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Demystifying the Bass Diffusion Model: the hidden role of distribution channel

Sungjoon Nam1

Rutgers Business School

Feb 2011

Abstract The goal of this paper is to uncover the hidden roles of distribution channels in the Bass Diffusion Model estimation. First, I show that the parameters in the BDM could be dramatically biased when a new product is launched in sequential rollout. This might partially explain commonly observed overestimation on contagion effects (WoM effects) in previous BDM literature. Second, I quantify the effect of distribution channel on parameters in the BDM model using a new micro level adoption patterns in a video-­on-­demand service controlling for internal and external communications, competition, and demographics.

Contrary to the widespread belief on the BDM model, the estimated results show that t tribution

not the Word-­of-­Mouth effect. The -­of-­Mouth)

and external (Advertising) communication channels. The two different

1 Sungjoon Nam is an Assistant Professor at Rutgers Business School, 1 Washington Street #992, Newark, NJ, 07102. sjnam@business.rutgers.edu

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communication roles (internal and external) cannot be separately identified in the usual settings in the absence of measure on Word-­of-­Mouth.

The managerial implications for the BDM model should be revised accordingly. Social media marketing and product quality should be emphasized in the early phage of a new product launch. In the late phage, distribution channel extension and local in-­store promotional activities should be actively managed.

I utilize the unique features of a video-­on-­demand service to control for other factors in a diffusion process. The data has mass media advertising expenditure and objective measures on signal quality that influence the social interaction among customers. The effects of distribution channels, competition and demographics on the diffusion process are investigated based on geographical information on customers, retailer stores, and DVD rental shops.

Keyword: Bass model, diffusion model, distribution channels, aggregation bias, video on demand service, social interaction, Word-­of-­Mouth effect.

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1. Introduction

Marketers have been curious about the roles of underlying drivers of the diffusion of a new

product. Marketing activities and social interactions are often referred to the two main

. The most famous and widely used

model is the Bass Diffusion Model proposed by Frank Bass (1969), one of the top ten most

influential papers published in the last 50 years of Management Science. More than 150

papers have been written based on the model (Mahajan et al. 1990). This model has done

very good jobs in forecasting the demand of new durable goods (Mahajan, Muller and Bass

1995), successive generations of technology (Norton and Bass 1987, and 1992, Hahn et. al.

1994, and Chintagunta et. al. 2009), pharmaceutical products (Lilien, et. al. 1981, Desiraju,

Nair and Chintagunta 2004) and new services (Horsky and Simon 1983, Libai, Muller, and

Peres 2009, Krishnan et. al. 2000). The underlying assumptions of the Bass Diffusion Model

could be expressed as follows.

The probability of adopting by those who have not yet adopted is a linear function of

those who had previously adopted

ion

market size

One of the fundamental questions is whether these assumptions on communication

channels are valid (Mahajan, Muller and Bass 1990).

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A question can be raised as to whether the Bass model really captures the

communications structure between the two assumed groups of adopters called

Due to the difficulty in measuring social interactions, and complex issues related to

testing the BDM model, the assumptions to identify communication roles were considered

to be true over 40 years.

Researchers have investigated the two different communication channels of the

diffusion of new products (Bulte and Stremersch 2004). They investigate new product

diffusion processes by comparing the coefficients of innovation and imitation across

products and across countries (Desiraju, Nair, and Chintagunta 2004, Talukdar, Sudhir

and Ainslie 2002, Gatignon et. al. 1989, Gatignon, Hubert 1989, and Bulte and Joshi 2004).

Various researchers focus on the effects of advertising (Horsky and Simon 1983, Simon, and

Sebastian 1987, Bass, Krishnan, and Jain 1994), word of mouth effects (Bulte et. al. 2007,

Easingwood et. al. 1983), pricing (Horsky 1990) and direct salesforce effort (Lilien, Rao, and

Kalish 1981) on diffusion process.

However there is paucity in BDM literature investigating the roles of distribution

channels. The lack of research in distribution channels in marketing literature is attributed

to difficulties to obtain the distribution channel information. Exceptionally, Ataman, Mela,

and Heerde (2008) extensively studies the effect of distribution channel, price discounting,

feature/display, and advertising using Bayesian dynamic linear model (DLM) of repeat

purchase diffusion of 225 new-­brand introductions. They show that access to distribution

breadth has the most impact on successful building of a new brand compared to price

discounting, feature/display, and advertising.

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The goal of this paper is to uncover the hidden roles of distribution channel in BDM. It

is possible that the cumulative customers might be correlated with unobserved

characteristics like the increasing patterns of distribution channels. I have shown the

importance of distribution channels by a simulation study and analyzing micro level

diffusion patterns in a new video-­on-­demand service data. I also test whether the coefficient

of imitation in the Bass Diffusion Model (BDM) really captures the internal (Word-­of-­

Mouth) communication channel.

dramatically biased when

national sales data is aggregated in sequential rollout. Firms often roll out new products

sequentially to minimize new product launch risks (Bronnenberg and Mela 2004). A firm

could launch a new product in a few test markets and then decide to roll out at national

level when the outcomes in those test markets turn out to be successful. Then the sales in

the late stage could be

customers although they barely communicate with each other.

Chintagunta, Gopinath and Venkataraman (2010) investigates the effect of online

movie user rating on offline movie sales of sequentially released new movies, and finds that

the valence of movie rating is significant on offline movie sales at local market level, but

becomes insignificant when data is aggregated at national level. In the later simulation

section, the non-­existing word of mouth effects become highly significant and overly

magnified.

Second, one of the biggest hurdles in the investigation of the different roles of the

diffusion processes is a measurement problem. Especially, we can hardly observe actual

social interactions (word of mouth) among consumers. Since social interaction is barely

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recorded, researchers usually rely on macro level social economics variables, and online

reviews.

Previous researchers compare the diffusion processes of a product across markets with

macro level social-­economics variables (Simon and Sebastian 1987, Gotignon et. al. 1989,

Talukdar et. al. 2002). However, different markets tend to have different distribution

channels, infrastructure, demographics, local marketing activities and different levels of

competition. Aggregation errors might explain the differences among p and q. Comparing

national diffusion patterns across countries is not appropriate to identify the two different

communication processes of new product diffusion.

