returns to scale.Next, we generalize the markup formula for non-constant returns.Then, we discuss the double markup implications given a feedback flow of input from the "downstream" industry to the "upstream" industry.
The downstream monopoly faces a constant elasticity demand function where ε is the constant elasticity of demand, pd is the price of the output Xd, and the subscript d indicates "downstream."Its cost function is C(Xd).
The monopoly chooses Xd to maximize its profit, Its first-order condition is We define the markup, M, as the price divided by marginal cost, MC = ∂C/∂Xd.Using the firstorder condition, Thus, the markup depends solely on the constant elasticity of demand, ε.

Constant Returns to Scale
We start by determining the double markup if the production functions exhibit constant returns to scale.The downstream monopoly buys its sole input, Xu, at price pu from the upstream monopoly.It uses one unit of Xu to produce one unit of its output: Xd = Xu.According to Equation 2, the downstream demand equation is pd = Mpu, because pu is its marginal cost.
Inverting the downstream demand function and using Equation 1, we find that the upstream inverse demand function is so the inverse demand elasticity, 1/ε, is the same upstream and downstream.
The upstream monopoly uses a single input X that it buys in a competitive market at price m.It produces its output Xu using the production process is Xu = X.Its objective is to choose Xu to maximize its profit πu = puXu -mXu =   1+1/ / -mXu.Substituting the upstream inverse demand function in the first-order condition, (1 + 1/ε)   1  Τ /m = 0 and rearranging terms, we find that pu = Mm.Thus, the upstream markup is also M because both the upstream and downstream firms face the same constant elasticity of demand, ε.Given that the upstream and downstream industries have the same markup, M, the markup of the downstream marginal cost, m, is squared: Equation 4 is the classic double-markup equation.

Non-constant Returns to Scale
How does the double markup change if firms have non-constant returns to scale?Now, the upstream production process is   =  ⬚   , where au is the returns to scale.The production process exhibits increasing returns to scale if au > 1, constant returns to scale if au = 1, and decreasing returns to scale if au < 1.Similarly, the downstream production function is where ad is its returns to scale.
Using the same type of reasoning as in the constant returns to scale analysis, we obtain the downstream price equation (which corresponds to Equation 4): 4 (5) Thus, the downstream price depends on the upstream firm's input price, m, the two returns to scale parameters, ad and au, and the demand elasticity, ε (because M depends solely on ε).If we set ad = au = 1 in Equation 5, we obtain the classic constant returns to scale double markup, Equation 4.
The following three examples illustrate that increasing returns to scale magnifies the double markup.Suppose m = 1 and ε = -2, so M = 2.With constant returns to scale pd = mM 2 = 4 The downstream firm's objective is . Substituting this expression into the first-order condition and rearranging terms, we obtain the upstream monopoly's inverse demand function, Thus, the upstream monopoly's profit-maximizing objective is Using the inverse demand function, we learn that its profit-maximizing price is −1 .Again using the upstream and downstream demand functions, we obtain the downstream price equation (5). 4. First, if ad = 1 and au = 1.1-that is, the upstream production function exhibits only a small amount of increasing returns to scale-then pd would increase from 4 to about 4.84.Second, if ad were also 1.1, then pd is about 5.39.Third, pd is nearly 19 if ad = 1 and au = 1.5.

Feedback
By restricting our analysis to input flows exceeding 6%, input flows in only one direction.How does this assumption affect our double-markup estimates?
In Appendix A, we extend this model to examine the effects of allowing a backward flow from a "downstream" industry to an "upstream" industry.We show that the Equation 5 markup may be a lower bound of the actual markup that accounts for a small backward flow.5

