Demand System Estimation and its Application 

To Horizontal Merger Analysis†*

Daniel Hosken 

Daniel O’Brien 

David Scheffman 

Michael Vita 

April, 2002 

Abstract 

The past decade has witnessed remarkable developments in the quantitative analysis of 

horizontal mergers. Increases in computing power and the quantity and quality of data 

available have substantially reduced the costs of estimating demand systems using 

econometric methods. Good estimates of retail demand elasticities can make an 

important contribution to assessing the potential effects of a manufacturer merger on 

consumer prices. While estimates of demand relationships can make substantial 

contributions to merger analysis, it is much like every other area of empirical economics, 

in that practitioners invariably are forced to confront and resolve a series of difficult 

econometric and conceptual issues. The purpose of this paper is to identify a number of 

these issues that we believe researchers and practitioners should address, as a general 

matter, and in specific applications in which these issues are pertinent, with the ultimate 

goal of improving the quality of antitrust analysis.

 

†

 This paper is a draft version of a paper that will be forthcoming in “The Use of 

Econometrics in Antitrust,” American Bar Association Section on Antitrust, J. Harkrider, 

ed. 

*

 We would like to thank Hajime Hadeishi, Christopher Taylor, Aileen Thompson, 

Shawn Ulrick, Matthew White, and members of the Department of Justice’s Economics 

Analysis group, particularly Greg Werden and Scott Thompson for their comments on the 

paper, and Sara Harkavy for excellent research support. We would like to thank Orley 

Ashenfelter, Luke Froeb, John Geweke, Jerry Hausman, Ariel Pakes, and David 

Weiskopf for their consultations on demand estimation. The opinions expressed in this 

paper are those of the authors and do not necessarily represent those of the FTC or its 

individual Commissioners. 
1

I. INTRODUCTION 

The past decade has witnessed remarkable developments in the quantitative analysis of 

horizontal mergers. Several factors account for these changes. The quantity and quality 

of data available to estimate the degree of substitutability among competing products has 

increased dramatically. This increase has been accompanied by a substantial decrease in 

the price of computing power required to analyze the data. A third factor is an increased 

focus on the possibility of competitive harm from “unilateral” market conduct, 

particularly in mergers involving differentiated products. However, understanding how 

consumers substitute among competing products also can contribute substantially to the 

analysis of possible competitive harm from “coordinated” market behavior. 

How consumers substitute across products as relative prices change is clearly relevant to 

understanding the potential price effects of mergers.1

 This information, contained in the 

own- and cross-price elasticities of demand at retail,2

 is most frequently used as means 

for predicting the “unilateral” incentives to increase prices post-merger. In the context of 

differentiated consumer goods, the term “unilateral effects” refers to the fact that a 

merger of competitors creates an incentive to increase price (ceteris paribus) to the extent 

that there are significant substitution possibilities that exist between the (now) jointlyowned products. In this setting, the existence of credible information about demand 

elasticities is clearly important. Having a good estimate of how substitutable these 

products are can help the analyst predict with much greater accuracy whether these 

unilateral incentives to raise price are substantial or minuscule.3

 

1

 Of course the own- and cross-price elasticities of the demand faced by manufacturers 

(“wholesale demand”) is more directly relevant to Guidelines market definition and 

competitive effects analyses. The properties of demand of consumers (i.e., the demand at 

retail) is relevant because they have implications for the demand at the manufacturer 

level. 

2

 The elasticity of some variable x with respect to another variable y is the percentage 

change in x that arises from a 1% increase in y. For example, the own-price elasticity of 

the demand for widgets is the percentage change in the quantity of widgets given a 1% 

increase in their price. 

3

 It has become conventional to analyze these unilateral pricing incentives using static 

oligopoly models in which firms compete on the basis of price. The static oligopoly 

game that models firms’ pricing decisions is sometimes referred to as the “Bertrand” 

pricing game after Joseph Bertrand (1883), who was the first economist to study it. This 

is the framework used most often to examine unilateral effects in merger analysis. 

Whether these static models provide an appropriate benchmark for predicting the 

consequences of a horizontal merger is somewhat controversial (see, e.g., Fisher (1989) 

and Shapiro (1989)); we do not address this controversy here. We note, however, the 

recent appearance of studies that attempt to test the validity of static oligopoly models 

(e.g., Nevo (2001); Pinske and Slade (2001); Hausman and Leonard (2000); Genesove 

and Mullin (1998); Wolfram (1999)). Most of these studies suggest that the static 

oligopoly models yield reasonably accurate predictions of pricing behavior. 
2

Until quite recently, economists had to rely on relatively simple quantitative analyses 

(surveys, analysis of shift in share, etc.) and qualitative information (for example, an 

internal company document stating that products X, Y, and Z all compete with each 

other) – that did not permit quantification of the degree of substitutability among the 

merging firms’ products. While these sources of information are useful and continue to 

play an important role in merger analysis, a well-executed econometric analysis of 

demand may enable an economist to infer not only that a set of goods are substitutes, but 

also to infer what volume of sales will switch from product X to product Y given (say) a 

specific price increase for product X. 

The value of information on demand elasticities is not limited to situations where 

attention is focused primarily on unilateral pricing incentives. Evidence bearing on the 

degree of substitutability among potentially competing products is also important in 

determining the incentive and ability to engage in coordinated post-merger pricing. 

In appraising the value of elasticity information gleaned from an econometric analysis of 

scanner data, is noteworthy that others, such as marketing professionals, also undertake 

similar analyses. For example, manufacturers of consumer products estimate systems of 

demand equations to help them determine optimal prices for their products. Clearly, 

scanner data, drawn from consumers’ actual purchases, provides a wealth of information 

that can be used to describe and analyze consumer demand.. 

While the quantitative estimation of demand relationships can make substantial 

contributions to merger analysis, it is much like every other area of empirical economics, 

in that practitioners invariably are forced to confront and resolve a series of difficult 

econometric and conceptual issues. The purpose of this paper is to identify a number of 

econometric and conceptual issues that we believe researchers and practitioners should 

address in order to make the quantitative estimation of demand relationships using 

scanner data more applicable to merger review. 

Briefly, we raise the following issues in this paper: 

1. What is the best way to aggregate data across observational units and across time? 

2. What are the consequences of choosing a particular functional form for an 

empirical demand curve? 

3. Is it necessary to address the possible endogeneity of explanatory variables? 

4. Is it possible to construct meaningful measures of the accuracy of predicted price 

changes? 

5. Can one easily translate elasticities estimated with retail-level data into wholesalelevel elasticities? 
3

These are difficult questions, and we do not attempt to provide definitive answers to 

them. Our purpose instead is to provoke further discussion and research into these issues, 

with the ultimate goal of improving the quality of antitrust analysis. 

II. DATA ISSUES 

A. Scanner Data Features 

The two leading providers of scanner data are A.C. Nielsen (Nielsen) and Information 

Resources Incorporated (IRI). Both firms provide a variety of retail information in a 

number of channels of distribution (supermarkets, drug stores, mass-merchandisers, and 

convenience stores) for various geographic regions throughout the U.S. The bases of 

these data sold by Nielsen and IRI are a sample of stores from which the data companies 

acquire all point-of-sale (POS) scanner data. The scanner data provides data on total 

revenue and total units sold by UPC code.4

 In addition, IRI and Nielsen collect a number 

of measures of price and of various measures of promotion for each retail outlet they 

sample, e.g., a specific chain and store location, and a measure of distribution 

penetration.5 

The data collected by IRI and Nielsen represent a sample of the retail outlets operating in 

the U.S., and both firms use different proprietary methods to project total sales. IRI and 

Nielsen cover some areas, and some distribution channels, better than others. Both IRI 

and Nielsen have very good coverage from supermarkets. There is significantly less 

coverage in the mass-merchandiser and convenience store channels. For products that 

have substantial sales outside the supermarket channel, the IRI and Nielsen data can 

present questions as to the representativeness of the data. However, to our knowledge, 

the data from IRI and Nielsen are the best available to study demand for these products. 

Although the “raw” data contains each individual POS transaction, the data Nielsen and 

IRI sell to their clients typically consists of aggregates of total sales in dollars and units 

by brand and UPC code. To our knowledge, IRI and Nielsen rarely sell (aggregated) 

price and quantity information from individual stores. Instead, they typically aggregate 

the quantity and revenue data up to either the level of the chain within a specific 

geographic area, e.g., Giant Foods in the Washington, DC metropolitan area, or, more 

 

4

 UPC refers to Universal Product Code. A UPC corresponds to a precise package 

size/brand of a consumer product. For example, a UPC would refer to a 15 ounce 

package of General Mills Cheerios cereal. The 10 ounce box of Cheerios would be a 

separate UPC as would the 15 ounce box of Honey Nut Cheerios. Within a single 

product category, e.g. ready-to-eat cereal, there are literally thousands of different UPCs. 

