Discussion Paper No. 36

The Ubiquitous Model for Dynamic Diffusion ofInformation Technology
Hirokazu Takada, Kaichi Saito, Nobuhiko Terui,and Masataka Yamada
February 23, 2015

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research

Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku

Sendai 980-8576, JAPANThe Ubiquitous Model for Dynamic Diffusion of Information Technology

Hirokazu Takada, Kaichi Saito, Nobuhiko Terui, and Masataka Yamada*February 23, 2015

*For correspondence, please contact Hirokazu Takada, Professor of Marketing, Zicklin Schoolof Business, Baruch College/CUNY, Box B12-240, One Bernard Baruch Way, New York, NY
10010, 646-312-3289 (office), 646-312-3271 (fax), Hirokazu_Takada@baruch.cuny.edu. Kaichi
Saito is Associate Professor of Marketing, Department of Economics, Meiji Gakuin University,
Tokyo, Japan. Nobuhiko Terui is Professor, Graduate School of Economics and Management,
Tohoku University, Kawauchi, Aoba-ku, Sendai, 980-8576, Japan. Masataka Yamada isProfessor of Marketing, Faculty of Commerce and Business, Nagoya University of Commerce
and Business, Nissin, Aichi, 470-0193, Japan.

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The Ubiquitous Model for Dynamic Diffusion of Information Technology

ABSTRACTThe recent information technology products with capability of performing multiple
functions owing to the digital convergence, e.g., smart phones with fast Internet connection,
provide ubiquitous access to the Internet for consumers. To model diffusion processes of suchproducts and services requires a comprehensive modeling framework. We address major issues
in the framework which include the consumer heterogeneity of diffusion modeling and market
segmentation determined by the adoption process, the need for more generalized model than the
successive generation substation theory, the distinction of the adoption processes based on thesequence of adopting different technologies, and the network externalities.
The comprehensive diffusion model based on the Bass Model was proposed, and thehierarchical Bayesian model was formulated for estimation. We conjecture that a segment could
be defined by the process of how consumers adopt the IT service, and we develop the diffusion
models for each of the segments. The proposed model thus consists of those segment specificmodels, and is capable of identifying the market potential for each segment.
The empirical analysis using data on Internet subscriptions via PC and digital cellular
phone in the U.S. and Japan shows that the proposed model can capture the interactive effectbetween two diffusion processes, and provides an excellent fit to the data. The hypotheses
developed in the theoretical framework are supported, and we discuss theoretical contributions
and managerial implications.
Key words: Diffusion, segmentation, Bass model.

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Everlasting quest for the ubiquitous access to the Internet leads to the innovation ofnewer generation digital information products. Smartphones, such as iPhones and Android
Galaxies, could be an answer to satisfy these needs by delivering faster and ubiquitous access to
the Internet with multiple capabilities attributable to the concept of digital convergence, i.e., thetechnological development of converging multiple functions into a single digital device.
Meanwhile, as processing huge amount of information available in the cyber space on portabledevices is getting quite cumbersome, more powerful devices such as desktop PCs may be a better
choice despite lacking portability. Laptop devices may bridge the gap between smartphones anddesktop PCs. How people are trying to achieve accessing the Internet may involve various
adoption patterns of these devices. The objective of this study is to try to build thecomprehensive diffusion model of those adoption behaviors for the access to the Internet. Ourinterest is not in the unit sales of these devices, but the subscription to the Internet by thesedevices. Building such a diffusion model is not a simple task because the adoption pattern may
involve more than a single device, and people may switch devices back and forth depending on
the situation. The widely used Bass model could be applied to this situation. However, thesubstitution model by Norton and Bass (1987) deals with only the switching behavior of
adoption from an old to a new generation, but not vice versa. Consider the scenario under whichpeople are using the desktop PC for their access to the Internet. Those consumers may later add
the cellular phone to supplement their access to the Internet. Since those people adopted theircellular phone after the PC, the cellular phone could be considered as the newer generation
device as opposed to the PC as the old generation. The NB model could capture this sequence
from an old to a new generation adoption. However, people are not quite abandoning their oldPCs, and rather they are using both devices as needed. This means that the NB model needs to3