Many Upstream and Downstream Industries
We want to measure how much upstream markups affect downstream prices across industries.To do so, we generalize our one-upstream-and-one-downstream-industry model in two ways.First, the downstream industry now uses inputs from several upstream industries, some monopolized and some competitive.Second, some upstream suppliers may buy inputs from industries further upstream.Thus, we account for direct and indirect effects of upstream market power.
We calculate the effect on downstream prices of reducing upstream prices, ignoring any possible downstream substitutions that would affect the upstream demand function.To conduct a full general equilibrium analysis, we would need a complete set of cross-elasticities of demand, which are unavailable.
However, this simplification is unlikely to create much bias.Although firms within an industry face substantial cross-elasticities of demand, the cross-elasticities of demand between manufacturing industries are likely to be extremely small.It is difficult to imagine any substitutability between, say, apparel and transportation or textiles and stone, clay & glass.
In our general model, a downstream monopoly in Industry  produces a single output   , which it sells at price   .The monopoly uses inputs,  = ሺ 1 ,  2 , … ,   ሻ, generated by the U upstream industries.The corresponding input prices are  = ሺ 1 ,  2 , … ,   ሻ.Each downstream monopoly has a Cobb-Douglas production function, where u indexes each of the U upstream industries.
As before, the downstream monopoly faces a constant elasticity of demand function, =     , so its profit-maximizing markup is   = 1/ሺ1 + 1/  ሻ.The downstream firm's objective is to maximize its profit: Its U first-order conditions are where  = 1, … , .Rearranging Equation 8, we can express Xu in terms of the input prices: Substituting for Xu from Equation 9 in the Cobb-Douglas production function, Equation 6, we find that the downstream quantity is where   = σ    =1 is the downstream industry's returns to scale, and ϕd = Md/(ad -Md).
Consequently, the downstream price is a function of the upstream input prices, the returns to scale parameters, and the elasticity of demand: (11)

The Price Effects of Eliminating or Reducing Double Markups
How large are double markups?We consider both a "global" and a "marginal" approach to assess their size.We first derive equations showing the price effects of eliminating markups.
Then, we determine the impact of a marginal reduction in the markups.
To facilitate this discussion, we write the upstream markup as Mu = 1 + μu.Because M = pu/MC, μu = (pu -MC)/MC.That is, μu is analogous to the Lerner measure, (pu -MC)/pu, where the marginal cost replaces the price in the denominator.We call μu the firm's market power.If μu = 0, the firm has no market power, so its markup, Mu, equals one, and the price equals marginal cost.
A reduction in an industry's market power by Δ (0, 1] lowers the markup to   * = 1 + ሺ1 − ሻ  .Setting Δ = 1 eliminates an industry's market power and markup,   * = 1. We consider the direct and indirect effects of eliminating one or more upstream markups on downstream prices.We initially discuss eliminating the upstream markups (Δ = 1) to keep the equations relatively simple.After deriving these equations, we show the more general equation for a reduction in the markup: Δ less than one.
Suppose we could eliminate one or all upstream markups, setting Δ = 1 so   * = 1 in the relevant industries.We want to calculate the downstream price effects considering upstream suppliers that buy inputs from other industries farther upstream.
To illustrate the issues that arise, consider the supply chain in Figure 3.A different set of upstream industries supplies each downstream industry d.Each industry may be upstream of some industries and downstream of others.In Figure 3, Industry 2 is a downstream industry for Industry 1 and an upstream industry for Industries 3 and 4.This example corresponds to the actual relationship in Figure 1, where Industry 1 is mining, Industry 2 is utilities, Industry 3 is prime metals, and Industry 4 is fabricated metal.
In Figure 3, Industry 3 buys directly from Industries 1 and 2. However, Industry 1 also supplies Industry 2, which directly supplies Industry 3. Thus, Industry 1 has both a direct and an indirect effect on Industry 3. Given that inputs flow in only one direction, we can calculate such second-and higher-order indirect effects.

Eliminating One Upstream Markup
First, suppose that we eliminate market power in a single upstream industry that directly supplies an input to a downstream industry.For example, consider the price effect of eliminating the markup in Industry 2, M2, on the downstream price in Industry 3, p3.
Before eliminating the markup, the price of Industry 2's output, X2, is p2 = M2m2, where m2 is the marginal cost of  2 .Using Equation 11, the price of the downstream monopoly in Industry 3 is where ϕ3 = M3/(a3 -M3).If we eliminate the upstream markup in Industry 2 by setting  2 * equal to one, the downstream price becomes Thus, using Equations 12 and 13, the percentage changes of the downstream price from eliminating market power in Industry 2 is With constant returns to scale, ሺ 3 * −  3 ሻ/ 3 = ൣ 2 − 32 ൧ − 1.