5

 A product’s percentage of “All Commodity Volume” (typically referred to as ACV) is 

defined to be the ratio of the revenue of retailer outlets carrying a product in a given 

geographic area to the sales of all retailers in that geographic area. For example, a food 

product with a percent of ACV of 70% in the Washington, D.C. metro area would be 

carried by retailer food outlets that account for 70% of food revenues in Washington, 

D.C. 
4

often, aggregate over all chains and stores within a geographic area for a given channel, 

e.g., revenue and quantity within the Washington, DC metropolitan area for all 

supermarkets. 

 

IRI and Nielsen also collect data on shelf prices; however, there are potential 

measurement problems with this data. The most important problems likely result from 

discounts (e.g., coupons or club) received by some consumers but not observed (or only 

imperfectly observed) in the data. For example, if a consumer purchased Coke at $3.99 

and used a $.50 coupon, the price would be recorded as $3.99. There is a similar problem 

for “club” or “loyalty card” purchases, which entitle a customer with a card to a 

substantial discount on promoted items. In some cases, the price is recorded as the most 

commonly occurring price (typically the price with a club card), in other times average 

revenue is recorded. An additional issue in both the IRI and Nielsen data results from the 

time interval over which data is collected. While both collect and report data weekly, 

different retailers change their prices on different days of the week, e.g. promotions at 

some retailers run Sunday to Saturday, while others run on a Thursday to Wednesday 

schedule. Thus, it is quite possible that the shelf price reported by IRI or Nielsen in a 

given week will only correspond to the actual shelf price for a portion of the reported 

week. 

 

IRI and Nielsen collect three general measures of promotional activity that can be used in 

demand studies.6

 First, the firms create measures of advertising of specific items in a 

retailer’s circular. Roughly speaking, an advertisement is coded as an “A” ad if it 

appears on the front or back cover of an advertising circular, a “B” ad if it appears inside 

the circular but has a graphical representation of the item, and a “C” ad if the item is 

 

6

 Retailers engage in a number of non-price promotional activities (often supported in 

some way by manufacturers) that can dramatically affect sales at a retailer. For example, 

a case study by Progressive Grocer reported that sales of household cleansers increased 

50% with a price cut and an advertisement, but increased by 1,900% when also given a 

display (see “The Real Power of Promotion” Progressive Grocer, page 39, December, 

1992). Market researchers and economists too have found that, holding price constant, 

promotional activities by retailers can have large incremental effects on sales 

(Montgomery (1997), Hoch, Kim, Montgomery, and Rossi (1995), Abraham and Lodish 

(1993), and Katz and Shapiro (1986) are just a few examples of papers in the marketing 

literature which explicitly incorporate measures of promotion and advertising in their 

estimation of demand systems). As an example, a weekly period in which Coke was sold 

at a discount price of $2.99 is likely to have significantly fewer sales than a weekly 

period in which Coke was sold at $2.99 accompanied by significant promotional activity. 

Economic theory does not give explicit guidance as to how this activity should be 

empirically modeled. For example, does promotional activity change the amount 

consumers would be willing to pay at any given price, or does promotional activity 

change the consumer’s price sensitivity? Given the empirical significance of advertising 

variables in marketing studies, it is likely the case that including information on 

advertising and promotion can improve the accuracy of demand studies used by antitrust 

economists. 
5

simply mentioned in the circular. Second, IRI and Nielsen record what proportion of 

stores have in-store promotional displays for items, e.g., an end of aisle display or some 

type of free-standing display. Finally, the firms record whether or not a coupon was 

released in a geographic area, typically as a “free-standing-insert” of the type found in the 

Saturday or Sunday edition of a newspaper. Including these measures of promotion can 

significantly enhance the accuracy of a demand study. However, if (as is typically the 

case) the data is aggregated across retailers, the aggregation to some extent “masks” the 

interactive effect between price promotions and other forms of promotions. For example, 

knowing that 50% of the retailers (by some measure of total sales) had an end aisle 

display does not allow us to match the price those stores set, since the measure of price is 

an average across the “market.” 

Because many antitrust practitioners have a vague notion of what exactly scanner data is, 

we believe it is beneficial to explicitly describe the data used by the FTC in a recent court 

case. In FTC v. Swedish Match, both the Commission and respondents presented 

estimates of the own-price elasticity for loose-leaf chewing tobacco based on monthly 

data from all retail channels (supermarkets, drug stores, convenience stores, and massmerchandisers) and aggregated across regions within a state. The data used by the FTC 

and Swedish Match in the studies presented to the Court was aggregated to the category 

level; that is, all UPCs of each brand (e.g, Red Man, Levi-Garret, or Beechnut Chewing 

Tobacco) were aggregated into a single number for loose leaf chewing tobacco. The data 

was also aggregated over: the time unit (from weekly to monthly), geography (all 

retailers within a state), retail channels (supermarkets, drug stores, mass merchandisers, 

convenience stores), retailers, brands, and UPC’s within the brand (package sizes). An 

example of an individual data point would be total dollar and unit sales of (all brands of) 

loose leaf chewing tobacco sold in Illinois in all measured retail channels for March, 

1999. Below we discuss the potential problems associated with the various types of data 

aggregation that are required to conduct an econometric analysis with scanner data. 

B. General Aggregation Issues 

One of the most significant issues in using scanner data to estimate demand estimates is 

the nature and extent of data aggregation. As discussed above, the data that is available is 

already aggregated across time (e.g., weekly), and also typically aggregated across 

retailers, often in a large geographic area. In addition, the researcher generally finds it 

necessary to undertake additional aggregations, to make the estimation tractable. For 

example, estimating demand for each individual size or variation of a given consumer 

product is generally not practical, and attempting to do so would often lead to imprecise 

parameter estimates. Unfortunately, aggregating the data requires the researcher to make 

assumptions which may have important effects on the parameter estimates. In this 

section of the paper we describe three major types of aggregation that in our experience 

can impact the demand estimates. 
6

1. Channel Aggregation 

Most consumer products are sold in a number of different channels, however, it is often 

the case that some channels of distribution are more important for a given product than 

others. For example, many food products are sold almost exclusively through 

supermarkets, e.g., canned soup, salad dressing, and cake mix. In these cases, simply 

using data from the supermarket channel should be sufficient to describe the demand 

system for the products. Other product categories have large sales of products through 

multiple channels, e.g., soft drinks and snack food are sold in significant quantities 

through convenience stores, grocery stores and mass-merchandisers. 

When consumers purchase the same consumer products through different channels, 

aggregation of sales and unit data across channels could lead to different elasticity 

estimates than if the elasticities were estimated separately by channel for at least two 

reasons. First, consumers choose to shop in different channels for different reasons. For 

example, consumers shopping at a convenience store likely have less elastic demand for 

products than those shopping at a supermarket. One would expect that consumers’ beer 

purchases through convenience stores would be less sensitive to price than purchases 

through grocery stores. The same pattern likely holds when comparing products carried 

by one channel more as a convenience (such as motor oil at a supermarket) to retailers 

that specialize in selling those products (such as motor oil through a mass-merchandiser). 

Second, the mix of package sizes of a given product/brand (e.g., Pepsi Cola) sold through 

different channels also varies significantly. For example, the share of single serve 

packages of cola (20 ounce bottles or 12 ounce cans) sold through convenience stores is 

much larger than that sold through supermarkets. If sales and revenue are calculated at 

the brand level (Pepsi) as opposed to the UPC level (20 ounce bottle of Pepsi, 2 liter 

bottle of Pepsi, 12 pack of Pepsi), then measures of revenue and sales from different 

channels will not be comparable because of differences in product mix across channels. 

In our experience, we have found for markets where substantial sales of the product occur 

in different retail channels of distribution, that the estimated demand elasticities can be 

quite different when estimated separately by channel. 

2. Aggregation Over Time 

In estimating demand systems for consumer products, staff often have access to weekly 

scanner data from supermarkets. There are two primary advantages to using weekly data 

as opposed to a more aggregated form (e.g., monthly or quarterly). First, because grocery 

stores tend to change their prices weekly (promotions typically last one or two weeks), 

weekly data most accurately relate consumer prices to their corresponding purchases. 

Second, the use of weekly data gives the researcher many more observations which 

increase the precision of elasticity estimates. On the other hand, for the purpose for 

which we perform these estimations, i.e., getting information about demand at the 
7

manufacturer level, the frequency of scanner data presents other problems. Unlike 

retailers, manufacturers do not change their wholesale prices on a weekly basis.7

 

Time aggregation also relates to another problem that we will discuss further below -- 

purchasing for inventory. Using weekly or even monthly data may overestimate 

elasticities because consumers often buy large quantities of items which are on sale and 

take them into household inventories; that is, the elasticities being measured are really 

short run purchasing elasticities not the consumption elasticities which are relevant for 

antitrust analysis. Economics and marketing researchers both find that inventory effects 

can be important.8 Because the goal of antitrust analysis is to measure the effects on 

consumer demand of permanent changes in price, it is important to measure elasticities 

that measure changes in consumer consumption due to changes in price. If inventory 

effects are important (this is likely to be the case if the predominate source of price 

variation are the sales which generate inventory effects), the estimated elasticities will 

likely be too large and should only serve as an upper bound for the demand elasticities for 

the purposes of antitrust analysis. 

