WORKING 

 PAPERS

Biases in Demand Analysis Due 

to Variation in Retail Distribution

Steven Tenn

John M. Yun

WORKING PAPER NO. 287

February 2007

___________________________________________________________________________

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author to protect the tentative character of these papers.

______________________________________________________________________________

BUREAU OF ECONOMICS

FEDERAL TRADE COMMISSION

WASHINGTON, DC 20580
Biases in Demand Analysis Due to Variation in Retail Distribution 

Steven Tenn*

Federal Trade Commission 

and 

John M. Yun 

Federal Trade Commission 

First Version: September 2003 

Current Version: February 2007

 

* Contact information for Steven Tenn (contact author): Federal Trade Commission, 600 Pennsylvania Avenue NW, 

Washington, DC 20580; phone: (202) 326-3243; fax: (202) 326-3443; and email: stenn@ftc.gov. We thank Chris 

Adams, Luke Froeb, Hajime Hadeishi, Daniel Hosken, Sam Peltzman, David Schmidt, Lawrence White, and 

participants of the EU/US Economic Workshop, the International Industrial Organization Conference, and the 

Federal Trade Commission seminar series. This paper does not necessarily reflect the views of the Federal Trade 

Commission or any individual commissioner. 
Biases in Demand Analysis Due to Variation in Retail Distribution 

Abstract 

 Aggregate demand models typically assume that consumers choose between all available 

products. Since consumers may be unwilling to search across every store in a given market for a 

particular item, this assumption is problematic when product assortments vary across stores. 

Using supermarket scanner data for five product categories we demonstrate that approximately 

one third of products have limited retail distribution, which account for one fourth of dollar sales. 

Monte Carlo analysis demonstrates that the level of limited product availability observed in the 

data can significantly bias the results of aggregate demand models that incorrectly assume all 

consumers in a given market face the same choice set. 

Keywords: retail distribution, demand estimation 
1 Introduction 

 Retail distribution is a requirement for retail sales. One would therefore expect demand 

studies to account for product availability in a careful manner. In practice, however, the role of 

retail distribution is implicitly determined by the level of data aggregation employed. Demand 

studies based on store-level data typically assume consumers limit their purchases to products 

available at a particular store. Previous research suggests this is a reasonable approximation for 

certain types of goods, such as grocery products (Rhee and Bell 2002). This highlights a 

potential problem in demand analyses that use regionally or nationally aggregated data, since 

they make the opposite assumption.1 Such studies assume consumers freely choose between all 

products available in a given market, even items carried by very few stores. They ignore search 

and transportation costs that may lead consumers to limit their choice sets to a subset of the 

available items. 

 The following example illustrates why this approach is potentially problematic. In 2000, 

the Federal Trade Commission (FTC) challenged the acquisition of Beech-Nut Nutrition 

Corporation by H.J. Heinz Company, both manufacturers of baby food. The district court judge 

noted that “nearly all supermarkets stock only two brands of baby food, not three...Gerber is 

invariably one of the two.”2 The fraction of stores that carried Gerber, Heinz, and Beech-Nut 

was approximately 100%, 40%, and 45%, respectively.3 Standard aggregate demand models 

would fail to control for this distribution pattern if consumers primarily substitute between 

products available at the same store. One would expect estimated cross-price elasticities 

between Heinz and Beech-Nut to be close to zero not because consumers are necessarily 

unwilling to substitute between them, but because few consumers visit stores where both are 

available. 

 1

 Throughout the paper, “aggregate data” refers to when sales from multiple stores are combined. 

2 FTC v. H. J. Heinz Co., 116 F. Supp. 2d (D.D.C. 2000) at 193. 

3 Id. at 194. 

1
 Our objective is to measure how frequently this problem occurs. The relevant issue is not 

whether a product is available, but rather to what extent it is available. Looking at five grocery 

categories, we show that far more products have limited distribution than one might expect given 

how little attention this issue has received in the demand estimation literature. While the baby 

food example is atypical, our results suggest that a more subtle form of this problem commonly 

occurs. Through Monte Carlo analysis, we show that typical levels of limited product 

availability can significantly bias the results of aggregate demand models that ignore product 

assortment heterogeneity across stores. 

 We conclude by exploring why products have limited retail distribution. As expected, 

many such items are niche products with de minimus sales. However, products with 

intermediate levels of retail distribution account for approximately 25% of total sales, which is a 

non-trivial amount.4 We highlight several reasons why this is the case. First, even though stores 

generally carry the same product lines, they select different assortments of product varieties from 

them. Second, it often takes many weeks for a retail-chain to introduce a new item across its 

stores. Lastly, even top-selling items have occasional stock-outs. 

 The paper is organized as follows. Section 2 reviews the literature on retail distribution 

and discusses how demand studies account for product availability. Section 3 describes the 

dataset employed. Section 4 demonstrates that many products have limited retail distribution, 

and section 5 considers the implications of this finding for demand analysis. Section 6 explores 

why limited product availability occurs. Section 7 concludes. 

2 Literature Review 

 Researchers widely recognize the importance of retail distribution. This is most evident 

in the vertical control literature, where the underlying maxim is that manufacturers require retail 

 4

 We define retail distribution as “intermediate” if a product is available at 50% to 90% of stores. See 

section 4 for further details. 

2
distribution to sell their products.5

 The search cost literature also highlights the importance of 

retail distribution. Rhee and Bell (2002) show that, over extended periods of time, consumers 

make the vast majority of their grocery purchases at a single store. Kumar and Leone (1988), 

Bucklin and Lattin (1992), and Pesendorfer (2002) look at whether promotions persuade 

consumers to switch grocery stores. Although there is some evidence of inter-store substitution, 

these studies suggest that consumers largely restrict their grocery purchases to those items 

available at a single retailer. 

 A number of marketing studies explicitly focus on retail distribution. Farris et al. (1989), 

Reibstein and Farris (1995), and Bronnenberg et al. (2000) analyze the relationship between 

distribution and market share. Cotterill et al. (2000) do the same for private label products. 

Olver and Farris (1989) consider distribution in the context of push and pull marketing. Curhan 

(1972) and Drèze et al. (1994) look at how shelf-space allocation affects sales. Draganska and 

Jain (2005) consider the impact of product assortment on the demand for yogurt. Stassen et al. 

(1999) analyze the relationship between product assortment and store choice. Bergen et al. 

(1996) investigate whether product proliferation within brands leads to higher retail distribution. 

 Despite widespread appreciation that retail distribution is a necessary precursor for retail 

sales, product availability plays a surprisingly minor role in demand estimation. One strand of 

the literature uses store-level data to estimate the demand for individual products (e.g., Besanko 

et al. 2003, Chintagunta et al. 2003, Gupta et al. 1996, Hoch et al. 1995). These papers assume 

each consumer visits a single store, and chooses from among the available items. This presumes 

inter-store substitution is sufficiently small that it can be ignored. A benefit of this modeling 

approach is that consumer choice sets are readily observed, since a product is either available in 

a given store, or it is not. 

 5

 Examples include Steiner (1976, 2004) and Villas-Boas (2005) who focus on vertical contracting, while 

Shaffer (1991) and Sullivan (1997) focus on the specific practice of slotting allowances. Asker (2004a, 2004b), 

Brenkers and Verboven (2004), Heide et al. (1998), and Ornstein and Hanssens (1987) examine vertical restraints, 

while Lafontaine (1992), Lafontaine and Slade (1997), and Lafontaine and Shaw (1999) cover franchising. 

3
 Many demand studies, however, rely on data aggregated across multiple retail outlets 

(e.g., all stores in a given city). Examples are Hausman et al. (1994), Hausman and Leonard 

(2002), Berry et al. (1995), Nevo (2001), and Petrin (2002). These analyses assume that 

consumer choice sets include all products available in a given market, even if an item is available 

in only a few stores. The plausibility of this assumption depends on the degree to which stores 

carry different sets of products. Consumers may be unwilling to search across many stores for a 

given item, especially if the search area contains hundreds or thousands of stores (which is often 

the case for regionally or nationally aggregated data). 

 To summarize, product availability plays a very limited role in demand estimation. 