Eliminating All Upstream Markups
More generally, suppose that we eliminate market power in all the upstream industries that directly supply inputs to the downstream Industry .Before eliminating the market power, the output price in each upstream industry  is pu = Mumu.If we eliminate all these markups, setting   * = 1 for all u, the change in the downstream price is Equation 15 shows only the direct effect of reducing all upstream markups.However, for example, eliminating the markup in Industry 1 in Figure 3 has both direct and indirect effects on price p3 in downstream Industry 3.The change in the downstream price is where  3 * is the price of  3 when the markup in Industry 1,  1 * , equals one.
Similarly, we can calculate higher-order effects for longer supply chains.For instance, the effect of setting all upstream markups equal to one on the downstream price  4 is where  4 * is the price of  4 when all upstream markups are set equal to one ( 1 * =  2 * =  3 * = 1).
In general, the change in the downstream price pd from eliminating all upstream markups is where h and i are intermediate industries.

Marginal Reduction in Upstream Markups
We also want to consider the price effects from marginal reductions in upstream markups.Given that our equations are nonlinear and our estimates hold locally, we have more confidence in calculating the price effects of marginal changes.
The change in the downstream price pd from reducing upstream market power by Δ is where h and i are intermediate industries.

Consumer Surplus
Because the upstream markups increase the downstream price, they decrease downstream consumer surplus.We account for direct and indirect double markups when calculating how a change in upstream markups affects downstream consumer surplus, as we did in the price analysis.
Let the original downstream equilibrium be (X, p).After reducing various upstream and

Estimation
To determine the size of double markups, we use (1) input flows between industries based on input-output and cost data; (2) estimates of markups and returns to scale in two-digit manufacturing industries and two other major industries that supply them; and (3) estimates of the Cobb-Douglas production functions.
We have already discussed the input flows.We start this section by discussing various methods of estimating market power and returns to scale, data and period issues, and our estimates.Then we discuss the production function estimates.

Methods to Estimate Market Power and Returns to Scale
The size of double markups depends critically on the estimates of markups and returns to scale at each stage of the supply chain.As the estimates from the literature vary, we consider several methods.
Many articles estimate industry markups.In his classic paper, Harberger (1954) calculated market power using the limited aggregate data on profits available at the time.He concluded that the U.S. economy had virtually no market power distortions: "Nothing to see here.Move along, folks." More recently, new empirical industrial organization (NEIO) papers used advances in theory, econometrics, and computing power as well as better data to estimate the degree of market power using sophisticated reduced-form and structural models (see the survey in Perloff, Karp, and Golan, 2007).Most of these papers found substantial market power.
To study the importance of double markups and returns to scale, we need estimates of industry markups and returns to scale for all relevant industries.Although the various papers De Loecker wrote with colleagues are excellent, they used firm-level data or non-U.S.data, so they do not provide industry-level estimates for U.S. manufacturing industries.6Thus, we focus on the Diewert and Fox (2008) and Hall (2018) methods to obtain our estimates using U.S. industrylevel data.7 Appendix B derives their estimating equations.Strikingly, both approaches estimated the same equation, but they interpreted the coefficients differently.The difference arises primarily because Diewert and Fox (2008)

Data
We want to compare the double markups implied by estimates of the Diewert-Fox and Hall models.We use a single data set to estimate both models to make this comparison clean.Diewert and Fox (2008) used data for the two-digit manufacturing industries.Hall (2018) examined most one-digit industries, including mining, utilities, and manufacturing, among others.To study double markups, we think looking at supply chains at the two-digit level makes more sense than at the one-digit level.Thus, we concentrate on two-digit manufacturing industries plus the one-digit mining and utilities industries, which supply manufacturing firms.the Törnqvist indexes for these two industries.

Period of Study and Instruments
To make the Diewert-Fox and Hall estimates comparable, we estimate both models for the same period.We also have to decide on whether to estimate the models using instruments or not.Diewert and Fox (2008)  Diewert and Fox argued against using instruments.They estimated their model with ordinary least squares (OLS).Although Hall (2018) employed instruments to examine a later period, we estimate his model for this earlier period using OLS for three reasons.First, not all of his instruments are available in some of the earlier years.Second, several of the remaining instruments are weak for at least some industries (see Duran-Micco 2020).Third, these instruments may not be exogenous to all macroeconomic fluctuations (Hall 1988 andRoeger 1995).
How do these decisions about the period and instruments affect our estimates?Duran-Micco (2020) estimated the Diewert and Fox (2008) and Hall (2018) models for several periods, with and without instruments.9She found that the returns to scale and markup estimates are sensitive to each of these choices.Using Hall's instruments available for the earlier period (oil price and military purchases of equipment, intellectual property products, and research and development) for Diewert and Fox's and Hall's methods produce very imprecise estimates.
Moreover, for several industries, the point estimates of the markup are implausibly negative.

