Market Roll-out and Retail Adoption for New Brands of

Non-durable Goods

by

Bart J. Bronnenberg∗ and Carl F. Mela

2 September 2002.

∗University of California at Los Angeles, e-mail bbronnen@anderson.ucla.edu, and Duke University, e-mailmela@duke.edu. We thank Xavier Dreze for comments on an earlier draft. Also, the comments provided by semi-nar participants at Dartmouth College, Duke University, MIT, UCLA, and the INFORMS Conference in Edmonton,Canada, are gratefully acknowledged. Finally, the authors would like to thank IRI for generously supplying the datafor this study.

1

Market Roll-out and Retail Adoption for New Brands of Non-durable Goods

Abstract

Retail distribution is a decisive early factor in new product success. This paper provides a spatialand network-diffusion model of how retail distribution for new brands of repeat purchase goodsspreads across time and markets in the United States. We focus on two aspects of this process,namely (1) the manufacturer roll-out decision, i.e., the sequence in which manufacturers enter localmarkets with new brands, and (2) chains’ decisions to adopt new brand(s). As retail chains’ tradeareas typically consist of multiple markets, these two decisions can be interrelated. For example,after a large chain approves a new brand for distribution in one market, a manufacturer may preferto roll-out to other markets within the trade area of the same chain. Hence, past chain adoption caninfluence market entry by the manufacturer. Conversely, manufacturer market entry decisions caninfluence a chain’s adoption decision via availability of the new brand. Using weekly data from 166chains and 95 domestic markets on the introduction of two very successful new brands in the frozenpizza category, Digiorno and Freschetta, we find that (1) manufacturers choose rollout markets basedon spatial proximity to markets already entered (spatial evolution), (2) manufacturers choose rolloutmarkets based on whether chains in those markets previously adopted elsewhere (selection), and (3)a typical chain adopts new brands based on the adoption decisions of competing chains within itstrade territory (network diffusion). We also find that manufacturers accelerate the rollout of newproducts once the first markets have been entered successfully. Additionally, we find manufacturersfirst introduce brands into markets where they have large category share. This conservative approachis inconsistent with at least one practitioner who claimed that early roll-out targets are marketswith a low brand development index. The combination of network diffusion, spatial effects, andmarket selection creates substantial diffusion or “installed base” effects on the distribution of newproduct distribution. We use our model to explore some implications of the U.S. geography and themultimarket location of U.S. retail chains for lead market selection in new product launch.Keywords: spatial diffusion, network diffusion, retail distribution, new products, launch strategy.

2

1 Introduction

The success of new product programs counts among the most important drivers of economic pros-

perity for manufacturers in the consumer non-durables industry. An important component of a new

product launch is obtaining distribution for a brand. In practice, distribution is obtained in phases,

via a roll-out strategy, i.e., as a sequence of manufacturer decisions of local market introductions.

Given the key role such decisions play in a new product launch, surprisingly little academic research

exists on these multimarket rollouts. In this study, we address this issue. More specifically, we model

how retailer distribution of new brands spreads across multiple markets and multiple retailers.1 The

unique aspect of our study is that we model new brand diffusion across time, geographical space,

and retailer trade areas. With the results of our study, we make recommendations about the choice

of lead markets in the rollout of new repeat purchase goods.

Focusing on the distribution aspect of new product growth abstracts from other important com-

ponents of new product strategy. To better position our study in the context of other work in this

domain we decompose —in Figure 1— new brand sales for repeat purchase goods into four underlying

components. As can be seen from this decomposition, other foci on new product growth exist, in-

cluding product assortment, product trial, and penetration depth. Because the decomposition above

is multiplicative, not additive, all aspects can be argued to be “make or break” factors in the success

of new products. Rather than dismissing these other aspects as beyond the scope of this study, a

justification to focus on the first factor is in order.

First, we focus on distribution because demand and profits for repeat purchase goods are condi-

tional on distribution being non-zero. Second, for many brand managers, obtaining retailer distri-

bution is the primary objective during the early stages of a product’s life cycle. Third, distribution

decisions are interesting in the context of repeat-purchase goods, because the decision by a retail

chain to distribute a non-durable product is often a durable commitment. Fourth, of all marketing

mix elements, distribution is studied the least in the context of consumer packaged goods. Indeed,

extant research in packaged goods focuses on “product,” “promotion,” and “price” but rarely on

“place.” Stated differently, much research on new products takes a consumer-centric perspective

and focuses on value proposition (price and product) and awareness (advertising). While these are

fundamental questions in marketing, the “place” dimension of marketing has remained understudied

1In this paper we use retailer and chain interchangably. That is, our use of retailer does not refer to a specificstore, but rather the entire set of stores operating under a chain name.

3

new brand salesit #carrying storesit=#carrying storesit

#brand SKUsit

#brand SKUsit

#trialsit

distributionproduct assort-

ment and qualityprice andpromotion

Push orientation Pull orientation

(this study)

#trialsit

new brand salesit× × ×

price andadvertising

Distributiondepth

Penetrationbreadth

Penetrationdepth

Distributionbreadth

Figure 1: Fit of the present study in new product research

empirically, notable exceptions notwithstanding (e.g., McLaughlin and Rao 1991, Montgomery 1975,

Reibstein and Farris 1995).

The scarcity of empirical work on distribution has at least two causes. First, the effects of

distribution are most readily observed during the launch of new brands when there is ample temporal

and spatial variation in distribution. However, given that the launch of new brands is a relatively

rare event, good observations of how distribution builds over time are scarce. Second, in order to

analyze the effects of distribution, spatially disaggregated data are necessary. Focusing merely on a

measure of nationally aggregated “all commodity volume” (ACV) distribution obscures the processes

underlying the evolution of product distribution.

Fortuitously, at least several new brands have been launched in the recent past and with the

introduction of multimarket store-level data by data providers such as Information Resources Inc.

(IRI) and AC Nielsen, it is possible to get high-quality information about at least two critical decisions

in the evolution of distribution for new brands. These are (1) the decision by manufacturers to enter

a specific local market (e.g., the New York market, the Los Angeles market, etc.), and (2) the first-

time adoption of a retail chain whose trade areas include such a market (e.g., Kroger or Albertsons,

respectively).

Obviously, market entry and chain adoption are linked and should be analyzed in a single compre-

hensive framework. The retailer’s adoption decision is conditioned on the manufacturer’s entry into

a local market. In turn, a manufacturer’s choice of which local market to enter is likely influenced

by the fact that markets are linked through retailer networks. For instance, a local market may be

4

a good candidate for entry if chains operating within it previously adopted elsewhere in their trade

areas. That is, Los Angeles may be an attractive market to enter for a manufacturer if Vons and

Albertsons (both high share retailers in Los Angeles) adopted the brand previously elsewhere, when

it became available in their trade areas (e.g., in Phoenix, where both chains operate).

We estimate a model of interdependent evolution of market entry and retail adoption using

multimarket store-level data for two highly successful introductions of new brands in the frozen

pizza category, Digiorno and Freschetta. We find the following stylized facts.

1. Market entry by manufacturers

(a) Local market entry is subject to “proximity” effects. Manufacturers seem to fan out from

selected lead markets and gradually move from one area of the United States to the next.

(b) In addition to these proximity effects, local market entry is also subject to a “selectivity”

effect. Manufacturers appear to enter markets of chains who have adopted in the past in

other markets.

(c) For a new brand roll-out in a given category, manufacturers first enter markets in which

their extant brands have high category share. Manufacturers seem to enter markets first

at a relatively slow pace, accelerating to faster market entry later on. Taken together,

this behavior seems conservative.

2. Adoption by retailers given market entry

(a) Adoption by a given retail chain is subject to “network” effects, i.e., past adoption by

other chains in one’s own territory tends to increase the likelihood of adopting.

(b) Adoption by a given retail chain is positively associated with the manufacturer-share in

the chain, the share of the category in the chain, and retailer size. Adoption also tends

to decelerate with time since the brand became available in a chain’s trade area.

3. Using a Monte Carlo experiment to account for spatial as well as network effects on lead market

selection, we find that good lead markets are serviced by large chains whos territories do not

overlap too much. In other words, good lead markets are on a common edge of the trade areas

of geographically separated large retail-chains.

The remainder of this paper is organized as follows. Section 2, summarizes relevant academic

research on diffusion, distribution, and retailer decisions. Section 3 gives an overview of the frozen

pizza industry. Section 4 states the spatial and network diffusion model. Section 5 contains the data

analysis. Section 6 uses the results of the data analysis to make recommendations for the choice of

lead markets and lead retailers. Section 7 concludes.

5

2 Academic research and background

Our work draws from several research streams, including academic research on diffusion, retailer

conduct, spatial statistics and sociology.

Starting with Bass (1969), marketing researchers have been interested in modeling the diffusion

of new products. Studies in this tradition have often sought to explain the category sales of durable

goods at some cross-sectionally aggregated level (e.g., the U.S. level) across time. Under almost all

circumstances, this aggregate is no longer informative about the cross-sectional processes that govern

the diffusion.2 We are interested in how new brands diffuse across markets (space) and competing

retailers (networks). Hence a key feature that distinguishes our paper from extant work on diffusion

is that, in addition to the temporal dimension of diffusion, we model diffusion across geographic

space and retailer networks.