Strong assumptions are made regarding the relationship between product availability and 

consumer choice sets without supporting evidence regarding their plausibility. As illustrated by 

the baby food example described in the introduction, this approach is problematic when there is 

significant heterogeneity in product availability across stores. The objective of this paper is to 

determine whether the degree of limited product availability that typically occurs is sufficient to 

bias significantly the results of aggregate demand models that incorrectly assume all consumers 

face the same choice set. 

3 Data 

 We utilize weekly scanner data provided by ACNielsen that covers five grocery 

categories: frozen novelties, shelf-stable pasta, hot dogs, ice cream, and salad dressing. The data 

reports sales from fourteen retailer-city combinations for the period December 1998 to June 2001 

(132 weeks).6

 For each UPC, the dataset reports dollar and unit sales, and the percentage of 

stores that carry that item. Recognizing that stores significantly vary by size, ACNielsen weights 

each store by its annual dollar sales (across all product categories) when calculating the 

percentage of stores where each product is available. This measure, known as “All Commodity 

 6

 A confidentiality agreement with ACNielsen prohibits retailer names from being revealed. 

4
Volume” (“ACV”), is the standard metric that brand managers and other practitioners use to 

quantify a product’s retail distribution. 

 In addition, the dataset reports the ACV of each product line, which is a collection of 

similar UPCs from the same brand. For example, “Ben & Jerry’s ice cream” and “Ben & Jerry’s 

frozen yogurt” are distinct product lines. A product line’s ACV reports the percentage of stores 

that carry at least one UPC from that line. In section 6, we use this measure to examine whether 

UPCs with limited retail distribution are secondary varieties or package sizes of widely available 

product lines. 

4 The Extent of Retail Distribution 

 Aggregate demand models consider a product “available” if it is sold in at least one store 

in a given market, irrespective of how many stores actually carry the particular item. We employ 

a finer categorization of each product’s availability. UPCs carried by less than 50% of stores are 

defined as having “low availability,” items carried in 50% to 90% of stores have “intermediate 

availability,” and products carried by at least 90% of stores have “wide availability.” Since a 

product’s availability changes over time, we categorize each UPC based on its median retail 

distribution (although in subsequent analysis we consider intertemporal variation in product 

availability). To make our definition comparable to how product availability is defined in 

aggregate demand models, this calculation is separately undertaken for each retailer-city 

combination. That is, the same UPC in a different retailer-city is treated as a distinct product. 

 Table 1 reports the percentage of products and dollar sales represented by each of these 

groups. Widely available products generally comprise less than one quarter of all items. The 

only exception is hot dogs, but even in that category, only 41% of products are widely available. 

Our finding that most products are not widely available may come as a surprise. Prior to 

analyzing the data, the impression from our own shopping experiences was that most items are 

available “everywhere.” While clearly not true, this perception is likely due to the finding, also 

from Table 1, that a majority of each category’s sales is derived from a small set of products that 

5
are widely available. Depending on the category, 62% to 81% of dollar sales come from 

products with a median retail distribution of at least 90% of stores. 

 Our findings indicate that while supermarket chains carry a fairly homogeneous set of 

popular items (i.e., widely available, top-selling items), stores have different assortments of lowselling products. To simplify the analysis, researchers commonly exclude low-selling items 

when estimating demand (e.g., Chintagunta 2002, Nevo and Hatzitaskos 2005). The fact that 

low-selling items often have low product availability is obviously immaterial when such 

products are excluded from the data sample. 

 However, a third set of products with intermediate distribution does pose a problem for 

demand estimation. Unlike products with low availability, this set of items constitutes a 

substantial fraction of dollar sales, 16% to 33% depending on the product category. Moreover, 

they constitute between 19% and 43% of all available products. Items with intermediate product 

availability are too numerous and too large a fraction of total sales to be reasonably ignored in 

demand analyses. However, since such products are not carried by a significant fraction of 

stores, inclusion of these items in aggregate demand models is similarly problematic (as 

demonstrated by the baby food example presented in the introduction). While a simple point, the 

literature has failed to recognize this problem. 

5 Monte Carlo Analysis 

 The previous section demonstrated that many products have limited retail distribution. 

We now explore the implications of this finding, specifically whether aggregate demand models 

that ignore product availability give biased estimates. Due to the difficulty of analytically 

determining the bias from estimating a mis-specified model, we rely upon Monte Carlo analysis. 

 The data used in the Monte Carlo simulations is generated assuming demand is 

determined by a standard logit framework. This specification is chosen for two reasons. First, it 

requires a small number of demand parameters. This is a key consideration when estimating 

demand for a large set of products since other commonly employed specifications, such as the 

6
constant elasticity or AIDS demand models, become unviable when the number of estimation 

parameters becomes too large. 

 A second feature of the logit demand model is that it can be quickly estimated. That is 

important since it is impractical to estimate a computationally burdensome model for a large 

number of Monte Carlo simulations. This requirement excludes the widely employed random 

coefficients logit demand specification (Nevo 2000). The popularity of that framework derives 

from its ability to accommodate more flexible substitution patterns than the standard logit model, 

where consumer substitution is proportional to market share. While the inflexibility of the 

standard logit model is a concern in empirical applications where proportional substitution may 

be violated, it is not a problem here since we generate the data employed in the Monte Carlo 

simulations assuming it is the correct framework.7

 The following details the demand specification employed. There exist markets 

m=1,2,...,M, where each represents a particular retailer-city for a given week. Consumer i in 

market m visits a single store and chooses either from among the products available at that store 

or chooses the “outside good.” We normalize the utility from purchasing the outside good to a 

mean value of zero, U = ω 00 mimi , where ω 0mi is i.i.d. Type I Extreme Value. For the 

remaining items, the utility derived from purchasing product j is a function of observed 

characteristics , unobserved characteristics X jm ε jm distributed i.i.d. , and an 

idiosyncratic stochastic term 

),0( 2 N σ

ωijm that is i.i.d. Type I Extreme Value. 

(5.1) XU β ε ++= ωijmjmjmijm

 The set of observed characteristics includes price and a retailer-city specific 

product fixed effect. We assume these characteristics do not vary across the stores in a given 

X jm

 7

 The problem of ignoring limited product availability when estimating aggregate demand is not specific to 

the logit framework. In a companion paper (Tenn 2006a), we show that very similar results can be obtained for the 

linear demand model (which, unlike the logit, accommodates flexible substitution patterns). Namely, cross-price 

elasticities are biased towards zero in the linear demand model when limited retail distribution is ignored. The 

extent of the bias depends on the probability a store carries one product conditional on it carrying the other. 

7
market. This precludes the possibility that each store charges a different price. Researchers 

routinely invoke this assumption when estimating demand using aggregate data (e.g., Nevo 2001, 

Hausman and Leonard 2002). They do so because aggregate datasets do not report store-level 

prices. We similarly maintain this assumption since its possible violation is tangential to our 

analysis of whether ignoring limited product availability leads to biased estimates.8

 Each market is composed of stores s=1,2,...,S, with each consumer randomly choosing to 

shop at a particular store. Stores vary solely with respect to the set of products, , that 

each carries. Let denote an indicator variable for whether product j is available in store s

in market m. The functional form assumptions provided above imply that product j’s market 

share 

mms ⊆ JJ

jms A

π jm is as follows. 

(5.2) = ∑

s

jm jms S , 1

π π where 

∑

∈

+

+

+ =

Jk m

X kmkm kms

X jmjm jms

jms eA

eA

εβ

β ε

π

1

It is straightforward to derive the following formulas for each product’s own- and cross-price 

elasticity at a particular store, where β p denotes the price coefficient from consumer utility 

function (5.1) and is product j’s price in market m. p jm

(5.3) )1( jjms jmp jms e −= β p − π , ms ∀ ∈ Jj

jmsjmpkjms = β pe π , ∀ , ∈ ms : ≠ kjJkj

 Researchers typically report the average cross-price elasticity between two products for 

the set of consumers who have both items in their choice set (e.g., Berry et al. 1995, Nevo 

2001).9

 Researchers do not report the average elasticity across all consumers, since doing so 

would underestimate the degree consumers view two products as substitutes. We follow 

 8

 Of course, conditional on there being one model mis-specification, a second mis-specification can either 

amplify or attenuate the bias. 