The other approach is to use consumer generated data, online reviews. Delarosa et. al.

(2007) investigates the diffusion patterns of 80 movies in the U.S market using a Bayesian

Hierarchical BDM model and shows

related to the valence of online movie user reviews. This research shows the relationship

between online word of mouth and the diffusion process in some way, but was not

release, so we can hardly tell whether it is really related to online word of mouth effects, or

unobserved marketing and media effects.

If these missing variables are correlated with the cumulative number of adopters, then

the parameters in BDM model could be biased. The Bass Diffusion Model usually relies on

yearly data. So it is quite possible that diffusion process could be affected by changes in

distribution channels, product characteristics, price (Narashinan 1989), substitutes, supply

chain (Ho et. al. 2002, Amini and Li 2011, and Jain et. al. 1991) and competition (Parker

and Gatignon 1994).

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Figure 1 shows the pattern of air conditioner diffusion from 1949-­1961, which is one of

the mostly replicated dataset in diffusion marketing literature (Bass 1969, and Srinivasna

and Mason 1986, and Van den Bulte and Lilien 1997, Schmittlein, and Mahajan 1982, Bass,

Krishnan, and Jain 1994, Easingwood et al. 1983, and Venkatasan et. al. 2004). The NLS

estimates for p and q are 0.0094 and 0.3748 implying a great role of social interactions

among customers.

However, there could be alternative explanations for the big social interaction effects. If

the coverage of distribution channels or the number of retailers increases with the

cumulative number of customers, the rate of imitation would capture not only social effects

among customers but also the extended distribution network. Figure 2 shows a dramatic

change in distribution channels of the Carrier air conditioner in Miami area from 1955 to

1964. As shown in Miami News advertisement, the number of retailers in these areas

jumped from 1 to 45 in 10 years.

To properly test the underlying processes of the Bass Diffusion Model, it is necessary to

rule out aggregation errors, to have objective measures on the social interaction among

customers, and to control other variables that could influence the adoption behaviors to

Otherwise it would be hard to rule out the

d variables. I use new micro level diffusion data

with exogenous shocks on word of mouth effect controlling for advertising, distribution

channels, competition and demographics.

The unique features in the data enable us to test the Bass Diffusion Model satisfying

these requirements. First, it is zip code level monthly adoption data. We aggregate the

street level adopters at the zip code level. Consequently, there is no sequential rollout in

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each market. Also the marketing activities are very similar across zip codes. The marketing

activities including TV advertising were determined at a broader market level (cities and

metropolitan areas), and there is little systematic difference across zip codes. The total

observation period is 13 months so that product characteristics and competitive

environments stay almost the same.

Second, we have geographical information about the offline distribution channels and

other competitors. The video-­on-­demand service was advertised using media like TV,

newspapers, and radio and was also shown with demonstration in consumer electronics

retail stores like BestBuy and Circuit City. We obtain the geographical information of

offline movie rental stores such as Blockbusters video stores in those markets. The detailed

information about distribution channels and competitors helps us to control for possible

endogeneity issues related to and other unobserved factors that

could influence the diffusion of a new product.

Third, we have objective measures on exogenous shocks on Word-­of-­Mouth effects

among consumers. It records signal quality information for the service. The number of new

movies available for the service relies on the signal strength and the noise level of the

signal the setup box receives from the terrestrial TV station. Since these are not observed

prior to activation, there is no other way for signal measures to affect adoption

decision but through social interaction activities. A detailed discussion about the

relationship between signal measures will follow in the data section.

Based on these properties, we test whether the ameter in the Bass

Diffusion Model is affected by breadth of retail distribution channels, signal quality levels

controlling for competition and demographics. Owing to the exogenous shocks on word of

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mouth effects across customers, we can separately control for the two different

communication processes. I apply the nonlinear square estimation for BDM model for the

micro level adoption data.

2. Simulation Study

This chapter tests whether Bass Diffusion Model could suffer from aggregation errors using

simulated data. Especially, we focus on the aggregation errors due to sequential rollout.

Basically parameters in the Bass Diffusion Model are identified from the shape of a

diffusion curve. Figure 3 shows various simulated diffusion (cumulative sales) patterns

given 1,000 adopters who vary in terms of the rate of innovation and imitation. We can

notice that a large q, the rate of imitation is associated with S shape of a cumulative sales

pattern, and a large p, the rate of innovation is associated with a concave diffusion pattern.

Meta-­analysis across 150 diffusion cases shows that the rate of innovation (p) is 0.03

and the rate of imitation (q) is 0.38 (Sultan, Farley, and Lehman 1990). These mean that

the effect of imitation on new product diffusion processes is much greater than that of

innovation.

However, these findings are not consistent with the results obtained at disaggregate

level analysis on adoption. Nam, Chintagunta and Manchanda (2010) investigates whether

that only 8% of new customers are acquired by word of mouth effect. In other words,

empirical researches based on macro level and micro level adoption data have contrasting

results.

The overestimation of social interactions was attributed to data truncation, ill-­

conditioning, and model misspecification (Bulte and Lilien 1997, and Bemmaor and Lee

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2002). Then the social contagion effect should be estimated consistently when data is fully

observed. However, this might not be true.

To test whether aggregation errors contribute the overestimation of contagion effect

(Word-­of-­Mouth), I simulate new product diffusion data without social interaction among

customers. The parameters for the BDM are set with p = 0.2 and q=0.0001 for all market

making no word of mouth effects in these simulated markets. The simulated time span is

13 years, which is commonly found in other literature (Srinivasan and Mason 1983).

We compare two cases in respect to the distribution channel rollout;; national rollout

and sequential rollout. We assume that there are hundred local markets with the same

potential market size. Each market has 100 potential adopters. We first simulate the

diffusion process without word of mouth effect for the 100 local markets. After the expected

adopter variables are generated, we add error terms following standard normal distribution

(with standard deviation equal to three). Then we aggregate the data with national and

sequential rollout settings.

