* Federal Trade Commission, Bureau of Economics. E-mail: stenn@ftc.gov. Telephone: (202) 

326-3243. Fax: (202) 326-3443. Address: 600 Pennsylvania Ave NW, Washington, DC 20580. 

Helpful comments from Hajime Hadeishi, Daniel Hosken, David Schmidt, Shawn Ulrick, and 

John Yun are greatly appreciated. The views expressed in this paper are those of the author, and 

do not necessarily represent the views of the Federal Trade Commission or any individual 

Commissioner. 

ESTIMATING PROMOTIONAL EFFECTS 

WITH RETAILER-LEVEL SCANNER DATA 

Steven Tenn* 

September 23, 2003 
- 1 - 

ESTIMATING PROMOTIONAL EFFECTS 

WITH RETAILER-LEVEL SCANNER DATA 

Abstract 

 Estimating cross-brand promotional effects with aggregate data requires knowledge of 

the joint distribution of each brand’s promotions. While such information is available in storelevel scanner data, it is not included in more aggregated scanner datasets. This paper presents a 

technique for overcoming this difficulty and develops a retailer-level model that incorporates 

both own- and cross-brand promotions. Promotional activity is integrated into the specification 

in a manner consistent with the way store-level models control for promotions, thereby avoiding 

the problem of aggregation bias. The proposed methodology extends the usefulness of retailerlevel scanner data by allowing it to answer important questions regarding how the promotions of 

competing products interact. 
- 2 - 

I. Introduction 

 The use of scanner data for analyzing the impact of promotional activity is widely seen as 

a “success story” by both academics and industry participants (Bucklin and Gupta 1999). A 

growing literature, however, questions whether aggregate-level scanner data can be reliably used 

for this purpose, or if store-level data is required instead (Allenby and Rossi 1991, Christen et al. 

1997, Chung and Kaiser 2000, Link 1995). A drawback of aggregate data is that stores with 

differing levels of promotional activity are combined together. This promotional heterogeneity 

raises two econometric issues. First, estimation of cross-brand promotional effects requires 

knowledge of the joint distribution of each brand’s promotions across stores, yet aggregate-level 

scanner data does not contain such information. Second, previous research demonstrates that 

demand estimation using aggregate data often leads to model misspecification known as 

“aggregation bias.” We develop a demand model that overcomes these two issues, allowing for 

consistent estimation of both own- and cross-brand promotional effects with retailer-level 

scanner data (e.g., the Jewel supermarket chain in Chicago).1

 The challenge of estimating cross-brand effects with aggregate data is easily 

demonstrated through a simple example. Suppose the manager of Brand A wants to estimate 

how a promotion by Brand B impacts his sales when Brand A is also on promotion. Aggregate 

scanner data only reports information regarding each brand’s own promotional activity (Link 

1995, Christen et al. 1997). While such data might indicate that Brands A and B are each on 

promotion in 50% of stores, it does not report the fraction of stores where Brands A and B are 

both on promotion. It could be the case that the two brands are never promoted at the same time 

in any given store. Alternatively, both brands may be on promotion in 50% of stores, with 

neither being promoted in the other half. Aggregate-level scanner data does not distinguish 

 1

 A confidentiality agreement with AC Nielsen prohibits retailer names from being revealed. This example 

does not indicate whether the dataset employed includes the Jewel supermarket chain in Chicago. 
- 3 - 

between these (or other) possibilities. Without information on the joint distribution of the two 

brands’ promotional activity, it is impossible to analyze how their promotions affect each other. 

 In this paper, we develop an econometric model that provides consistent estimates of both 

own- and cross-brand promotions when used in conjunction with retailer-level scanner data. 

First, a store-level model is constructed that controls for the promotional activity of each brand. 

Product demand at each store is then added together to obtain retailer-level demand in a given 

city. Aggregation to the retailer-level is made possible by the development of a technique for 

estimating the joint distribution of each brand’s promotions across stores. This is accomplished 

using information regarding the univariate distribution of each brand’s promotions that is 

typically included in scanner datasets. By explicitly modeling store-level promotional 

heterogeneity, and then incorporating such activity into the aggregate demand specification in an 

internally consistent manner, aggregation bias is avoided for both own- and cross-brand 

promotional effects. 

 This methodological approach requires several modeling assumptions. To facilitate 

aggregation, it is assumed that all stores within a retail chain that have the same promotional 

activity for a given product also charge the same price. While price homogeneity clearly does 

not hold at the market level, for many products it will (approximately) hold for stores within the 

same retail chain in a given city.2

 This motivates the paper’s focus on retailer-level scanner data. 

Additionally, it is assumed that the model parameters are homogeneous across stores. This is 

required since retailer-level scanner datasets do not include any information on particular stores, 

which makes it difficult to meaningfully incorporate parameter heterogeneity into the model. 

When these two conditions are satisfied, we demonstrate that retailer-level scanner datasets 

contain sufficient information to consistently estimate the effect of own- and cross-brand 

promotional activity. 

 2

 For example, Chevalier et al. (2003) conclude that there is relatively little inter-store price heterogeneity 

despite the presence of multiple price zones in their data. 
- 4 - 

 Many important questions relate to how the promotions of competing products interact 

(Blattberg et al. 1995, Bucklin and Gupta 1999): How do the promotions of other brands impact 

one’s own sales? Do cross-brand promotions enhance or diminish the promotional activity of 

your brand? Does this effect depend on the particular type of promotion? The methodology 

developed in this paper greatly enhances the usefulness of retailer-level data by allowing these 

issues to be addressed. The paper concludes with an empirical analysis demonstrating how 

retailer-level data can provide significant insight into cross-brand promotional effects. For 

example, we show that for two brands of premium ice-cream, each brand’s promotional activity 

greatly diminishes the impact of the other’s promotions. This likely explains why supermarkets 

rarely promote the two brands at the same time. 

 The paper is organized as follows. Section two details the reasons why aggregation bias 

arises in demand estimation. A demand model that is consistently estimated with retailer-level 

data is presented in section three. Section four uses the model to estimate the impact of 

promotional activity for two brands of premium ice-cream. Section five concludes. 