Spatial diffusion hold that the likelihood of innovations spreading from one point to another

is inversely related to distance. This diffusion concept has been applied to research questions in

the atmospheric sciences (Niu and Tiao 1995), epidemiology (Cliff et al 1981), and spatial statistics

(Stoffer 1986). It has as of yet received little attention in marketing. This is not to say that marketing

researchers do not acknowledge the potential importance of spatial diffusion as is apparent in the

work on international diffusion by Dekimpe, Parker and Sarvary (2000), and Putsis et al (1997).

Dekimpe, Parker and Sarvary (2000) make within-country adoption of technologies dependent on

the cross-country diffusion of such technologies. In turn, cross-country adoption is not explicitly

related to pair-wise proximity measures among countries (e.g., social similarity or distance). Putsis

et al (1997) allow local adoption to depend directly on adoption in another country but the cross-

country effects are equally strong for all pairs of countries. Our contribution vis-a-vis these papers

is that we explicitly model the effects of spatial and social proximity.

Network diffusion seeks to formalize the communication links between potential adopters and

traces diffusion of innovations along these links. Network diffusion is closely related to spatial

diffusion (especially with discrete spaces) and has roots in research on innovations (e.g., Valente

1995) and —more broadly— on sociology (e.g., Wasserman and Faust 1994). The contribution of this

paper to this literature is (1) the implementation of network effects in a new product diffusion model

2An exception occurs when the non-linearities in the individual level behavior aid in identification at the aggregatelevel (see e.g., Zenor and Srivastava 1993).

6

and (2) a test of alternative operationalizations of the network of multimarket retailers spanning the

continental United States.

Another, smaller, contrast to extant diffusion models is that our interest is with brand-level

diffusion and not category-level diffusion. However, at the retailer level, multiple brands can (and

do) achieve almost complete penetration of their target markets because retailers stock multiple

brands. As a consequence, we use a diffusion model with multiple brands, each of which can strive

for distribution by all retailers.

The managerially interesting aspect of diffusion in the context of business research on innovations

is that a portion of new product sales is generated through “inexpensive” word-of-mouth, or more

colloquially, that there is a “free lunch” or “windfall” created by the installed base of the product.

This “windfall” is managerially interesting because it depends on a manager’s choice of lead users

(in terms of how many potential users they may convert to adoptees). Sociological research deals

with suitable choices of “opinion leaders” or “lead users.” Specifically, Wasserman and Faust (1994)

formalize networks of potential adopters and seek to find those individuals with the highest degree

of centrality and prestige. The concepts of actor centrality and actor prestige are then used to select

those users that are the most effective “sources” of social contagion, e.g., will help diffuse the product

the quickest (for examples see Strang and Tuma 1993).

An important albeit somewhat stylized difference between the marketing tradition and the soci-

ology tradition in innovation research is that the former has predominantly dealt with diffusion of

new products across time, whereas the latter has predominantly dealt with diffusion across actors

or cross-sectional units. Indeed, most research in the marketing tradition has ignored differences

in users in terms of their efficacy in providing word-of-mouth, whereas the research tradition in so-

ciology often uses purely cross-sectional data. Vandenbulte and Lilien (2001) show that inferences

about what constitutes social “contagion” and simply cross-sectional covariation is confounded. As

perhaps the most clearly identifiable strength of this paper, we combine both streams to model the

spatio-temporal patterns in retailer adoption of new brands.

While the current paper is not about durable goods from a consumer-centric perspective, from

a retailer perspective, the distribution of a repeat purchase good is durable. Therefore we treat the

retailer decision to adopt a brand for distribution as a durable good. McLaughlin and Rao (1991)

study retailer adoption decisions of new brands. They find that retailer acceptance of new products is

7

related to a variety of variables ranging from marketing spending by vendors to product and vendor

status. Montgomery (1975) found that the percentage of competition carrying the new brand is

important in the adoption decision. However, both studies are cross-sectional.

3 The industry

Because our application uses data from the Frozen Pizza category, it helps the interpretation of the

empirical results to briefly discuss the industry and visualize the diffusion patterns of the main new

brands in this category. In addition to the presence of new product launches over our observation

window, we selected frozen pizza industry for our analysis because we have access to managers in-

volved with the new product launch. Finally, the Frozen Pizza category is sizable and manufacturers

have a large direct sales force thereby having greater control over their roll-out strategy and timing.

3.1 General description

Consumers. The frozen pizza (FP) industry accounted for roughly $2.8 billion of sales in the year

2000 in the United States. The category has the highest penetration of all frozen prepared foods:

57 percent of all American households buy frozen pizza. Frozen pizza consumption is highest among

18-44 year olds. There is little difference in consumption rates between single and married people

and no difference between black and white ethnic groups (Holcomb 2000). The market for frozen

pizza was forecasted to grow at a compounded annual rate of 8.9 percent per year between 1997 and

2002 (Holcomb 2000). Frozen pizza consumptions tends to be higher in the Midwest than elsewhere

in the United States. Supermarket sales account for 90 percent of frozen pizza sales.

Products. Prior to 1996, most sales occurred in the so-called “regular” frozen pizzas. The leading

two brands in this market were Tombstone and Tony’s, which were marketed by Kraft and Schwan’s

respectively. The latter manufacturer also produces the Red Baron brand. Each of these two leading

brands offers a variety of recipes and crusts. Prior to 1996 Kraft’s share of the industry was 33.7

percent, whereas Schwan’s had 23.5 percent market share (Holcomb 2000).

Manufacturer actions. From personal interviews, we learned that managers involved in these

launches choose lead markets for new brands very deliberately. Among the decision variables that

are frequently mentioned are transportation cost, low brand development index (BDI)3 for the man-

3The brand development index is measured as the sales of brands relative to all commodity volume scanned in a

8

ufacturer’s other brands accompanied by a high category development index (CDI)4 in local markets,

cannibalization, and funding constraints. Obviously, retailers on these lead markets play a crucial

role in the selection of which markets to target first. According to at least one Kraft manager,

a good lead market should be to some extent isolated, i.e., it should have smaller retail accounts

(predominantly from a cost perspective). In addition, another manager made the observation that

the Digiorno product sought to expand the frozen pizza category by competing with take-out pizza,

which may or may not have played a role in the selection of lead markets.

Retailer decisions. Retailers who adopt a new product do so typically once for all markets in

which they operate. For example, Kroger will approve to distribute a new Kraft brand, e.g., Digiorno,

for all its markets at once. That is to say, an important mile-stone in the diffusion of new products

through the retailer network, is whether the retailer approves the product at the chain level.

3.2 The introduction of Digiorno and Freschetta

Timing. Both Kraft as well as Schwan’s developed and launched a “premium” frozen pizza with

rising crust. First, Kraft introduced the Digiorno brand in 1995, followed a year later by Schwans’

introduction of the Freschetta line. These two introductions are the main focus of our study. Figures

2 and 3 visualize the diffusion of supermarket distribution for these two brands in the continental

United States.

Diffusion patterns. In both instances, brands are launched in a selected number of lead markets.

In the case of Digiorno, the brand is launched in Denver, Seattle, St. Louis and Atlanta. Two of these

markets (Denver and St. Louis) belong to the top-10 metropolitan areas in frozen pizza consumption

per capita (Holcomb 2000). In the case of Freschetta, the brand is launched in Omaha, St. Louis,

Minneapolis, and Kansas City. The first three launch cities belong to the same top-10. The launch

of Freschetta seems more local than that of Digiorno in the sense that Digiorno initially spans a

large area of the US with a select number of “lead markets” and fills in the empty space between

these cities through subsequent introductions. An alternative to this policy is to first create a dense

concentration of lead markets and expand —radially— from this “base.” There appears to be some

indication that initially Freschetta uses such a policy, expanding from north to south. Regardless, in

both cases there appears to be a strong local component to sequential market entry. For instance, in

given market. A high BDI means that relative to other markets the brands sell well.4CDI is the category sales divided by total sales over all categories.

9

(a) September 1995 (b) May 1996

(c) August 1996 (d) April 1998

25% ACV 50% ACV 75% ACV 100% ACV

Figure 2: Spatio-temporal development in retail distribution for Digiorno Pizza

Figure 2, we see that Digiorno expands from the Seattle market to three neighboring markets between

May and August 1996. Likewise, in Figure 3, it can be seen that Freschetta seeks to move south

from Atlanta into the Florida markets between April and October of 1997. Ample other examples

like this can be found in the graphs.

Success of the launches. Both launches were very successful and achieved national distribution

in 1 to 2 years with Freschetta starting later but rolling out faster than Digiorno. Currently, both

brands are important profit generators for their respective parent companies.

4 Model

We develop a model to represent the manufacturer’s decision to introduce a brand in a market, and

conditional on this decision, of the chain’s decision to carry the brand. Our modeling strategy consists

10

(a) January 1997 (b) April 1997

(c) October 1997 (d) July 1998

25% ACV 50% ACV 75% ACV 100% ACV

Figure 3: Spatio-temporal development in retail distribution for Freschetta Pizza

of representing these decisions as hazards with a survival probability following a probit specification.