Estimated Markups and Returns to Scale
We report OLS estimates for both models in Table 1.The table does not show hypothesis tests for Diewert and Fox's market power estimates.Those estimates are a transformation of their returns to scale estimates, so the hypothesis tests correspond to the returns-to-scale tests.In the table, the null hypothesis for all tests is that the coefficient equals one: either constant returns to scale or no market power.
The estimates for the Diewert and Fox method replicate their results for the manufacturing industries because we use their period, data, and estimation method.We cannot compare our results to those in Hall's paper because he used a later period and did not estimate markups for two-digit manufacturing industries.
Despite having different underlying theories, Hall (2018) and Diewert and Fox (2008) estimated the same regression equation (see Appendix B).However, they interpret the parameters of the equation differently.Hall estimated the price markup conditional on assuming constant returns to scale.The Diewert and Fox estimates of returns to scale are the same as Hall's estimates of the price markup (as the first two columns of Table 1 show).Diewert and Fox then use the estimated returns to scale to determine the price markup.For example, Hall's estimated markup for mining is 1.320.Diewert and Fox's estimated returns to scale estimate is 1.320, and their estimated price markup is 1.601.The Hall-method markup estimates are systematically smaller than Diewert and Fox's.
Using either set of estimates, we cannot reject the hypothesis that the markup equals one in the apparel, textile, utilities, and wood industries at the 5% level.Nonetheless, we use the (nearly one) point estimates for these industries in the following analyses.
Given that the markup in a monopoly industry is M = 1/(1 + 1/ε), we use the estimated markups to infer the elasticities of demand: ε = M/(1 -M).Thus, in our calculations of the double markups, the demand elasticities vary with the method we employ to estimate the markups.

Estimated Cobb-Douglas Production Functions
We use a two-step procedure to estimate our Cobb Douglas production function, Equation 6, coefficients.For downstream Industry d, sdu is the share of total cost, C(Xd) spent on input Xu: .
We calculate these input shares using BEA input-output and total costs data.By construction, these input shares sum to one: σ   = 1  .
With the Diewert and Fox approach, we use their estimates of the downstream industry's returns to scale   .Hall's method assumes constant returns to scale, ad = 1.
Using the values for sdu and ad, we calculate the Cobb-Douglas production function parameters for the downstream industry as adu = adsdu.Consequently,   = σ    .

Downstream Price Effects from Reducing Market Power
We want to determine the distortion due to double markups.To do so, we conduct counterfactual exercises to determine how reducing market power would lower downstream prices.First, we examine the price effects of eliminating market power (setting Δ = 1 so that the markup equals one) in a single upstream market, all upstream markets, and all upstream and downstream markets.Second, we calculate the downstream price effects of reducing market power in a single upstream market by 1% (setting Δ = 0.01).