9

 Note, however, while we assume consumers choose only between those products available at a particular 

store, the cited authors assume each consumer’s choice set includes any product available in at least one store in a 

given market. 

8
standard practice and calculate the average elasticity across the subset of consumers for which a 

given pair of items is in their choice set. 

(5.4) = = = )1,1|( kmskjmsmskj AAeEe jms

 This “heterogeneous store logit” framework is assumed to be the true model in the Monte 

Carlo analysis. We compare this framework to a “representative store logit” model that is 

otherwise identical, but assumes all stores carry the entire set of available products . In that 

specification product j’s market share is as follows. 

Jm

(5.5) 

∑

∈

+

+

+

=

Jk m

X kmkm

X jmjm

jm

e

e

εβ

β ε

π

1

~

Store- and aggregate-level elasticities take the following form in the standard logit model. 

(5.6) ) ~ 1( ~e β p −−= π jmjmpjjm , ∀ ∈ Jj m

β pe π jmjmpkjm ~ ~ = , ∀ , ∈ m : ≠ kjJkj

(5.7) ),| ~( ~ = kjmmkj ∈ JkjeEe m

 A comparison of the elasticity formulas for the two models suggests three reasons one 

might obtain biased results if the representative store model is employed when the heterogeneous 

store framework is the correct specification. First, while the heterogeneous store logit recognizes 

that only a subset of stores in a market may carry a given pair of products, the representative 

store model assumes that either all or no stores in a given market carry both items. This can lead 

to the type of situation described in the introduction regarding baby food. It could be the case 

that no store carries both Heinz and Beech-Nut. If so, the cross-price elasticity between the two 

would not be defined in the heterogeneous store logit model. In contrast, the representative store 

logit would still produce an estimate for this (non-existent) cross-price elasticity. 

 A second difference pertains to how a product’s market share is calculated. In the 

heterogeneous store logit model elasticities depend on a product’s market share in those stores 

where it is available. In contrast, elasticities in the representative store model depend on a 

9
product’s average market share across all stores. These two measures coincide when all stores 

are identical. When that assumption is violated, however, market shares in the two models can 

substantially diverge. 

 The last potential difference between the two models relates to price coefficient β p . If 

the true model is the heterogeneous store logit, but one instead employs the representative store 

logit framework, one might expect to obtain a biased estimate for this parameter (although the 

direction and magnitude of the bias is hard to predict). 

 It is difficult to determine analytically the net impact of these factors. To provide some 

intuition for the Monte Carlo results presented below we consider a special case. Suppose 

product j is available only in market m, and this product is carried by a fraction of stores 

in that market. In addition, assume that product j’s market share is identical across all stores 

where it is available. Let 

ACVjm

1/ ~ jjjj −= bias

jj eee denote the percent bias of the own-price elasticity 

estimate from the representative store model when the heterogeneous store logit is the correct 

framework (where and are defined in equations (5.4) and (5.7), respectively). This term 

simplifies as follows in our simple example, where denotes the percent bias in the price 

coefficient. 

jj e jj e

~

bias β p

(5.8) 1

1

1

)1( −

−

− +=

jm

jm

bias jm

p

bias

jj

ACV

e

π

π

β

 Bias in the own-price elasticity is the product of two factors. The first is the percent bias 

in price coefficient β p , which can be in either direction. The second term, 

jm

jm

jm

ACV

π

π

−

−

1

1 , 

depends on a product’s market share in those stores where it is available as well as its market 

share across all stores. This term causes the own-price elasticity to be (weakly) upwards biased 

(too elastic). Since can be positive or negative, however, it is impossible to sign the 

overall bias. Consider the case where each product has a small market share in those stores 

bias β p

10
where it is available. The term 

jm

jm

jm

ACV

π

π

−

−

1

1

 limits to a value of one as a product’s market share 

grows increasingly small, so that the own-price elasticity bias approximately equals . 

While it is not possible to predict the direction of bias, one would expect each product’s ownprice elasticity to be similarly biased since 

bias β p

β p is not a product-specific parameter. This special 

case is empirically relevant when estimating the demand for a large number of products, where 

often no single product has a large market share. In our data, 

jm

jm

jm

ACV

π

π

−

−

1

1

 has a value extremely 

close to one for most products and is never larger than 1.03.10 As such, in our Monte Carlo 

results one would expect the bias in each product’s own-price elasticity to approximately equal 

. As discussed below, this is what we find. bias β p

 We now consider the bias in the cross-price elasticity estimate from the representative 

store model when the heterogeneous store logit is the correct framework. Let / 1 ~ kjkj −= bias

kj eee

denote the percent bias in the cross-price elasticity. This term depends on , the fraction 

of stores in market m that carry both products k and j. In our simple example, simplifies as 

follows. 

ACVkjm

bias

kj e

(5.9) += )1( −1

km

bias kjm

p

bias

kj ACV

ACV

e β , ∀ ∈ m : ≠ kjJk

 As before, bias in price coefficient β p can be in either direction. The second factor, 

km

kjm

ACV

ACV

, is the probability that product j is available conditional on product k being available. 

This term causes the cross-price elasticity to be (weakly) downwards biased. In the Monte Carlo 

results, for most products this latter term dominates. The cross-price elasticity estimates are 

 10 To calculate market shares researchers typically make an assumption regarding per-capita consumption, 

and then calculate a market’s size using population data. Since we do not know the number of people who visit each 

retail chain, we follow Tenn (2006b) and instead assume each retailer-city’s market size is ten times average 

category sales. 

11
therefore biased towards zero on average, albeit with significant variation depending on the 

extent of a product’s availability.11

 We now turn to the Monte Carlo analysis, which allows us to consider situations where 

the bias from ignoring limited distribution cannot be analytically determined. To calibrate the 

model, we use the scanner data described in section 3 to estimate the heterogeneous store logit 

framework and obtain estimates for model parameters β and σ . When doing so we restrict the 

data to products with either intermediate or wide distribution (i.e., products with median 

availability of at least 50% of stores). Although many products have low availability, they 

account for a very small fraction of dollar sales (see Table 1). As discussed earlier, the limited 

retail availability of such products is less of a concern since researchers often exclude low-selling 

items when estimating demand. To be conservative we follow this practice and remove such 

products. If we were to include them, however, our results would show an even larger bias from 

ignoring limited product availability. 

 Calibration of the heterogeneous store model requires three steps. First, we choose which 

stores in a market carry a given set of products. We assume each market is composed of 100 

stores, and then randomly assign which products are available in a particular store.12 For 

example, if a product is available in 50% of stores, we randomly select which 50 stores carry that 

item. Following Berry (1994), we then define δ = X β + ε jmjmjm and iteratively solve for the 

set δ }{ ∀ ,mjjm so that predicted market shares exactly equal observed market shares. Lastly, we 

estimate the linear equation δ = X β + ε jmjmjm by ordinary least squares to obtain estimates of 

model parameters β and σ . 

 11 As detailed below, in the Monte Carlo analysis we assume each product’s retail availability is 

independently distributed. Equation (5.9) simplifies to when 

. 

+= −1)1( jm

bias

p

bias

kj e β ACV

ACVkjm = ACVACV jmkm

12 As discussed later in the section, alternative assumptions for the joint distribution of product availability 

can lead to either smaller or larger bias. 

12
 These estimates are taken as the “true” parameter values from which we construct 

simulated data for each Monte Carlo simulation. We recognize that the obtained demand 

estimates might be biased for a variety of reasons, such as endogeneity bias, omitted variables 

bias, and the use of a restrictive functional form. Nonetheless, it allows us to calibrate the model 

in a way that approximates a real-world setting, and from which we can conduct a Monte Carlo 

analysis that by construction does not suffer from any of these potential biases.13

 We conduct 2,500 Monte Carlo simulations, each of which is carried out as follows. 