We use an autoregressive representation of network and spatial effects. Figure 4 shows the main

model components. It shows that the spatial and network dependencies in the model are introduced

by allowing these individual level decisions to depend on similar decisions made by actors at other

points in geographical or social space and/or at earlier points in time. For instance, we allow the

adoption of a new brand by a given retailer to depend on the past adoption decisions of “neighboring”

retailers. Along the same lines, we allow for the entry of a given market to be influenced by past

entry in “neighboring” markets. Below, we first describe and operationalize the models for market

entry and retailer adoption, and then we define the neighborhood effects. Note that the spatial unit

of diffusion is different for entry decisions (markets) than for retailer adoptions (multimarket trade

areas). Therefore their respective definitions of neighborhood effects are different.

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chain adoption given entry in at

least one market of its trade area

Chains that haveadopted by t-1

Chains adopting at t

Markets that havebeen entered by t-1

exogenous effectson chain adoption

exogenous effectson market entry

network effectson chain adoption

spatial effectson market entry

market selectionbased on retailer

adoption

Adoption in trade-area by

chains

local market entry by the manufacturer

Markets beingentered at t

(a) mental model of diffusion (b) empirical operationalization

time delay

timedelay

timedelay

Figure 4: The main features of the model

4.1 Market entry model

Denote the presence of the brand in a market by yimt, where i = 1, ..., I indexes brands, m = 1, ...,M

indexes markets, and t = 1, ..., T indexes time. The variable yimt is discrete and assumes the value

1 if the brand is present in market m, at time t, and 0 else. Market entry is treated as an absorbing

event because the data do not cover situations where the manufacturer retracts a new brand from a

market. Each market m eventually adopts.

The basic model with which we formalize entry into market m by manufacturer i in week t is a

probit model with an absorbing state.

Pr(yimt = 1) = [Φ (Uimt)]1−yimt−1 , (1)

in which Uimt is the attraction of market m in week t for manufacturer i, and Φ is the CDF of

the standard normal distribution N (0, 1). The power in this specification implements the absorbing

nature of market entry. This is consistent with a hazard interpretation of the probit model. A direct

consequence of this model is that observations of yimt are irrelevant for inferences after the brand

has been introduced in market m.

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A flexible model of Uimt is obtained using a variance components model that includes fixed and

random effects of brand, market and time variables. Specifically, let

Uimt = Xyimt · θ + βm + γit, (2)

so that in addition to fixed effects Xyimt · θ, we allow for random components at the market level

βm that are common across brands and time, and for random components γit that are common to

markets but vary across brands and time.

Fixed effects. With respect to fixed effects we use the following operationalizations (for a short

overview of all the variables used in the model see Table 1). First, we allow for brand specific

intercepts for the brands considered in this study.

Second, the probability of market entry may be affected by the category development index,

CDIymt. We define the category development index in this study as the weekly category dollars as a

percentage of the total weekly dollars scanned in a market. In the same vein, we believe that the

probability of market entry may be affected by the manufacturer development index, MDIyimt. This

variable is defined as manufacturer i’s dollar share of the category in market m and week t. To the

extent that transportation costs play a role in the entry of markets, we use distance to manufacturing

site DSMyim (in 1000 miles) as the covariate for this component.

Next, we define the spatial effects, SPTyimt as the spatially autoregressive effect of market entry

in neighboring markets. These neighboring markets can be coded in an M ×M matrix Ws whose

rows add to one, and whose entries [m,m′] are 0 if m and m′ are not neighbors and positive if they

are. Next, arraying the market entry variables of t− 1 across markets into the M × 1 vector yit−1,

we define SPTyimt as the mth element of the spatially and temporally lagged (see Bronnenberg and

Mahajan 2001) market entry variables.

SPTyit =

(M×1)Ws·yit−1. (3)

In practical terms, SPTyimt is the weighted average of past entry in neighboring markets. The weights

are defined in a subsequent section. We expect the spatial effects of SPTyimt on entry to be positive,

i.e., we expect entry to be close to previously entered markets.

Another variable of interest in this study is market share of chains who have adopted previously

in another market, PRVyimt. This variable is defined as the sum of market shares in market m of

chains who adopted manufacturer i′s new brand in any market prior to t. Formally, we use an M by

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K matrix H containing the ACV share of chain k in market m. In other words, in each row m, the

matrix H lists the share of all retailers in market m. Absence of a chain k from market m equates

to an ACV share of 0. Rows of H add to unity, i.e., shares add to 1 within each market. Last, H

can be interpreted as a representation of the geographical structure of U.S. retail chains. Denote the

distribution status of brand i by zikt = 1 if chain k adopted before or in week t and zikt = 0 if the

chain did not adopt up until week t. Array across chains to obtain a K × 1 vector zit. Then, we

define PRVyimt as the mth element of

PRVyit =

(M×1)H · zit−1. (4)

PRVyimt can be interpreted as a weighted average of past adoption among retailers that are in market

m. This measure is between 0 (none of the chains in market m has adopted the brand in the past

anywhere else) and 1 (all chains on market m have already adopted the brand previously in some

other market m′ �= m).

Random effects. Equation (2) contains two random components, βm and γit. These components

allow for market specific and brand-time specific influences on market entry. In turn, each of these

components contains descriptors of markets and brand-time interactions respectively. None of the

random components can contain an intercept because such an intercept would be confounded with

the intercepts in the fixed effects (see Vines, Gilks, and Wild 1996).

For the market specific random effects, we use three relevant market descriptors. We define

the size, ACVym, of the market measured as the average weekly volume sold on a given market in

millions of dollars. Then, we define the market level concentration, HRFym, of the retail-industry as

the Herfindahl index of the market shares based on all-commodity-volume (ACV) for the retailers

in market m. Finally, we use the fraction of the size of the market, SNIym, that is sold through

retail-chains rather than independent stores.5 The variable SNIym is a proxy for how “connected” a

market is in the network of retailers. That is, the larger the market share of independent stores is in

a given market, the less ties will exist across markets because such independent stores do not have

multi-market presence.

Through the brand-time random components we allow for the probability of market entry for

each brand to be time dependent. We define the variable TSIyit as the time since manufacturer i

introduced the brand in the first local market. If, for example, manufacturer 1 first introduces a

5 SNI stands for Shares of Non-Independent chains

14

new brand in week 201 in, say, St.-Louis, MO, then the variable TSIy1t counts the weeks after that

initial introduction for market other than St.-Louis. This variable allows for increasing or decreasing

hazard rates (e.g., Johnson and Kotz 1970, p. 283) for each brand, i.e., allows for acceleration or

deceleration of market entry. To summarize the discussion above, the complete specification of the

market entry model used in this study is as follows:

Uimt = θi + θ3CDIymt + θ4MDIyimt + θ5DSMyim + θ6SPT

yimt+

θ7PRVyimt + βm + γit, i = {1, 2}

(5)

with

βm ∼ N(φ1ACV

ym + φ2HRF

ym + φ3SNI

ym, σ2

β

)γit ∼ N

(λTSIyit, σ

2γ

) . (6)

4.2 Chain adoption model

Similar to the model of market entry, we propose a probit model to represent the probability that

a retail chain adopts the brand. For each chain k, brand i, and week t we let zikt = 1 if the brand

is adopted at or before week t and zikt = 0 if the brand is not adopted. Adoption can only occur

if the brand is made available by the manufacturer in at least one market that belongs to chain k’s

territory. Formally, if we let Ck be the set of markets on which chain k operates, and we write yiCkt

be an indicator variable that assumes the value 1 if brand i is available at week t on at least one

market m in Ck and 0 in all other cases, then adoption by retailer k of manufacturer i’s brand in

week t is modeled as a probit model with an absorbing state.

Pr(zikt = 1) = yiCkt · [Φ (Vikt)]1−zikt−1 , (7)

The multiplication by yiCkt expresses that entry in a retailer’s trade area is necessary for adoption.

The power 1 − zikt−1 implements that adoption is an absorbing state (retailers do not disadopt in

our data). Defining the moment of earliest entry into the trade area of retailer k by tavailk , and the

moment of first time adoption by the retailer by tadoptk , we write

Pr(zikt = 1) =

0 if t < tavailk

Φ(Vikt) if tavailk ≤ t ≤ tadoptk

1 if t > tadoptk

. (8)

15

Thus, the relevant observations for inference fall between (1) the moment of manufacturer entry in

the retailer’s trade area and (2) adoption by the chain somewhere in its trade area (inclusive of the

moment of adoption).

Analogous to the market entry model above, we specify that Vikt contains fixed and random

effects,

Vikt = Xziktµ+ bk (9)

This model is the same as the market entry model (2) except for the fact that the time brand

interaction is absent. Rather than being influenced by the time since introduction, we believe that

retailers k may be influenced in their adoption of brand i by the time that has elapsed since the

manufacturer entered its trade area. This is not a two-way i, t interaction, but a three way interaction

between time, retailer and brand which will be specified in the fixed effects.

Fixed effects. Among the fixed effects are brand specific intercepts µi, i = 1, 2, for each of the

two brands considered in this study.

Second, we allow the time difference between brand-availability and brand-adoption at the retailer

level to be dependent on the category development index, CDIzkt, at the retailer level. This variable

is defined as the weekly retailer level sales of the entire category as a percentage of the retailer’s

total volume (for short reminders of the definitions of this and other variables, see Table 1). We

expect retailers with higher CDIzkt to adopt earlier, i.e., the effect of the category development index

of the retailer on adoption is expected to be positive. Next, we allow for effects of the manufacturer

development index, MDIzikt, at the retailer level. This variable is manufacturer i’s dollar-share of

the category with retailer k. We expect retailers with a higher share of i’s extant brands to adopt a

new brand by manufacturer i earlier than with a lower share of i’s existing brands. As argued before

acceleration or deceleration of the tendency to adopt is controlled by introducing a variable, TSAzikt,

that measures the time since the brand became available in retailer k’s trade area (in weeks). We

have no a priori expectation of the effect of time since availability on adoption.