be extended to cope with a sequence of usage of a new generation product as well as an old
generation product. This is just a single example of the daunting tasks that we need to deal withto construct a comprehensive diffusion model.
Theoretical underpinning of our proposed model lies in the behavioral premise that
adopters would be grouped into different segments based on how they choose devices to accessto the Internet. The majority of diffusion models use the macro level of data by aggregating
adopters. We conjecture that the likely adoption process of gaining Internet access at the microlevel can be used as the segmentation base to group adopters into distinct segments. By
aggregating the segment level diffusion models we come up with the comprehensive unified
model. As the proposed model thus consists of separate models which corresponds to diffusion
processes of different market segments, we formulate the simultaneous equation model.
Despite the increasing amount of diffusion research (for review of diffusion research
literature, see Muller 2014 and Peres, Muller, and Mahajan 2010), to the best of our knowledge,
the unified and comprehensive modeling to disentangle complex diffusion processes of accessing
the Internet via different devices built upon the behavioral premises of segmentation is the firstattempt.
The limited number of observations available for estimation often confronts researcher in
diffusion studies. Our solution to this problem is to develop the hierarchical Bayesian (HB)
model. It is well known that the HB model is capable of yielding very effective and efficientestimation results, and has been widely applied to marketing studies, but not so in diffusion
studies.
Empirical analysis using the subscription data in the U.S. and Japan yields the plausible
results with excellent fit to the data which lend support to the majority of hypotheses developed4

in the theoretical framework, confirming the existence of the large segment of consumers who
are utilizing different devices to achieve ubiquitous access to the Internet.
In the following sections, we present the theoretical and modeling framework, followedby the proposed model and empirical results. We derive managerial implications based on theempirical results, and conclude with discussions on the limitations of this study along withdirections for future research.
Theoretical and Modeling Framework
We organize the theoretical and modeling framework proposed in this study with respect
to the following six major areas: (1) consumer heterogeneity and segmentation to be defined byadoption process, (2) the successive segmentation substation theory and the need for moregeneralized and comprehensive model, (3) identification of initial and conditional adoptions, (4)diffusion acceleration and the learning effect hypothesis, (5) cross-country diffusion research,and (6) the network externalities. The proposed framework, along with the pertinent literature,empirical results, and implications, is summarized in Table 1[Insert Table 1 about here]
Consumer Heterogeneity and Segmentation
We conjecture that the market consists of different segments, thus assuming aheterogeneous market, as opposed to the underlying assumption among the prior diffusion
models as a single potential market with one user segment. Our approach based on theheterogeneous market assumption is to bridge the gap between the homogeneous market
assumption and the individual based assumption for modeling of the diffusion processes.
We define the segments by identifying the patterns of gaining Internet access, i.e., howconsumers access the Internet. For illustrative purpose, we follow the previous scenarios of5

accessing the Internet by PC or cellular phones, or utilizing both devices, as illustrated in Figure
1 where two segments, namely the independent and ubiquitous segments, are identified. The
independent segments consist of subscribers either utilizing their PCs or cell phones alone. The
ubiquitous segment corresponds to the overlapping area where subscribers are using both devices.
Furthermore, those subscribers are divided into two groups depending upon the sequence of
which device is chosen for access to the Internet.
[Insert Figure 1 about here]
We do not label the ubiquitous segment as the complementary segment, since the‘complementarity’ in economics literature is defined in contrast to the substitution, and theformer refers to the case where a product requires another product to function properly, e.g.,
DVD players and software, PC and the operating system with software. The ubiquitous segment
definition is thus to better represent the characteristics of this segment.
Ubiquitous segment hypothesis (H1). We expect that the ubiquitous segment would be
the dominant and growing segment, larger than the aforementioned independent segments. We
derive this hypothesis based on behavioral and technological rationales. First, consumers’
preference for being connected to the cyberspace is easily comprehended because of growing
popularity of cyber communication and huge amount of information available on the Internet.
Formally this is explained by the concept of network externality which we will explore further inthe subsequent section. Simply put, the network externality posits that the more consumers areconnected to each other, the higher pressure consumers feel to adopt the innovation so as tofacilitate communication via the same type of innovation. Thus network connectivity enabled by
PC and cell phone in the ubiquitous environment is expected to stimulate non-adopters to adopt
the same technology.