Using the parameter estimates and control variables (but not the unit sales data) from the 

heterogeneous store logit model, we simulate a new dataset. We then use the simulated data to 

estimate the representative store logit model. The Berry inversion method is again relied upon to 

estimate the model via ordinary least squares, although δ }{ ∀ ,mjjm is now calculated 

analytically. By comparing the estimated results to the true parameter values, we analyze 

whether ignoring limited retail distribution leads to biased findings. 

 The first panel of Table 2 reports the parameter estimates used to calibrate the 

heterogeneous store logit model. The average own-price elasticity ranges from -1.97 to -2.22, 

depending on the category. Cross-price elasticities are generally very small across all five 

product categories. The reason is that most products have relatively small market shares. Such 

products tend not to be close substitutes, since substitution is proportional to market share in the 

logit demand model. 

 The second panel in Table 2 reports the percent bias of the estimates produced by the 

representative store logit framework when the heterogeneous store logit is the correct model. 

Bias is estimated as the percent difference between the true value and the average estimate across 

the 2,500 Monte Carlo simulations.14 Note that due to the large number of products in each 

 13 Alternatively, we could have simply picked parameter values in a completely arbitrary manner. 

14 Since we employ a large number of simulations, variation due to random sampling has a negligible 

impact on the reported results. 

13
category, it is not possible to report the percent bias for each individual own- and cross-price 

elasticity. Instead, we report the average percent bias across all products in each category. In 

addition, we report the standard deviation of the percent bias to measure the extent the bias 

varies across products. 

 The average own-price elasticity bias ranges from 4.2% to 18.3%, depending on the 

category. There is very little heterogeneity in the percent bias across products, with the standard 

deviation ranging from 1.3% to 2.2%. The special case considered earlier provides the intuition 

for why this occurs. Since most products have relatively small market shares, the percent bias 

approximately equals for most items. bias β p

 The average cross-price elasticity bias is somewhat larger, ranging from -10.6% to 

-20.7% depending on the category. Moreover, there is substantially more variation in the degree 

of bias across products. The standard deviation in the percent bias ranges from 16.1% to 19.7%. 

Again, the special case considered earlier suggests why this occurs. Recall that the cross-price 

elasticity bias largely depends on the extent of a product’s availability. Since the median retail 

distribution of the products in the data sample ranges from 50% to 100% of stores, one would 

also expect the percent bias in the estimates to vary widely across products. 

 To provide a better indication of this, Figure 1 presents a histogram of the cross-price 

elasticity percent bias in the hot dog category. While the percent bias is positive for a few items, 

the cross-price elasticity is biased towards zero for most products. The degree of bias widely 

varies, however. While a percent bias close to zero most frequently occurs, percent biases as 

large as -50% are relatively common. We selected this category since the percent bias is not 

particularly big or small; histograms for the other product categories reveal a similar pattern. 

 The poor performance of the representative store model raises the issue of whether one 

might instead estimate demand using a framework that explicitly accounts for product assortment 

heterogeneity across stores, such as the heterogeneous store logit model employed above (or, 

more likely, a random coefficients variant that accommodates flexible substitution patterns). The 

problem with doing so is that the heterogeneous store model has informational requirements that 

14
go beyond what is reported in aggregate datasets. Specifically, evaluation of equation (5.2) 

requires the joint distribution of retail availability across all products (i.e., the fraction of stores 

that carry only a particular subset of items). Aggregate datasets typically used in demand 

estimation, such as scanner data produced by ACNielsen and IRI, do not report this joint 

distribution. They report only the univariate distribution of product availability (i.e., the fraction 

of stores that carry a particular item). We deal with this data deficiency in the Monte Carlo 

analysis by assuming each product’s retail availability is independently distributed, so that the 

(observed) univariate distribution is sufficient to construct the (unobserved) joint distribution. 

While an interesting baseline case to consider, this independence assumption may be violated in 

empirical applications. 

 It is impossible to model heterogeneity in consumer choice sets without knowing the joint 

distribution of product availability. A continuum of joint distributions can potentially arise given 

a set of observed univariate distributions. Aggregate datasets do not report any information that 

identifies which of the many possible joint distributions is correct. Obviously, one cannot 

control for heterogeneity in product assortment across stores if the fraction of stores that carry a 

given set of items is not known. 

 One solution to this problem is to obtain better data. While ACNielsen and IRI do not 

report the joint distribution of product availability in the aggregate datasets they produce, this 

information is reported in their store-level datasets. Unfortunately, such data is far more 

expensive, and these vendors are often unwilling to provide data for a large number of stores 

(Boatwright et al. 2004). The widespread use of aggregate data to estimate demand likely 

indicates many researchers lack access to store-level data. 

 When store-level data is unavailable, an alternative approach is to estimate the 

heterogeneous store model under a wide range of assumptions for the joint distribution of retail 

availability. One would have greater confidence in those estimates that are insensitive to the 

joint distribution assumed. Conversely, the data contains insufficient information to identify the 

estimates that significantly vary depending on the joint distribution employed. 

15
 An alternative approach is to rely upon a representative store model, but then undertake 

sensitivity analysis regarding the likely bias from doing so. Consider the example discussed 

earlier for which equation (5.9) reports , the percent bias of the cross-price elasticity 

estimate from the representative store logit model when the heterogeneous store logit is the 

correct framework. The degree of bias crucially depends on , the fraction of stores in 

market m that carry both products k and j. As discussed above, is not reported in 

aggregate datasets. Nonetheless, one can place bounds on the range of values can take. 

The smallest possible value for this term is , while the 

largest possible value is . 

bias

kj e

ACVkjm

ACVkjm

ACVkjm

,0max( 1) min = km jm −+

kjm

ACV ACV ACV

min( , ) max

km jm kjm

ACV = ACV ACV

 When contains a narrow range of values, one has a good sense of 

the likely bias from using the representative store model. For example, suppose products k and j 

are each available in 50% of stores. Further, assume the percent bias in the estimated price 

coefficient is sufficiently small that it can be ignored (i.e., ). In this case, equation 

(5.9) implies . The estimated cross-price elasticity might be unbiased, or it 

could be underestimated by 100%. Since we do not know the true magnitude of the bias, the 

estimated cross-price elasticity has little informative value. In contrast, suppose products k and j 

are each available in 95% of stores. Equation (5.9) implies . Since lies 

in a fairly narrow range, one would have a much better idea of the bias in the estimated crossprice elasticity for this latter example. 

[ , ] min max

kjm kjm

ACV ACV

≈ 0 bias β p

−∈ 0%,100[ %] bias

kj e

−∈ %,10[ 0%] bias

kj e biaskj e

 To summarize, aggregate data lacks the requisite information to explicitly model 

heterogeneous product availability across stores. In some situations, this is a fatal shortcoming 

since the estimated elasticities crucially depend on the unobserved joint distribution of retail 

availability. In other cases, this joint distribution plays less of a role. Researchers can undertake 

the sensitivity analyses suggested above to determine whether an aggregate demand model might 

be successfully employed in a particular situation. 

16
6 Explanations for Limited Distribution 

 In this section, we explore why so many products have limited retail distribution. We do 

so for two reasons. First, a better understanding of the empirical determinants of product 

availability would clearly be useful given that retail distribution touches on a number of distinct 

literatures as mentioned in section 2. The second reason is directly applicable to the focus of this 

paper; by obtaining a better understanding of why products have limited distribution, researchers 

may be more attuned to whether limited product availability is likely to be a significant problem 

in a particular demand application. 

 As discussed earlier, products with low retail distribution pose only a minor problem 

when estimating demand. Such products account for a small percentage of sales, and therefore 

can be reasonably omitted from the analysis altogether. For that reason, in this section we focus 

on products with intermediate distribution. Also, note that new and discontinued items are 

excluded from the analysis, except for when we explicitly consider them. Doing so allows us to 

differentiate between reasons why products have limited retail distribution on a transitional basis, 

as opposed to consistently having limited distribution. 