Central to this study, we introduce a variable that allows the adoptions by chains to be related

to past adoptions by other chains. This variable, DIFzikt, is defined by specifying an autoregressive

effect of adoption by retailers that are “close” in the network of overlapping retail trade areas ( see

e.g., Bronnenberg and Sismeiro 2002). Closeness can be captured in a K × K matrix Wn (to be

defined) whose rows add to one, and whose entries [k, k′] are 0 if k and k′ do not compete in the same

16

geographic markets and positive if they do compete directly. Going back to the definition of DIFzikt,

array the K distribution variables zikt−1 at t− 1 across markets into the K × 1 vector zit−1. Next,

DIFzikt is the kth element of the spatially and temporally lagged (see Bronnenberg and Mahajan

2001) chain adoption variables.

DIFzit =

(K×1)Wnzit−1. (10)

These variables can be interpreted as weighted averages of past adoptions by competing retailers. The

weights capture the degree of influence by each direct competitor in one’s trade area. Consistent with

the central hypothesis in innovation diffusion research, the expectation is that the effect of DIFzikt

on the adoption of brand i by retailer k in week t is positive.

Random effects. The components bk contain the retail chain effects on adoption timing. As

before, the components bk are modeled as a hierarchical model with covariates. We use two retailer-

level covariates. First, we define ACVzk as the total size of the retail chain in $MM aggregated across

all markets in k’s trade area and averaged over weeks. We expect the effect of chain size on adoption

to be positive. Second, the variable HRFzk measures the degree of spatial concentration of a retailer’s

ACV over the markets on which it operates. It is measured as the Herfindahl index of total retailer

volume across markets. For example, Dominicks is a retailer whose volume is very concentrated in

Chicago and is an example of a retailer with a high HRFzk. On the other hand, Kroger is a retailer

whose total volume is spread across many markets in the Eastern United States and is an example

of a retailer with a low HRFzk.

To summarize our retailer adoption model, we use a probit model (8), with the following opera-

tionalization

Vikt = µi + µ3CDIzkt + µ4MDIzikt + µ5TSAzikt + µ6DIFz

ikt + bk, i = {1, 2} (11)

with

bk ∼ N(ψ1ACV

zk + ψ2HRF

zk, σ

2b

). (12)

Obviously, from a diffusion perspective, special interest is with the parameter µ6. If this parameter is

positive this means that retailers tend to be influenced by past adoptions of retailers that are “close”

in the retailer network

17

4.3 The representation of geographic proximity

The spatial variable SPTimt uses a weight matrix Ws. We propose to use a discrete definition of

geographical space. Therefore the weight matrix identifies which locations are neighbors. Ws is also

called a spatial lag operator (see e.g., Anselin 1988). Generally, the rows of Ws add to 1. If so, the

matrix is said to be standardized. In this study, we use a standardized spatial lag operator Ws.

The definition of a set {Vi} of neighbors of market i must follow from a suitable discretization

of geographic space. We use the simple concept of Voronoi polygons (Okabe, et al. 2000 ), which

divides geographic space (e.g., the United States) exhaustively into mutually exclusive areas around

centers (e.g., local markets such as New York, Los Angeles, etc.) whose interior points are closest to

these centers. We define as a neighbor two local markets, whose Voronoi polygons have a common

edge. Thus, a given market can not be a neighbor of itself. For an illustration of Voronoi polygons

to define spatial autoregression in multimarket data using local U.S. markets, see Bronnenberg and

Mahajan (2001). For other illustrations of using geographic neighbors in marketing models, see e.g.,

ter Hofstede, Wedel and Steenkamp (2002).

We specify two alternative definitions for the weights in Ws. Defining the number of markets in

the neighbor-set {Vi} as Ni, these definitions are

ws,N (i, j) =

1/Ni if j ∈ {Vi}

0 elseand ws,acv(i, j) =

ACVj/∑

k∈{Vi}ACVk if j ∈ {Vi}

0 else(13)

The first definition takes the influence of each market on market entry to be equal, while the second

gives higher weight to larger markets.

4.4 The representation of the retailer network and network effects

The U.S. retail industry consists of many different retail chains. Some of these chains compete

directly in the same geographical markets, while others are separated from each other by distance.

Because we wish to measure the role of retailer connectedness in the diffusion of new products, it

will be useful to propose a definition of the degree to which pairs of retailers are “linked.” A useful

definition for such network links utilizes the overlap in trade areas between two retailers as a measure

of link-strength. More precisely, let retailer r operate in a set of markets m ∈ Cr, with Cr being

its retail trade area. Denote the average dollar-sales volume per week by retailer r in market m by

ACVrm. Then, the link-strength of r′ to retailer r is defined by the former’s share of ACV in the

18

latter’s territory. Specifically, a useful definition of the link-strength of retailer r′ to retailer r is

wn,acv(r, r′) =

∑m∈Cr

ACVr′m∑r′′ �=r

∑m∈Cr

ACVr′′m

and wn(r, r) = 0 ∀r. (14)

This measure is between 0 and 1 and adds to 1 over all competitors r′ for any retail chain r. The link

wn(r, r′) is 0 for all pairs of retail-chains whose trade-areas do not overlap and becomes larger with

the degree to which the trade areas of two retailers coincide. This definition also expresses that, for

any given retail-chain, large direct competitors have more influence than small direct competitors.

An alternative definition of the link between retailer r′ and r takes into account the size of the

retailer r to express that the influence of r′ on r is larger in markets where both are large. This

definition implies that greater weight is accorded to competing chains that operate within a chain’s

core (i.e., large share) markets. This interaction can be expressed as

wn,inter(r, r′) =

∑m∈Cr

ACVr′m ·ACVrm∑r′′ �=r

∑m∈Cr

ACVr′′m ·ACVrm

and wn(r, r) = 0 ∀r. (15)

Figure 5 helps to explain these definitions. This figure represents a hypothetical situation with 3

markets, and 3 retail chains. Retailer 1 operates in markets A and C, and it faces competition from

retailer 2 in market A and from retailer 3 in market C. The definition for wn,acv above states that

the relative influence on chain 1 is equal to

wn,acv(retailer 1, retailer 1) = 0

wn,acv(retailer 1, retailer 2) =ACV2A

ACV2A +ACV3C

and (16)

wn,acv(retailer 1, retailer 3) =ACV3C

ACV2A +ACV3C

In other words, the relative influence on retailer 1 by retailers 2 and 3 is proportional to the size of

the latter retailers in the former’s trade area.6 Taking the size of the circles proportional to market

size, retailer 3 is a larger retailer than retailer 2 in retailer 1’s trade area. Our definition for wn,acv

in equation (14) then implies that retailer 3 has more influence on retailer 1’s adoption than retailer

2 has.

In practice, the influence of retailers is not symmetric. Our definition allows for this. For example,

consider two retailers: H-E-B and Albertsons. Albertsons is a retailer with a very large trade area

6 If we use the definition based on the market-specific interactions between chains, then we would find for examplethat wn,inter(retailer 1,retailer 2) =ACV2A·ACV1A/(ACV2A·ACV1A+ACV3C ·ACV1C).

19

RETAILER 1

RETAILER 1

RETAILER 2RETAILER 2

RETAILER 3

RETAILER 3

MARKET A

MARKET B

MARKET C

Figure 5: Overlapping retail territories and market links

that spans the entire West and South of the continental U.S. (see also Figure 5). Because of the

size of its trade area it faces many competitors. H-E-B on the other hand is a high share retailer

located in several Texan markets. Given its geographic concentration it faces far fewer competitors.

Therefore, among all competitors of Albertsons, H-E-B’s share is relatively small because H-E-B is

present in only a few markets of Albertsons’ trade area. On the other hand, Albertson’s is present in

every market on which H-E-B operates. Among H-E-B’s competitors Albertson’s has an ACV share

of 0.258. We take this to imply that if network effects are important, all else equal, the influence of

Albertsons on H-E-B’s decision to adopt a new brand may be higher than vice versa.

All possible combinations for pairs of retailers span a K ×K matrix Wn, as follows:

Wn =

0 wn(1, 2) · · · wn(1,K)

wn(2, 1) 0 · · · wn(2,K)...

.... . .

...

wn(K, 1) wn(K, 2) · · · 0

This sparse matrix, i.e., which contains many wn(k, k

′) = 0, represents the network of retailers as a

sociomatrix with asymmetric links (see, e.g., Wasserman and Faust 1994, ch. 4).

20

4.5 Discussion

The model as operationalized herein presents a testable account of the spatial and temporal patterns

with which two recent national rollouts took place. The model is a reduced form model containing

equations for market entry by manufacturers and retail chain adoption given availability in its trade

area.