II. Aggregation Bias 

A common problem when estimating demand using aggregate data is that model 

misspecification leads to “aggregation bias.” This section details the primary reasons why 

aggregate-level data often produces biased estimates. For a detailed consideration of these 

issues, Theil (1954) and Krishnamurthi et al. (1990) analyze the linear model; Lewbel (1992), 

Christen et al. (1997), and Chung and Kaiser (2000) analyze the constant elasticity model; and 

Allenby and Rossi (1991) and Krishnamurthi et al. (2000) analyze the Logit model. Stoker 

(1993) provides a general review of empirical approaches to the data aggregation problem. 

Aggregation bias arises when the wrong explanatory variables are used to estimate 

product demand. This is easily demonstrated through a simple example. Suppose there are two 

types of stores that differ solely by the price each charges for a given product. In each time 

period t, let a fraction φ ∈ (0,1) of retailers charge price t p1, , with the remaining stores charging 
- 5 - 

price t p2, . All stores have the same demand curve: q = μ +αp . Suppose that the only sales 

data available is aggregated across both types of stores. Adding up product demand implies that 

the average quantity sold per store is t t q = μ +αp , where t t t p p p 1, 2, = φ + (1−φ) . Note that 

aggregate demand is a function of the average price across stores. Commonly available 

aggregate datasets, such as market-level scanner data, do not report this measure of price. 

Rather, average price is typically calculated as total dollar sales divided by total quantity sold, 

i.e., the volume-weighted average price. The use of this price measure to estimate aggregate 

demand leads to model misspecification. One cannot reliably estimate the model using volumeweighted average price simply because product demand is not determined by this variable. For 

this particular example, the estimated αˆ obtained using volume-weighted average price can be 

biased in either direction depending on the model calibration. 

Linear demand is a special case where store and aggregate-level demand have the same 

functional form. For non-linear models, this will generally not be true. Consider the previous 

example, but with a constant elasticity store-level demand curve: ln q = μ +α ln p . Average 

store sales takes a different form: ln ln( (1 ) ) 2, ln 1, ln t p t p

t q e e μ α μ α

φ φ

+ + = + − . Further, 

aggregate demand is not a function of either store-weighted or volume-weighted prices. To 

properly estimate this demand specification, one must separately obtain the price in each type of 

store, and one must observe the fraction of stores that are of each type (φ and 1−φ ). Further, 

the model must be estimated using the aggregate-level demand specification implied by the 

store-level model, rather than with a constant elasticity demand model. Otherwise, the aggregate 

demand model will be incorrectly specified, and aggregation bias will likely occur. 

An additional cause of aggregation bias is parameter heterogeneity across stores. 

Suppose that each type of store faces a distinct demand curve. For any given price p, let demand 

in the first type of store be determined by q p 1 = μ1 +α1 . Product demand in the second type of 

store is q p 2 = μ2 +α 2 . Unit sales per store is equal to 

t t t t q p p p 1 1, 2 2, = μ +α +φ(α −α ) + (1−φ)(α −α ) , where 1 2 μ = φμ + (1−φ)μ and 

1 2 α = φα + (1−φ)α . This demand function takes a similar form to store-level demand, but 
- 6 - 

contains two additional terms. If one estimates the linear model t t q = μ +α p , the obtained 

estimate αˆ will be a biased relative to α unless the last two terms of the aggregate-level model 

are jointly uncorrelated with t p . A special case where this occurs is when φ = 1 2 and prices 

are independently and identically distributed across each type of store.3 In general, however, 

parameter heterogeneity will result in aggregation bias. This finding is not an artifact of linear 

demand; aggregation bias similarly arises when the store-level model is non-linear. 

 To summarize, one can obtain aggregate-level demand estimates that are untainted by 

aggregation bias under the following conditions. One must estimate aggregate demand using a 

functional form that is consistent with store-level demand. One must estimate the model using 

the correct variables, where the variables of the aggregate model may not be simple averages of 

their store-level counterparts. Lastly, one must take into account that the aggregate-level model 

may be a complex function of the store-level model’s parameters. 

 Researchers have concluded that aggregation bias is less problematic when data is 

aggregated across stores with homogeneous marketing activity (Christen et al. 1997). The above 

discussion provides the intuition for this conclusion. First, homogeneity often implies that 

aggregate demand has the same functional form as store-level demand. For instance, if storelevel demand is of the linear or constant elasticity form, then aggregate demand has the same 

specification when stores are identical (and face the same demand curve). Second, aggregate 

demand is often a function of the same variables (price, etc.) as store-level demand, simply 

because there is little or no variation in these variables across stores. This leaves store-level 

parameter heterogeneity as the leading determinant of aggregation bias. Store homogeneity in 

marketing activity does not necessary imply homogeneity in the demand-side response to 

 3

 These requirements may seem overly strict to readers familiar with Christen et al. (1997), which cites 

Krishnamurthi et al. (1990) as showing that a “bias exists only if there is (1) heterogeneity in both the parameters 

and the independent variables, and (2) a non-zero covariance between these two model elements.” The non-zero 

covariance requirement must hold in finite sample for each observation across the units of aggregation. This 

condition is violated when the control variables and parameters are drawn from distributions that are independent of 

each other. 
- 7 - 

promotions (Hoch et al. 1995). Therefore, parameter heterogeneity can potentially lead to bias 

(relative to the average parameter values) even when data is aggregated across stores that 

undertake identical promotion and pricing decisions. The degree of bias depends on the model 

employed. Allenby and Rossi (1991) find that in the Logit model, parameter heterogeneity does 

not lead to significant aggregation bias under certain conditions, one of which is homogeneity in 

marketing activity. Krishnamurthi et al. (2000) conclude, however, that this finding is not robust 

to time-series variation in parameter heterogeneity. 

Link (1995) suggests that aggregation bias be avoided by employing data that has been 

aggregated across stores with homogeneous marketing activity. Doing so does not eliminate 

aggregation bias due to parameter heterogeneity. Link argues, however, that data aggregation 

across stores with heterogeneous marketing activity is the most significant source of bias in 

practical applications. However, even if one obtains data that is aggregated across stores where a 

brand’s own promotions are homogenous, heterogeneity in the promotions of competing 

products may still remain. Thus, Link’s approach does not account for aggregation bias in crossbrand effects. 