In national rollout, a firm decides to launch a new product for every market at the

same time (year 1). In sequential rollout, a firm does the same at different times increasing

the breadth of the distribution channels. We simulate that 20% of markets are covered in

year 1, 30% in year 4, and 50% in year 7 by the sequential rollout. Then the aggregate level

market sales are obtained. Figure 4 shows the simulated aggregate level diffusion pattern

in sequential rollout.

After we obtain two different aggregate level sales data, we run the standard Bass

Diffusion Model based on nonlinear least square estimation (Srinivasan and Mason 1986).

The results are shown in Table 1 with the average estimates over simulated 100 local

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markets. For the national rollout setting, the parameters are recovered consistently. The

rate of innovation is significant and the rate of imitation is not. In contrast, the parameters

in sequential rollout have dramatic changes in the parameters in the BDM. The magnitude

of the rate of innovation, p decreases to less than one tenth of the true value, and its

significance level is significantly weakened. Strikingly, the rate of imitation, q becomes

very significant with a magnitude 4,000 times higher than the true value. In fact, the

simulated data was generated without word of mouth effects. In other words, sequential

rollout could dramatically change the magnitudes and the significance levels of the

parameters in the BDM model.

These findings raise serious questions about the validity of previous research

investigating the rolls of internal and external communications relying on national level

diffusion data. Previous literature (Talukdar et. al. 2002, Gotignon et. al. 1989, and Bulte

and Stremersch 2004) investigates the effect of socio economic variables like urbanization,

Gini index,

using multinational product diffusion patterns. Even if the BDM model assumptions are

right, we say anything about communication channels because these national sales

data were obtained in the absence of sequential rollout information. A high rate of imitation

might just reflect the degree of sequential rollout of the country.

In summary, we address fundamental data collecting problems that could cause serious

systematic biases on the parameter estimates in the Bass Diffusion Model. I show that

BDM model when a new

product is launched in sequential rollout.

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In the next chapter, we will investigate the ability of identifying

communication rolls using a new micro level data that does not suffer from aggregation

errors.

3. Data

The data comes from a new type of video-­on-­demand service which receives the new movie

information through the terrestrial TV signals2. The data is observed from October 2003 to

November 2004 in three test markets.

street level addresses. I match these addresses and obtain the zip-­code level demographics

from the Census data. The location information about the competitors and retail channels

is (Figure 5, and

Table 2). Since we have a relatively short time span, we aggregate the data at a monthly

basis. Summary statistics is reported in Table 3.

To apply the Bass Diffusion Model, we first need to define the scope of a market. For

simplicity and availability of demographics information, we choose zip-­code level as a base

analysis unit3. In Figure 6, each boundary represents the market size of zip codes, and the

color shows the number of adopters in that area. We observe that there are significant

differences in adoption across zip code level areas. In total, there are 155 zip codes in three

test markets, Jacksonville FL, Salt Lake City, UT, and Spokane WA. On average, there are

25.3 adopters in each zip code and the penetration rate is 0.35% (Table 3). Given the fact

2 Due to confidentiality reasons, we cannot reveal the actual name of the service.

3 If we want more micro level data, we could aggregate at the census track level, but the number of observation

in each area is too small.

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that the total video on demand service category share is less than 1% at that time, this

penetration rate is not surprisingly low. In Figure 7, we can see that a lot of markets do not

have many adopters. If there are too many zeros in the data, the BDM model would not

work well. Accordingly, we restrict the data set to the markets, which have at least 20

adopters. The number of markets is reduced from 155 to 75. We do not find systematic

differences on the selected samples. The average number of total adopters in each market

increases from 25.3 to 43. The percentage of zeros in the number of monthly adopters is

12%.

Figure 8 shows the product diffusion patterns across zip code level markets. The solid

lines represent the number of actual adopters and the dotted lines are the predicted

adopters based on the BDM model. We can notice that the BDM model predicts the actual

adoption pattern quite well.

Based on the zip code level information, we obtain the number of retail stores including

BestBuy, Circuit City, Sears, and other local stores (Table 2). The caveat is that the location

of these stores might be determined entailing the unobserved (for researchers) local

characteristics. Retailers could strategically enter a market based on market potentials and

potential competition among other retailers (Zhu et. al. 2009). If the locations of the

retailers for the video-­on-­demand service are determined with these strategic and local

unobserved characteristics, the parameter estimates for distributional channels might be

biased due to these correlated factors.

To test these correlated errors, I check whether the presence of these stores has

similar effects on the new product adoption over time. If the static local characteristics are

the main drivers, then we should not observe time varying effects of the distribution

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channels. Also the main effects of retail shops would be similar across different retailer

shops.

The table 4 shows the NBD regression results of the total number of adopters across zip

codes given a specific month. Interestingly, not all stores have significant effects on

adoption. BestBuy stores have insignificant effects all over the periods. Sears and local

stores show significant effects only for the first and second month respectively. It is likely

that these stores might have local or in-­store promotions to attract new adopters for this

video-­on-­demand service. Otherwise we would not observe the time varying effects of

distribution channels unless there were time varying unobserved promotional activities

specifically for those markets. Most of the promotional activities (93%) in this data is spent

on mass medias like TV advertising (64%), newspaper (15%), and radios (14%).

Circuit City stores tend to promote the new product the most. We find significant effect

of Circuit City in 3rd, 4th, 6th, 7th, and 12th months. These imply that there would be local

or in-­store promotional activities in Circuit City stores. To quantify the different effect of

retail stores, we treat Circuit City and the other stores as two separate variables. The

number of shopping malls is also used for controlling for unobserved local characteristics

associated with potential endogenous retailers locations.

To control competition level across micro level areas, we obtain the number of DVD

rental stores like Blockbusters and Hollywood stores, and, and conventional and digital

cable TV penetration information to control other alternative entertainment options. On

average, there are 1.06 DVD rental stores, and 0.32 shopping malls in a zip code level

market. The average cable and digital cable penetrations are 35% and 12%. The retailers,

competing DVD rental shops and shopping malls are depicted in Figure 8.

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Other demographics information like the number of households, income, single, black,

silver (over 55 years old) is obtained from Census survey data. On average, 20%, 7.2%, and

17% are singles, black, and silver respectively. The average income is $58,720 with S.D. of

$16,934. The average number of households across zip codes is 7,592 with maximum 22,127

and minimum of 52.