The simple structure of the model originates from the use of time lags. The selection effect on

market entry yit (M × 1) at time t is based on the retailer adoption zit−1 (K× 1) at time t− 1. This

assumption follows from noting that the sample rate of the data is high (weekly) compared to the

decision process to enter a market or to adopt a brand for distribution. It is therefore reasonable to

assume that same-week selection effects are absent, because adoption by retailer k in week t can not

cause same-week entry by the manufacturer in the other markets on which k operates. For a similar

point regarding the modeling of events in time and space, see Cressie (1993, p. 450). Likewise,

the spatial effects on yit are captured through spatial dependence on yit−1. Finally, the network

effects relate zit to zit−1. Because our observations include weeks up to and including the moment of

adoption, the model does not contain circularities. Statistically the two equations are even unrelated.

We offer a very selective justification on the variables in the equations (many of these variables

lie at the intersection of the factors enumerated by management and the measures in the data). The

variables in the market entry models are possibly related to launch cost. Indeed, it may be cheaper

for manufacturers to concentrate on markets (1) which are concentrated (fewer retailers), (2) which

are located close to markets that were entered before, or (3) on which many retailers operate who

adopted previously. If the selection effect is important, we additionally expect manufacturers to

enter markets with small shares of independent stores early (which also implies a positive effect of

the variable that measures the market level share of multi-market retailers, SNIkm).

Finally, consistent with the model in Figure 4, the selection effects and the market entry con-

straints on adoption decisions create a feedback loop among market entry and retailer adoption. In

other words, the evolution of retailer distribution in this model is path dependent and makes that

lead market selection matters for the speed of diffusion. We investigate lead-market selection explic-

itly after the estimation results of the model are discussed. We now turn to the empirical analysis

that produces these results.

21

5 Empirical analysis

5.1 Data

The data used in this study consist of sales data from the Frozen Pizza category for a national sample

of 1900 supermarket stores across 166 retailers and 95 local markets. We use the IRI definition for

what constitutes a market. Typically, an IRI market is either a metropolitan area (e.g., New York) or

a region (e.g. West Texas/New Mexico). Retailers are designated by a retailer code. Large retailers

may have region-dependent codes. Because, our interviews with Kraft managers indicated that

even these large retailers first take a central decision in approving the brand chain wide, such region

dependent codes were unified. The sample of stores and chains are subject to attrition and expansion

in our data, which we assume to be independent of the category under investigation. Retailers for

which first time adoption is not observed (i.e., retail chains that adopted prior to entering the sample)

add no information about adoption-timing and were not used in the analysis (there are a few small

retailers for which this holds). Also, independent stores were dropped from the analysis,7 because

they do not constitute a retail chain.

The data span 5 years of weekly store-level sales data. During this time two major new brands

were launched. First, Digiorno was launched in 1995. This Kraft-Foods brand, which established

the “premium” frozen pizza segment, was very successful. A year later Freschetta was launched by

Schwan’s as Digiorno’s direct competitor. Both brands obtained national retail distribution coverage.

As explained, the dependent variables central to this study are (1) the timing of market entry and

(2) the timing of retailer adoption given availability, i.e., entry in at least one market of a retailer’s

trade area. These variables are in principle unobserved to the analyst. Nonetheless, the available

IRI data allow for high quality proxies for the timing of these two decisions. First, we define the

moment of market entry as the week of first time sales in a given market. Second, the moment of

chain adoption is taken as the earliest week across all markets belonging to a retailer’s trade area in

which sales was recorded.8 While there may be small deviations between the first time we observe

sales and the actual decision moments by manufacturers and retailers, the variation in the proxies

7 The data on independents was however used in the computation of several variables. For instance, the variableSNIym measures the percentage of ACV in each market that is moved by chains with multi-market presence.

8 In a few instances, these definitions synchronize the initial market entry by manufacturers with the initial adoptionsby retailers. However, this simultaneity is uncommon and ample empirical observations exist to identify the two stagesin the model.

22

across retailers and markets is clearly beyond any reasonable measure of observation error within

retailers and markets. For instance, across markets, entry occurs on average 62 weeks after the first

market was entered for Digiorno and 28 weeks for Freschetta. Hence, the observed variation in entry

timing is very large compared to the time it takes to make such a decision. As a consequence, we

take the observed entry to be informative about the actual entry decisions by manufacturers. Along

the same lines, the deviation across retailers in adoption timing since availability is 15 weeks for

Digiorno and 17 weeks for Freschetta.9 We therefore believe that these observed adoption times are

informative about retailer adoption timing, because it is unlikely that a delay of 3 months or more

in adoption is coincidental or manufacturer driven.

––– Table 1 about here –––

Table 1 lists some descriptive statistics of the variables used in this study. The descriptive

statistics report on averages and standard deviations over all relevant observations of market entry

yimt and retailer adoption zikt. For instance, the market level category development index, CDIymt,

averages 0.67 and has a standard deviation in the data of 0.46. Hence, on average across markets,

0.67% of all scanned items by IRI are of the frozen pizza category.

5.2 Estimation

We estimate the hierarchical variance components model in equations (5) and (11) using an MCMC

approach. To implement this estimation approach, we specify the full-conditional distributions of

all model parameters and their prior distributions. Appendix A contains the full conditionals, while

appendix B contains the MCMC algorithm. The prior distributions are of two types and are chosen

to be uninformative. For all model parameters other than variance terms, we use IID N (0, 10000)

distributions. The variance terms of the model have an IG(1, 1) prior distribution.

A couple of notes about implementation of the MCMC chain deserve mentioning. Poor mixing,

i.e., the phenomenon that the parameters meander slowly, may occur with models of the type con-

tained in equations (5) and (11). Taking for instance the model in (5), an immediate problem is

9 The large variation in the data also helps to dispell the possibility that the differences in adoption across retailersare manufacturer controlled. This would for instance happen if manufacturers initially make their brand selectivelyavailable to a subset of retailers in a given market. From a cost perspective, it makes little sense to “hold back” newbrands selectively (for as long as multiple quarters) from some retailers, given that many launch costs are forceblymade at the market level (e.g., advertising or transportation).

23

that one can add a constant to all βm and subtract this from the intercept term in the θ vector

without altering the likelihood of the data (Gilks, Richardson, and Spiegelhalter 1996; Vines, Gilks

and Wild 1996). Fixes to this problem exist such as reparametrizing the model with a zero-mean for

βm (across m) at every pass through the sampler (Vines, Gilks, and Wild 1996). Alternatives to this

so-called sweeping are hierarchical centering (Gelfand, Sahu, and Carlin 1995), or block sampling

(Chib and Carlin 1999). In our application, we control for poor mixing by avoiding the use of too

many random factors.10,11

We executed the MCMC chain for 500,000 draws, used the first 50,000 draws for burn-in and

then sampled every 50th draw from the MCMC chain for further analysis. Thus a total of 9,000

draws are used in the computation of the parameter estimates.

We estimated all 4 combinations of models with Ws based on the number of neighbors (Ws,N )

or size of neighbors (Ws,acv), and with Wn based on the local size of rival chains (Wn,acv) or the

interaction of own size with the size of rival chains (Wn,inter). In addition, to contrast our model

to one where we just care about retailer adoption, we estimated the model based on equation (11)

only. In the latter model, all spatial and temporal evolution in market entry is attributed to retailer

adoption through Wn.

5.3 Results

5.3.1 Adoption conditional on market entry. The four operationalizations of the full model

were compared using Bayes Factors. We computed these factors using the method proposed by

Gelfand and Dey (1994) and Raftery (1996). The best operationalization of the weight matrices

uses contiguity relations based on market size (Ws,acv) and the local size of rival chains (Wn,acv). A

close second is the model with spatial lags defined by Ws,N and with Wn,acv. The models with the

retailer network effects based on the interaction between own and rival chains (i.e., using Wn,inter)

performes less on the Bayes factor criterion. Estimation results for the best model are in Table 2.

Market entry The vector θ contains the regression effects of the market entry model. Both

10 We also estimated the model using an orthogonalization by demeaning the covariates of the random componentsin the model. The parameter estimates were found to be identical except for a shift in the intercept to reflect the sweapof the mean. The convergence with sweeping is markedly quicker than without.

11 For instance, estimation of more and more random factors in addition to βm and γit makes the chain mix lessand less efficiently. Contemplate, for instance, a factor δim. Such a factor is very hard to distinguish from βm becausethere are only few brands. Hence, estimates of the sum of βm and δim will be stable, but their separate estimates areconfounded in practice.

24

brands have negative intercepts, because market entry is a relatively low probability event. The

intercept for Freschetta, θ2, is higher than that of Digiorno, θ1 (although the distributions overlap

somewhat). This means that while rollout is slow, Freschetta rolls out faster than Digiorno.

The effect θ3 of the category development index, CDIymt, on market entry yimt is not different from

0. In other words, the two manufacturers do not seem to enter markets in increasing or decreasing

order of category importance (although the lead markets are high-CDI markets).

In contrast, the effect θ4 of the manufacturer development index, MDIyimt, is significant and

positive. Manufacturers have a tendency to first enter markets on which they have a large extant

share. While this seems logical, prima facie, the effect is least unexpected, on reflection. It seems

conservative of a manufacturer to launch a new brand first where it already has high shares with

extant brands. The potential for cannibalization is highest in such markets. On the other hand, if

the new brand is targeted to a new market segment that is not currently served,12 there are potential

reputation benefits in markets with high MDIyimt. This is, in turn, a plausible reason for early entry

among all possible markets.