6Second, the rapid advancement of IT products/services is likely to induce consumers toyarn faster and convenient communication and connection in 24/7 and at anywhere possible.
Recent 4G technology enabled cell phones and smartphones enable consumers to achieve higher
level of ubiquitous communication.
In summary, the proposed model attempts to capture diffusion processes by conjecturingthat these different segments are gaining access to the Internet with varying sequence of using
technologies. The comprehensive models were formulated by aggregating the specific models
for each of the segments into the unified simultaneous equation model. This approach isconsistent to the study by Wind, Robertson, and Fraser (1982) which contends that if the
diffusion patterns vary by segment, the single market assumption is inappropriate. Furthermore,marketing plan and forecasting of new technologies can be improved by properly understanding
the market heterogeneity caused by the different segments. The proposed model is capable ofidentifying various characteristics of different segments from the aggregate data, whereas theprevious studies require separate data for each segment.
From the Successive Generation Substitution Theory Model to the Comprehensive Model
The successive generation substitution model developed by Norton and Bass (1987)
along with the subsequent extended studies has a significant contribution to the literature by
expanding the arena of diffusion research on the high technology innovation. The basic premiseof NB model is that a new product is technologically more advanced and attractive than an
existing product, such that consumers are switching to the new product. The NB model is, thus,
developed based upon the homogeneous segment assumption in which all the consumers adopt
the new generation of the product, and does not explicitly consider the existence of the multiple

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heterogeneous segments. Therefore, the restrictive homogeneous segment assumption needs tobe extended to fully cope with the heterogeneous adoption behaviors across various segments.
In order to capture the recent phenomena of ubiquitous access via multiple devices withthe mixed generations, the new models will be called for, since the ubiquitous segment isutilizing the existing (e.g., PC) as well as the new generation devices (e.g., the cellular phone)simultaneously to satisfy their desire of ubiquitous access to the information in the cyberspace.
The proposed model is formulated by expanding the NB model within a more comprehensive
framework.
The Conditional Adoption Concept for the Ubiquitous Segment
Adoption process of subscribing to the Internet would become complex if consumers
attempt to gain access ubiquitously using different devices. We introduce the concept of initialand conditional adoption process in the proposed model. The initial adoption refers to the casein which consumers first adopt the innovation, whether the adopted innovation could be an
existing or newly introduced device/service. Whenever consumers start the Internet access witheither PC or cellular phone, this is defined as the initial adoption, as illustrated in Figure 2, wheretime horizon of the horizontal axis spans from the time when an Internet access by PC became
available (  P  0 ). The time when an Internet access by cell phones became available is denotedby (  C ).
[Insert Figure 2 about here]
The conditional adoption occurs within the ubiquitous segment where consumers with
the initial adoption subsequently add another innovation, whether an added innovation could be
an existing or newly introduced device/service, so as to facilitate their desires to gain ubiquitousaccess to the Internet. The conditional adoption is thus defined as the adoption conditional upon8

the initial adoption. For example, if the PC subscription is the initial adoption for consumers in
the ubiquitous segment, their subsequent conditional adoption is the cellular subscription to theInternet access. The proposed model can deal with both cases, i.e., the initial adoption could be
the cellular or PC subscription, similarly for the conditional adoption as well within theubiquitous segment.
Accelerating Diffusion among the Ubiquitous Segment
We hypothesize that consumers within the ubiquitous segment would accelerate theconditional adoption process because of the learning effect derived from the prior experience
with the initial adoption. The accelerating hypothesis (H2) is consistent with the diffusion
theory (Rogers, 2003) and international diffusion literature that diffusion rate is accelerated forthe innovation later introduced across different countries because of the time and learning effect(Putsis, Balasubramanian, and Sen 1997). The proposed model is formulated to measure theinitial and conditional adoption rates separately, thus enabling the hypothesis test of this effect.
Cross-country Diffusion Research
In order to contribute to the empirical generalization (Bass 1995, Ehrenberg 1995), we
conduct the empirical analysis using the aforementioned subscription data collected from theUnited States and Japan, the culturally vastly different yet the largest economies in terms of GDP
among the non-communism countries in the world. The parameter estimates will be examined in
the context of the cross-country diffusion research findings.
The flattening effect hypothesis (H3). We contend that the diffusion process of the IT
products/services across different countries tend to exhibit similar patterns, resulting comparable
parameter values, the so-called flattening phenomenon of diffusion of the information technology
products in the global market (Friedman 2006), whereby the diffusion process of these products