 Christen et al. (1997) propose a methodology to “de-bias” demand estimates based on 

aggregate data. First, demand is estimated using simulated store-level data that has been 

aggregated across stores. The average difference between the true and estimated parameters 

from the simulation is then added to the estimates from an empirical application, so as to de-bias 

the results. A shortcoming of this approach is that it can be difficult to reliably estimate the 

magnitude of aggregation bias, as one may have insufficient information to calibrate the 

simulated data to the actual data. This is particularly problematic for cross-brand effects. 

Calibration of the simulated data requires knowledge of the joint distribution of each brand’s 

promotions across stores, information which is not contained in aggregate-level scanner datasets. 

The de-biasing procedure may not entirely eliminate aggregation bias, and if done poorly, could 

exacerbate the problem. 
- 8 - 

A number of authors have analyzed the impact of aggregation bias in the following 

manner (Allenby and Rossi 1991, Christen et al. 1997, Chung and Kaiser 2000, Krishnamurthi et 

al. 2000). First, a store- or consumer-level model of demand is posited to be the true demand 

specification. The aggregate-level model is then obtained by adding up demand across each 

store (or individual). This specification is then compared to an alternative aggregate-level model 

to assess whether the latter is biased relative to actual aggregate demand. A commonly 

employed choice for the alternative model is the store-level model evaluated at the average value 

of each store-level variable. While this approach has been broadly employed to demonstrate the 

presence of aggregation bias, it can also be used to directly formulate an aggregate-level model 

of demand. Rather than addressing whether an alternative model is biased, one can simply 

estimate the aggregate-level model implied by the store-level model (Stoker 1993). While 

conceptually straightforward, data limitations complicate the estimation of the aggregate model. 

The following section presents an aggregate demand model that is based on this approach, and 

which is estimable with retailer-level scanner data. 

III. Econometric Demand Model 

This section develops a general demand specification that is consistently estimated with 

city specific, retailer-level data. First, a store-level model of demand is presented. This 

framework is then aggregated to the retailer-level, so that it can be feasibly estimated. 

Store-Level Model

 Each store s within a retail chain sells a set of brands B, with the total measure of stores 

normalized to one.4

 Denote the marketing activity of brand i, in store s, at time t, by mist ∈ M . 

Typical examples of marketing activity are “No Promotion,” “Feature,” “Display,” and “Feature 

 4

 The model assumes brands are composed of a single product. This is relaxed in the empirical example 

presented in section four, which controls for the number of different products contained within each brand (e.g., 

distinct flavors). 
- 9 - 

& Display.”5

 The set consisting of each brand’s marketing activity is denoted by 

st mist i B g = { , with } ∈ gst ∈G . For example, if M contains four types of marketing activity and 

B contains two brands, then G consists of 16 pairs of marketing activity. Similarly, the set of 

prices across all brands is defined as st ist i B p = { . Store-level unit sales p } ∈ ist q is determined 

by demand specification d, which is a function of price st p , promotional activity st g , and a 

vector i δ of demand parameters:6

(3.1) ) ( , ; ist st st i q = d p g δ . 

Retailer-Level Model

 Without store-level data, one cannot directly estimate model (3.1). Rather, one must 

aggregate the model to the level of the available data. For each g ∈G , let π gt denote the 

fraction of stores with said marketing activity. To facilitate aggregation, assume that an identical 

price is charged at all stores with the same promotional activity for a given brand: 

(3.2) p p s mist m m

ist = it , . ∀ : =

Note that price homogeneity is only required across stores within a given retail chain. Price 

homogeneity across retail chains is not a model requirement. 

Denote the vector of cross-brand prices that corresponds to each g ∈G by g

t p . Further, 

let ) m (g i be the element of g corresponding to brand i. Model (3.1) implies that total unit sales 

for brand i, across stores with marketing activity m, can be written as follows: 

(3.3) ( , ; )

: ( )

i

g

t

g G mi g m

gt

m

it q ∑π d p g δ

∈ =

= . 

 5

 A “Feature” is typically defined as an advertisement in a promotional circular. A “Display” is a 

secondary sales location within a store which is used to draw special attention to a given product. 

6

 The model can accommodate additional control variables. The empirical application of section four 

provides such an example. 
- 10 - 

 Model (3.3) defines average quantity sold m

it q as a function of each brand’s price and 

marketing activity. Econometric models of demand account for deviations from expected sales 

through the use of an error term. A straightforward approach is to assume that the model can be 

written as follows, for a given function f, where m

it q denotes actual quantity sold: 

(3.4) m

it

m

it

m

it f ( . q ) = f (q ) + ε

Although a standard assumption for the error term is ) ~ (0, 2

i

mε it N σ , one can estimate the 

model using any distribution. If store-level demand is linear, then an obvious choice for f is the 

identity function ( f (x) = x) . When store-level demand takes the constant elasticity form, one 

would likely choose f to be the natural log function ( f (x) = ln x) . Under these specifications for 

f, the error term enters model (3.4) in an analogous manner to the error term in the linear and 

constant elasticity specifications. 

Homogeneity Assumptions

 A key model requirement is pricing assumption (3.2). The empirical validity of price 

homogeneity, conditional on a given level of marketing activity, will depend on the application 

at hand. A potential violation is when a retailer employs more than one price zone within a city. 

For example, Hoch et al. (1995) report that the Dominick’s supermarket chain in Chicago uses 

multiple price zones. 

The model also assumes that stores have the same demand specification. Since a store 

can be defined in terms of “store-equivalent units,” stores are allowed to differ in size so long as 

demand for all products uniformly scales up or down. For instance, if a store sells twice as much 

of each brand as the others, it can simply be viewed as two separate stores without violating the 

model assumptions. 

Whether one can reasonably assume parameter homogeneity across stores is potentially 

problematic (Boatwright et al. 2001). However, research concerning the use of pooled datasets 
- 11 - 

concludes that a violation of parameter homogeneity is not overly troublesome so long as the 

condition is close to being satisfied (Wallace 1972, Bass and Wittink 1975). 