The distance to the manufacturing site, DSMyim, has no impact on the timing of entry or the

order in which markets are entered (θ5 is not different from 0). This is not unreasonable, because

one would expect the distribution cost to impact local market prices (Anderson and de Palma 1988)

and not necessarily the order of market entry.

The values of θ6 and θ7 represent the spatial and selection effects on market entry. The value

of θ6 is positive, and hence entry of markets depends positively on whether neighboring markets

have been entered in the past. We therefore infer that manufacturers tend to launch brands close

to markets that were already entered. A possible explanation for this entry pattern is more efficient

use of multimarket resources in the distribution channel such as distribution centers, transportation

carriers, etc.

Finally, the effect θ7 of PRVyimt is also positive. This means that markets are more likely entered

if retailers that operate on them have adopted in the past (i.e., in other markets). This effect is

interpreted as a “selection” effect, because it is the manufacturers’ choice to select markets with

chains that have already approved the brand in the past. Importantly, it is this selection effect that

12 There is some support for this condition. According to a Kraft manager, Digiorno was developed and marketed tocompete with take-out pizza and not with frozen pizza brands that were already on the market. The Digiorno slogan“It’s not delivery, it’s Digiorno!” reflects this positioning.

25

creates a feedback from retailer adoption to market entry.

A potential empirical concern with these two effects is their proper separation or discriminant

validity. Such a concern would be especially valid if many retailers are common to two neighboring

markets and, conversely, if two markets that have retailers in common, are also located close to

each other. Namely, if this were the case, the effects of PRVyimt and SPTy

imt would be confounded.

However, taking into account the actual retail structure in the United States, i.e., the M ×K matrix

H, the latter statement is not generally true. Whereas neighboring markets do share retailers,

markets with common retailers do not necessarily have to be spatially close. For example, Safeway is

large in San Francisco and in Washington D.C. (see Figure 5) but these markets are separated by a

large distance. As a result the variables SPTyimt and PRVy

imt are only moderately (0.32) correlated.

Hence, the spatial effects θ6 and selection effects θ7 measure different things.

With respect to the random factors βm and γit, we discuss the effects of their covariates. First

the effect φ1 represents the impact of market size, ACVym, on the random effect βm. The parameter

φ1 is not different from 0, and hence market size does not impact βm and by extension does not

impact the timing of market entry.

Second, because φ2 < 0, we infer that concentration of the retail industry in a given market,

HRFym, has a negative significant impact on market entry. Hence, markets that are not very con-

centrated, i.e., have many retailers, are entered earlier than markets that have one very dominant

retailer. It therefore seems that during early launch among manufacturers avoid reliance on only one

or few retailers. This seems consistent with the Kraft manager who stated that lead markets were

chosen such as to avoid markets with a single large retail chain. This approach seems to make the

manufacturer less dependent on any given retailer in early success of the brand.

The effect of the share of retail chains as opposed to independent stores, SNIym, is positive, that

is, φ3 > 0. This variable measures the strength of connection among markets due to multi-market

presence of retailers. Its large positive effect seems to indicate that manufacturers seek to enter

markets early that are “central” or “well-connected” through retailers.13

Finally, the factor γit has one covariate. The effect, λ, of time since introduction, TSIyit, is positive

and significant. This suggests that the rate at which markets are entered increases with time. This

13 Interestingly, and counter to what we find, in one interview with a Kraft manager, it was suggested that earlymarkets were selected for being relatively “isolated,” so that the cost of retailer incentives would be low. We do notfind this in the data.

26

“acceleration approach” is consistent with a conservative launch strategy (i.e., starting slow).

––– Table 2 about here –––

Chain adoption Given availability, Digiorno and Freschetta are adopted at base rates that are

comparable although Digiorno is adopted slightly faster than Freschetta. However, the intercepts µ2

for Freschetta and µ1 for Digiorno are not significantly different.

Retailers adopt a brand faster if the frozen pizza category is an important one. That is to say, the

effect, µ3, of the category development index, CDIzkt, at the retailer level is positive and significant.

Hence, retailers with a larger revenue share of frozen pizza (as a % of retailer ACV) adopt a new

brand earlier than retailers with a smaller revenue share of this category. One explanation for this

effect is that retailers with a large frozen pizza category are economically more motivated to try

innovations belonging to this category than retailers with a small frozen pizza category (see also

Rogers 1983). Additionally, retailers with a large frozen pizza category are likely to have more

available cooler equipment to shelf a new brand without having to rearrange the entire category.

Retailers also adopt a brand faster if the manufacturer has a large category share with the retailer.

That is to say, µ4, the effect of manufacturer i’s development index with retailer k,MDIzikt, is positive.

Retailers will likely have a tendency to adopt the brand from a high share manufacturer because this

manufacturer appears to be the preferred one among consumers from the retailer’s perspective.

Retailer adoption decelerates with the time since the brand is available in its trade area, TSAzikt,

i.e. µ5 < 0. In other words, the longer it takes for a retailer to adopt, the less likely it is that they

ever will.

Importantly, the network-diffusion effect among retailers, µ6, is positive. This means that retailers

have an increased tendency to adopt the brand if other retailers in their trade area have done so in

the past. This effect accords with what Bass (1969) calls a “word-of-mouth” or installed base effect.

While the network diffusion effect is significant, there are other effects (retailer specific characteristics

such as MDIzikt) that have greater on chain adoption.

Next we discuss the random effects bk. These random effects have two covariates. First, the

retailer level random effects are driven by retailer size (measured by ACVzk). Because ψ1 > 0, we

infer that the larger a retailer, the higher the probability is that it will adopt early. Rogers (1983)

27

notes, supportive of this effect, that early adoption of industrial goods is related to the size of the

adopter.

Finally, the effect ψ2 of concentration of retailers across markets, HRFzk, i.e., whether a retailer

is concentrated in one or two markets (e.g. Jewel in Chicago) of its trade area, or whether its total

size is spread across many markets (e.g., Kroger) is not different from 0.

5.3.2 Adoption confounded with availability The results discussed above are obtained from

the two-stage model where retailer adoption timing is conditioned on availability. Most diffusion

models, even individual level models (e.g., Lattin and Roberts 2000), do not take this condition

into account. In our specific case, the omission of the availability condition leads to very different

inferences for the adoption behavior of retailers. Table 3 shows the estimation results of a model

which ignores availability as a necessary condition for adoption. In such a model, the attribution is

made that manufacturer delays in market entry are in fact retailer delays in adoption. This leads to

the following differences in inferences compared to the conclusions above.

––– Table 3 about here –––

First, and most importantly, the influence of network diffusion (µ6) becomes more than three

times as large as before. Most likely this is because the spatial contiguity of retail-trade areas

can substitute in part for the spatial roll-out patterns of manufacturer entry. In fact, the network

diffusion effect is now larger than the effect of for instance MDIzikt.

Second, when availability is ignored, the adoption rates no longer decrease with time but instead

increase with time. This is likely caused by the fact that markets are entered progressively by

manufacturers, (i.e., λ > 0), and that the timing of entry and the timing of adoption are now

collapsed into one variable.

Third, and finally, instead of being zero, the effect of retailer concentration, ψ2, is now negative

and significant. This means that the degree to which retailers are concentrated in one or few markets

impacts the combination of entry and adoption negatively. This spurious effect can less clearly be

traced back to a single aspect of market entry but rather is a combination of omitting the influence

of connectedness (SNIym) and market concentration (HRFym) at the market level.

28

In sum, by ignoring the marketing actions (launch strategy) of manufacturers, the role of network

diffusion is very substantially overstated. Interestingly, and in a different context Vandenbulte and

Lilien (2001) also find that taking the marketing actions of manufacturers in to account tends to

weaken estimates of the “external” or word-of-mouth influence.14 Hence, it is very important that

efforts be made to include the marketing activity of firms in models of diffusion.

6 The selection of lead markets

With every new product rollout, managers need to select lead markets. To guide such decisions, we

designed a numerical experiment that focuses on the implications of the spatial—, and the selection

effects (SPTyimt and PRVy

imt) and the network effects (DIFzikt) on lead-market attractiveness.

The experiment initiates in each of the M markets a rollout at t = t0 by making the new brand

available in that market. After initialization in a candidate lead market m = 1, ...,M, other markets

are entered, and chains k = 1, ...,K adopt, probabilistically guided by the models (5) and (11). At

the same time, the three variables above, SPTyimt, PRV

yimt and DIFz

ikt, are updated recursively based

on markets entered and retailers that adopt. To isolate the effects of the U.S. geography and the

geographical retail structure, we set the parameters for all other variables to 0, while the effects

of SPTyimt, PRV

yimt and DIFz

ikt were set at 2, 1, and 0.5 respectively (e.g., their rounded empirical

values).

Given the probabilistic simulation of market entry and retailer adoption, not all sample paths

of diffusion for a given lead market m are identical. Indeed the number of possible diffusion paths

through the 166 retailers and 95 markets presents a formidable combinatorial problem. Therefore, we

approximated the variability of sample paths by running for each candidate lead marketm = 1, ...,M

400 replications, � = 1, ..., 400. For each combination of m and �, the number of weeks, Tm�, was

stored at which all 95 markets were entered and minimally 50% of all chains had adopted.15

To report on the findings of the experiment, we order the markets m = 1, ...,M on the mean (of

a left quantile to be chosen)16 of Tm� for each m. For instance, below we report the mean of the

best 10% of the completion times Tm� for each market. Figure 6 visualizes the location of the lead

14 However, this is not universally true, see e.g., Bass, Krishnan and Jain (1994).15 Other criteria were used with similar results.16 We use a left-quantile because, in the spirit of lead market selection, interest is with the “best” diffusion paths

not with the “average” path.