Empirically, we have found that elasticity estimated using weekly data are often larger 

than those estimated using monthly data. 

3. Aggregation Across Product Sizes and Varieties 

Many types of consumer products are sold in different package sizes, with the price per 

unit of weight or volume generally declining with package size. Further, it is sometimes 

the case that different package sizes are sold more through some channels of distribution 

than others. For example, mass-merchandisers focus more on selling large package sizes 

(either through better pricing or enhanced in-store promotion and display), while 

convenience stores typically sell a product’s small package sizes. 

As a practical matter, when estimating a demand system, a researcher is required to make 

some aggregation choices to minimize the number of parameters to be estimated. In 

some markets aggregation across package sizes is not very important because most sales 

are made through one package size, e.g. shaving cream, motor oil, and shampoo. 

However, in other markets significant volume is sold through multiple package sizes, 

e.g., pet food, ready-to-eat cereal, and soda. Further, substitution between package sizes 

within a brand is often empirically important. In our merger investigations, we have seen 

 

7

 Although manufacturers may offer discounts to retailers during promotions during 

discrete time periods, e.g. a month, which may be viewed as a temporary discount on the 

wholesale price. 

8

 Pesendorfer (2002) develops a model of intertemporal price discrimination and finds 

evidence that lagged prices affect the current level of demand (consistent with consumer 

inventory behavior). Hosken and Reiffen (1999) also develop a model of intertemporal 

price discrimination and discuss the effects of such a model on estimating demand 

systems. Hendal and Nevo (2001) provide empirical evidence on the importance of 

inventory effects. 
8

firms conduct sophisticated studies trying to determine how much substitution will take 

place between different package sizes of their own brands. In terms of estimating 

demand systems, we have observed that different aggregation rules (e.g., average price 

per pound, the creation of a price index, or estimating elasticities separately by package 

size) can lead to very different estimated demand elasticities. The fixes to this problem 

are not obvious or easy to undertake.9

 

C. Price Specification and Aggregation 

The scanner data that is typically used in estimating demand curves is aggregated over 

some geographic area, e.g., a census region, state, or metro area, and across retailers, by 

channel, in that area. Obviously, if independent pricing decisions are made by stores 

within the geographic areas the price and quantity observed in the data (typically price 

defined as average revenue, and units defined as the sum of all units in the area) will not 

correspond to the prices charged (quantities sold) by any individual firm. There are two 

distinct types of problems that result from aggregation across retailers. The first comes 

from the observation that the aggregate price, as measured by average revenue, and 

aggregate output will not correspond to a point on the aggregate demand curve because 

average revenue is a non-linear function of each retailer’s average revenue. The second 

set of problems are the result of un-modeled phenomena (e.g., sales, promotion, and 

other forms of retail competition) that cause consumers to not face the aggregate price as 

measured by average revenue. As discussed in more detail below, the second set of 

problems leads to more difficult questions on how to appropriately use price and quantity 

data to correctly estimate elasticities which manufacturers are likely to face. 

 

A simple example can demonstrate how measuring price as average revenue can lead to 

biased elasticity estimates when demand curves are linear demand. Assume that there are 

three retailers operating in a geographic area, and, for simplicity, assume that the firms do 

not compete with one another because they are in separate geographic markets. The price 

and quantity data that the researcher observes is aggregated from the three firms. To be 

explicit assume that: 

Firm 1's demand curve is: Q = 1000 - 5*P 

Firm 2's demand curve is: Q = 1000 - 8*P 

Firm 3's demand curve is: Q = 1000 - 10*P. 

The aggregate demand firm for the region will be: 

Q = 3000 - 23*P. 

 

9

 In principal, one could attempt to formally incorporate the non-linear budget set into 

the econometric model, e.g., Reiss and White (2001). However, in the time required to 

estimate a demand system in a merger investigation this approach is not currently 

feasible. Instead, the approach BE has taken is to check the robustness of our results to 

different measures of price. 
9

When we estimate a demand curve, we estimate a relationship like 

Q = A - B*P, 

where A and B are parameters to be estimated, and we use a single measure of price 

(aggregated in some manner; e.g., average revenue) 

If each firm charges the same price at every point in time, we can correctly estimate the 

demand curve using average revenue as the measure of price. However if the three firms 

charge different prices at the same point in time, then the estimated aggregate demand 

curve will not correspond to the true aggregate demand curve. 

To illustrate the misspecification we conduct a simple simulation with 1500 price (and 

corresponding quantity) draws for each firm where firms 1, 2, and 3 set prices 

independently (but where prices were drawn from the same distribution), and find that the 

least squares estimate of the demand curve using the average unit price as the measure of 

price is: Q = 2687 - 19.3*P, which represents a significant underestimate of the true 

slope of the demand curve (see Figure 1 which presents a plot of the average price and 

total quantity data).10

 

10 In the simulation we model each retailer as randomly drawing prices from a uniform 

distribution with prices between 0 and 100. 
10

Figure 1: Average Price and Total Quantity, Aggregate Three Demand Curves 

with Different Slopes but the Same Intercept

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500 3000 3500

Quantity

Price
11

This example shows that even though each individual demand curve is linear, the 

relationship between aggregate quantity and market-level average revenue is not. Thus, 

estimating an aggregate demand curve using a similarly aggregated average price 

measure can provide misleading inferences about the aggregate demand sensitivity.11, 12

Most of the scanner data used in estimating demand curves combines price and quantity 

data across retailers within a broad geographic area, such as a metro area. As described 

above, because retailers charge different prices, the price and quantity data aggregated 

across retailers do not represent the prices faced by any consumer.13 A further problem 

arises because of non-price competition that varies across retailers within a market at a 

 

11 This example is intended merely to demonstrate the potential bias resulting from 

aggregation. However, strictly speaking, the model presented above is not internally 

consistent. An aggregate demand curve is only well defined if the products being 

aggregated are homogeneous. Presumably, the fact that the different firms charge 

different prices violates the homogeneity assumption. However, since we know that 

different retailers in different areas charge very different prices at the same time (see 

Hosken and Reiffen, 1999), the example indicates that the aggregation across markets can 

“matter,” and that the aggregation choices typically made by researchers could be 

problematic. 

12 The problems associated with aggregating demand curves across consumers (or 

equivalently collections of consumers) has been well known for some time and was the 

subject of much research on demand estimation (Gorman’s (1959) work was some of the 

first to deal with these issues. Deaton and Muellbauer’s (1980) book Economics and 

Consumer Behavior provides an excellent description of the problems of aggregation and 

the estimation of demand systems). However, this earlier literature did not address the 

problems created by consumer paying different prices. The problem of price aggregation 

in analysis of scanner data is discussed in Scheffman (1992). As a practical matter, not 

much can be done to solve this problem other than trying to get access to more 

disaggregated data or making very specific assumptions about the structure of demand 

(e.g., AIDS). 

13 Recall that the raw data consist of innumerable individual transactions that may differ 

during the reporting period in the prices paid by consumers. For example, if the reported 

data, as is typically the case, aggregates across supermarkets during the period, the 

reported aggregated data would sum up transactions at Chain X selling the particular 

UPC code at $1 with transactions at Chain Y at $1.30. The typical estimate of price 

would be average revenue, i.e., total sales divided by total units. Clearly, this measure 

does not capture the variability in prices across stores. For example, if sales were split 

evenly between Chain X and Chain Y, the estimate of price would be $1.15. But this 

would be the same measure of price if both X and Y had prices of $1.15 during the 

reporting period. As will be discussed below, this may present significant issues in 

attempting to estimate consumer (retail-level) demand. 
12

point in time. For example, it is well known that advertisements in circulars and in-store 

promotional activity (e.g., end of aisle displays) have large effects on unit sales.14 

If a given chain charges approximately the same prices and offers similar promotions 

within a metro area, chain-specific data should accurately reflect the price and non-price 

attributes facing consumers in a given week. IRI and Nielsen do maintain these data; 

however, they have rarely been used in antitrust investigations. 