To control for the communication channels, we obtain measures on external and

internal communication variables in the new product adoption. The external influence is

captured by dollar amount in TV advertising spending. The company spent about 64% of

the all the advertising budget in TV advertising almost proportionally across markets.

Other radios and newspapers are also recorded, but dropped in the estimation due to lack of

variations over time. The internal influence (Word of Mouth effect) is identified by the

signal quality measures the new video-­on-­demand service data records periodically.

The service comes with a set-­up box connected to a conventional TV set. The setup box

is designed to automatically download ten new movies per week. To watch a movie, a

subscriber needs to get an authorization from the service provider through a phone line.

Since the setup box is connected to the service provider through the phone line, it also

transfers the level of signal information to the service provider. There are two measures of

signal;; signal quality and signal strength. These are correlated. The correlation between

signal quality and strength is 0.5. If the signal strength is high but contaminated with

noises, it might not decode the movie information well from the terrestrial TV signals.

When we analyze the relationship between usage and signal measures, we find that the

signal quality primarily determines the level of usage.

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In Figure 9, we can see that signal quality varies across zip code areas. The signal

quality varies from 0 to 2.4 and also has variation within subscribers. If an area has bad

signal qualities, the subscribers in that area might have bad experience about the service

and would not recommend the service to other potential subscribers. In general, the higher

the signal quality is in a zip code, the higher the penetration rate is. We can also observe

the effect of signal quality on the diffusion curves (Figure 10). When we regress the rate of

penetration on signal quality, the signal quality is very significant (t-­value is above 4). It is

evident that the higher signal quality effectively boosts the new product adoption.

One of the main questions of this paper is whether coefficient of imitation represents

question, it is essential to argue that the signal quality affects only Word-­of-­Mouth effects.

Signal quality is unknown prior to activation and service provider cannot target it. As a

result, the only way in which signal quality plays a role in adoption is the social interaction

activities. If the service provider could customize their marketing activities based on the

future signal quality level, then the signal quality would affect both the rates of innovation

and imitation together. However, it is not the case. The advertising marketing activities

were determined at the market level, a broader area level, and they cannot target each

customer because even the service provider is unable to know the exact level of signal

quality level prior to activation. Details about the link between signal quality and word of

mouth effects are discussed in Nam, Manchanda, and Chintagunta (2010).

Since signal quality is affected by location of the household, weather conditions, and

other environments such as facing south or north, or being blocked by big buildings and

trees, it is rarely correlated with the demographics, the level of competition, and the

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distribution channel. Table 5 shows the regression results of signal quality on the

demographics, the number of DVD rental shops (competitors: Blockbuster, Hollywood Video

Store), the number of consumer electronics stores (offline retail channels: BestBuy, Circuit

City) and market dummy variables. All the variables are not significant except the Spokane

market dummy variable. The joint null hypothesis of sum of all the variables cannot be

rejected (Prob>F=0.735) and supports that signal quality is exogenous shocks on word-­of-­

mouth effect.

However, the signal quality is not stationary. In Table 6, we can see the monthly

average of signal quality increase over time. In contrast, signal strength does not increase

over time. We use signal strength as an instrument variable for signal quality in the

estimation. To graphically illustrate the word of mouth effects, it is better to use the

predicted signal quality based on the instrument variables. I will discuss the details in the

estimation section.

For a quick glance of the diffusion process, I run the simple ordinary BDM model

separately in each market and estimate the parameters (p, q, m). Figure 11 shows the box

plot of the rate of imitation, q by number of retailers, and Figure 12 shows the scatter plot

of q by the predicted signal quality (the blue points are significant at 95% level and the red

ones are insignificant). It looks that more likely correlated with distribution

channels rather than signal quality (word of mouth effect). Figure 13 shows q by both the

number of retail stores and the predicted signal quality. We rigorously test the main

hypotheses of identifying distribution channels and communication channels controlling for

other possible correlated variables.

4. Model

We discuss model structure and model specification in following sections.

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4.1. Model Specification

We specify a model to

communication channels, distribution channels, competition, and demographics. To do that,

first of all, we need to discuss some issues about the market definitions and the

identification strategies for distribution channels and communication channels.

First, I assume that the zip-­code level markets are independent in terms of distribution

channels and communication channels. One might argue that the potential adopters in a

zip code level market might buy the product in adjacent Then the

effect of distribution channel might be weakened. But the influence of retail stores would be

smaller as customers live far away from the retailer in distance. In that sense, our

estimates would be the lower bounds for the distribution channels effects. In respect to

internal communication channels, there are randomly generated exogenous shocks on word

of mouth effects across subscribers. The independence assumption among markets at zip-­

code level would not be a big problem that produces potential bias on the parameter

estimates. We are identifying the word of mouth effect mainly through the exogenous

variations in signal quality in the video on demand service.

Second, the locations of distribution channels could be endogenous as discussed in the

data section. However, the retailers for this service are selling thousands of products not

specifically designed to sell this video-­on-­demand service. Also the retailers have been

operated long before the launch of this new service. Then the endogeneity issues of the

retail location might not be great. I identify the effect of retail distribution not only by the

main effect of the number of retailers, but also by the interaction of the number of a retailer

and promotion time dummies belong to the specific distribution channel.

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As discussed in the previous section, we separate the number of retail stores into

Circuit City stores and other retailers and treat those as separate variables. Circuit City

stores significantly boost sales in the middle and late stage of product diffusion. To account

for this retailer promotional activities, an interaction term between the number of

Circuit City stores and time dummies (1 for significantly boosted months and 0 for the

others) is also used. If the interaction affects the BDM model parameters, then it is very

likely that the distribution channels influence the diffusion pattern in a new product launch.

Given these assumptions on distribution channels, communication channels,

competition, and demographics are modeled in a multiplicative way using exponential

transformations. The identification of the external communication channel (TV advertising)

comes from time varying trends, and those of internal communication channel,

distributional channels, competition and demographics comes from cross-­sectional

variations . The promotional activities for

Circuit City are identified by the interaction of time variations and cross-­sectional

variations.