Product-Line Length

 One explanation for why products have limited availability is that it is impractical for 

retailers to carry entire product lines due to space limitations and consumer preference 

heterogeneity across stores.15 Rather, they typically carry only a subset of the UPCs contained 

within each line of products (e.g., Lemon-Lime Gatorade but not Lemonade Gatorade). We 

explore whether heterogeneity in product assortment explains why so many items are available 

in most, but not all of a retailer’s stores. If products with limited distribution are secondary 

 15 Retailers often optimize the product assortment at a particular store to account for heterogeneity in 

consumer preferences. Since this issue is addressed in previous research, such as Stassen et al. (1999), we do not 

focus on that explanation here. 

17
package sizes or varieties of widely available products, that could explain why many stores do 

not carry such items. 

 The dataset includes three types of product characteristics that describe each UPC. The

first defines the set of UPCs that constitutes a given product line. For example, “Ben & Jerry’s 

ice cream” and “Ben & Jerry’s frozen yogurt” are distinct product lines. The other 

characteristics describe each product’s package size and variety. In the ice cream category, for 

example, variety is measured by characteristics such as flavor (e.g., vanilla), fat-content (e.g., 

“low-fat”), and sugar-content (e.g., “no sugar added”). Each UPC within a product line is 

defined by a unique combination of package size and variety characteristics. 

 We use these characteristics to compute statistics regarding whether the other members of 

a UPC’s product line are widely available. As indicated earlier, we employ a data sample 

composed of products with intermediate distribution (i.e., products with median availability of 

50% to 90% of stores). The first row of Table 3 reports the fraction of UPCs that are part of 

widely available product lines. This is defined as product lines where at least 90% of stores 

carry a UPC from that line (although each store may carry a different assortment of UPCs). A 

large percentage of UPCs with intermediate distribution, 64% to 93% depending on the category, 

are part of widely available product lines. The second row of Table 3 shows that depending on 

the category, 22% to 66% of UPCs with intermediate distribution are from product lines where at 

least one UPC is widely available. The large difference between the first two rows of statistics 

demonstrates that even though stores largely carry the same product lines, they carry a different 

subset of items. Heterogeneity in product assortment is so extensive that it is often the case that 

no single UPC from a widely available product line is itself widely available. 

 The third and fourth rows of Table 3 examine whether product assortment heterogeneity 

is due to differences in product variety or package size. We find that only a small fraction of 

items are alternative package sizes of widely available product varieties. Depending on the 

category, this is the case for only 1% to 12% of UPCs. In contrast, 20% to 64% of UPCs are 

from product lines that contain a widely available item with the same package size, but a 

18
different variety. Thus, product assortment differences are primarily due to certain stores not 

carrying all of the varieties contained within a product line, rather than from stores not carrying 

secondary package sizes. 

New Product Introductions

 Another reason many products have limited retail distribution is that the process of 

introducing and discontinuing items often takes place over many weeks. Even if a product 

eventually becomes widely available, during a transition period it is typically carried by only a 

subset of a retailer’s stores. To show this, we look at how long it takes a new product to become 

widely available. One slight complication is that we have only 132 weeks of data, which leads to 

a truncation problem for products introduced towards the end of the dataset. To avoid truncation 

bias, we estimate a duration model and then calculate the probability of a given introduction spell 

length using the estimated model parameters. 

 We restrict the data sample to newly introduced products, and then estimate the following 

model. Let denote an indicator variable for whether product j is available in at least one 

store in retailer-city r in week t (i.e., ). Similarly, let denote an indicator 

variable for whether product j is widely available (i.e., ). We rely on a two 

equation discrete-time duration model where and are the dependent variables, 

respectively, is a set of observed product characteristics, and 

Ajrt

> 0 ACVjrt W jrt

≥ %90 ACVjrt

Ajrt W jrt

X jrt Λ denotes the logistic 

cumulative distribution function. 

(6.1) )()1|1( = AAP tjrjrt −1, Λ== X jrtβ1

)()0,1|1( jrt == WAWP tjrjrt −1, = = Λ X jrtβ 2

Becoming widely available ( =1) and being discontinued ( Wjrt = 0 Ajrt ) are both terminal 

conditions that end the introduction spell. This spell continues for as long as a product remains 

available, but not widely available (or the dataset ends, in which case the introduction spell is 

truncated). 

19
 To accommodate either positive or negative duration dependence, the set of control 

variables includes a fourth order polynomial in the number of weeks since a product was 

introduced. In addition, it consists of a set of dummy variables for the calendar month, and a set 

of retailer-city dummy variables that control for heterogeneity with respect to how quickly 

retailers introduce or discontinue items. Lastly, we include the four variables shown in Table 3, 

which control for whether an item is from a widely available product line, whether that line 

includes a widely available item, and whether that line contains a widely available UPC of the 

same variety or package size. We construct these measures using data from the week prior to 

when an item is first introduced. They are included in the set of control variables since the 

availability of related products potentially speaks to whether a newly introduced item will itself 

become widely available. 

X jrt

 The estimation results from the two logit models are presented in Table 4. It is difficult 

to tell from the parameter estimates what the fourth order polynomial in the number of weeks 

since a product was introduced looks like. Therefore, we briefly describe its profile, which is 

similar across the five product categories. In the first model where the dependent variable is 

, the probability of being discontinued is highest for products that have just been introduced. 

It gradually decreases until approximately 20 weeks following the product introduction, after 

which the probability starts to increase again. Similarly, when is the dependent variable, 

the probability of becoming widely available in a given period peaks at around 10 weeks and 

then gradually declines. As shown in the table, mixed results are obtained for the remaining 

control variables that measure the availability of the other items in the same product line. In 

some categories a new product from a widely available product line is more likely to become 

widely available itself, while the opposite is true in other categories. 

Ajrt

W jrt

 For each product j, the set of control variables and parameters X jrt β1 and β 2 are used 

to predict the likelihood of a given spell outcome and duration. The first panel in Table 5 reports 

the probability of becoming either widely available or being discontinued in the first year, as 

well as the probability that the introduction spell has not been completed by the end of the first 

20
year (i.e., a product is available, but not widely available). While the results vary somewhat by 

product category, on average approximately one third of new products become widely available 

in the first year, and an additional one third are discontinued. That leaves the remaining one 

third of products, which continue to be available, but with limited distribution. Depending on the 

category, in its first year a new product has limited product availability an average of 21.4 to 

36.1 weeks. 

 The second panel of Table 5 presents the probability of becoming widely available in a 

given week, conditional on a product becoming widely available in its first year. Many products 

quickly become widely available, with 18% to 43% of products doing so in their first month, 

depending on the category. Nonetheless, most products take substantial longer, with an average 

of 8.6 to 14.2 weeks. The third panel of Table 5 presents the probability of being discontinued in 

a particular week conditional on a product being discontinued in its first year. In general, it takes 

longer for a new product to be discontinued, with an average of 16.1 to 21.1 weeks depending on 

the category. 

 To summarize, product introductions are not an instantaneous process. To the contrary, 

new products undergo a lengthy transition where approximately two thirds are either 

discontinued or become widely available within a year. Since that transition often takes many 

weeks, a new product typically has limited retail distribution for much of its first year. 

Other Sources of Intertemporal Variation

 Even established products often experience temporary changes in distribution. One 

reason is that widely available UPCs occasionally have stock-outs. To demonstrate this, we 

restrict the data sample to widely available products. Table 6 shows that very few of these 

products are widely available every week. Depending on the category, 66% to 79% of UPCs are 

available in 50% to 90% of stores during at least one week. However, few of these products are 

ever available in less than 50% of stores. Depending on the category, this is the case for only 7% 

to 19% of UPCs. 

21
 While creating an exhaustive list of reasons for why retail distribution changes over time 

is beyond the scope of this paper, it is worth pointing out that nearly all products undergo 

extensive intertemporal variation in product availability. To show this we estimate the following 

model, separately for each product j. 

(6.2) , where . jrtjrjrjrjtjrt ACV tt ++++= εααδδ 2

21 ln( ) 2 )( Var = σε jjrt

Each product’s log distribution (ACV) is regressed against a set of fixed effects for time t and 

retailer-city r, and a retailer-city specific quadratic time trend. The root mean squared error 

(RMSE) from the regression, σ j ˆ , measures the extent distribution is changing over time after 

accounting for these factors. We include these controls to demonstrate that distributional 

changes are idiosyncratic, and are not implicitly controlled for in models that account for 

underlying trends or seasonality. Since time fixed effects and quadratic time trends are 

commonly used, that is the specification we chose to employ. 