While retailer-specific data reduce the problem of measurement error, the demand 

parameters estimated from retailer-specific data do not necessarily correspond to the 

parameters of interest to antitrust economists. The goal of the demand study is to 

determine the demand elasticities facing the manufacturer, not its retailers. As a matter 

of simple economic theory, we know that the demand curve facing competing retailers in 

a region will be more elastic than the aggregate demand curve for the entire market. For 

example, assume that there is a highly perishable product for which consumer demands 

are virtually completely inelastic (e.g., milk), and also that some fraction of consumers 

are loyal to shopping at their favorite store, while others shop at the store with the lowest 

milk price. Assume further that supermarket chains compete for the non-loyal customers 

by offering milk at discounted prices (in some kind of mixed- price equilibrium).15 In the 

data, when a chain happens to have the lowest price for milk in a given week it will 

experience a surge in sales (because it captures all of the non-loyal consumers), while the 

total quantity of milk sold in the market is unchanged. Thus, the demand elasticity for 

milk estimated using chain data will be large, while the market level elasticity (correctly 

measured using market level data) is zero. 

Whether the analysis should use chain-specific or market-specific data will depend on the 

question being asked. As described above, if the analyst is trying to infer the market 

level demand for a product and consumers are likely to change retailers to purchase that 

product given small changes in that product’s price, then chain-specific data may not 

yield good elasticity estimates. However, if consumers are unlikely to change retailers to 

purchase a product at a promoted price, then market/chain specific data is probably 

preferable to market-level data aggregated over chains. 

III. Functional Forms in Demand Estimation and Merger Simulation 

A. Introduction 

Empirical estimation of market-level demand equations requires the analyst to specify 

functional form for the equation prior to estimation. A number of criteria must be 

considered in making this choice. Most researchers wish to preserve “flexibility” (i.e.,

they wish to avoid predetermining the pattern of substitution possibilities among the 

 

14 Meaning, in a regression setting, holding price constant, the presence of advertising or 

in-store displays increases unit sales significantly. 

15 See Varian (1980) for an example of such a model. 
13

commodities being analyzed by the particular choice of functional form) – or to put it 

more simply, they want to allow the data to tell them whether two goods are substitutes, 

and if so, whether they are close or distant substitutes). 

The problem researchers face is that “flexibility” is expensive, in the sense that a great 

deal of data is required to estimate demand equations that have this property. If a 

researcher is estimating the demand relationships among, say, five different products, he 

or she must estimate 25 own- and cross-price elasticities. If there are 10 products, the 

number of price elasticities (own and cross) that must be estimated increases to 100. 

Given that the typical antitrust economist usually only has access to several years of data, 

it can become difficult to estimate with acceptable precision the demand elasticities for 

even a modest number of products.16 And, as these demand elasticities are the critical 

inputs into calculating the predicted post-merger price change, imprecision in the former 

naturally translates into imprecision in the latter. 

In what follows, we briefly review and summarize the current state of knowledge about 

the implications of choosing particular functional forms. 

 

16 In Bresnahan (1987) there were 100 different auto models analyzed, yielding 10,000 

elasticities. 
14

B. Choosing Functional Forms 

Here we will focus principally on the functional forms that have experienced widespread 

use in merger simulations; readers seeking a more general discussion are referred to 

Deaton and Muellbauer (1980). 

In estimating demand at retail, the researcher must choose the mathematical formula 

(functional form) that expresses the demand relationship. The statistical estimation, 

itself, does not “choose” the functional form. In theory, there is a “true” functional form 

that generates the purchase data, and of course it is important that the functional form 

chosen for estimation approximates the “true” functional form. As a matter of practice, 

assessing the validity of the functional form chosen for estimation is done through 

various statistical tests and testing alternative functional forms. 

In the typical antitrust setting in which demand estimation and merger simulation occurs, 

the researcher will have data for a number of different cities (e.g., 30 of the largest cities 

in the U.S.). For each product (or brand) analyzed, the dataset will consist of the number 

of units sold in some particular time period (e.g., a week), a measure of the price that 

prevailed during that period,17 and also measures of promotional activity for each 

product. Using standard econometric techniques,18 the researcher will estimate a 

statistical relationship between the quantity of the good purchased and the price and 

promotional activities and other determinants of demand (such as the size of the market). 

Choice of functional form can have major implications for the magnitude of predicted 

prices. Crooke et al. (1999) show that different functional forms can produce 

substantially differing predictions about post-merger equilibria. For example, if the 

researcher assumes that the demand functions exhibit constant elasticities, the predicted 

post-merger price increases will be much larger than if linear or logit demands are 

assumed. 

One possible functional form is the linear demand system. One major advantage to the 

linear demand system is that it makes computation of the merger’s competitive effects 

relatively easy (see Werden (1996) for details). There are numerous drawbacks to the 

linear demand system. First, there is no guarantee that the estimated parameters will have 

the “right” sign. If the different brands are substitutes, then the cross-price terms should 

be positive, in order to yield a positive cross-elasticity. However, it is frequently the case 

in applied work that the estimated cross-price coefficients will be negative, which calls 

into question the validity of the empirical exercise. 

 

17 As discussed above, the measure of “price” typically used is average revenue (= 

(p*q)/ q), which often will not give an accurate measure of the prices actually faced by 

consumers during that week. For purposes of the present discussion, however, we will 

ignore this issue. 

18 We defer to Section III the economic and econometric issues associated with 

endogeneity of the price and promotion variables. 
15

A second, more subtle problem is identified by Crooke et al. (1999), who found that 

simulations conducted with linear demand systems sometimes can yield negative

predicted quantities. 

An alternative to linear demand systems is the log-linear (i.e., constant elasticity) demand 

function. This system is estimated by regressing the natural logarithms of the quantity 

variables on the natural logarithms of the price and demand-shifting variables. The appeal 

of the constant elasticity system is that the regression coefficients are the elasticities – no 

further computations are required. There are several disadvantages to this functional 

form. First, the “adding-up” restriction of demand theory (i.e., the requirement that 

expenditure shares sum to unity) cannot be satisfied by the constant elasticity demand 

system (Deaton and Muellbauer, 1980, p. 17). Second, many researchers prefer to allow 

demand elasticities to vary as prices and quantities vary (e.g., as in the linear, logit, and 

AIDS demand systems, where demand becomes more elastic as one moves up the 

demand curve). If the true demand system is not constant elasticity, yet the researcher 

assumes otherwise for the purpose of merger simulation, the resulting predicted price 

increases can substantially overstate the likely price effects (Crooke et al. (1999)). A 

third disadvantage is that, depending on the values taken on by the elasticities, merger 

simulations may lead to a situation in which post-merger equilibrium does not always 

exist (Crooke et al. 1999). Last, the log-linear system, like the linear system, cannot 

guarantee that the parameters have the “right” signs. 

The disadvantages of the linear and log-linear systems are sufficiently large that many 

researchers now use alternative functional forms in merger analysis.19 One popular 

choice is the Almost Ideal Demand System (popularly termed the “AIDS” model), first 

proposed by Deaton and Muellbauer (1980), and advocated by Hausman et al. (1994) as a 

basis for empirical merger analysis. In the AIDS model, expenditure shares of each 

product are regressed on the logarithms of the prices of the different goods and the log of 

total expenditure (deflated by a price index). The principal disadvantages are that, like 

other functional forms (e.g., linear), it requires the estimation of a large number of 

parameters, and it does not guarantee (at least without further restrictions) that crosselasticities have the “right” signs. Additionally, although AIDS allows elasticities to 

adjust as equilibrium prices and quantities vary, it restricts somewhat the way these 

adjustments take place; consequently, the predictions of models estimated using the 

AIDS specification do not vary greatly from those estimated under an assumption of 

constant elasticities (Crooke et al. (1999, Table III)). 

The burden of estimating a large number of parameters can be addressed by employing 

functional forms that have fewer free parameters. Werden and Froeb (1994) and Werden 

et al. (1996) have advocated the use of the logit model. The appeal of the logit model is 

found in its analytical tractability and its relatively modest data requirements. The logit 

model assumes that consumers make a discrete choice from a set of (exhaustive) 

alternatives. For example, if the good being analyzed is breakfast cereals, it is assumed 

 

19 It is of interest to note, however, that market researchers who develop estimates of 

elasticities for grocery manufacturers often do use linear or log linear models. 
16

that the consumer chooses the brand of cereal yielding the highest utility (he also has the 

alternative of choosing “none of the above,” which is referred to as the “outside good.”). 

With aggregate share data, the parameters of a simple logit model can be estimated as 

follows: 

log(Sj/SO) = β*xj + α*pj + γ*log(Sj|g) + εj

Here, Sj is the market share of product “j”; SO is the share of the “outside good;” xj are 

characteristics of good “j”; pj is the price of good “j”; and Sj|

g is the market share of 

product “j” within segment “g”. To illustrate with an example, Irwin and Pavcnik (2001) 

analyze the competition between Boeing and Airbus within the market segment 

consisting of wide-bodied aircraft. Here, the typical Sj is the share (out of total aircraft, 

narrow and wide-bodied) of a particular plane, such as the Airbus A-320; SO is the share 

of all narrow-bodied aircraft; Sj|

g is the share of the A-320 in the wide-bodied segment; 

the xj are the observable (to the econometrician) characteristics of the A-320; and pj is its 

price. Once the parameters α, β, and γ are estimated, own- and cross-price elasticities can 

be easily computed. 