4.2. Model Structure

I discuss how the model is structured to test the Bass Model

communication channels. I model the number of monthly adopters for each zip code to

follow the standard Bass Model (F. Bass 1969, equation 2) where p(>0) and q(>0) are

F(t) is cumulative

distribution function of the number of adopters, and f(t) is the derivative of F(t).

(1)

The number of adopters, yit in zip code i at time t is given by:

))(1))((()( tFtqFptf

19

itiiiiiiit utntFtFmy )())()(( 1 (2)

))()(())(()()( tNmtNmqtNmp

dttdNtn iii

i

iiiit

ii

The closed form for the number of adopters is expressed in equation (3) where is an

additive error term with variance .

ittqpiit

tqpiitit

iit ueqp

eqppmyiit

iit

2)(

)(2

)()( (3)

The error term represents sampling errors, unobserved excluded variables which

include economic conditions, local advertising efforts, and other type promotions.

Srinivasan and Mason (1986) shows that the Maximum Likelihood Estimation approach

significantly underestimates the standard errors of the estimated parameters because the

error term in the MLE does not account for other errors but the sampling errors. They have

shown that the Nonlinear Least Square (NLS) approach performs better to produce the

valid standard error estimates.

I use the Hierarchical Nonlinear Least Square estimation allowing the parameters, p, q

and m to be functions of other variables following Talukdar, et. al. (2002). Since the data

include time-­varying marketing activities, I use

parameters to be exponential functions of the linear combination of demographics,

marketing activities, and the competition related variables (equation 4). The difference

from Talukdar, et. al. (2002) is that we use nonlinear least square (NLS) rather than

Bayesian estimation which assumes a likelihood function and prior distributions of

parameters. As stated earlier, Srinivasan and Mason (1986) shows that the estimation

based on MLE (based on the likelihood function) could seriously underestimate the

i tu

2

i tu

20

standard errors of the estimates parameters. Therefore, Hierarchical NLS is a more

conservative way to test the effects of covariates on the parameters of BDM model than

other estimation methods that involves a likelihood function of error terms (MLE and

Bayesian).

(4)

indicates the number of Circuit City, prom is the time dummy

variables associated with local or in-­store promotional activities. The interaction term

would help to identify the influence of distribution channels in new product diffusion. The

shows the number of the other stores. As shown before, Sears and local stores

tend to promote the new video-­on-­demand service only in the early phage.

One of the problems in the estimation of effect of signal quality is that the signal

quality tends to increases over time which raises endogeneity issues. Since the parameters

of a BMD model are estimated from the time varying slope of the diffusion curve, the

systematic movement in repressor over time could be problematic. The service provider

might upgrade the software of the setup box and increase the ability to filter out the noisy

signal to update more new movies. We need to control for

errors. As I mentioned in the data section, there are two measures of signals: signal quality

and signal strength. Table 6 shows the household level signal quality and signal strength

over time. The first column shows the signal quality level and the second column shows the

signal strength. Unlike the signal quality, signal strength does not increase over time

imitmo th ersmtmmi

iqitqipiqo th ersqtqqi

ipitptipipo th ersptppit

ZretpromC CC Cmm

ZressigretpromC CC Cqq

ZadressigretpromC CC Cpp

0

0

0

)log(

)log(

)log(

21

whereas the correlation between the two at zip code level is relatively high (0.5). Therefore,

it would be a good instrumental variable for the signal quality. I use zip code level signal

strength and market dummies as instruments for a control function of signal quality. The

control function is easily implemented in BDM model. After running a regression of the

endogenous signal on instruments, the residual terms need to be included as another

repressor of the main BDM model. The control function technique is found to be effective to

control the endogeneity issues in a non-­linear choice model setting in individual level, and

aggregate level data (Goolsbee and Petrin 2004, and Petrin, and Train 2010). In equation

strength and market dummies. These residual terms

correcting the coefficient of signal quality effect on BDM parameters.

In short, we test whether the rate of imitation is significantly affected by distribution

channels and communication channels controlling for the endogeneity issues arising from

retailers

Competition and demographics are included in Z. Given these parameters and

covariates, I can simulate the diffusion process across all the micro level markets. The

estimation procedure minimizes the square of the difference between the predicted adopters

and the actual adopters. The objective function to minimize is given below. X represents the

whole vector of ad, sig, res, and Z, a indicates all the parameters. I denote the number

of monthly adopters as yit.

2)(min itit Xfy (5)

22

The NLS estimates are consistent and asymptotically normal. The standard deviations

could be obtained based on the derivative of the gradient of the diffusion function. The final

result is expressed below.

serror term of variance ,),( ),1(plim where,

),0(~)(2

00

000

10

20

Xfn

Q

QNn

oo

o

a

(6)

I use R code to manipulate this procedure and use BFGS algorithm for the optimization.

The parameter estimates results will be discussed in the following section.

5. Results and Discussion

Table 7 shows the estimation results. The first to third columns show the NBD regression

results of the total number of adopters and the fourth to sixth columns show the BDM

model results of zip code level diffusion data. The parenthesized values represent the

standard deviation of the parameter estimates. The significance levels are shown with

starts.

The first column demonstrates the null NBD regression results without a control

function. The effect of signal quality is significant at 90% confidence level. The effect of the

number of retail stores, the number of households, and income is positive and significant

(12%, 6.6%, and 5.75% by a retailer, 1,000 HH, and $10,000 respectively). Senior population

and Salt Lake City and Spokane market dummies have negative effects.

The first and second columns show the difference with a control function for signal

quality. As I have discussed in the previous section, the results without considering the

instruments can produce biases in parameter estimates due to reverse-­causality. After

controlling the correlated errors, the magnitude of signal quality doubles and the

23

significance level improves to 95% level. A 10% increase in signal quality increases the

adoption of the new service by 18.3%.

The third column represents differences in the heterogeneous effects of different

distribution channels. The third column model treats the numbers of Circuit City and other

retail stores as separate variables. The magnitude of the effect of Circuit City quadruples,

and the estimate of other retailers becomes insignificant. This result demonstrates the

importance of retail efforts to promote a new product. Just showing a new product

might not attract customers enough to buy it. Product demonstrations, adequate in-­store

salesforce training, and displays would be important factors that determine the success of a

new product launch.