9tends to exhibit a converging, rather than varying, pattern between the different countries. The
major rationale behind this hypothesis stems from the glowing global communication acrosscountries generate the homogenized preferences and tastes among consumers, in particularamong younger generation for their desire to adopt high tech products with standardized features.
This is contrary to the prior findings in the cross country diffusion research literature (Putsis,
Balasubramanian, and Sen1997, and Gatignon, Eliashberg, and Robinson1989) that parameter
estimates tend to vary across countries reflecting differences of macro environment factors suchas socio-cultural, economic, geopolitical, and technical environments in the countries. The
flattening effect hypothesis is in accord with the premise of standardization strategy in theinternational marketing research literature that an existence of the homogenized segments acrossvarious countries lends support for its strategy leading to the lower cost and better control for
multinational firms (Levitt 1983). This converging diffusion pattern is expected to emerge
whether diffusion occurs across countries with or without time lags of certain magnitude.
Network Externalities
The network externalities are extensively studied by marketing scholars (c.f., thereferences therein Goldberg, Libai, and Muller 2010) since the notion of the network effect was
first introduced in economic literature (Rohlfs 1974). The IT products, such as the Internet, PC,and cellular phones, are well recognized to exhibit a higher level of direct network externalities,
wherein the utility that a consumer derives from buying a product or service is directly affectedby the number of other users, as opposed to the indirect network externality in which the utility
depends on the number of other users of complementary products (e.g., Katz and Shapiro 1985).
Consequently the primary focus of this study is on the direct network externalities.

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The diffusion studies in the marketing literature with rigorous investigation into the
network externalities are sparse, despite that the well-recognized existence of the network
externalities, due to several grounds. First, the Bass model formulation already captures the
network externality as well as other effects with its imitation coefficient (q), since Bass (1969)
conceptualizes that imitators are influenced by the number of previous buyers, i.e., the direct
network externality effect, although the network externality was not mentioned in his original
paper since his original paper was published earlier than the network externality has been
investigated in the economic literature. Second, identifying the network effects bydisaggregating the parameters into the network effects and other components sounds
theoretically appealing, but it is a formidable task to recover the network externalities from theBass model parameter estimates with aggregate data, because the network externalities deal with
the individual contagion effects, and thus require the micro level individual data in order toproperly capture interactions among consumers, whereas the studies based on the Bass model
including the current research employ the aggregate data for estimating parameters.
The study by Goldenberg, Libai, and Muller (2010) is cited among the first in theliterature to try to separate the word-of-mouth process from network effects in the diffusion of
new products by developing an agent-based cellular automata model (Stremersch, Lehmann, andDekimpe 2010). Nonetheless commentaries on this study raise limitations associated with thestudy, such as the effect of threshold on the empirical evidence of the chilling effect as an artifact
rather than the true state of diffusion network externalities. Authors state that agent-basedmodels are equivalent to the discrete version of the Bass model if a homogenous population andlarge market potential are assumed. Our study is explicitly dealing with the heterogeneous
population, namely different segments defined by the adoption processes of innovation.

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The network effect hypothesis (H4). Based on these reviews and considerations, wehave decided to investigate the direct network externality, separately from the proposed model
formulation. Furthermore, we must note that since the primary objective of this study is todevelop the ubiquitous diffusion model based on the segments, the extension of the alreadycomplex proposed model does not warrant for a more complex modeling with extra parameters.
Nonetheless, empirical investigation of the network effect based on the well-establishedmethodology in the literature still calls for in our study. We hypothesize that the positive direct
network effect exists in our study.
ModelsAs outlined in the theoretical framework in Table 1 and illustrated in Figure 1, we
consider that the market consists of the following four segments: two independent and two
ubiquitous conditional segments, and defined as follows:
Independent segments:
Segment PC:

Subscribers to the Internet using the PCs, but not via
cellular phones.