The major analytical criticism of the logit model is that it embodies the restrictive 

assumption of the Independence of Irrelevant Alternatives.20 In the context of logit 

models of demand, the IIA property implies that if the price of one good increases, 

consumers switch to other goods in proportion to the latter's market shares. This is a 

highly restrictive assumption that clearly will not be valid in many instances.21

To avoid the highly restrictive pattern of cross-elasticities embodied in the simple logit 

model, but at the same time preserving its parsimony in terms of parameters requiring 

estimation, researchers have developed alternative models of demand that not only allow 

for much greater flexibility in substitution patterns, but which also allow the researcher to 

take into account heterogeneous consumer preferences and the likely endogeneity of 

product prices. Berry, Levinsohn, and Pakes (see Berry (1994); Berry, Levinsohn, and 

 

20 Hausman and Leonard (1997, p. 322) note that “[a]s has been known for many years, 

the logit demand model makes the IIA assumption, which implicitly restricts the demand 

structure by constraining the pattern of demand structure by constraining the pattern of 

demand substitution between products. Indeed, it has been known for over twenty years 

that the logit demand system makes the assumption of identical cross-price elasticities for 

all products with respect to a given product . . . restricting the demand substitution 

patterns [in this way] would seem to defeat the purpose of performing unilateral effects 

analysis.” 

21 There is another possible empirical problem with the logit specification. Many studies 

of household behavior indicate that the same household often regularly purchases 

multiple brands. (Recall that the purchasing unit is probably best viewed as the 

household, with the grocery shopper(s) making purchases on behalf of all the household 

members). 
17

Pakes (1995); Nevo (2000)) have proposed a random coefficients logit model that 

assumes that products can be viewed as bundles of characteristics (e.g., automobiles 

might be characterized by horsepower, passenger space, and air conditioning). 

Accordingly, their empirical model is specified in terms of the demand for these 

characteristics, which are far fewer in number than the number of products (or brands) 

that compete in the market at any given time. The data required to estimate the random 

coefficients logit model may not always be particularly demanding – in some cases, they 

can be estimated with market-level price and quantity data, data on product 

characteristics, and information on the distribution of consumer attributes (e.g., income, 

education) – but the estimation procedure itself is complex and time-consuming. The full 

details of the BLP approach are too complex to be presented in detail here. Nevo (2000) 

provides an excellent summary. 

IV. Estimation Issues 

A. Endogeneity 

For statistical analysis of sample data to produce “reliable” results -- that is, results that 

accurately convey information about the underlying population -- certain conditions must 

hold. The data we use in the estimation is the product of both demand-side and supplyside factors. Care must be taken to insure that what is actually being estimated is the 

demand relationship rather than some combination of demand and supply. One important 

issue is whether explanatory variables in the demand relationship (e.g., price) are 

correlated with “disturbances” that shift the demand relationship. For example, if stores 

change prices during the period of data reporting in response to “unexpected” changes in 

the volume of purchases, we would say that prices are “endogenous,” as opposed to a 

situation in which stores set their prices in advance of the data period and do not change 

prices during the data period, despite occasional unexpected changes in the volume of 

sales. 

Even if prices (or other explanatory variables, such as promotions variables) are 

endogenous, there are statistical methods that, in principle, can produce reliable 

estimates. Although there a number of approaches to addressing the problem of 

endogeneity, perhaps the most commonly used method is some variant of what is known 

as “instrumental variables” estimation. An instrumental variable is some variable that the 

researcher believes is correlated with the explanatory variable of interest (here, price) but 

uncorrelated with the unobserved “disturbances” that shift the demand curve. Good 

candidates for instrumental variables would be the prices of inputs used in the production 

of the product, since they are likely to be correlated with the supply curve (at retail) but 

not disturbances that shift the demand curve. Such data series are generally termed 

“costs shifters.” 

In the context of demand estimation with scanner data, however, it is usually difficult to 

find enough cost shifters, since the analyst would need as many different costs shifters 

are there are prices in the demand system. One commonly used estimation strategy is 
18

that proposed by Hausman et al. (1994) and Hausman (1997).22 To use this approach, the 

analyst assembles data on prices and quantities for a number of different cities for a given 

time period. Under the assumption that unobserved shocks to product costs affect all 

cities equally (i.e., there are no city-specific cost shocks) but that there are city-specific 

demand shocks (and not nationwide demand shocks), the prices in other cities can serve 

as valid instruments for the price in any particular city (i.e., the prices of soft drinks in 

(say) Detroit, Minneapolis, and Denver can serve as instruments for the price of soft 

drinks in Chicago). 

The legitimacy of this proposed solution to the endogeneity problem is controversial. 

Bresnahan (1997a, 1997b), for example, contested its validity in the context of ready-toeat cereals demand estimation. Bresnahan argues (1997a, pp. 241-2) that if, for example, 

there are national advertising campaigns whose effectiveness is imperfectly measured by 

the econometrician, there will be a national component to the demand disturbance, which 

will in turn invalidate the restrictions necessary for implementation of the Hausman 

method. If Bresnahan’s criticism is correct, the resulting estimates of the relationship 

between price and quantity will be biased towards zero (Bresnahan (1997, pp. 241-2)). 

Nevo (2000, pp. 535-36) makes a similar point. 

It can be argued that endogeneity of prices is not a major issue in the econometric 

estimation of retail demand functions using supermarket scanner data. For example, 

Hausman (1997, 219-20) has argued that if supermarkets do not adjust weekly prices to 

equilibrate demand and supply, and if supply curves are flat, prices can be treated as 

econometrically predetermined, thus obviating the need for instrumental variables 

estimation procedures. The validity of this reasoning also has been questioned. 

Bresnahan (1997a, p. 241) has argued that this reasoning assumes that the (common) 

demand shocks (e.g., from national ad campaigns) cannot be foreseen when retail prices 

are set, an assumption that he regards as unlikely. Bresnahan also argues that short-run 

retailer supply curves may be upward-sloping, rather than flat, because of retailer market 

power or inventory-adjustment costs. 

B. Inference 

Statistical inference – drawing inferences about a population from information contained 

in a sample drawn from that population – requires the analyst to carry out two tasks: 

first, he must compute the statistic of interest (e.g., the sample mean); and second, he 

must compute some measure of the accuracy of that statistic as an estimate of the 

corresponding population value (i.e., the population mean). Unless the analyst has this 

second piece of information, he has no idea whether his estimate of the truth is likely to 

be fairly close, or substantially off the mark. As recently stated by Koenker and Hallock 

 

22 The method used in Hausman et al. (1994) and Hausman (1997) was derived by 

Hausman and Taylor (1981). The Hausman-Taylor article proposes an instrumental 

variables method for estimating the coefficients on time-invariant characteristics in a 

panel data setting. 
19

(2001, p. 153), “[i]t is a basic principle of sound econometrics that every serious estimate 

deserves a reliable assessment of precision,” [emphasis original]. 

 Suppose, for example, that the analyst wished to know the average retail price of a 1-litre 

bottle of Coca-Cola sold in the Washington, D.C. metro area. He could visit 50 retail 

locations, record the price at each location, and compute the mean for the sample. Using 

standard statistical techniques, he could compute the estimated variance of the sample 

mean, and construct a confidence interval, which would give a sense of how precisely the 

sample mean likely approximates the true population mean (i.e., the mean that would be 

computed if the researcher visited every retail location where Coke is sold). 

This basic approach to gauging the accuracy of a sample statistic extends in a 

straightforward manner to more complicated settings, such as estimating a set of linear 

regression coefficients – or linear functions of these coefficients – and their associated 

variances. The formulas for carrying out these computations can be found in every 

econometrics text, and standard econometric software packages calculate them 

effortlessly. But matters quickly become analytically and computationally difficult if the 

researcher is interested in nonlinear functions of the regression coefficients. In these 

circumstances, the analyst must rely on alternative methods for approximating the 

variances. These methods may or may not convey useful information about the true 

variance, and may prove computationally difficult to carry out. 