We find that the signal quality (a proxy for the word of mouth effects), distribution

channels and some demographics significantly influence the new product adoption. The

next step is to test whether these variables have consistent effects on new product diffusion

process.

The fourth to sixth rows show the intrinsic parameter estimates for the coefficients of

or p or q, and the potential market size or m in the BDM model.

The first row indicates the intrinsic values of p, q, and m (0.086, 0.01, and 10.9 respectively).

By considering time varying and time invariant covariates, the predicted means and

standard deviations of p, q, m across markets are 0.124 (0.076), 0.010 (0.045), and 55.5

(23.1) respectively. The estimated potential market size is 20% higher than the average of

the total number of subscribers acquired during the observation period (43).

When we compare these estimates to the average values (p=0.03 and q=0.38) of the

meta analysis across 213 published applications of the Bass model and its extensions

24

(Sultan et al. 1990), the estimated p is very high, but q is small. This is consistent with the

simulation study as shown in the previous section. This micro level adoption data would not

suffer from the aggregation biases, which make the estimates for p smaller and q bigger.

We find significant effect of distribution channe

service in early phage and Circuit City does in the late phage, we find different

distributional effects on p and q. A retail store (not Circuit City) increases the rate of

varying local promotional activities. The interaction effect of the

presence of Circuit City and its promotional time dummies has significant and positive

local or in-­store promotional activities such as display, employee education, and fliers.

These results mean that the breadth of distribution channels and depth of its local or in-­

store promotional activities can effectively boost the adoption of a new product.

The main goal of this research is to test whether the rate of imitation

with Word-­of-­Mouth effect or distribution channels. Following the BDM model assumptions,

I hypothesize that by signal quality. However, the

estimated results show that the coefficient of imitation is not affected by the signal

quality, but by the interaction term associated with distribution channels. In other words,

-­store promotional

activities in the late phage of product diffusion process not the degree of word of mouth

effect among customers.

25

One might argue that we might not observe the role of signal quality on the coefficient

in this data set because the word of mouth effect is weak at the early stage of

product diffusion. The data is collected on a monthly basis, and time span is much shorter

than usual research in in the BDM literature. If the argument is true, we would not find

the strong effect of signal quality on the penetration rate in these markets (Table 7), nor

would we observe the significantly different diffusion patterns over time by signal quality

level (Figure 10). T cumulative adopters) is just 20% of

the total potential market size, thus it is not right to treat this diffusion process as an early

phage of new product adoption.

In short, the estimated results of the effect of signal quality on p and q do not support

the BDM model capability to capture the communication structure in a new product

diffusion process. Moreover, the TV advertising and signal quality (word of mouth effects)

are both captured . So we cannot separately identify the roles of

communication channels in usual setting prevalent in previous literature lacking adequate

measures of word of mouth effects.

Advertising is significant and positive only for the

advertising does not have to correlate with cumulative adopters, we do not include

BDM model. An increase of $100,000 TV advertising would increase the innovation rate by

18.4%.

Potential adopters with easier access to offline DVD rental stores or cable TV programs

26

might not be as excited as those without alternative options for a video-­on-­demand service.

The effect of digital cable and shopping malls are insignificant. Interestingly these

alternative options do not decrease the potential market sizes. For managers, it would not

be a wise decision not to enter new markets worrying about competition. Competition slows

the diffusion processes but does not shrink the potential market sizes.

For the demographics, we find consistent results in Hierarchical BMD model with NBD

regression of total number of adopters. The number of households in each zip code

innovation. A market with 1,000 more households would have 4.6% higher potential market

size. Income also has significant and positive effects on . Potential subscribers with a

higher income could afford to buy a new service without much burden, so the early phage

adoption would be easier. Single and senior populations have significant and effects on p

-­2.4% decrease in the market

6. Conclusion

This paper uncovers the hidden roles of distribution channels in the Bass Diffusion Model.

This paper especially investigates the potential errors due to sequential rollout of

distribution channels. I also empirically tests whether the Bass Diffusion Model can

capture the underlying communication structure with national level sales data. Since it is

hard to observe the Word-­of-­Mouth effect and hard to

previous literature have limitations to test these assumptions.

underlying assumptions on communication channels were believed to be true over 40 years.

27

I test whether the aggregation errors in national level data could make the BDM

estimation biased. Firm often sequentially rollout distribution channels for new products. I

simulate diffusion process in sequential rollout setting without Word-­of-­Mouth effects. The

simulation study shows that the word of mouth effect could be dramatically overestimated

due to aggregation errors. These results may partially explain why previous literature

overestimates the contagion effects in new product diffusion process in the absence of

information of distribution channels .

I find that the ith the breadth of retailer

distribution stores and its local or in-­store promotional activities in the late phage of

product diffusion process. The effect of distribution channels is not the same across

distribution channels. BestBuy stores have insignificant effects on new product adoption.

Circuit City stores which promoted in late phage increase

the other stores which promoted in early phage increase in

BDM model.

Owing to the exogenous signal quality measure of the VOD service, I identify the effect

of word of mouth (signal quality) o based on

micro level adoption data. However, the estimated results do not support for the

hypothesized assumptions on the BDM model on communication channels. The signal

quality (word of mouth) is found to be significant in the , not in

T both internal

(word of mouth) and external (advertising) influences. This means that the Bass model

cannot separately identify the communication structure in new product diffusion

(innovation vs. imitation) in usual setting lacking measure on Word-­of-­Mouth.

28

For managers who want to successfully increase a new product s penetration in the

long run, it is crucial to broaden retail distribution channels and actively manage local and

in-­store promotions. Products should be shown in the right location with effective display

and salespeople should be well educated and incentivized to promote new products. Just

putting the new products in a retail store does not automatically yield sales. In the early

phage of a new product launch, social media marketing and product quality should be

emphasized to facilitate new product diffusion through Word-­of-­Mouth effects.