The Price Effects of Eliminating the Market Power in One Upstream Industry
How much would eliminating upstream market power in one upstream industry affect downstream prices?In Table 2, we simulate the effects of eliminating upstream market power in one upstream industry at a time.We set the upstream markup equal to one, so its price equals its marginal cost.We are not arguing that eliminating all market power is feasible.Instead, we are using these simulations to understand the magnitude of double markups.
Figures 1 and 2 show that the mining and chemical industries are upstream from virtually all the other manufacturing industries.The top section of Table 2 shows the downstream price effects for industries downstream from mining in Figure 1.In this section, we eliminate upstream market power in mining, primary metal, fabricated metal, and computer and electronics industries one at a time (as the first column of Table 2 shows).The bottom section shows the price effects for those industries downstream from the chemical industries in Figure 2.
These downstream price effects reflect both the direct and indirect effects of eliminating the market power in an upstream industry.For example, primary metal is upstream from fabricated metal.Both are upstream from machinery.Thus, eliminating market power in primary metal affects the downstream price of machinery directly and indirectly through its effect on fabricated metal.
We present simulations using three methods to illustrate the roles of markups and returns to scale in determining the downstream price.The DF-IRS column uses Diewert-Fox's jointly estimated markups and returns to scale.We refer to these estimates as DF-IRS because all the industries exhibit increasing returns to scale (IRS).The DF-CRS column uses the Diewert-Fox estimated markups that were jointly estimated with returns to scale, but where we set the returns to scale parameters equal to one (constant returns to scale, CRS).The final column uses Hall's method, which imposes CRS.
Because the Diewert-Fox estimated markups are larger than Hall's, the DF-IRS and DF-CRS price reductions from reducing the double markup exceed the Hall price reductions.For each downstream industry, price effects are the smallest for the Hall method, followed by DF-CRS and DF-IRS.
Accounting for returns to scale (DF-IRS) substantially increases the double markup price effect estimates relative to the CRS methods (DF-CRS and Hall).The DF-IRS estimates are much larger than the DF-CRS or Hall estimates.For example, the first row shows our estimates of the downstream fabricated metal price effect from eliminating market power in mining upstream.With constant returns to scale, the DF-CRS estimate is -0.97%, and the Hall's is −0.57%.In contrast, the estimated price effect for the DF-IRS estimate is -14.26%.
The range of downstream price effects is -5.76% to -73.23% using DF-IRS, -0.34% to −30.75% for DF-CRS, and -0.27% to -20.9% for Hall.The two largest DF-IRS price effects are from eliminating the mining markup on petroleum and coal and the chemical markup on plastics.
Eliminating chemical and paper markups greatly affect downstream industries due to their large markups and increasing return to scale.To illustrate the role of downstream returns to scale, compare the effects of eliminating the chemical markup on printing and textile prices.The estimated price effect for the DF-IRS estimate are similar, -33.18% for printing and −34.40% for textiles.However, the estimated price effects for the DF-CRS estimates differ substantially: -0.60% for printing and -25.82% for textiles.Textiles is one of the few industries with no significant markup nor increasing returns to scale.In contrast, printing has a large markup and substantial increasing returns to scale.

The Price Effects of Eliminating All Double Markups
What would be the downstream price effects if we could eliminate all upstream market power?We use Equation 17to calculate the effects of removing double markups by setting all upstream markups equal to one so that only downstream markups remain.
Table 3 shows the percentage change in downstream prices from eliminating all upstream market power.The table does not include the chemical, computer and electronics, mining, or wood industries because they are not downstream from any of our other industries.
According to the DF-IRS method, eliminating the double markup causes substantial reductions in downstream prices.The price decrease exceeds 50% for three industries: plastic (73%), petroleum and coal (70%), and printing (63%).The big petroleum and coal effect is due to the large input flow: Mining supplies 78% of its inputs.Printing's substantial price decrease reflects its increasing returns to scale.Plastic's hefty effect is due to multiple factors.
Again, the price reductions from decreasing double markups are substantially lower with constant returns to scale (DF-CRS and Hall).For instance, the price reduction in petroleum and coal with the DF-IRS method of 70% falls to 31% if we impose constant returns to scale (DF-CRS) or 19% using Hall's method.Indeed no double markup exceeds 31% with the DF-CRS method or 21% with Hall's.Imposing constant returns to scale with the Diewert-Fox markup estimates cuts the double markup at least in half in all industries except textiles and utilities.It often cuts the double markup by much more.
With the DF-IRS method, eliminating double markups would reduce downstream prices by between 10% and 73% across 13 industries, with prices falling by more than 25% in 10 industries and more than 40% in 6 industries.With the Hall approach, downstream prices would fall between 2% and 21% and more than 15% in 3 industries.Printing provides a dramatic example of the roles of direct and indirect effects.The chemical industry supplies the paper industry, which in turn supplies the printing industry.Table 2 shows that reducing market power only in the chemical industry reduces the paper price by 44.82% and the printing price by 33.18% (DF-IRS).Table 3 shows that the printing price falls by 62.57% if we eliminate the markup in both the chemical and paper industries.

The Price Effects of Eliminating all Upstream and Downstream Market Power
Eliminating all market power upstream and downstream has a much larger price effect than only eliminating it upstream.Consider the DF-IRS results.Table 4 shows that eliminating all market power would lower prices by 50% or more in nine industries.In contrast, that large a reduction occurs in only three industries in Table 3, which captures the effects of eliminating only the double markup.Given constant returns to scale in the DF-CRS and Hall estimates, the price decreases are smaller but still substantial.Only one industry (apparel) had its price drop by less than one-fifth with the DF-CRS estimates, and only three did with the Hall estimates.
What part of the total price reduction from decreasing market power is due to only upstream effects?Table 5 shows the percentage share of the total downstream price reduction from eliminating only the upstream markup.This share in the DF-IRS model is at least 50% for all industries except stone, clay and glass, and utilities.These results are due to a small input flow in the stone, clay, and glass and constant returns to scale in utilities.It is over 80% for four industries and 92% for plastic.These shares are much greater for DF-IRS than for DF-CRS.
They are also bigger than the Hall method except for textiles and utilities.Four industries have a share greater than 50% with both the DF-CRS and Hall approaches.Thus, according to any of these methods, double markups are substantial.