Data Requirements

 The data used to estimate model (3.3) must meet several key requirements. Importantly, 

the dataset must separately provide price and unit sales for each brand by each type of marketing 

activity. Retailer-level scanner datasets typically report unit and dollar sales by promotion, 

where the set of marketing activity M contains four elements: “No Promotion,” “Feature,” 

“Display,” and “Feature & Display.” One can calculate price m

it p as dollar sales for promotion 

m divided by unit sales. Note that equation (3.2) implies that the use of volume-weighted 

average price will not result in specification error, since prices are homogeneous across stores 

with a given level of marketing activity. 

 Through a variable known as “All Commodity Volume,” or ACV, scanner datasets 

include an empirical proxy for the fraction of stores in which a brand has a given level of 

promotional activity. A product’s ACV is the percentage of total sales, across all product 

categories, which are accounted for by the stores that carry that product. Similarly, the ACV for 

a given level of promotion is the fraction of all category sales that are accounted for by those 

stores where the brand has said promotional activity. The ACV for each level of promotion can 

be used as an empirical counterpart to m π it , the fraction of stores in which a brand has marketing 

activity m. However, scanner datasets do not directly report {π gt}g∈G , which is the joint 

distribution of each brand’s marketing activity across stores. This data deficiency can be 

overcome by postulating that the joint distribution of marketing activity is a function h of the 

distribution of each brand’s promotions: 

(3.5) ) {π } ({π } ;θ

m M

i B

m

gt g G it h

∈

∈ = ∈ . 

Parameter θ is included in the model specification, and allows the joint distribution of marketing 

activity to be flexibly estimated. Alternatively, one can assume that each brand’s promotions are 
- 12 - 

independently distributed. Doing so eliminates the need for θ , since ∏

∈

=

i B

g mi

gt it

( ) π π does not 

require any parameterization. 

Model Estimation

The specification detailed above provides sufficient structure to estimate the model with 

retailer-level scanner data. Given a store-level demand function d, a function h that calculates 

the joint distribution of each brand’s promotions across stores, and a function f that details how 

the econometric error term enters the demand equation, one can estimate the model parameters 

{{ , } , } 2 δ σ θ i i i∈B via maximum likelihood. An important property of maximum likelihood is 

that under standard conditions, it provides a consistent estimate of the model parameters (Greene 

1997). An example of such estimation is provided in the following section. 

IV. Empirical Application 

 The econometric model developed in the previous section is used to estimate the demand 

for premium ice-cream. The dataset employed is described below. Details concerning 

functional form assumptions and estimation technique are then provided. This is followed by a 

presentation of the results. 

Data Description

 The analysis utilizes retailer-level supermarket scanner data corresponding to AC 

Nielsen’s “premium ice-cream” category. The dataset includes two of the five largest brands of 

premium ice-cream. Sales data for each brand is separately reported for four types of 

promotional activity: “No Promotion,” “Feature,” “Display,” and “Feature & Display.” A 

confidentiality agreement with AC Nielsen prevents brand or retailer names from being revealed. 

Henceforth, the two brands are referred to as “Brand A” and “Brand B.” The dataset includes 

weekly scanner data for ten retailer-city combinations, covering the period December 1998 
- 13 - 

through June 2001 (132 weeks). Since premium ice-cream is predominantly sold in a half-gallon 

container, the dataset is restricted to items of that size. This limits potential bias when 

calculating the average price across SKUs, since each brand’s ice-cream flavors for a given 

container size are line-priced. 

Model Specification

A widely employed specification for store-level demand is the model presented in 

Wittink et al. (1988), where ist q is the unit sales, ist p is the price, and mist is the marketing 

activity of brand i, and where m Zit is a set of additional control variables:7

(4.1) i

mist

it

j M B m

ij m jst m

j B

qist = μi + ∑αij p jst + ∑ ∑ γ + Z β

∈ ∈

=

∈

( ) ln . ln 1

This specification is relatively inflexible in how promotional activity affects unit sales. 

Promotions impact the intercept of the demand curve, but do not alter own- and cross-price 

elasticities. 

 An alternative approach is to let the model parameters vary by the promotional activity of 

each brand. As before, gst ∈G denotes the set consisting of each brand’s marketing activity. 

Since there are two brands and four distinct types of marketing activity m, the set G contains 16 

pairs of marketing activity. A generalization of (4.1) is the following specification: 

(4.2) i

mist

it

j B

jst

st g

ij

st g

ist i q = μ + ∑α p + Z β

∈

ln . ln

Each g ∈G has its own set of model parameters } { , g

ij

g

i μ α . This allows promotions to impact 

product demand in a flexible manner. The disadvantage of this specification is that a large 

number of parameters must be estimated. As is typical, there is a trade-off between model 

flexibility and model precision (Greene 1997). Too restrictive a model can lead to 

 

7

 In order for the model to aggregate to the retailer-level, the set of controls m Zit cannot vary by individual 

store s. 
- 14 - 

misspecification and bias, while excessive flexibility leads to parameter estimates that are too 

imprecise to be informative. 

 As a balance between these two factors, the empirical analysis employs a model that is 

less restrictive than (4.1), but has far fewer parameters than (4.2). This is accomplished by 

employing a set of parameter restrictions: 

(4.3) 

, , , s.t. .

, , ( )

g G i j B i j

g G i B

g

ij jj

g

ij

mi g

ii

g

ii

= ∀ ∈ ∀ ∈ ≠

= ∀ ∈ ∀ ∈

α α α

α α

The first restriction requires that own-price elasticities only vary by a brand’s promotional 

activity. This restriction assumes that a brand’s own promotions dominate consumer response to 

changes in its price, rather than the promotions of competing products. The second restriction 

implies that any two price changes by brand j that have the same effect on brand j’s sales, also 

have the same impact on brand i’s sales. Suppose a 10% price increase leads to a 20% sales 

decrease for brand j when it is not on promotion, but only a 10% decrease when brand j is on 

“Feature.” Since the fraction of consumers that discontinue their purchases in response to the 

price increase is twice as large when brand j is not on promotion, the second restriction implies 

that the percentage sales increase for brand i is also twice as large. Through these restrictions, 

the model produces relatively precise estimates while still remaining quite flexible.8

 One must make additional assumptions regarding the specification of the econometric 

error term. It is assumed that m

it ε is i.i.d Normally distributed. The variance of the error term is 

allowed to differ by a brand’s own marketing activity: ) ~ (0, 2

im

mε it N σ . Additionally, the 

 8

 An attempt was made to test whether restrictions (4.3) hold in this empirical application. The LikelihoodRatio test did not reject these restrictions. However, this test is statistically valid only under the assumption of an 

i.i.d error term. As discussed below, the estimation procedure allows for a general serially correlated error process. 