A simple example may help illustrate. Suppose we are estimating a simple regression 

equation using ordinary least squares 

V I

E

X

y X

2

0 1

[ ]

[ ] 0;

ε σ

ε

β ε

β β ε

=

=

≡ +

= + +

If we have N observations on y and x, the OLS estimate ofβ1 (denoted as b (= [b0 b1]’) is 

(X’X)-1X’y, and its variance (Σ ) equals 2 σ (X’X)-1. Since the parameter is unknown, it 

must be replaced with its estimate s2

 (= e’e/(n-1), where e = y - Xb). Thus armed with 

the estimated regression coefficients (b) and their estimated variances s2

b [ s

2

 (X’X)-1], 

the analyst can proceed to test hypotheses about the true regression parameters. If the 

analyst is prepared to assume that β1  is distributed multivariate normal, then in small 

samples linear functions of b and its estimated standard error (sb) will have a tdistribution. If the distribution of  β1 is unknown, then (provided the sample is 

sufficiently large) the analyst can invoke the asymptotic (large sample) properties of the 

least squares estimator and use the normal distribution to test hypotheses about β1 . A 

common hypothesis test is whether β1 = 0; the test statistic is b1/sb, and the “critical 

values” are obtained (depending on the sample size) from the tabulated values of the t- or 

standard normal distributions. 
20

Suppose now that the analyst is not interested in testing hypotheses about regression 

parameter β1 , but is instead interested in the elasticity of y with respect to x, defined as 

η = β1(x / y ). In empirical applications, it is common to calculate this elasticity by using 

the estimated parameter (b1) and the sample means for x and y . While it is easy to 

compute this estimated elasticity, it is not readily apparent how to compute its standard 

error, a necessary ingredient for hypothesis testing, nor is it obvious what the distribution 

of η  will be, even if the small sample distribution of b1 is known. 

One approach, known as the “delta method” (see Greene (1997), p. 280; Goldberger 

(1991), p. 102), uses asymptotic distribution theory to show that ifb ~ N( β , Σ), then 

asymptotically f(b) is distributed normally with mean f(β) and variance f’(b)V(b)f’(b)’. 

There are two possible problems with the use of the delta method. First, it is valid only 

asymptotically; if the sample is insufficiently large, one cannot necessarily infer that the 

functions of b are normally distributed, and the asymptotic standard errors may provide a 

poor approximation of the standard errors in small samples. Second, and perhaps more 

important in the context of demand estimation, the functions that researchers are 

interested in (own- and cross-elasticities) are highly complex nonlinear functions of the 

regression parameters, which is a particular problem when the researcher uses a 

functional form such as the Almost Ideal Demand System (AIDS; see Green and Alston 

(1990)). And researchers are typically not interested in the elasticities themselves, but 

rather in functions of those elasticities (e.g., to compute predicted post-merger prices). It 

becomes computationally burdensome to calculate the variance matrix of the elasticities. 

Moreover, the delta method is based on the fact that the linear approximation to a 

function, and the function itself, has the same asymptotic distribution at a particular point. 

As one moves away from this point – as one might, for example, when simulating the 

effects of a merger – the asymptotic equivalence of these two distributions might no 

longer hold. Perhaps for these reasons, it is uncommon for researchers to provide 

estimated standard errors of the predicted price effects of mergers. 

An alternative approach to computing standard errors for nonlinear functions is the 

“bootstrap” method (see Efron and Tibshirani (1993); Brownstone and Valletta (2001) 

provide a nontechnical discussion). The statistical theory behind the bootstrap is 

complex and will not be discussed here. Instead, we will describe its mechanics and 

comment on its utility in the particular application of merger simulation. Return to our 

example of computing the average price for a 1-litre bottle of Coke, with a sample of 50 

prices. One could compute the sample mean and variance using the standard formulas 

found in any statistics textbook, and use these numbers to carry out tests of hypotheses 

about the mean price, to construct confidence intervals, etc. The alternative method for 

computing the variance is to use the bootstrap. For example, a confidence interval can by 

calculated by drawing a large number (e.g., 10,000) of “bootstrap samples” of size 50 

(sampling is done with replacement) and computing the mean for each of these samples. 

The .025 and .975 percentiles of the distribution of the bootstrap sample means can then 

be used as the boundaries of the 95 percent confidence interval on the mean. 
21

Why use the bootstrap? The bootstrap’s appeal derives from (1) under fairly general 

conditions, the bootstrap approximations of the sampling distribution are at least as 

accurate – and under some conditions, more accurate – than the distributions obtained 

from asymptotic approximations; and (2) the bootstrap is relatively easy to implement. 

One of the difficulties in using the bootstrap in the context of demand estimation is that 

the data are typically in the form of a “panel” – this is, time series-cross section data (e.g.,

3 years of monthly data on 50 cities). Because there may be serial correlation among the 

disturbances in the data, the normal bootstrap technique of random sampling from the 

data will be inappropriate. One possible solution to this problem would be to transform 

the data using standard procedures for autocorrelation (e.g., the Cochrane-Orcutt 

procedure, suitably modified for panel data; see Green (1997), pp. 638-39) so that the 

variance matrix of the transformed disturbances no longer exhibit autocorrelation, and 

then carry out the bootstrap operations on the transformed data. Capps, Church, and 

Love (2001) propose an alternative method, based on a method originally developed by 

Freedman and Peters (1984). 

V. Using Retail Price Data to Analyze Mergers of Manufacturers 

A. Overview 

The widespread availability of retail scanner data has made it possible to estimate 

demand systems and use the estimates to draw inferences about the potential effects of a 

merger. Most of the mergers that come before the agencies, however, occur at the 

manufacturer level, one or two stages upstream from retail pricing, which is determined 

at the retail level. An issue that is almost always ignored in the demand analyses that 

come before the agencies is the relationship between the demand elasticities estimated 

from retail data and the effects of a merger among upstream producers.23

We discuss two of issues here that we think deserve more attention. First, the 

own- and cross-elasticities of demand facing retailers are generally not the same as the 

own- and cross elasticities facing upstream wholesalers and manufacturers. Specific 

assumptions or analysis beyond that which is typically done is required to determine the 

demand elasticities facing upstream firms from estimates of retail elasticities. 

Second, competition between upstream firms often takes place through more 

complicated contracts than the competition between producers of most final goods. The 

“prices” manufacturers charge retailers are often more complex than linear (i.e., per-unit) 

wholesale prices. They often include fixed fees of various types, quantity discounts, 

minimum or maximum purchase commitments, etc. In practice, payments between 

manufacturers and retailers are often broken into two components --- “list” prices and 

trade promotions. The list price is the unit price adjusted for any standard discounts and 

allowances, such as volume, prompt payment, etc. Trade promotions are various forms 

 

23 This is discussed Scheffman (1992) and in Scheffman and Spiller (1996). See, also, 

Steiner (1973, 1993, 2001). 
22

of reductions from the list price and/or net payments from the manufacturer in various 

forms for features, displays, promotions, more favorable shelf space, etc. All of these 

factors can give rise to “nonlinear” payments (i.e., payments that are not made on a perunit basis) between the manufacturer and the retailer, and this may have important 

implications for the analysis of a merger. In the next two subsections, we discuss these 

issues in more detail.24

B. Derived Demand Elasticities 

When a manufacturer sells a product through retailers, the demand for its product is the 

quantity that retailers purchase to resell to final consumers. The quantity that retailers 

purchase depends on how profitable they think the product will be, which in turn depends 

(in part) on the “final demand” for the product from consumers. The demand facing the 

manufacturer is called a “derived demand” because it is “derived” from retailers’ 

purchasing decisions, which are governed in part by the final demand for the product. 

The elasticities (own and cross) that are relevant for the manufacturer’s pricing decision 

are the elasticities of the derived demand for its product. 

It is well known that the elasticities of the derived demand facing manufacturers are 

generally not the same as the elasticities of the final demand estimated at the retail level. 

In general, the relationship depends on the form of the retail demand functions, the cost 

conditions of retailers, and the nature of retailer competition. Since we are often 

interested in the elasticities of derived demand, either for defining markets or for 

simulating manufacturer mergers, it is important to understand the nature of this 

relationship in specific environments. 

A small amount of formal structure is useful. Suppose that the product in question is 

widgets, which a manufacturer sells to retailers for resale to final consumers. Denote the 

retail price for widgets as p and the wholesale price that retailers pay the manufacturer for 

 

24 A third issue that we do not discuss here is that the terms of exchange between 

manufacturers and retailers are determined through bargaining more often than the prices 

of final goods. Bargaining can have implications for the effects of mergers because a 

merger may change the bargaining positions (or “bargaining power”) of the merging 

parties relative to firms on the other side of the market. See Horn and Wolinsky (1988), 

who examine the incentives for mergers between independent upstream firms (firms that 

do not compete with each other) and competing downstream firms when wholesale prices 

are negotiated. We are not aware of any literature on the effects of horizontal mergers 

between competing upstream manufacturers when wholesale prices are determined 

through bargaining. 