The Price Effects of Reducing the Market Power by 1% in One Upstream Industry
We now examine the downstream price effects from a marginal reduction in upstream market power of 1% (Δ = 0.01) rather than eliminating market power.One might be willing to put more weight on these estimates than those from eliminating market power because the market power and returns to scale estimates hold locally.
Table 6 shows the (sum of the direct and indirect) downstream price effects of reducing market power by 1% in a single upstream industry.For example, reducing the mining markup by 1% would reduce the downstream fabricated metal price by -0.12% (first row).That is, the price elasticity from a reduction in the upstream markup is -0.12.
The price elasticities across industries are all smaller than -1 in absolute value.The largest elasticities for all the methods are for mining-petroleum and coal.It is -0.97 for DF-IRS, -0.29 for DF-CRS, and -0.19 for Hall.Some CRS estimates are close to 0, but the smallest DF-IRS elasticity is -0.05, and most exceed -0.1.Table 6's exercise corresponds to that in Table 2, in which we eliminate market power in one upstream industry.The results in Table 6 are roughly proportional to those in Table 2.For example, in row 1 of Table 2, eliminating the upstream market power in mining would cause the downstream price of fabricated metal to fall by -0.57(Hall), -0.97 (DF-CRS), or −14.26 (DF-IRS).The corresponding numbers in Table 6, where we reduce market power by one percent, are -0.01,−0.01, and -0.12.In this industry pair, the downstream price effect from eliminating market power is more than 100 times those of reducing the market power by one percent because our equations are nonlinear.However, the price effect from eliminating market power is not always more than 100 times the effect of a one percent reduction.For example, the DF-IRS plastic price effect from eliminating market power in the chemical industry is -73%, but it is −0.84% from a one percent reduction.

Robustness Experiments
We have already discussed the effects of relaxing our feedback and returns to scale assumptions.Our results also depend on the downstream markup and the demand elasticity.
You can use an interactive simulation model, https://elisaduranmicco.shinyapps.io/Sensitivity/, to examine the sensitivity of the downstream price and consumer surplus to these variables.The simulation model allows you to adjust the input flow between mining and petroleum & coal (P&C).It then shows how the P&C price or consumer surplus varies with the P&C returns to scale, market power, and demand elasticity.
These simulations demonstrate how much the downstream price and consumer surplus increase with the returns to scale and decrease with the markup or the demand elasticity.

Consumer Surplus Effects from Reducing All Upstream Markups
Lowering prices by reducing market power would have consumer surplus benefits.To illustrate the magnitude of the double markup on consumer surplus, we ask how much consumer surplus would rise if we reduced all upstream markups by 1%.
These consumer surplus changes depend on our estimated price effects (Table 6) and revenue in the downstream market (measured in 2000 dollars).Table 7 shows the change in consumer surplus in millions of dollars.
Using the DF-IRS method, a one percent reduction in market power in mining would increase consumer surplus in petroleum and coal by $2.236 billion per year.Across all downstream industries, a one percentage point upstream reduction in market power would increase consumer surplus by between $58 million and $2.236 billion per year.Reducing mining market power's consumer surplus effect on petroleum and coal is the largest.The effects range from $6 to $433 million for the Hall method and $8 to $671 million for the DF-CRS approach.
Obviously, larger market power reductions would have more substantial consumer surplus effects.