29

markets which performed best on this criterion. To facilitate interpretation, these lead markets are

placed relative to the trade areas of four of the main retailers in the United States.

From both a geographical and a retailer-network standpoint Denver is an attractive lead market.

This is not because of its central location in the United States —many such “central” markets fair

poorly— although that fact does contribute. Rather, Denver is in the trade area of three major

retailers, and is on the edge (convex hull) of two of them, opening up a large set of markets in the

United States (through the selection effect of PRVyimt).

Two of the best geographical lead markets are on the spatial edge of the U.S.. The market named

“Louisiana” is large and is in the trade area of both Kroger and Albertsons. Together, these two

retailers cover the majority of the US markets. Washington DC is an attractive market in our model

because Safeway operates on it and gives the brand potential exposure on both coasts. So, whereas

Washington DC is an “edge-market” in Euclidean space, from a retailer perspective it is a more

“central” market.

Many attractive lead markets are located in the trade area of Cubs Foods. This retailer has

excellent coverage in the central and Northern United States. In addition, the trade areas of retailers

in the East, South, and West of the United States all connect through the trade area of Cubs Foods,

giving it a high degree of what is called “betweenness centrality” (Wasserman and Faust 1994, p.

189-191).

The results for the average of other quantiles of Tm� are reasonably robust. For instance, the

correlation between the average completion time based on the 10th percentile correlates in excess of

0.8 with the average based on the 25th percentile. While the exact ordering of markets on average

completion time may change somewhat, markets tend to perform consistently well or consistently

poor. For example, the unique location of the Denver-market, central both from a geographic as

well as a retailer-network viewpoint, makes it the best market in any quantile of the distribution

of completion times. Other markets that score consistently high are Washington DC, and Omaha.

The Louisiana market tends to loose some ground in other quantiles, i.e., there is more variability

in the completion times than with other markets. This is because of the possibility to take an initial

step into the Florida markets which is an edge both geographically as well as in the retail-network.

A market that gains ground in other quantiles is the El-Paso/Albuquerque market (located directly

below Denver in Figure 6) which is in the Safeway and Albertsons trade-areas.

30

Figure 6: Lead markets and trade areas in the continental United States

A caveat of our simulation results is that the values of the parameters guiding the simulation are

estimated from the observed paths of manufacturer roll-outs and chain adoptions. It is implicitly

assumed that estimated manufacturer policies for the targeting of markets are invariant to the path.

Given the complexity of a formal optimization in a dynamic, spatial, and stochastic setting, the

condition that managers are not very strategic is likely a good approximation.17 Thererfore, the

results of this experiment can be interpreted as an exploration of several reasonable assumptions

about how manufacturers role out new brands and how retailers adopt them in the context of lead-

market selection.

7 Conclusion

We present and estimate a model of diffusion of retail distribution for new brands of repeat purchase

items in the United States. This model studies the important element of retail distribution. It

represents the evolution of retail distribution as an interactive sequence of manufacturer’s decisions

to enter local markets and retail chains’ decisions to adopt the brand.

17 For instance, our discussions with the managers involved in the launch of one of the brands suggest that the rolloutsequence is heuristically determined using the factors we model, as opposed to “optimized.”

31

In the confines of our empirical data, market entry by manufacturers is positively affected (1) by

the existing share of the manufacturer in the market at hand, (2) by spatial proximity to markets

already entered in the past, and (3) by the share of retailers who have adopted in the past (on other

markets). Further, markets entered early tend to contain many retailers (are not concentrated) with

multimarket trade areas (as opposed to independent stores). Finally, markets are entered in an

accelerated fashion, i.e., slow at first and faster later on. These results are suggestive of the fact that

manufacturers in our empirical application seem conservative. Their early focus in the new product

launch is on “home-markets” on which they are already large, and they seem to roll out slowly at

first.

Adoption of the brand by retailers is positively affected (1) by the importance of the category

to the retailer, (2) by the size of the manufacturer in the retailer’s outlets, and (3) by the adoption

of the brand by rival retailers. In addition, adoption is positively associated with retailer size and

negatively with time since availability. Hence retailers seem to adopt because of the importance of

the manufacturer (the combined effect of CDIzkt and MDIzikt) and because of competitive pressures

(the effect of DIFzikt).

Taken together, our paper suggests the presence of spatial—, selection—, and network effects in the

diffusion of new product distribution. These concepts have a broader applicability than the strict

interpretation in which they are applied here. For instance, in terms of future research, the most

obvious empirical extension of this paper is to model the evolution of other key performance variables

in new product launch. Candidates for such other variables are the three remaining ratios in Figure

1, i.e., assortment breadth, consumer trial, and consumer repeat purchase for new brands of repeat

purchase goods. Given the findings in this paper, another plausible extension is to conduct a more

formal dynamic spatial stochastic optimization of roll-out paths for the manufacturer.

We investigate lead market selection when chains approve new brands based on contagion from

other chains, and that manufacturers tend to roll the product out geographically. While we acknowl-

edge other selection criteria for lead markets, we find that markets that are located “central” in the

network of retail-chains, or on the edge of multiple large chains are especially appealing candidates,

all other factors held constant.

A potential limitation of the paper is caused by the fact that we have no data on manufacturer

incentives offered to the retailers. At the same time, the success of the brand with rival retailers

32

seems to be a more important and enduring incentive to adopt a brand than a one-time manufacturer

incentive. In sum, while manufacturer incentives may play a role initializing new product distribution,

it is unlikely that they replace the network effects found in this paper.

Finally, to our knowledge this paper is the first to empirically model spatial or network diffusion

in marketing. We hope that the current paper represents a constructive step towards modeling

many other contexts in which spatial and network dependencies may play a role. Such contexts

range from viral marketing applications and fashions or fads, to the diffusion of new technologies

and new products.

33

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35

A Full conditional distributions

A.1 The market entry model.

• [yimt|yimt,rest]

The first distribution to specify is that of the latent probit variables yimt such that yimt > 0

if and only if yimt = 1 and yimt ≤ 0 if and only if yimt = 0. The variables yimt conditional

on the outcomes yimt have truncated Normal distributions. Specifically, we obtain for all

weeks that fall between the moment of global launch of the brand and entry in m, i.e., for

Tglobal launch of i ≤ t ≤ Tenter in m, that

[yimt|yimt, rest] ∼ N (Xyimt · θ + βm + γit, 1)

left-truncated at 0 if yimt = 1

right-truncated at 0 if yimt = 0(A.1)

• [θ|rest]

Define yθimt by yimt − βm − γit. Construct the array yθ and the matrix Xy by stacking over

brands, markets, and time. The full conditional for θ is proportional to

[θ|rest] ∝ [θ|yθ,Xy][θ0]

with [θ|yθ,Xy] ∼ N((Xy′Xy)−1

Xy′yθ, (Xy′Xy)−1)and prior [θ0] ∼ N (0,Vθ0) . This conju-

gate pair leads to the following full conditional

[θ|rest] = N (mθ,vθ)

mθ = vθXy′yθ (A.2)

vθ =(V−1

θ0 +(Xy′Xy

)−1

)−1

• [β|rest]

Define yβimt = yimt−Xyimt·θ−γit. Array all covariates of the hierarchical model for βm in a 1×Pβ

row vector Xβm (in the operationalization below equation (5) Xβm = [ACVym HRFy

m SNIym].

Array these covariates further into the M × Pβ matrix Xβ = [X′

β1 · · ·X′

βm · · ·X′

βM ].′ Finally,

define an index matrix Im of size Ny ×M which maps each observation yimt into m. Then, the

vector β of random factors βm has the following full conditional distribution.

[β|rest] = N (mβ,vβ) (A.3)

mβ = vβ

(I ′

myβ+1

σ2β

Xβφ

)

vβ =

(I ′

mIm +1

σ2β

IM

)−1

• [φ|rest]. The full conditional for φ is proportional to

[φ|rest] ∝ [φ|β,Xβ][φ0]

36

with [φ|β,Xβ] ∼ N

((X′

βXβ

)−1

Xββ,(X′

βXβ

)−1

)and prior [φ0] ∼ N (0,Vφ0) . This conju-

gate pair leads to the following full conditional

[φ|rest] = N (mφ,vφ) (A.4)

mφ = vφXββ

vφ =

(V−1

φ0 +1

σ2β

X′

βXβ

)−1

• [σ2β|rest]

The full conditional distribution for the variance σ2β is proportional to the product of the

distribution [β] = NM

(Xβφ, σ

2βIM

)and the prior [σ2

β] = IG(qβ, rβ),i.e.,

p(σ2β) =

rqββ

Γ(qβ)

(σ2β

)−(qβ+1)

e−rβ/σ2

β

This distribution and the multivariate Normal distribution forms a conjugate pair and results

in

[σ2β|rest] = IG

(qβ +

M

2, rβ +

1

2(β −Xβφ)

′(β −Xβφ)

)(A.5)

• [γ|rest]

Define yγimt = yimt − Xyimt · θ − βm. Array all covariates of the hierarchical model for γit in

a 1 × Pγ row vector Xγit (in the operationalization below equation (5) Xγit = [TSIyit]. Array

these covariates further into the M × Pγ matrix Xγ = [X′

γ11 · · ·X′

γ1T1X′

γ21 · · ·X′

γ2T2].′ Finally,

define an index matrix Iit of size Ny × (T1 + T2) which maps each observation yimt into i, t.