One can test the validity of restrictions (4.3) under this error structure by estimating the model without imposing the 

restrictions, and then employing a Wald test. Doing so requires an estimate of the variance matrix for the parameter 

estimates. For this empirical application, the estimated standard errors for the unrestricted parameters are 

implausibly small. This commonly occurs when one employs variance estimates that are only asymptotically valid 

in situations where certain parameters are identified by a small number of observations, as is the case for the 

unrestricted model. Since restrictions (4.3) cannot be formally tested, little can be said regarding their validity. 
- 15 - 

function f that determines how the error term enters the demand specification is chosen to be the 

natural log function: ) f (x) = ln(x . This specification allows the error term to enter the demand 

specification in a manner analogous to the error term in the constant elasticity model. 

The parameterization of the error term assumes that there is no serial correlation. This 

assumption is a result of the dataset being an unbalanced panel of observations. The number of 

observations, for a given retailer in a given week, depends on how many different types of 

promotions have positive sales. This number ranges from between one observation (“No 

Promotion” only), to up to four observations (“No Promotion,” “Feature,” “Display,” and 

“Feature & Display”). An unbalanced panel makes it difficult to formulate a sensible 

characterization of a serially correlated error process. However, as detailed in the following 

subsection, the standard errors of the parameter estimates are adjusted so as to correct for a 

general form of serial correlation. 

 These assumptions lead to the following retailer-level demand specification, subject to 

the constraints embodied in equation (4.3): 

(4.4) 

where , and ~ (0, ).

ln( ) ln( ( ) ) ln( )

2

: ( )

( ln )

: ( )

im

m

it

g G mi g m

gt

m

it

m

i it

m

it

m

it j B

g

jt p g

ij

g

i

g G mi g m

m

it

m gt

it

N

q e Z

π π ε σ

π β ε

π

π μ α

∑

∑

∈ =

∑

∈

+

∈ =

=

= + + +

The first term is the log of the weighted average of unit sales across each set of promotional 

activity g. The subsequent term proportionally scales up unit sales by each brand’s distribution 

m π it . The homogeneity assumptions of section three imply that this variable exhibits constant 

returns to scale, as seen by its unit coefficient. This is relaxed by including ) ln( m π it as one of the 

variables in mZit (see below). One can thereby test whether distribution exhibits constant returns, 

rather than simply asserting unit elasticity of distribution. 
- 16 - 

 The variable m π it is empirically measured as the fraction of each brand’s “Total 

Distribution Points,” or TDP. That is, 

∑

∈

=

m M

m

it

m

m it

it

TDP

TDP

~

π ~ . The variable m TDPit is the sum, across 

all SKUs, of brand i’s ACV at time t that has promotional activity equal to m. TDP is an overall 

measure of product distribution, incorporating both the breadth and depth of a brand’s 

availability. For example, a TDP of 300% is the distribution equivalent of a brand having three 

SKUs distributed at every store. 

 To fully specify the model, one must choose a particular function h to use in equation 

(3.5). Recall that this function specifies the cross-brand distribution of promotions, {π gt}g∈G , 

as a function of the univariate distribution of promotions for each brand, 

m M

i B

m

it

∈

{π } ∈ . One 

possibility in defining h is to assume that promotions are independently distributed across the 

two brands. To allow for greater flexibility, the following approach is taken instead.9

 Denote 

the fraction of stores in which brand i is being promoted (“Feature,” “Display,” or “Feature & 

Display”) by π it

~ . Since probabilities are restricted to [0,1], the probability that Brand A and 

Brand B are both on promotion in a given store must be between ] ~, ~[ min max π t π t , where 

1) ~ ~ max(0, ~ Brand A,t Brand B,t

min π t = π +π − and ) ~, ~ min( ~ Brand A, Brand B,max π t = π t π t . One can then 

specify the probability that both brands are simultaneously on promotion in a given store by 

, min ~max (1 ) ~

t t

p p

t π =θπ + −θ π , where θ is a model parameter that takes a value between zero and 

one. The probability that Brand A is on promotion, but Brand B is not, is equal to 

p p

t

p

t

p np

t ,

Brand A,

, π = π −π . Similarly, the probability that only Brand B is on promotion is 

p p

t

p

t

np p

t ,

Brand B,

, π = π −π . The probability that neither brand is on promotion is given by 

np p

t

p np

t

p p

t

np np

t , , , , π = 1−π −π −π . To complete the specification, it is assumed that 

conditional on whether Brand A and Brand B are each on promotion the particular type of 

promotion is independently distributed. 

 9

 Strictly speaking, this approach is not “more general” since the former is not nested within it. 
- 17 - 

 The estimation procedure employs several additional control variables. For each brand, a 

set of time and retailer-city fixed effects is included in the specification.10 As mentioned above, 

ln( ) m TDPit is also included as a control variable. This variable is a measure of each brand’s 

retail distribution at those stores where it has promotional activity m. 

Estimation

 All parameters from the eight equations of the model are jointly estimated via maximum 

likelihood (four types of promotion multiplied by two brands). As detailed above, the error 

structure assumes that m

it ε is i.i.d Normally distributed. After obtaining the maximum likelihood 

estimates through the usual means, possible correlation between error terms is accounted for 

when the variance matrix of the parameter estimates is calculated. This adjustment is known as 

“Quasi Maximum Likelihood Estimation,” or QMLE (White 1982, Hamilton 1994).11 A NeweyWest (1987) assumption on the error structure is employed, with a maximum lag difference of 

four weeks. That is, any two residuals that are from time periods within four weeks of each other 

are allowed to be arbitrarily correlated.12 Robustness checks indicated that the estimated 

standard errors are not sensitive to the particular choice of how many time lags are allowed for. 

By constructing the variance matrix in this manner, robust standard errors are obtained without 

having to specify a particular process for the model’s error structure. 