Conclusion
We systematically estimate the price effects of double markups across two-digit manufacturing industries, mining, and utilities.Because the results depend on the estimated markup in each industry, we compare results based on the estimation methods of Diewert and Fox (2008) and Hall (2018).
The Diewert and Fox approach provides estimates of markups and returns to scale.The Hall markup estimates are conditional on constant returns to scale.The Diewert and Fox markup estimates are bigger than the Hall estimates, so our Diewert and Fox double markup estimates are larger for that reason alone.However, the double markup estimates are even more substantial with the Diewert and Fox approach because their method produces estimates of increasing returns to scale in all industries, dramatically increasing our estimates of the double markup's effects.
To measure the size of double markups, we simulate the downstream price effects of eliminating or reducing upstream market power.Eliminating all upstream markups-that is, the double markups-would reduce downstream prices by between 10% and 73% across the 13 industries using the Diewert and Fox approach, but by only 2% to 21% with the Hall method.
Lowering all markups, including downstream, has enormous price effects with both approaches.The downstream prices fall by 25% to 81% with the Diewert and Fox approach and 9% to 54% with the Hall method.
Much of the total downstream markup is due to upstream markups, that is, double markups.If we could eliminate all upstream and downstream markups, upstream markups would account for between 26% and 92% of the downstream price reduction using the Diewert-Fox method and 7% to 91% using Hall's method.
We calculate the price effect of a marginal reduction in market power as an alternative to eliminating all market power.Reducing market power by 1% in a single upstream industry would lower downstream industries 'prices by between 0.1% and 1% in the Diewert and Fox approach and between 0.01% and 0.2% with the Hall method.
The price decreases from reducing or eliminating market power would substantially increase consumer surplus.The largest annual consumer surplus increase from a one percent reduction of market power upstream is $2.2 billion for the mining-petroleum and coal pair.
Overall, our results suggest that double markups are enormous.The practical implications of this finding are four-fold.First, typical estimates of market distortions in particular firms or industries are substantially biased downward because they ignore double markups.Second, the new macroeconomic debate on whether market power is increasing should account for changes in double markups.Third, vertical or quasi-vertical integration might ameliorate these double markup distortions.Fourth, because the Illinois Brick decision requires assessing all antitrust damages downstream, knowing the role of double markups is crucial.
We made four simplifying assumptions that future work could relax.First, we did not explicitly account for the small feedback flows between industries.Appendix A argues that doing so may make our double markup estimate a lower bound for a single small feedback flow.
However, a formal analysis of the effects of having several small feedbacks (which occurs for four industries) might be desirable.
Second, we assumed that none of these industries exercise monopsony power when purchasing from the other industries.While studies have found evidence that manufacturing industries have monopsony power in labor markets, we know of none reporting monopsony power between these U.S. industries, but the possibility remains.
Third, we ignored any possible cross elasticities between these industries, which we think is plausible.It is difficult to imagine substitutability between, say, apparel and transportation.
Nonetheless, this assumption should be tested.
Fourth, we modeled the industries as monopolies, arguing that such an approach could approximate the outcomes of other market structures.However, modeling specific industry structures could result in more precise estimates.The upstream monopoly's first-order condition is Rearranging terms, this condition is 0 (  −) Thus, ∂pd/∂θ > 0 for small θ.For example, the only relatively large feedback (5.47%) is from utilities to mining.Here, θ = 0.028, which is less than audad/(Mau) = 0.03937651, so the inequality holds.Without market power and constant returns to scale, this inequality implies that θ < aud < 1.
We can express this equation in terms of Törnqvist indexes.The logarithm of the Törnqvist quantity index for output growth between periods t -1 and t is    ሺ −1  −1 ,     ,  −1 ,   ሻ ≡ [   −   −1 ]. (B.8) The logarithm of the Törnqvist input price index for input price growth between t -1 and t is The implicit logarithm of the Törnqvist input quantity index between periods t -1 and t is

(
possibly) downstream markups, the new downstream equilibrium is (X*, p*).The change in consumer surplus in the downstream industry is because  +1 = .We can rewrite this change in consumer surplus as 19 and that the demand function is  =   , Equations 19 and 22, revenue (pX)  from our data set, and our estimates of εd, we can calculate the change in consumer surplus.
estimated the returns to scale andHall (2018) assumed constant returns to scale.Diewert and Fox (2008) estimated markups and returns to scale.They assumed that each industry functions as a monopoly.They used a nonconstant-returns-to-scale translog cost function with neutral technical change, decomposing productivity growth into contributions from returns to scale and technological progress.Treating input prices as given, they estimated their model using ordinary least squares.They argued that likely productivity shocks show up primarily in output variables, most likely instruments are not entirely exogenous, and these instruments are weakly correlated with some inputs for some industries.Hall (2018) estimated markups by determining marginal costs as the ratio of the observed change in cost to the observed change in output.He implicitly assumed constant returns to scale by setting an input's share of total costs equal to its share of total revenue (see Appendix B).Hall estimated his model using five instruments: military purchases of equipment, military purchases of ships, military purchases of software, military expenditures on R&D, and the oil price.
used 1949used  -2000used   data, whereas Hall (2018used  ) used 1987used  -2015       data.Several studies, includingDe Loecker, Eeckhout, and Unger (2020) andHall (2018), argued that markups have increased over time and provided various explanations.Examining BLS and BEA data between 1949 and 2016 indicates that a distinct structural shift started around 2000.Appendix C shows that a pronounced plunge in input and output indexes occurred in many industries then.Given this significant change in trends, the greater variability, and the limited number of years in the post-2000 period, we use theDiewert and Fox period, 1949-2000, to   estimate both models. 8