 Table 7 presents the distribution of the RMSE estimates obtained from equation (6.2).16 

The results show substantial variation in product distribution over time, with a median RMSE of 

9% to 16%, depending on the category. Most products have either intermediate variability 

(RMSE between 10% and 20%) or high variability (RMSE of 20% or more). Not only is limited 

product availability extremely common, but the extent of most products’ retail distribution 

significantly varies over time. 

7 Conclusion 

 Aggregate demand models typically assume all consumers in a given market shop at the 

same “representative store,” and therefore face the same choice set. We find little empirical 

support for this assumption. Across the five grocery categories in our dataset, products with 

 16 Equation (6.2) requires a sufficient number of observations to estimate the RMSE with reasonable 

precision. The approach taken here is to include all products with at least 156 weeks (three years) of observations 

(out of a maximum possible 1,848 pooled weeks). The results are not sensitive to this choice of sample selection. 

22
limited retail distribution represent a large percentage of category sales. Thus, consumers in the 

same market have very different choice sets depending on where they shop. 

 Monte Carlo analysis shows that the observed level of limited retail distribution is 

sufficient to bias significantly own- and cross-price elasticity estimates in models that do not 

control for the extent of a product’s retail distribution. While it is obvious that limited product 

availability can affect demand analysis in highly atypical conditions such as the baby food 

example discussed earlier, our results indicate the bias from ignoring limited retail distribution 

can be quite large even under ordinary conditions. 

 We find support for three hypotheses regarding why so many products have limited retail 

distribution: (1) stores carry select varieties of popular product lines, rather than the entire line; 

(2) new product introductions often take place over a period of months—not weeks; and (3) even 

top-selling, widely distributed products have occasional stock-outs that temporarily reduce their 

retail distribution. By providing a better understanding of why products have limited retail 

distribution, we hope researchers will be more attuned to whether this is likely to be an issue in a 

particular demand application. 

 Finally, while our results show that representative store aggregate demand models may 

perform quite poorly, researchers who lack store-level data have few alternatives since aggregate 

datasets contain insufficient information to control for product assortment heterogeneity across 

stores. Nonetheless, the sensitivity analyses we suggest allow researchers to assess the likely 

magnitude of the bias. This gives researchers some degree of certainty regarding whether an 

aggregate demand model might be successfully employed in a particular circumstance, or 

whether store-level data is ultimately required. 

23
References 

Asker, John, “Measuring Advantages from Exclusive Dealing,” working paper, April 2004a. 

Asker, John, “Diagnosing Foreclosure Due to Exclusive Dealing,” working paper, October 

2004b. 

Bergen, Mark, Shantanu Dutta, and Steven M. Shugan, “Branded Variants: A Retail 

Perspective,” Journal of Marketing Research 33 (1996), pp. 9-19. 

Berry, Steven T., “Estimating Discrete-Choice Models of Product Differentiation,” RAND 

Journal of Economics 25 (1994), pp. 242-262. 

Berry, Steven, James Levinsohn, and Ariel Pakes, “Automobile Prices in Market Equilibrium,” 

Econometrica 63 (1995), pp. 841-90. 

Besanko, David, Jean-Pierre Dubé, and Sachin Gupta, “Competitive Price Discrimination 

Strategies in a Vertical Channel Using Aggregate Retail Data,” Management Science 49 (2003), 

pp. 1121-38. 

Boatwright, Peter, Sanjay Dhar, and Peter E. Rossi, “The Role of Retail Competition, 

Demographics and Account Retail Strategy as Drivers of Promotional Sensitivity,” Quantitative 

Marketing and Economics 2 (2004), pp. 169-90. 

Brenkers, Randy, and Frank Verboven, “Liberalizing a Distribution System: The European Car 

Market,” working paper, November 2004. 

Bronnenberg, Bart J., Vijay Mahajan, and Wilfried R. Vanhonacker, “The Emergence of Market 

Structure in New Repeat-Purchase Categories: The Interplay of Market Share and Retailer 

Distribution,” Journal of Marketing Research 37 (2000), pp. 16-31. 

Bucklin, Randolph E., and James M. Lattin, “A Model of Product Category Competition Among 

Grocery Retailers,” Journal of Retailing 68 (1992), pp. 271-93. 

Chintagunta, Pradeep K., “Investigating Category Pricing Behavior at a Retail Chain,” Journal of 

Marketing Research 39 (2002), pp. 141-54. 

Chintagunta, Pradeep K., Jean-Pierre Dubé, and Vishal Singh, “Balancing Profitability and 

Customer Welfare in a Supermarket Chain,” Quantitative Marketing and Economics 1 (2003), 

pp. 111-47. 

Cotterill, Ronald W., William P. Putsis, Jr., and Ravi Dhar, “Assessing the Competitive 

Interaction Between Private Labels and National Brands,” Journal of Business 73 (2000), pp. 

109-37. 

24
Curhan, Ronald C., “The Relationship Between Shelf Space and Unit Sales in Supermarkets,” 

Journal of Marketing Research 9 (1972), pp. 406-12. 

Draganska, Michaela and Dipak Jain, “Product-Line Length as a Competitive Tool,” Journal of 

Economics and Management Strategy 14 (2005), pp. 1-28. 

Drèze, Xavier, Stephen J. Hoch, and Mary E. Purk, “Shelf Management and Space Elasticity,” 

Journal of Retailing 70 (1994), pp. 301-26. 

Farris, Paul, James Olver, and Cornelis De Kluyver, “The Relationship Between Distribution and 

Market Share,” Marketing Science 2 (1989), pp. 107-28. 

Gupta, Sachin, Pradeep Chintagunta, Anil Kaul, and Dick R. Wittink, “Do Household Scanner 

Data Provide Representative Inferences from Brand Choices: A Comparison with Store Level 

Data,” Journal of Marketing Research 33 (1996), pp. 383-98. 

Hausman, Jerry A. and Gregory K. Leonard, “The Competitive Effects of a New Product 

Introduction: A Case Study,” Journal of Industrial Economics 50 (2002), pp. 237-63. 

Hausman, Jerry, Gregory Leonard, and J. Douglas Zona, “Competitive Analysis with 

Differenciated Products,” Annales D’Économie et de Statistique 34 (1994), pp. 159-80. 

Heide, Jan B., Shantanu Dutta, and Mark Bergen, “Exclusive Dealing and Business Efficiency: 

Evidence From Industry Practice,” Journal of Law and Economics 41 (1998), pp. 387-407. 

Hoch, Stephen J., Byung-Do Kim, Alan L. Montgomery, and Peter E. Rossi, “Determinants of 

Store-Level Price Elasticity,” Journal of Marketing Research 32 (1995), pp. 17-29. 

Kumar, V. and Robert P. Leone, “Measuring the Effect of Retail Store and Promotions on Brand 

and Store Substitution,” Journal of Marketing Research 25 (1988), pp. 178-85. 

Lafontaine, Francine, “Agency Theory and Franchising: Some Empirical Results,” RAND 

Journal of Economics 23 (1992), pp. 263-83. 

Lafontaine, Francine and Kathryn L. Shaw, “The Dynamics of Franchise Contracting: Evidence 

from Pane Data,” Journal of Political Economy 107 (1999), pp. 1041-80. 

Lafontaine, Francine and Margaret Slade, “Retail Contracting: Theory and Practice,” Journal of 

Industrial Economics 45 (1997), pp. 1-25. 

Nevo, Aviv, “A Practitioner’s Guide to Estimation of Random-Coefficients Logit Models of 

Demand,” Journal of Economics and Management Strategy 9 (2000), pp., 513-548. 

Nevo, Aviv, “Measuring Market Power in the Ready-to-Eat Cereal Industry,” Econometrica 69 

(2001), pp. 307-42. 

25
Nevo, Aviv and Konstantinos Hatzitaskos, “Why Does the Average Price of Tuna Fall During 

Lent?,” NBER Working Paper No. 11572, August 2005. 