 
23

each widget as w. The elasticity of the derived demand for the manufacturer’s widgets 

can be written as25

 ( ) p

M R ER Ew Pass through rate

p

w E E × − = × 













 = ×

where EM is the elasticity of the derived demand facing the manufacturer, ER is the 

elasticity of final demand facing the retailer, and Ep

w is the elasticity of the retail price 

with respect to the wholesale price. This equation shows that in a retail environment, 

where one unit of the intermediate good (widgets) translates into one unit of output 

(widgets), the elasticity of the manufacturer’s derived demand equals the elasticity of the 

retail demand times the ratio of the wholesale and retail prices, w/p, times the passthrough rate. The ratio of the wholesale and retail prices times the pass-through rate is 

just the elasticity of the retail price with respect to the wholesale price, as indicated by the 

last equality in the equation. 

From this relationship we can derive several special cases of interest. If the retail market 

is perfectly competitive, then the retail price equals the retailer’s marginal cost, and the 

pass-through rate equals 1 (because the retail price adjusts one-for-one with the wholesale 

price). Suppose we make the simplifying assumption that the wholesale price is the only 

source of marginal cost at the retail level. This assumption is almost never literally true, 

but it may be a reasonable approximation for products in which the wholesale price 

constitutes the majority of the retailer’s marginal cost. Under this assumption, perfect 

competition between retailers yields p=w (i.e., price equals marginal cost). In this 

special case, the equation above shows that the elasticity of the derived demand is equal 

to the elasticity of the retail demand. Of course, the retail markets in which scanner data 

are available are typically not perfectly competitive, and the wholesale price does not 

constitute 100 percent of the marginal cost incurred by retailers in selling most 

products.26 Thus, the practical value of this special case seems remote. 

 

If retailers set prices to maintain constant percentage mark-ups, then the elasticity of the 

retail price with respect to the wholesale price is equal to 1. Under this assumption, the 

equation above also shows that the derived demand elasticity equals the retail elasticity. 

Constant percentage mark-ups are profit maximizing for single-product retailers that face 

constant elasticity demand and incur no (marginal) costs other than the wholesale price. 

 

25 Formally, let DR(p) be the final demand facing a retailer for some product, where p is 

the retail price, and let w be the wholesale price the retailer pays the manufacturer for 

each unit that it purchases and resells to final consumers. Let p(w) be the price the 

retailer charges given a wholesale price of w. The derived demand facing the 

manufacturer is then DM(w) = DR(p(w)). Differentiating DM with respect to w, putting the 

expression in elasticity form, and recognizing that DM=DR yields the expression in the 

text. 

26 Retail mark-ups over the wholesale price typically range from 20 to 80 percent, 

depending on the product, contradicting the implication that p=w in this special case. 

 
24

These are strong assumptions that might be plausible in some applications, but clearly not 

in all settings. 

 

Outside of these special cases, the relationship between the elasticities at different levels 

in the production chain is not one-to-one. In general, the relationship depends on the 

shape of demand curves and the nature of competition. Given assumptions about these 

factors, it is possible to calculate the relationship. For example, in the special case of 

linear demand, a retail marginal cost of w, and monopoly at the manufacturer and retail 

levels, it can be shown that w/p = 2/3 and that the pass-through rate is 1⁄2. In this case the 

derived demand elasticity is one-third the retail elasticity. Other common demand curves 

(e.g., semi-log, AIDS, and constant elasticity) yield pass-through rates that exceed 1⁄2. 

The derived demand elasticity is closer to the retail elasticity in these cases than it is 

under linear demand, other factors equal. 

The relationship becomes considerably more complicated for multi-product retailers that 

compete with one another. We discuss three complications here that relate to institutions 

that are prevalent in the retailing environment. 

One complication is the “one-stop shopping” nature of retail outlets, which generates 

demand-side complementarities among products on the shelf that are unrelated to 

consumers underlying preferences for the products. For example, a lower price for milk 

might draw customers into the store where they then decide to purchase detergent while 

they are there. This makes milk and detergent complements in demand from the 

perspective of the grocery store, even though consumer preferences for these products are 

probably unrelated. 

A second complication is the extensive use in retailing of frequent, but temporary 

discounts on alternative sets of products over time.27 As far as we know, there has not 

been any work on how retail sales behavior affects the elasticities of the derived demand 

for the products they sell.28 This issues was discussed above at the beginning of this 

section (Section V. A., 1-3). 

A third complication that arises in the retailing environment is that retailers have scarce 

shelf space and can sometimes use this to their advantage to discipline the pricing 

behavior of suppliers. The reader may have noticed that in all of the examples we have 

discussed so far, the elasticity of demand facing the manufacturer of some product A is 

no larger than the elasticity facing retailers. This is the “normal” case for products that 

are not subject to the risk of being dropped from the shelf by retailers in response to a 

small increase in the wholesale price. However, if retailers can credibly threaten to 

remove a product from their shelves when faced with a price increase, the elasticity of 

demand for a product at the manufacturer level can exceed the elasticity at the retail level. 

 

27 See, for example, Hosken and Reiffen (2000). 

28 Sporadic sales behavior may also complicate the estimation of retail demand 

elasticities by inducing consumers to purchase products on sale and hold them in 

inventory. See the discussion on aggregation in section I.B. 
25

A simple example illustrates this point. Imagine a market in which four manufacturers---

A, B, C, and D, compete for two “slots” at a retail outlet. To keep things simple, assume 

that the retailer is a monopolist, that the manufacturers have the same costs, and that all 

manufacturers know that their rivals have the same costs.29 Assume further that the four 

products are symmetric in the sense the retailer expects to make the same sales and earn 

the same profits regardless of which two products it carries.30 Manufacturers compete to 

have their products stocked by announcing their wholesale prices. The retailer then 

selects the two products it will carry, sets retail prices, and pays the winning 

manufacturers the wholesale prices that they announced for each unit sold.31

This situation is analogous to an auction in which four identical bidders, (the four 

manufacturers) “bid” for two identical items (the two slots on the shelf). Since there are 

more bidders than items, and the bidders have complete information about their rivals, 

this auction will yield the perfectly competitive outcome. That is, the bidding process 

will result in a wholesale price equal to the manufacturers’ marginal cost. Suppose that 

the winning bidders are manufacturers A and B. What is the elasticity of the derived 

demand facing manufacturers A and B? 

To answer this question, we need to consider what would happen if one of the winning 

bidders attempted to raise its wholesale price. Suppose that manufacturer A did so. 

Because the losing bidders, C and D, each stands ready to sell a product with a sales and 

profit potential equal to that of product A, the retailer would respond to A’s price increase 

by replacing product A with product C or D. That is, a wholesale price increase by 

manufacturer A would cause it to lose all of its sales. This means that the elasticity of 

demand facing the manufacturer A is very high (in this example, infinite), even though 

the elasticity of the consumer demand for product A could be very low. The reason for 

the large own elasticity for product A is the high cross elasticity between product A and 

other products C and D that are not currently carried by the retailer.32

Now consider the effects of a merger between the two winning bidders, A and B. After 

the merger, there will still be three independent firms bidding for two slots. The postmerger auction will still yield the competitive outcome, so the merger will have no effect 

on the wholesale price. Notice that this conclusion is independent of the own and cross 

elasticities of the consumer demand (i.e., the demand facing retailers) for the merging 

firms’ products. 

 

29 The insights from this example are relevant for more complicated markets. 

30 Note that this assumption does not mean that the products are homogenous. They 

could be differentiated or even independent products that have the same retail profit 

potential. 

31 In practice, competition for shelf space often involves more complicated payment 

schedules than simple linear prices (see the next section on nonlinear contracts). 

However, this simple example is rich enough to convey the point we want to make here. 
26

This example shows that retail shelf-space constraints can have important implications 

for manufacturer-level demand elasticities. In particular, retail demand elasticities may 

understate manufacture-level elasticities if retailers respond to a wholesale price increase 

by dropping the manufacturer’s product. Note that an important implicit assumption in 

this example is that the shelf space allocated to any one product is inelastic with respect 

to the product’s profitability. For items that receive only one facing, this may be true, but 

for items that receive multiple facings, the space allocated to the product can be reduced 

if it becomes less profitable. The importance of shelf-space effects is likely to vary from 

case to case. The key question is whether the wholesale price charged by the 

manufacturer is constrained at the margin by the retailer’s threat to drop the product from 

its shelves, or by the reduction in sales caused when the retailer passes part of the 

wholesale price increase on to consumers. We suspect that for some products where 

brand loyalty is not particularly strong, retailers’ threats to displace products will provide 

strong disciplining effects on manufacturer price increases. In such cases, retail-level 

elasticities may understate manufacturer-level elasticities. On the other hand, some 

strong brands would not be dropped by retailers without a large increase in the wholesale 

price. In these cases, retail-level elasticities may overstate manufacturer-level elasticities. 

Many of the demand system estimations presented to Agencies use the multi-stage 

budgeting approach with the AIDS (Almost Ideal Demand System) demand specification. 

The AIDS system is not of the constant elasticity form, and retailers nearly always sell 

multiple products. Thus, constant mark-ups generally do not reflect profit maximizing 

behavior by retailers in the AIDS analyses that are typically done, suggesting that the 

upstream and downstream elasticities will not be equal. A common response to this 

concern is an empirical observation that “retailers tend to follow constant mark-ups.” 