.
where, M = 1/(1 + 1/ε) is the downstream monopoly's markup of price over marginal cost, pd/MC.Because   =     , Substituting this expression into Equation A.5 and rearranging terms, we obtain the upstream monopoly's inverse demand function, Equations A3, A6, and   =     to obtain the second equality.
* ሺ −1 ,   ,  −1 ,   ሻ =  ሺ  ,   , ሻ −  ሺ −1 ,  −1 ,  − 1ሻ −  ሺ −1 ,   ,  −1 ,   ሻ. (B.10) Substituting Equations B.8 and B.9 in Equation B.7, we obtain Diewert and Fox's main regression equation,    ሺ −1  −1 ,     ,  −1 ,   ሻ =  −1   * ሺ −1 ,   ,  −1 ,   ሻ +  −1 .(B.11) Hall's Method Hall (2018) estimated markup uses the price to marginal cost ratio.He stated that a natural measure of this ratio is the change in cost not associated with changes in input prices divided by the change in output not associated with the change in Hicks-neutral productivity.To compare models, we use Diewert and Fox's notation.Total cost is change in output not associated with the change in Hicks-neutral productivity is  −    .(B.17)The price to marginal cost ratio is the change in cost not associated with changes in input prices divided by the change in output not associated with the change in Hicks-neutral productivity.In other words, the markup factor is price divided by the ratio of Equation B.is the share of input  in total revenue,   =      Τ .(B.20)For discrete periods, we can write Equation A.19 as ∆   =  −1 σ   ∆     =1 + ∆  , (B.21) which is Hall's main regression equation.Connecting the Diewert and Fox and Hall Methods We now show that Hall and Diewert and Fox estimated the same regression equation.Only their interpretations of the parameters differ.Hall used this equation to estimate the markup,  −1 , whereas Diewert and Fox used it to estimate the returns to scale factor,  −1 .We start with Diewert and Fox's approach.Using Equation B.5,  =  −1  σ      =1 .Also, using Equation B.6,   =     / σ    production function, this equation is the same as Diewert and Fox's Equation B.11.The left-hand side is the logarithm of the Törnqvist quantity index for output growth.The first right-hand side term is the logarithm of the Törnqvist input quantity index, Equation B.10, and the last term is the productivity growth rate.Hall used this regression equation to estimate the markup,  −1 , by assuming constant returns to scale:   =   .

Figure
Figure C.1: BLS Input and Output Indexes for Various Manufacturing IndustriesInput IndexOutput Index Because pd > 0 and ε < 0, the sign of ∂pd/∂θ is positive if the term in the brackets is negative:If ሺ  − ሻ > 0, then this expression holds if (noting that au0 + aud = au) Diewert and Fox assumed that a monopoly maximizes its profit in each period,     ሺሻ − ሺ  , , ሻ, where   is the observed period t price.The inverse of the markup factor in period ,   is determined by     = ሺ  ,   , ሻ/.Thus, an estimate of the firm's (inverse) returns to scale  in each period t is the ratio of the markup-adjusted revenue divided by total cost.The observed cost share of input  in period  is    =       / σ

Table 1 Estimates of Price Markups and Returns to Scale Diewert and Fox Hall Returns to Scale Markup Markup
Diewert and Fox (20082018)andDiewert an-2000 (2008) methods for 1949-2000.** * Reject the null hypothesis that the coefficient equals one at the 1 percent level.** Reject the null hypothesis at the 5 percent level.* Reject the null hypothesis at the 10 percent level.Although the table does not show hypothesis tests for Diewert and Fox's market power estimates, these estimates are a transformation of the returns to scale estimates, so the hypothesis tests correspond to the returns to scale tests.