It is desirable for future research to investigate the effect of distribution channel and

promotional activities on new product diffusion process in other product categories. The

findings in this paper might be category specific in the sense that the video-­on-­demand

service is high tech products where product changes are rapid. Digital revolution enables

researcher to collect detailed information about retail stores and its in-­store promotional

activities like salesforce compensation scheme, and display on the micro level purchase

behaviors.

This paper contributes to new product diffusion marketing literature by uncovering the

hidden role of distribution channel. The aggregation errors could partially explain the

commonly observed overestimation of contagion effect in the Bass Diffusion Model. The rate

29

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33

Table 1. Simulation of National Rollout vs. Sequential Rollout

Variables True Value National Rollout

Sequential Rollout

P(innovator) 0.2 0.193 0.017

(0.006) (0.005)

q (imitator) 0.0001 0.012 0.423

(0.023) (0.065)

m (market size) 10,000 10,067 8,971

(280) (845) *Launch a new product at market 1 (20%) in year 1 at market 2 (30%) in year 4, and at market 3 (50%) in year 7), total period 13 years. All the parenthesized numbers show the average standard errors over 100 iterations.

34

Table 2. Summary Statistics by market

Jacksonville, FL

Salt Lake City, UT

Spokane, WA

Adoption Total Population 1,080,925 1,764,891 448,533 Total Households 428,511 557,061 191,255 Total Number of subscribers 2,147 2,061 559 Address Matched observations 1,727 1,696 497

HH Penetration (%) 0.50% 0.37% 0.29% Advertising ($spending) TV 745,233 1,301,159 496,482 Radio 217,242 310,678 71,142 Newspaper 261,188 172,738 120,587 FSI 109,301 91,381 54,629 Distribution Channels BestBuy 2 4 2 Circuit City 3 5 5 Sears 3 5 2 Local Stores 9 15 2 Total 17 29 13 Competition DVD rental shop 62 85 15 Shopping Malls 20 20 9 Cable 51% 25% 33% Digital Cable 17% 10% 9% Demographics Income 56,420 63,831 52,800 Single(%) 20 21 18 Black (%) 21.2 1 1.2 Silver (%), over 55 yr 19 14 20

35

Table 3. Summary Statistics

Variable Obs Mean S. D. Min Max #Subscribers 155 25.30 22.72 1 111 Penetration(%) 155 0.36 0.23 0.01 1.92 TV ad ($10k) 13 2.27 1.17 1.2 3.4 Signal quality 155 1.59 0.32 0 2.25 Signal strength 155 3.01 0.36 0 3.36 # of households 155 7,592 4,971 52 22,127 Income* 155 58,717 16,934 22,408 117,596 Single* 155 0.20 0.06 0.12 0.47 Silver* 155 0.17 0.06 0.01 0.39 Black* 155 0.07 0.15 0 0.97 Cable* 155 0.35 0.22 0 0.87 Digital cable* 155 0.12 0.09 0 0.34 DVD rental 155 1.06 1.20 0 6 Retail stores 155 0.34 0.80 0 4 Circuit City 155 0.06 0.25 0 1 BestBuy 155 0.05 0.22 0 1 Sears 155 0.06 0.25 0 1 Local stores 155 0.17 0.47 0 2 Mall 155 0.32 0.75 0 5 SLC 155 0.44 0.50 0 1 SPK 155 0.25 0.44 0 1

Notes: *Demographic information is based on 2002 Census Tract level

Income Mean Income level ($)

Single the proportion of population of single (never married)

Silver the proportion of population over 55 years old

Black the proportion of population of black (non hispanic)

Cable the proportion of population with conventional Cables

Digital Cable the proportion of population with digital Cables

36

Table 4number of adopters (monthly)

(1) (2) (3) (4) (5) (6)

Month1 Month2 Month3 Month6 Month9 Month12 hh(1,000) 0.0812*** 0.110*** 0.0342* 0.0888*** 0.0381 0.0871** (0.0158) (0.0196) (0.0151) (0.0229) (0.0340) (0.0305) Bestbuy -­0.280 -­0.461 -­0.164 -­0.248 -­0.0576 -­0.772 (0.219) (0.269) (0.209) (0.319) (0.507) (0.447) CC 0.231 0.401 0.552** 0.797** -­0.309 0.777*

(0.199) (0.236) (0.170) (0.259) (0.463) (0.353) Sears 0.418* 0.326 0.167 0.276 0.340 0.0695 (0.164) (0.209) (0.180) (0.250) (0.372) (0.327) Localstore 0.0898 0.270** 0.0667 -­0.0701 -­0.00668 -­0.279 (0.0809) (0.0977) (0.0800) (0.126) (0.195) (0.168) Rental -­0.0646 -­0.106 0.102* -­0.0401 0.143 0.0433 (0.0456) (0.0573) (0.0421) (0.0651) (0.0961) (0.0974) Mall -­0.0754 -­0.0340 -­0.206* -­0.153 0.0846 0.0933 (0.0732) (0.0828) (0.0807) (0.111) (0.129) (0.126) Slc -­0.462* -­0.312 -­0.434* 0.222 0.509 -­0.0854 (0.180) (0.227) (0.174) (0.278) (0.448) (0.354) Spk -­0.496* -­0.135 -­0.568** -­0.562 -­0.0314 0.527 (0.221) (0.250) (0.220) (0.371) (0.434) (0.396) Const. 1.790* 0.611 0.466 -­0.336 -­3.336* 1.250 (0.754) (0.929) (0.721) (1.106) (1.607) (1.525) Log(alpha) -­16.89 -­2.903*** -­16.75 -­5.714 -­15.39 -­15.29 (591.0) (0.647) (773.4) (12.67) (711.0) (875.6) N 73 73 73 73 73 73

Coefficients for demographics are suppressed for brevity.