Olver, James M. and Paul W. Farris, “Push and Pull: A One-Two Punch for Packaged Products,” 

Sloan Management Review 31 (1989), pp. 53-61. 

Ornstein, Stanley I. and Dominique M. Hanssens, “Resale Price Maintenance: Output Increasing 

or Restricting? The Case of Distilled Spirits in the United States,” Journal of Industrial 

Economics 36 (1987), pp. 1-18. 

Pesendorfer, Martin, “Retail Sales: A Study of Pricing Behavior in Supermarkets,” Journal of 

Business 75 (2002), pp. 33-66. 

Petrin, Amil, “Quantifying the Benefits of New Products: The Case of the Minivan,” Journal of 

Political Economy 110 (2002), pp. 705-29. 

Reibstein, David J. and Paul W. Farris, “Market Share and Distribution: A Generalization, A 

Speculation, and Some Implications,” Marketing Science 14 (1995), pp. 190-202. 

Rhee, Hongjai and David R. Bell, “The Inter-Store Mobility of Supermarket Shoppers,” Journal 

of Retailing 78 (2002), pp. 225-37. 

Shaffer, Greg, “Slotting Allowances and Resale Price Maintenance: A Comparison of 

Facilitating Practices,” RAND Journal of Economics 22 (1991), pp. 120-35. 

Sullivan, Mary W., “Slotting Allowances and the Market for New Products,” Journal of Law and 

Economics 40 (1997), pp. 461-93. 

Stassen, Robert E., John D. Mittelstaedt, and Robert A. Mittelstaedt, “Assortment Overlap: Its 

Effect on Shopping Patterns in a Retail Market When the Distributions of Prices and Goods Are 

Known,” Journal of Retailing 75 (1999), pp. 371-86. 

Steiner, Robert L., “The Prejudice Against Marketing,” Journal of Marketing 40 (1976), pp. 2-9. 

Steiner, Robert L., “The Evolution and Applications of Dual-Stage Thinking,” Antitrust Bulletin

49 (2004), pp. 877-909. 

Tenn, Steven, “Demand Estimation under Limited Product Availability,” working paper, August 

2006a. 

Tenn, Steven, “Avoiding Aggregation Bias in Demand Estimation: A Multivariate Promotional 

Disaggregation Approach,” Quantitative Marketing and Economics 4 (2006b), pp. 383-405. 

Villas-Boas, Sophia B., “Vertical Contracts Between Manufacturers and Retailers: Inference 

with Limited Data,” CUDARE Working Paper 943R2, July 2005. 

26
27

Table 1 

Percent of Products, by Median Product Availability 

Available in % of Stores:

Frozen 

Novelty

(N=3,123)

Pasta

(N=5,127)

Hot Dog

(N=1,176)

Ice Cream

(N=6,345)

Salad 

Dressing

(N=6,436) Average

Low Availability:

0% to 10% 9% 26% 10% 8% 17% 14%

10% to 20% 8% 18% 6% 10% 14% 11%

20% to 30% 5% 7% 5% 7% 7% 6%

30% to 40% 5% 5% 3% 7% 5% 5%

40% to 50% 6% 4% 3% 8% 5% 5%

Sub-total 33% 60% 28% 40% 48% 42%

Intermediate Availability:

50% to 60% 7% 4% 5% 9% 6% 6%

60% to 70% 9% 4% 6% 10% 7% 7%

70% to 80% 12% 5% 7% 10% 9% 9%

80% to 90% 15% 7% 13% 11% 11% 11%

Sub-total 43% 19% 30% 40% 34% 33%

Wide Availability:

90% to 99% 14% 10% 17% 11% 10% 12%

99% to 100% 10% 12% 24% 9% 9% 13%

Sub-total 24% 21% 41% 19% 18% 25%

Percent of Dollar Sales, by Median Product Availability 

Available in % of Stores:

Frozen 

Novelty Pasta Hot Dog Ice Cream

Salad 

Dressing Average

Low Availability:

0% to 10% 0% 1% 0% 0% 0% 0%

10% to 20% 0% 2% 0% 1% 1% 1%

20% to 30% 0% 2% 1% 1% 1% 1%

30% to 40% 1% 2% 1% 1% 1% 1%

40% to 50% 2% 2% 1% 3% 1% 2%

Sub-total 4% 8% 3% 6% 4% 5%

Intermediate Availability:

50% to 60% 2% 2% 1% 4% 2% 2%

60% to 70% 5% 2% 2% 6% 3% 4%

70% to 80% 9% 4% 4% 8% 6% 6%

80% to 90% 17% 9% 8% 14% 12% 12%

Sub-total 33% 17% 16% 33% 23% 24%

Wide Availability:

90% to 99% 32% 24% 25% 25% 22% 26%

99% to 100% 30% 51% 56% 37% 51% 45%

Sub-total 63% 75% 81% 62% 73% 71%

Notes: N = number of products, which is defined as a UPC in a given retailer-city. Each column sums to 

100%. 
28

Table 2 

Monte Carlo Results 

A. Heterogeneous Store Logit Calibration

Frozen Novelty Pasta Hot Dog Ice Cream 

Est Est Est Est 

Price Coefficient -0.75 -1.70 -0.75 -0.62 

σ 0.44 0.39 0.45 0.40 

# of Observations

Avg Std Dev Avg Std Dev Avg Std Dev Avg Std Dev 

Own-Price Elasticity -2.22 0.62 -2.11 0.92 -2.16 1.28 -2.13 0.60 Cross-Price Elasticity 0.002 0.001 0.001 0.001 0.003 0.003 0.001 0.001 B. Percent Bias of the Representative Store Logit when the Hetergeneous Store Logit is the Correct Model

Frozen Novelty Pasta Hot Dog Ice Cream 

Est Est Est Est 

Price Coefficient 3.8% 6.3% 7.4% 16.8% 

σ 30.0% 20.4% 13.5% 29.0% 

Avg Std Dev Avg Std Dev Avg Std Dev Avg Std Dev 

Own-Price Elasticity 4.2% 1.3% 6.8% 1.3% 8.2% 1.3% 18.3% 2.2% Cross-Price Elasticity -20.7% 17.9% -13.5% 17.4% -10.6% 16.1% -11.9% 19.7% 

200,004 239,575 86,573 372,466 

Notes: Panel A reports the parameter values used to simulate the data employed in the Monte Carlo analysis. Each obser

analysis corresponds to a particular UPC in a given retailer-city in a given week. Panel B reports the average percent difference be

estimated values across the 2,500 Monte Carlo simulations. 
29

Table 3 

Percent of Intermediate Available Products, by Product Line Availability 

Frozen 

Novelty

(N=559)

Pasta

(N=579)

Hot Dog

(N=139)

Ice Cream

(N=1,037)

Salad 

Dressing

(N=948) 

Product Line is Widely Available 80% 81% 64% 93% 86% Product Line Contains a Widely Available UPC 22% 50% 44% 66% 61% Product Line Contains a Widely Available UPC of the Same Variety

1% 8% 5% 5% 12% 

Product Line Contains a Widely Available UPC with the Same Package Size

20% 39% 27% 64% 49% 

Notes: N = number of products, which is defined as a UPC in a given retailer-city. The data sample is restricted to produ

availability, which is defined as median retail distribution of 50% to 90% of stores. Widely available is defined as median retail di100% of stores. 
30