However, economists are generally uncomfortable with models based on ad hoc

assumptions like constant mark-ups without an explanation of how they emerge from 

rational behavior.33 These studies also ignore the three complications just discussed---

demand complementarities from one-stop shopping, retailer sales behavior, and retail 

shelf-space constraints. These issues clearly deserve more attention.

C. Nonlinear Payment Schedules 

The foregoing discussion demonstrates that the relationship between the elasticities of 

derived and final demands is not straightforward. This complicates the chain of inference 

between retail demand estimation and the competitive effects of upstream mergers, even 

under linear pricing. This subsection considers a second factor that complicates the 

inference chain --- nonlinear payment schedules. 

Nonlinearities are pervasive in the transactions that govern exchange in intermediate 

good markets. A simple example is a two-part tariff, which involves both a fixed fee and 

a per-unit wholesale price. Fixed fees can be positive (e.g., a franchise fee) or negative 

 

33 An explanation of the use of constant mark-ups when retail demand is of the AIDS 

form would appear to require some notion of bounded rationality. 
27

(e.g., a slotting allowance)34. If the fixed fee is positive, the average payment declines 

with the amount purchased (quantity discount); if the fixed fee is negative, the average 

payment increases with the amount purchased (quantity premia). A wide range of fees 

exchanged by manufacturers and retailers affect the marginal and/or the fixed (or 

“inframarginal”) payment from the retailer to the manufacturer. Examples include 

presentation fees (paid for the privilege of making a sales presentation); display fees 

(paid for special merchandising and the display of products);35 pay-to-stay fees (paid to 

have the retailer continue stocking and displaying a product); and failure fees (paid when 

a product does not meet expected goals). Other common components of nonlinear 

payment schedules include volume discounts, minimum and maximum purchase 

commitments, and liquidated damages. 

The complication introduced by nonlinear payments goes beyond simply trying to draw 

inferences about derived demand elasticities from retail data. Competition in nonlinear 

payment schedules is fundamentally different from competition in per-unit prices. 

Perhaps the easiest way to see this is through a simple example, which is based on 

models examined by O’Brien and Shaffer (1997)36 and Shaffer (1991). The example 

illustrates that nonlinear payment schedules can have important implications for the 

effects of mergers among upstream suppliers. 

O’Brien and Shaffer consider a model in which two differentiated suppliers compete in 

nonlinear contracts to sell through a single retailer. The authors show that the 

equilibrium contracts involve nonlinear payments in which the marginal transfer price 

(the per-unit component) paid by the retailer for each unit purchased equals the 

manufacturer’s marginal cost. For the special case of two-part tariff contracts, this means 

that the wholesale price equals the manufacturer’s marginal cost. Thus, nonlinear pricing 

allows the upstream firms to avoid double-marginalization,37 analogous to the wellknown case of nonlinear pricing under bilateral monopoly.38

 

34 Slotting allowances are payments from manufacturers to retailers to induce the retailer 

to shelve the product. The use of these fees is found throughout the food retailing 

industry. A related practice is that of “pay-to-stay” fees, which are made in periods 

subsequent to the initial stocking decision so that the retailer continues to shelve the 

manufacturer’s products. 

35 Display fees are for special displays or favored placement. Examples include special 

end aisle displays, “display pyramids” (such as for 12-can boxes of soft drinks), and 

preferred position on shelves (e.g., eye-level for bread). 

36 See also Bernheim and Whinston (1998), who studied a similar model. 

37 “Double-marginalization” refers to the pricing distortion that occurs when a retailer 

adds its own (supra-competitive) mark-up to an upstream firm’s own (supra-competitive) 

mark-up. 

38 A basic result in the economics of vertical control is that bilateral monopolists can 

avoid double-marginalization (cf. note 12) using two-part tariffs. 
28

This result has important implications for the effects of upstream mergers when nonlinear 

contracts are feasible. Suppose the two upstream firms in the O’Brien/Shaffer model 

merge. The combined firm is a multi-product monopolist that can employ sophisticated 

contracts to sell through a downstream monopolist. This problem was analyzed formally 

by Shaffer (1991). He showed that the upstream firm (the merged firm in our context) 

cannot extract all the surplus from the retailer with standard nonlinear contracts in which 

the payments for each product depends only the amount purchased of that product. The 

reason for this is that the retail monopolist can credibly threaten to carry only one of the 

products if the manufacturer attempts to capture all of its surplus. Given this constraint, 

Shaffer finds that the merged firm will charge wholesale prices greater than marginal cost 

to capture some additional surplus, trading this benefit off against the cost of introducing 

double-marginalization. On the other hand, if the manufacturer can use more 

sophisticated contracts, such as aggregate rebates, full-line forcing, under which the 

retailer’s payment for each product may depend on the amount purchased of both 

products, then the manufacturer will charge wholesale prices equal marginal cost. The 

idea is that by effectively bundling its products, through “aggregate rebates” (rebates 

based on the aggregate purchases) or full-line forcing (making the payment terms 

contingent on the purchase of both products), the monopolist is able to capture more 

surplus without introducing a double marginalization distortion. 

Combining Shaffer’s results with the result in O’Brien and Shaffer, we see that the 

effects of an upstream merger depend critically on the nature of the contracts employed 

by the manufacturers. If the merged firm is restricted to standard nonlinear contracts, the 

merger leads to an increase in wholesale prices. On the other hand, if the merged firm 

can employ more sophisticated contracts, such as aggregate rebates or full line forcing, 

then the merger will have no effect on wholesale prices. The only affect of the merger in 

the latter case is to transfer surplus from the retailer to the manufacturers. Since the 

wholesale price does not change, the retail price does not change either, so the merger has 

no effect on consumer welfare.39

 

 

39 This is a rather extreme example because it ignores informational and contracting 

imperfections that might prevent firms from writing contracts that eliminate doublemarginalization completely. However, the example does illustrate that nonlinear pricing 

may have important implications for the effects of upstream mergers. 
29

The literature on competition in nonlinear contracts in intermediate good markets is still 

developing.40 More work needs to be done, both theoretical and empirical, before we 

will be in a position to say with confidence how nonlinear pricing alters the effects of 

horizontal mergers. As the literature continues to advance in this area, the best strategy 

for merger analysis is probably to continue to employ models that assume linear pricing. 

We have no empirical basis at this point for concluding that the predictions of these 

models are inherently biased one way or another. Our intuition is that models based on 

linear pricing will probably overstate the anticompetitive effects of horizontal mergers, 

because multi-product nonlinear pricing tends to eliminate double marginalization 

distortions (as suggested by the example above). However, the precise nature and 

importance of any bias awaits additional theoretical and empirical work. 

VI. CONCLUSION 

Economists have made substantial progress in applying econometric techniques to the 

analysis of horizontal mergers. As a commentator recently observed, econometrics has 

much to offer as to means for “illuminating critical issues in antitrust investigations and 

litigation.”41 In this paper, we have attempted to identify some aspects of this approach 

that could benefit from additional analysis and research by both academic and practicing 

antitrust economists. We do not intend to indicate that we believe that econometric 

analyses of scanner data are not useful. At the FTC we regularly conduct such analyses 

and have found them to be useful, when combined with the other evidence developed in a 

merger investigation. This paper, however, has highlighted issues that in some contexts 

are likely to require specific attention in assessing the viability and utility of the 

estimates. 

 

40 The theoretical literature on buyer-specific nonlinear contracts has focused mainly on 

cases with oligopoly at either the upstream or downstream level and either a single seller 

or perfect competition at the other level. It has also focused on different issues than 

horizontal mergers. For example, O’Brien and Shaffer (1997) and Bernheim and 

Whinston (1998) examine incentives for exclusive dealing when the downstream firm is a 

monopolist. O’Brien and Shaffer (1992) and McAfee and Schwartz (1994) examine the 

role of vertical restraints and nondiscrimination clauses for a single supplier selling 

through competing retailers. Hart and Tirole (1990) consider buyer-specific contracting 

with duopoly at both stages, but they focus on the effects of vertical integration and 

exclusive contracts. There is no published empirical work on how to predict the effects 

of horizontal mergers when firms negotiate nonlinear contracts. An interesting step in 

this direction is taken by Villas-Boas (2001). She estimates the retail demand for yogurt 

using the discrete choice methodology of Berry (1994) and Barry, Levinsohn and Pakes 

(1995) and attempts to distinguish between different models of (linear and nonlinear) 

input pricing using a non-nested hypothesis test, as in Bresnahan (1987). Using this 

technique, it would be possible in principle to distinguish between different models of 

input pricing and to use that model to predict the effects of upstream mergers. 

41 Werden (2002), p. 47. 
30

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