37

Table 5. Regression of signal quality on demographics

Est. S. E. t-­value

HH(1,000) 0.001 0.009 0.15 HH size -­0.045 0.198 -­0.23 Income ($10,000) 0.003 0.039 0.09 Education 0.453 1.174 0.39 Single -­0.607 0.631 -­0.96 Child -­0.020 0.365 -­0.05 Silver -­1.032 0.903 -­1.14 Black 0.494 0.732 0.68 Cable -­0.077 0.217 -­0.36 Digital cable 0.388 0.484 0.8 Rental -­0.004 0.032 -­0.13 Retail 0.026 0.038 0.69 Mall -­0.048 0.038 -­1.25 SLC 0.122 0.116 1.05 SPK 0.239 0.106 2.24 Income*black 0.025 0.211 0.12 Const. 1.778 0.459 3.88

Number of obs. 155, R2=0.08

F( 16, 138)= 0.75, Prob > F = 0.7349

38

Table 6. HH level Signal Quality and Strength

actvmonth signal quality signal strength

mean S.D. Mean S.D.

1 1.566 0.495 3.059 0.401

2 1.574 0.507 3.062 0.351

3 1.596 0.490 3.074 0.337

4 1.609 0.485 3.074 0.367

5 1.615 0.504 3.064 0.293

6 1.646 0.492 3.071 0.322

7 1.694 0.517 3.054 0.322

8 1.699 0.448 3.048 0.254

9 1.729 0.580 3.003 0.502

10 1.763 0.560 3.101 0.224

11 1.793 0.563 3.057 0.342

12 1.927 0.538 3.066 0.333

13 2.098 0.424 3.109 0.389

14 2.291 0.068 3.156 0.135

Correlation of signal quality and signal strength: 0.5027

39

Table 7. Regression results

NBD Hierarchical NLS #adopters #adopters #adopters p q m Const. 2.482*** 1.978*** 1.978*** 0.086 0.01 10.909*** (0.421) (0.550) (0.522) (0.066) (97.368) (3.329) Communication Channels TVad($100k) 0.184*** (0.027) Quality (WOM) 0.372' 0.725* 0.763* 1.008* -­1.403 (0.207) (0.324) (0.307) (0.395) (3143)

Resid. (control function).

-­0.588 -­0.642 -­1.07 0.768 (0.417) (0.397) (0.506) (3555)

Distribution Channels #Retail 0.119*** 0.112*** (0.0321) (0.0320) #Circuit City 0.375*** -­0.097 4.871 0.106 (0.0905) (0.145) (454) (0.106) #Other Retail 0.0477 0.185** -­2.813 -­0.002 (0.0365) (0.066) (1034) (0.046) CC_prom 0.272 1.152* 0.314*** (0.184) (0.521) (0.088) Competition #DVD_rental 0.0253 0.0199 0.00370 -­0.121** 4.07 0.05 (0.0258) (0.0258) (0.0249) (0.044) (943) (0.032) #mall -­0.0589 -­0.0495 -­0.0472 0.013 -­0.61 -­0.044 (0.0366) (0.0369) (0.0350) (0.089) (300) (0.064) Cable -­0.204 -­0.154 0.00936 -­0.983** -­0.852 0.098 (0.269) (0.268) (0.259) (0.447) (7662) (0.301) Dcable 0.663 0.487 0.408 -­1.352 -­1.007 1.072 (0.494) (0.503) (0.476) (1.164) (3990) (0.841) Demographics HH(10k) 0.657*** 0.661*** 0.667*** 0.312' 0.731 0.46*** (0.0926) (0.0914) (0.0862) (0.166) (2506) (0.118) Income(10k) 0.0572** 0.0524** 0.0469* 0.084* -­2.25 0.024 (0.0193) (0.0194) (0.0184) (0.036) (532) (0.025)

Single -­0.830 -­0.942 -­1.172' -­9.046*** -­0.564 5.419***

40

(0.741) (0.736) (0.704) (1.374) (35737) (1.086) Black 0.169 0.168 0.142 -­0.742 -­0.386 0.294 (0.271) (0.268) (0.254) (0.841) (4284) (0.683) Silver -­1.687** -­1.775** -­1.957** 0.868 -­0.824 -­2.421** (0.637) (0.632) (0.602) (1.423) (13854) (1.003) Slc -­0.241* -­0.231* -­0.204* -­0.65** -­0.691 -­0.097 (0.108) (0.106) (0.101) (0.183) (2935) (0.134) Spk -­0.279* -­0.319** -­0.333** -­0.462' -­0.413 -­0.19 (0.119) (0.121) (0.114) (0.268) (893) (0.185) ln(alpha) -­3.718*** -­3.768*** -­4.005*** (0.307) (0.313) (0.347) N 73 73 73 975 975 975 BIC 585.7 588.0 583.2 MSE 4006.5

Standard errors in parentheses

* p<0.001

41

Figure 1. Sales of air conditioners between 1949-­1661

42

Figure 2. Air conditioner Ads in Miami News

1955 June 1964 April

43

Figure 3. Diffusion Simulation varying p and q parameters

Given q=0.1

Given p=0.02

44

Figure 4. Simulated data with sequential rollout

Figure 5. Distribution Channels and Competition

45

Figure 6 Zip code level adoption pattern (Jacksonville, FL)

Figure 7 Histogram of the total number of adopters by zip code

# of adopters

Freq

uenc

y

0 20 40 60 80 100 120

010

2030

40

46

Figure 8 Micro level adoption and bass model fits

2 4 6 8 10 12

01

23

45

6

month

# ad

opte

rs

2 4 6 8 10 12

24

68

10month

# ad

opte

rs2 4 6 8 10 12

01

23

4

month

# ad

opte

rs2 4 6 8 10 12

02

46

812

month

# ad

opte

rs

2 4 6 8 10 12

510

15

month

# ad

opte

rs

2 4 6 8 10 12

05

1015

20month

# ad

opte

rs

2 4 6 8 10 12

02

46

810

month

# ad

opte

rs

2 4 6 8 10 12

12

34

56

month

# ad

opte

rs

2 4 6 8 10 12

13

57

month

# ad

opte

rs

47

Figure 9 Zip code level signal quality pattern (Jacksonville, FL)

Figure 10 Diffusion Pattern by signal quality

*given total subscribers>30

48

Figure 11. The rate of imitation and the number of retailers

Figure 12. The rate of imitation and signal quality

49

Figure 13. The effect of signal quality and # retailers on q

pred_qual

q

0.5

1.0

1.5

2.0

2.5

1.4 1.5 1.6 1.7 1.8

retail0

1

23

4