Table 4 

Logit Estimates, Product Introduction Duration Model 

A. Dependent Variable: Product is Available

Frozen Novelty Pasta Hot Dog Ice Cream 

Est SE Est SE Est SE Est SE 

Intercept 4.36 (0.39) *** 3.51 (0.23) *** 3.13 (0.54) *** 4.06 (0.30Time Elapsed 22.25 (3.92) *** 20.48 (2.52) *** 22.53 (6.20) *** 27.52 (3.17Time Elapsed^2 -103.23 (17.61) *** -73.04 (11.06) *** -88.44 (31.56) *** -124.52 (14.0Time Elapsed^3 159.96 (28.77) *** 99.69 (17.52) *** 128.00 (57.45) ** 190.60 (22.4Time Elapsed^4 -81.96 (15.53) *** -48.42 (9.07) *** -63.19 (33.54) * -96.52 (11.8Product Line is Widely Available -0.15 (0.25) 0.61 (0.17) *** -1.64 (0.64) ** 0.19 (0.13Product Line Contains a Widely Available UPC 0.17 (0.28) -0.05 (0.28) 2.04 (0.72) *** -0.30 (0.19Product Line Contains a Widely Available UPCof the Same Variety -0.14 (0.33) -0.81 (0.32) ** -0.26 (0.73) 0.30 (0.62Product Line Contains a Widely Available UPCwith the Same Package Size 0.21 (0.22) -0.43 (0.27) -0.47 (0.45) 0.30 (0.16# of Observations 36,454 82,987 9,067 77,732 

B. Dependent Variable: Product is Widely Available

Frozen Novelty Pasta Hot Dog Ice Cream 

Est SE Est SE Est SE Est S

Intercept -7.60 (0.50) *** -7.20 (0.39) *** -6.37 (0.74) *** -5.19 (0.24Time Elapsed 15.55 (3.58) *** 18.02 (5.15) *** -5.09 (5.08) 20.14 (2.57Time Elapsed^2 -141.76 (26.69) *** -129.76 (35.50) *** -53.81 (37.75) -183.36 (19.4Time Elapsed^3 305.25 (63.45) *** 228.88 (78.58) *** 180.19 (89.22) ** 381.47 (45.7Time Elapsed^4 -194.25 (46.21) *** -121.57 (53.77) ** -140.62 (64.84) ** -233.69 (33.2Product Line is Widely Available -0.33 (0.21) 0.60 (0.35) * 0.39 (0.70) -0.53 (0.12Product Line Contains a Widely Available UPC 0.23 (0.23) 1.76 (0.36) *** 0.21 (0.70) 0.63 (0.14

Product Line Contains a Widely Available UPCof the Same Variety -0.73 (0.31) ** 0.25 (0.27) 0.29 (0.42) -0.01 (0.27Product Line Contains a Widely Available UPCwith the Same Package Size -0.09 (0.16) 0.76 (0.18) *** 0.27 (0.24) -0.18 (0.10# of Observations 37,462 83,851 9,318 79,667 

Notes: The data sample is restricted to new products. Each observation corresponds to a particular UPC in a given retailer-city in a giv

include a set of dummy variables for the calendar month and a set of retailer-city fixed effects. Robust standard errors that are clustered by prodlevels correspond to *=10%, **=5%, ***=1%. For clearer presentation, “time elapsed” is rescaled by dividing by 132 weeks, so that this variab
31

Table 5 

Spell Length Predicted Probabilities for New Product Introductions 

A. Outcome in First Year Following Product Introduction

Frozen 

Novelty

(N=1,340)

Pasta

(N=1,631)

Hot Dog

(N=358)

Ice Cream

(N=2,581)

Salad 

Dressing

(N=2,634) Average

% of Products

% Widely Available 17% 27% 49% 51% 26% 34%

% Available, But Not Widely Available 34% 57% 27% 34% 41% 39%

% Discontinued 49% 17% 24% 15% 33% 28%

Total 100% 100% 100% 100% 100% 100%

Weeks in First Year with Limited Distribution

Average weeks 25.3 36.1 21.4 25.5 30.6 27.8

Median weeks 15.0 52.0 10.0 16.0 33.0 25.2

B. Duration, Conditional on Becoming Widely Available in First Year

Frozen 

Novelty Pasta Hot Dog Ice Cream 

Salad

Dressing Average

% of Products

1-4 weeks 29% 18% 43% 26% 19% 27%

5-8 weeks 26% 20% 23% 26% 21% 23%

9-12 weeks 19% 16% 13% 18% 19% 17%

13-26 weeks 20% 33% 15% 24% 32% 25%

27-39 weeks 4% 10% 4% 4% 7% 6%

40-52 weeks 2% 3% 2% 1% 2% 2%

Total 100% 100% 100% 100% 100% 100%

Average weeks 10.1 14.2 8.6 10.3 12.8 11.2

Median weeks 8.0 11.0 5.0 8.0 10.0 8.4

C. Duration, Conditional on Being Discontinued in First Year

Frozen 

Novelty Pasta Hot Dog Ice Cream 

Salad

Dressing Average

% of Products

1-4 weeks 20% 21% 28% 25% 17% 22%

5-8 weeks 16% 18% 19% 16% 15% 17%

9-12 weeks 11% 12% 11% 9% 10% 11%

13-26 weeks 19% 23% 18% 14% 22% 19%

27-39 weeks 13% 13% 11% 11% 16% 13%

40-52 weeks 21% 13% 13% 24% 20% 18%

Total 100% 100% 100% 100% 100% 100%

Average weeks 20.1 17.5 16.1 20.1 21.1 19.0

Median weeks 14.0 12.0 9.0 12.0 16.0 12.6

Notes: N = number of products, which is defined as a UPC in a given retailer-city. 
32

Table 6 

Percent of Widely Available Products, by Minimum Product Availability 

Available in % of Stores:

Frozen 

Novelty

(N=532)

Pasta

(N=968)

Hot Dog

(N=386)

Ice Cream

(N=965)

Salad 

Dressing

(N=1,024) Average

Low Availability:

0% to 10% 3% 1% 5% 2% 2% 3%

10% to 20% 2% 1% 5% 2% 1% 2%

20% to 30% 1% 1% 2% 1% 1% 1%

30% to 40% 1% 1% 3% 2% 1% 2%

40% to 50% 6% 2% 4% 4% 3% 4%

Sub-total 12% 7% 19% 12% 8% 12%

Intermediate Availability:

50% to 60% 10% 7% 8% 12% 9% 9%

60% to 70% 20% 15% 11% 18% 18% 16%

70% to 80% 27% 25% 24% 25% 24% 25%

80% to 90% 22% 28% 24% 20% 24% 23%

Sub-total 79% 75% 66% 74% 76% 74%

Wide Availability:

90% to 99% 8% 16% 12% 11% 12% 12%

>99% 1% 2% 2% 3% 4% 2%

Sub-total 9% 18% 15% 14% 16% 14%

Notes: N = number of products, which is defined as a UPC in a given retailer-city. The data sample is restricted to products 

with wide availability, which is defined as median retail distribution of 90% to 100% of stores. Each column sums to 100%. 
33

Table 7 

RMSE of Log Product Distribution 

% of Products

RMSE:

Frozen 

Novelty

(N=178)

Pasta

(N=349)

Hot Dog

(N=91)

Ice Cream

(N=336)

Salad 

Dressing

(N=335) Average

Low Variability:

0% to 5% 3% 21% 24% 6% 9% 13%

5% to 10% 22% 36% 25% 15% 18% 23%

Sub-total 25% 56% 49% 22% 26% 36%

Intermediate Variability:

10% to 15% 25% 19% 20% 30% 21% 23%

15% to 20% 16% 12% 14% 19% 19% 16%

Sub-total 40% 31% 34% 49% 39% 39%

High Variability:

20% to 25% 15% 8% 7% 13% 15% 11%

>25% 20% 5% 10% 17% 20% 14%

Sub-total 34% 13% 16% 30% 34% 26%

Mean RMSE 18% 11% 12% 17% 17% 15%

Median RMSE 15% 9% 10% 15% 16% 13%

Notes: N = number of products, which is defined as a UPC. The table reports the root mean square error 

from regressions using log ACV as the dependent variable. A set of retailer-city and time fixed effects are 

employed, along with a retailer-city specific quadratic time trend. Each column sums to 100%. 
34

Figure 1 

Histogram of the Cross-Price Elasticity Percent Bias for 

Products in the Hot Dog Category 

-100 -80 -60 -40 -20 0 20 40 60 80 100

0

500

1000

1500

2000

2500

3000

3500

4000

4500

% bias

Notes: The hot dog category contains 250 UPCs, which results in 25,528 cross-price elasticity 

pairs. The mean bias is -10.6%, with a standard deviation of 16.1%.