 10 The inclusion of time fixed effects eliminates seasonal variation from the data. Due to a lack of 

instruments for price, it is important to do so to remove endogenous price variation related to seasonal demand 

changes. 

11 This is a special case of “Generalized Method of Moments,” or GMM, estimation (Hansen 1982). The 

first order conditions from the log-likelihood function are used as moment conditions. 

12 The model “residual” is the gradient of the portion of the log-likelihood function that corresponds to a 

given observation. 
- 18 - 

Results

 The remainder of this section details the results from estimating the model. To introduce 

the data, Table 1 presents the fraction of unit sales, revenue, and “Total Distribution Points” 

(TDP) that is accounted for by each type of promotion.13 These percentages are calculated from 

variable totals for each retailer-city combination. The reported statistics are un-weighted 

averages across the 10 retailer-city combinations. 

Promotions clearly play a significant role in the marketing of both brands. 

Approximately one half of unit sales are sold on promotion, with a “Feature” being the most 

common type of promotion. Unit sales are high, relative to distribution, for each level of 

promotional activity other than “No Promotion.” This is potentially due to several distinct 

effects. First, promotions lead to an upward shift in the demand curve for a given brand. 

Promotional activity in the ice-cream category is also typically associated with a price reduction, 

which itself leads to increased sales (i.e., movement down the demand curve). In addition, 

promotions most often occur in the summertime, which is when demand for ice-cream is highest. 

See Blattberg et al. (1995) for a review of the empirical literature that considers the effect of 

promotions. 

The price distribution for each type of promotional activity is reported in Table 2. Each 

retailer-city / week combination is given equal weight when constructing this distribution. For 

each retailer, all prices are re-scaled so that the modal price when not on promotion equals $1.00. 

This transformation is used throughout this section to disguise the identity of each brand. On 

average, each brand’s price is substantially lower when on promotion, particularly when on 

“Feature” or “Feature & Display.” It is quite common for a promotional price cut to be 50% or 

more. Each brand is sometimes promoted with only a small price reduction, however. Thus, 

there is substantial price heterogeneity within each type of promotional activity. This allows the 

 13 A confidentiality agreement with AC Nielsen prevents other summary statistics from being presented. 
- 19 - 

impact of promotions that are supported by a major price reduction to be separately identified 

from the impact of promotions that are not (see below). 

 Table 3 reports summary statistics from the estimation procedure. For both brands, the 

variance of log unit sales is highest when each brand is on “Display.” This potentially indicates 

that there is substantial heterogeneity in the quality of displays. While an end-of-aisle display 

may have a significant impact on sales, a display in a less attractive location likely has a much 

smaller effect. The low variance of log unit sales when on “Feature & Display” suggests that 

featured displays are uniformly high quality. This is consistent with the expectation that heavily 

promoted products receive a premier location within a store. 

 The model provides an estimate of the joint distribution of promotions across the two 

brands, which is presented in Table 4A. On average, neither brand is on promotion in 62% of 

stores. It is relatively common for one brand to be on “Feature” when the other brand is not 

being promoted. Rarely, however, are both brands simultaneously on promotion in a given store. 

For each month, Table 4B reports the fraction of stores that simultaneously promote both brands. 

As expected, retailers are relatively likely to do so in the summertime. In particular, 

simultaneous promotions are more likely to occur in August than in any other month. 

 Table 5 reports the impact of each brand’s distribution level (TDP). The estimates 

indicate that distribution has a highly significant effect on unit sales. For Brand A, a 1% increase 

in distribution leads to a .99% increase in sales (se=.03%). That is, distribution is (nearly) 

constant returns to scale for this brand. Although statistically distinct from one at conventional 

levels, the distribution elasticity of Brand B is close to constant returns to scale. A 1% 

distribution increase for Brand B leads to a .90% increase in unit sales (se=.04%). Note that each 

brand’s level of distribution is determined by the number of flavors that a supermarket carries for 

that brand. These results indicate that expanded distribution of an ice-cream flavor leads to a 

significant increase in brand sales, rather than simply a cannibalization of a brand’s other SKUs. 

This is consistent with previous research that documents the sales expansion effects of lineextensions (Reddy and Holak 1994, Lomax and McWilliam 2001). 
- 20 - 

 Next, consider the impact of each brand’s promotional activity on its own sales. To 

separate the direct effect of promotional activity from that of a promotional price decrease, Table 

6 presents the impact of a promotion that is not accompanied by any price change. Parameter 

estimates from the demand model are used to predict the percentage change in unit sales from a 

promotion, relative to “No Promotion,” while holding price constant at $.80. This is at the lower 

end of the price distribution when each brand is not on promotion, and is at the upper end of the 

distribution when each brand is being promoted (see Table 2). 

Promotions generally have a significant impact on each brand’s sales, even when not 

accompanied by a price reduction. The exception is when Brand B is on “Display,” which has a 

statistically insignificant effect of only -1.2% (se=15.0%). This contrasts with a 52% sales 

increase when Brand A is on “Display” (se=10.9%). Brand A’s price on “Display” is typically 

one half of its non-promoted price. Brand B is most commonly displayed without any price 

reduction (see Table 2). Since they are more often associated with significant price cuts, Brand 

A’s displays may be of higher quality (e.g., end-of-aisle). This potentially explains why the 

impact of a display for Brand B is much smaller. 

 The parameter estimates from the demand model are used to predict the impact of a 

competing brand having a “Feature,” relative to not having a promotion.14 As before, each 

brand’s price is held constant at $.80 when making these calculations. The results shown in 

Table 7 indicate that a “Feature” by one brand has little effect on the sales of the other when it is 

not on promotion. For example, when Brand A is not on promotion, its sales are reduced by only 

2% (se=4.7%) when Brand B changes from “No Promotion” to being on “Feature.” When both 

brands are simultaneously on promotion, however, each brand’s promotions generally have a 

negative impact on the other. When Brand A is on “Feature”, its sales fall by 36.9% (se=12.4%) 

when Brand B’s promotional activity changes from “No Promotion” to “Feature.” These results 

 14 The cross-brand impact of other types of promotions is imprecisely estimated. This is a result of 

“Display” and “Feature & Display” occurring far less frequently than a “Feature.” 
- 21 - 

indicate that although a brand’s own promotional activity draws in additional consumers, a 

competing promotion takes away much of the increase.15 This likely explains why retailers 

rarely promote Brand A and Brand B at the same time (see Table 4). Note, however, that not all 

of the cross-brand promotional effects are statistically significant at conventional levels. 