Then, the vector γ of random factors γit has the following full conditional distribution.

[γ|rest] = N (mγ ,vγ) (A.6)

mγ = vγ

(I ′

ityγ+

1

σ2γ

Xγλ

)vγ =

(I ′

itIit +1

σ2γ

IM

)−1

• [λ|rest]. The full conditional for λ is proportional to

[λ|rest] ∝ [λ|γ,Xγ ][φ0]

with [φ|γ,Xγ ] ∼ N((

X′

γXγ

)−1

Xγγ,(X′

γXγ

)−1

)and prior [φ0] ∼ N (0,Vφ0) . This conjugate

pair leads to the following full conditional

[φ|rest] = N (mφ,vφ) (A.7)

mφ = vφXγγ

vφ =

(V−1

φ0 +1

σ2γ

X′

γXγ

)−1

37

• [σ2γ |rest]

The full conditional distribution for the variance σ2γ is proportional to the product of the

distribution [γ] = NM

(Xγφ, σ

2γIT1+T2

)and the prior [σ2

γ ] = IG(qγ, rγ). This distribution and

the multivariate Normal distribution forms a conjugate pair and results in

[σ2γ|rest] = IG

(qγ +

T1 + T22

, rγ +1

2(γ −Xγλ)

′(γ −Xγλ)

)(A.8)

A.2 The chain adoption model.

• [zikt|zikt,rest]

As above, we specify is the distribution of the latent probit variables zikt such that zikt > 0 if

and only if zikt = 1 and zikt ≤ 0 if and only if zikt = 0. The variables zikt|zikt are distributed

truncated Normal. Specifically, for all weeks that fall between the moment of trade area

availability and adoption of the brand by retailer k, i.e., for Tavail,k ≤ t ≤ Tadopt,k, that

[zikt|zikt, rest] ∼ N (Xzikt · µ+ bk, 1)

left-truncated at 0 if zikt = 1

right-truncated at 0 if zikt = 0(A.9)

• [µ|rest]

Define zµikt by zikt − bk. Construct the array zµ and the matrix Xz by stacking over brands,

retailers, and time. The full conditional for µ is proportional to

[µ|rest] ∝ [µ|zµ,Xz][µ0]

with [µ|zµ,Xz] ∼ N((Xz′Xz)−1

Xz′zµ, (Xz′Xz)−1)and prior [µ0] ∼ N (0,Vu0) . This conju-

gate pair leads to the following full conditional

[µ|rest] = N (mµ,vµ) (A.10)

mµ = vµXz′zµ

vµ =(V−1

µ0 +(Xz′Xz

)−1

)−1

• [b|rest]

Define zbikt = zikt − Xzikt · µ. Array all covariates of the hierarchical model for bk in a 1 × Pb

row vector Xbk (in the operationalization below equation (11) Xbk = [ACVzk HRFz

k]. Array

these covariates further into the K × Pb matrix Xb = [X′

b1 · · ·X′

bk · · ·X′

bK ].′ Finally, define an

index matrix Ik of size Nz ×K which maps each observation zikt into k. Then, the vector b of

random factors bk has the following full conditional distribution.

[b|rest] = N (mb,vb) (A.11)

mb = vb

(I ′

kzb+

1

σ2b

Xbψ

)vb =

(I ′

kIk +1

σ2b

IK

)−1

38

• [ψ|rest]. The full conditional for ψ is proportional to

[ψ|rest] ∝ [ψ|b,Xb][ψ0]

with [ψ|b,Xb] ∼ N((X′

bXb)−1

Xbb, (X′

bXb)−1

)and prior [ψ0] ∼ N (0,Vψ0) . This conjugate

pair leads to the following full conditional

[ψ|rest] = N (mψ,vψ) (A.12)

mψ = vψXbb

vφ =

(V−1

ψ0 +1

σ2b

X′

bXb

)−1

• [σ2b |rest]

The full conditional distribution for the variance σ2b is proportional to the product of the distri-

bution [b] = NM

(Xbψ, σ2

bIK)and the prior [σ2

b ] = IG(qb, rb). The full conditional distribution

makes use of this conjugate pair and results in

[σ2b |rest] = IG

(qb +

K

2, rb +

1

2(b−Xbψ)′(b−Xbψ)

)(A.13)

B The MCMC algorithm

The full conditional distributions are all closed form. Hence, the algorithm uniquely consists of Gibbs

steps. Draws from the joint posterior distribution of the parameters are obtained by passing through

the following conditional distributions while updating the parameters on which these depend by the

most recent posterior draws.

1. Market entry model

(a) draw from [yimt|yimt,rest] (see equation A.1)

(b) set yθimt = yimt − βm − γit, draw from [θ|rest] (see equation A.2)

(c) set yβimt = yimt −Xyimt · θ − γit, draw from [β|rest] (see equation A.3).

(d) draw from [φ|rest] (see equation A.4)

(e) draw from [σ2β|rest] (see equation A.5)

(f) set yγimt = yimt −Xyimt · θ − βm, draw from [γ|rest] (see equation A.6)

(g) draw from [λ|rest] (see equation A.7)

(h) draw from [σ2γ|rest] (see equation A.8)

2. Retailer adoption model

(a) draw from [zikt|zikt,rest] (see equation A.9)

(b) set zµikt = zikt − bk, draw from [µ|rest] (see equation A.10)

(c) set zbikt = zikt −Xzikt · µ., draw from [b|rest] (see equation A.11)

(d) draw from [ψ|rest] (see equation A.12)

(e) draw from [σ2b |rest] (see equation A.13)

39

Table 1: Description of the variables

Model Variable name units mean std

category development index CDIymt %cat. salesmt/ACVm 0.67 0.46

manufacturer development index MDIyimt mfr. salesimt/cat.salesmt 0.25 0.14

distance to manufacturing site DSMyim 103 Miles 0.70 0.46

market spatially lagged entry SPTyimt [ ] 0.16 0.24

entry share of previous adopters PRVyimt % market ACV 0.35 0.34

market size ACVym MM$/week 4.19 3.38

retailer concentration in market HRFym [ ] 0.31 0.15

share of multi-market chains SNIym % market ACV 0.88 0.15

time since introduction TSIyit weeks 56.39 37.04

category development index CDIzkt %cat.saleskt/ACVk 0.50 0.37

manufacturer development index MDIzikt mfr. salesikt/cat.saleskt 0.16 0.16

retailer time since availability TSAzikt weeks 34.79 39.64

adoption network lagged adoption DIFzikt [ ] 0.77 0.27

retailer size ACVzk MM$/week 2.20 4.10

market concentration in retailer HRFzk [ ] 0.74 0.30

40

Table 2: Estimation results of the full model

percentile 2.5% 50% 97.5%

symbol variable name Market Entry

θ1 Digiorno DIGy -7.758 -6.331 -5.095

θ2 Freschetta FREy -6.516 -5.192 -4.016

θ3 category development index CDIymt -0.262 0.064 0.392

θ4 manufacturer development index MDIyimt 0.651 1.373 2.093

θ5 distance to the site of manufacturer DSMyim -0.253 0.063 0.368

θ6 spatial proximity SPTyimt 1.174 1.575 1.990

θ7 share of previous adopters PRVyimt 0.530 0.925 1.347

φ1 all commodity volume ACVym -0.080 -0.027 0.023

φ2 Herfindahl index HRFym -2.548 -1.337 -0.203

φ3 share of multimarket chains SNIym 0.971 2.213 3.633

λ time since introduction TSIyit 0.011 0.018 0.025

σ2β variance market component 0.166 0.304 0.540

σ2γ variance time component 0.399 0.651 1.085

Chain Adoption

µ1 Digiorno DIGz -3.044 -2.526 -2.041

µ2 Freschetta FREz -3.148 -2.634 -2.155

µ3 category development CDIzkt 0.332 0.528 0.730

µ4 manufacturer development index MDIzikt 1.435 1.906 2.404

µ5 time since availability TSAzikt -0.010 -0.005 -0.001

µ6 network effect on chain adoption DIFzikt 0.143 0.483 0.827

ψ1 all commodity volume ACVzk 0.036 0.074 0.113

ψ2 Herfindahl index HRFzk -0.229 0.219 0.684

σ2b variance chain component 0.216 0.344 0.531

41

Table 3: Estimation results ignoring market entry

percentile 2.5% 50% 97.5%

symbol variable name

µ1 Digiorno DIGz -4.442 -3.954 -3.450

µ2 Freschetta FREz -4.037 -3.581 -3.086

µ3 category development index CDIzkt 0.206 0.372 0.530

µ4 manufacturer development index MDIzikt 1.154 1.529 1.909

µ5 time since availability TSAzikt 0.004 0.007 0.009

µ6 network effect on chain adoption DIFzikt 1.463 1.738 2.047

ψ1 all commodity volume ACVzk 0.055 0.091 0.125

ψ2 Herfindahl index HRFzk -1.012 -0.466 -0.074

σ2b variance retailer 0.234 0.364 0.545

42