 We know from Table 6 that promotions have a major impact on sales even when not 

accompanied by a price reduction. Table 8 shows that price reductions have a highly significant 

impact as well. For both brands, the own-price elasticity when not on promotion is 

approximately -2. Each brand’s own-price elasticity on “Display” is a less elastic -1.4. The 

results for “Feature” and “Feature & Display” differ by brand. Brand B has elastic demand 

during these promotions (-2.1 and -2.3, respectively), while Brand A’s own-price elasticity is 

significantly smaller in magnitude (-1.5 and -1.3, respectively). Previous research offers mixed 

evidence concerning the relative magnitudes of promotional and non-promotional price 

elasticities (Guadagni and Little 1983, Lattin and Bucklin 1989, Mulhern and Leone 1991). 

Understanding their general relationship is an area that deserves additional attention (Blattberg et 

al. 1995, Bucklin and Gupta 1999). 

 Table 9 presents the effect of a price reduction by the competing brand. The results 

reveal substantial cross-price elasticities, with a price reduction in one brand leading to a 

substantial sales decline for the other. The cross-price elasticities vary between .17 and .43, 

depending on the competing brand’s promotional activity. This corroborates the findings 

presented in Table 7, which indicate that Brand A and Brand B are substitutes for each other. 

 Tables 10 and 11 summarize each brand’s demand curve as a function of its price and 

promotional activity. Each brand’s demand curve is constructed under the assumption that the 

other brand is not on promotion. The demand curve for each level of promotional activity is 

shown for prices between the 10th and 90th percentile of the distribution for each type of 

 15 See Van Heerde et al. (2003) for a decomposition of promotional effects according to cross-brand 

substitution, cross-period substitution, and category expansion effects. 
- 22 - 

promotion (see Table 2). For confidentially reasons, unit sales are normalized to one when each 

brand is not on promotion and has a price of $1.00. These tables clearly demonstrate that 

promotions and price reductions both lead to significantly higher unit sales. For each brand, the 

combination of a 50% price cut and a “Feature & Display” yields sales that are more than six 

times typical sales when not on promotion. 

V. Conclusion 

 Estimating cross-brand promotional effects requires knowledge of the joint distribution of 

each brand’s promotions, but this information is not reported in aggregate-level scanner data. 

We develop a model that overcomes this difficulty under certain conditions, namely parameter 

homogeneity and price homogeneity conditional on a given level of promotional activity. Two 

main factors make this possible. First, the model is consistent with adding up from store-level 

demand. This avoids misspecification due to estimating the “wrong” model. Additionally, the 

proposed framework is described in terms of store-level promotional activity. This is facilitated 

by the development of a technique for estimating the joint distribution of each brand’s 

promotions across stores. These factors allow an internally consistent demand model to be 

estimated with retailer-level scanner data. The model’s usefulness lies in the wide availability of 

such data. When store-level data is unavailable, or too costly to obtain, it provides a practical 

methodology for estimating both own- and cross-brand promotional effects with retailer-level 

scanner data. 

 A major benefit of disaggregate data is its ability to provide insight into how the 

promotional activity of one brand affects another. When store-level data is available, it is 

straightforward to estimate how different combinations of promotions for a given set of brands 

impact consumer demand. Aggregate-level scanner datasets do not contain information 

regarding the joint distribution of promotions, which has hereto precluded estimating cross-brand 

effects with such data. This paper illustrates how to use retailer-level scanner data to estimate 

not only the joint distribution of promotional activity, but also how the distribution of 
- 23 - 

promotions impacts consumer demand for each product. The presented empirical application 

demonstrates how aggregate data can provide useful insights in this respect. For example, the 

results indicate that the impact of a brand’s promotions on a competing product is far greater 

when that product is also on promotion. 

 Estimation of the model with market-level scanner data violates a key model requirement 

that price be homogenous conditional on a given level of promotional activity. Given the lack of 

alternative means for estimating both own- and cross-brand promotional effects with marketlevel data, however, application of the model may prove to be useful. Since price heterogeneity 

is the only assumption that is clearly violated by market-level data, the model should be able to 

provide (nearly) unbiased estimates of promotional effects when the use of volume-weighted 

average price does not significantly contaminate the estimates for the other variables. A 

promising area for future research is to analyze under what circumstances the model provides 

accurate results when estimated with market-level data. 
- 24 - 

Table 1 

Summary Statistics 

Brand A

No 

Promotion Feature Display

Feature & 

Display

% of Unit Sales 57.1% 34.9% 1.9% 6.1%

% of Revenue 67.5% 26.5% 1.5% 4.4%

% of TDP 81.3% 16.6% 0.7% 1.5%

Brand B

No 

Promotion Feature Display

Feature & 

Display

% of Unit Sales 46.6% 43.0% 0.9% 9.4%

% of Revenue 56.3% 35.3% 0.9% 7.5%

% of TDP 74.5% 22.1% 0.5% 2.8%

Notes: N=1,320, corresponding to a panel of 10 retailer-city combinations and 132 weeks. 

Percentages are calculated from variable totals for each retailer-city combination. The reported statistics 

are un-weighted averages across the 10 retailer-city combinations. Each row sums to 100%. 
- 25 - 

Table 2 

Price Distribution by Promotional Activity 

Brand A

No 

Promotion Feature Display

Feature & 

Display

Average 0.95 0.63 0.69 0.57

Mode 1.00 0.50 0.50 0.50

Minimum 0.48 0.30 0.22 0.30

10th Percentile 0.72 0.49 0.50 0.47

25th Percentile 0.95 0.50 0.50 0.50

50th Percentile 1.00 0.60 0.61 0.54

75th Percentile 1.00 0.72 0.83 0.64

90th Percentile 1.03 0.75 1.00 0.75

Maximum 1.19 1.02 1.13 0.83

Number of Obs. 1,279 319 294 211

Brand B

No 

Promotion Feature Display

Feature & 

Display

Average 0.97 0.63 0.85 0.59

Mode 1.00 0.50 1.00 0.50

Minimum 0.47 0.25 0.35 0.25

10th Percentile 0.79 0.47 0.49 0.47

25th Percentile 0.98 0.50 0.69 0.49

50th Percentile 1.00 0.60 0.99 0.60

75th Percentile 1.01 0.75 1.01 0.67

90th Percentile 1.05 0.76 1.05 0.75

Maximum 1.13 1.03 1.12 1.04

Number of Obs. 1,090 338 244 254

Notes: Brand A has 2,103 observations across all types of promotions. Brand B has 1,926 

observations. For each retailer-city combination, the modal price of each brand when not on promotion 

is normalized to $1.00. 
- 26 - 

Table 3 

Estimation Summary 

Brand A Brand B

Number of Obs. 2,103 1,926

Number of 

Est. Parameters

Root MSE 

by Promotion:

0.37 0.35

(0.02) (0.03)

0.42 0.51

(0.03) (0.04)

0.62 0.70

(0.03) (0.04)

0.45 0.46

(0.03) (0.04)

333

No 

Promotion

Feature &

 Display

Feature

Display

Notes: Standard errors are reported in parentheses. 
- 27 - 

Table 4A 

Joint Distribution of Promotional Activity 

Brand B Promotional Activity

No 

Promotion Feature Display

Feature & 

Display Total

No 

Promotion 61.8% 18.4% 0.4% 2.4% 83.0%

Feature 13.0% 1.9% 0.1% 0.2% 15.1%

Display 0.4% 0.1% 0.0% 0.0% 0.6%

Feature &

 Display 1.2% 0.1% 0.0% 0.0% 1.3%

Total 76.4% 20.5% 0.5% 2.6% 100%

Brand A 

Promotional 

Activity

Table 4B 

Average Percentage of Stores that Simultaneously Promote Both Brands 

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

January February March April May June July August September October November December

Notes: The reported statistics in Table 4A are un-weighted percentages across the 10 retailer-city 

combinations and 132 weeks. Table 4B reports un-weighted average percentages across retailer-city 

combinations for those weeks contained within each month. 
- 28 - 

Table 5 

Distribution Elasticity 

Brand A Brand B

0.99 0.90

(0.03) (0.04)

Notes: Standard errors are reported in parentheses. 
- 29 - 

Table 6 

Impact of Own-Brand Promotional Activity, 

Relative to “No Promotion” 

Own-Promotion Brand A Brand B

Feature 21.8% 22.0%

(5.1%) (5.2%)

Display 52.3% -1.2%

(10.9%) (15.0%)

80.1% 38.1%

(9.6%) (11.7%)

Feature & 

Display

Notes: Each estimate is the predicted percentage change in unit sales from a brand’s own 

promotional activity, relative to “No Promotion.” The other brand’s promotional activity is held 

constant at “No Promotion.” All estimates assume a price of $.80 for each brand. Standard errors are 

reported in parentheses. 
- 30 - 

Table 7 

Impact of a “Feature” Promotion by the Competing Brand, 

Relative to “No Promotion” 

Own-Promotion Brand A Brand B

-2.0% 5.8%

(4.7%) (6.1%)

Feature -36.9% -41.5%

(12.4%) (14.8%)

Display -27.9% 7.6%

(15.5%) (13.1%)

-14.9% -36.5%

(13.4%) (18.5%)

Feature & 

Display

No 

Promotion

Notes: The first column reports the effect on Brand A’s unit sales from Brand B having a “Feature,” 

relative to “No Promotion,” as a function of Brand A’s own promotional activity. The second column 

reports counterpart results for the effect of a “Feature” by Brand A on Brand B’s unit sales. All 

estimates assume a price of $.80 for each brand. Standard errors are reported in parentheses.
- 31 - 

Table 8 

Own-Price Elasticity by Own-Brand Promotional Activity 

Own-Promotion Brand A Brand B

-1.92 -2.01

(0.10) (0.15)

Feature -1.53 -2.11

(0.16) (0.19)

Display -1.40 -1.38

(0.19) (0.25)

-1.31 -2.28

(0.22) (0.22)

Feature & 

Display

No 

Promotion

Notes: Standard errors are reported in parentheses. 
- 32 - 

Table 9 

Cross-Price Elasticity by Competing Brand Promotional Activity 

Cross-Promotion Brand A Brand B

0.25 0.43

(0.09) (0.12)

Feature 0.27 0.34

(0.09) (0.10)

Display 0.17 0.31

(0.07) (0.09)

0.29 0.29

(0.10) (0.09)

No 

Promotion

Feature & 

Display

Notes: The first column reports the cross-price elasticity of Brand A with respect to a price increase 

in Brand B, as a function of Brand B’s promotional activity. Column two reports the cross-price 

elasticity for Brand B. Standard errors are reported in parentheses. 
- 33 - 

Table 10 

Brand A Demand Curves 

01234567

0.49 0.52 0.55 0.58 0.60 0.63 0.66 0.69 0.72 0.75 0.78 0.81 0.84 0.87 0.90 0.93 0.95 0.98 1.01 1.04

relative price

relative quantity

No Promotion Feature Display Feature & Display

Notes: All prices are rescaled so that the modal price when not on promotion equals $1.00. Unit sales when not o

promotion, and when the price is $1.00, are normalized to one. The demand curve for each level of promotional activshown for prices between the 10th and 90th percentile for each type of promotion (see Table 2). The promotional activ

Brand B is held constant at “No Promotion.” 
- 34 - 

Table 11 

Brand B Demand Curves 

01234567

0.49 0.52 0.55 0.58 0.60 0.63 0.66 0.69 0.72 0.75 0.78 0.81 0.84 0.87 0.90 0.93 0.95 0.98 1.01 1.04

relative price

relative quantity

No Promotion Feature Display Feature & Display

Notes: All prices are rescaled so that the modal price when not on promotion equals $1.00. Unit sales when not o

promotion, and when the price is $1.00, are normalized to one. The demand curve for each level of promotional activshown for prices between the 10th and 90th percentile for each type of promotion (see Table 2). The promotional activ

Brand A is held constant at “No Promotion.” 
- 35 - 

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