Segment Cell:

Subscribers to the Internet using the cellular phones, but
not via PCs.

Ubiquitous conditional segments:
Segment PC-Cell:

PC subscribers who subsequently add cellular subscriptions
once the cell service becomes available.

Segment Cell-PC:

Cellular subscribers who subsequently add pc subscriptionsat any time. We assume that PC subscription service has

12been available from the beginning of the time horizon
under study.
The usual stationarity assumption is in order such that consumers are supposed to remain withina particular segment over the period of interest, and would not shift from the original segment to
the other.
As shown in Figure 1, PC subscribers, SP(t), consist of three segments: an independent
PC Segment and two ubiquitous conditional Segments, and can be expressed as follows:(1)

S P  t   S PPC  t   S PPC-Cell  t   S PCell-PC  t 

Similarly the model for cell phone subscribers, SC(t), is:(2)

Cell - PCt   SCPC -Cell t  .
SC t   SCellC t   S C

where superscripts identify the segment as shown in Figure 1. The model is developed on adiscrete time basis, and a time interval (t-1, t] is denoted as, time t. In order to properly accountfor the interactive effects between these two equations, we formulate the two equations as thesimultaneous equation model. The proposed model is more comprehensive than the model by
Norton and Bass (1987), and for a comparison purpose between two models, the proposed model
can be collapsed to the following equations which are the NB model:





(3)

SP t  SPPC-Cell t ,(4)

SC t  SCellt  SCPC-Cell t .
C







The first equation corresponds to the first generation model, while the second equation to thesecond generation model. Our proposed model considers not only the successive generation
substitution as in NB model, but also the opposite generation shift from new to old as well.

13This is a necessary condition for modeling the ubiquitous segment, because subscribers demanda seamless connection to the Internet utilizing devices from different locations. Another notabledifference from the NB model is the unit of measurement as pointed out in the theoreticalframework. The NB model uses the unit sales, whereas our model is using the subscription data.
Diffusion Models for Market Segments
We conjecture that the whole adoption process could be classified into the initial andconditional processes, as we defined previously. For an illustration purpose, the PC subscription
model (Equation 1) is used. (1) The initial subscription process refers to the case where
consumers have adopted a PC subscription for the first time. This process occurs within the firsttwo segments: Segments PC and PC-Cell. (2) The conditional subscription process corresponds
to the situation where consumers choose the PC subscription after experience with the cell phone
subscription, i.e., the PC subscription is conditional upon the prior cell subscription. This
adoption process prevails within Segment Cell-PC. The distinction between the initial andconditional subscriptions is important because it affects the model development which we
describe in the following section.
The initial PC subscribers in Segments PC and PC-Cell, SPPC t  and SPPC -Cell t  , the first
two terms in Equation 1, are derived by multiplying the probability of the initial PC subscription
with the potential segment size as follows:











(5)

SPPC t  m PC FPInitial t   P  FPInitial t   P 1 , and(6)

SPPC-Cell t  m PC-Cell FPInitial t   P  FPInitial t   P 1 











where mh is the potential market size of segment h (h = {PC, Cell, PC-Cell, and Cell-PC }),analogous to the definition of potential market size of the Bass model, m; FPInitial t  is cumulative
14

distribution function of initial PC subscription, and P denotes the time when the PC subscription
service becomes available. Since the PC subscription service occurs at the onset of the time
considered, P = 0.
The conditional PC subscribers in Segment Cell-PC are expressed as follows following
Norton and Bass (1987):





- PC
t   m Cell - PC FCInitial t   C  1 FPConditional t   P   FPConditional t   P  1
SCell
P

(7)

Conditional

where FPfor t   C t is cumulative distribution function of conditional PC subscription and  isC

the time when cell phone subscription service becomes available. Note that FPInitial t   C  1  0
for t   C .
As previously discussed, the initial subscription by the ubiquitous Cell-PC Segment iswith cell phone followed by PC subscription. Thus, potential PC adopters in Segment Cell-PC isdetermined by the cell phone subscribers. The term in Equation (7), m

Cell-PC

FCInitial t   C 1 ,shows the cumulative cell phone subscribers, i.e., the potential and actual PC subscribers at time
t in Segment Cell-PC. The number of conditional PC subscribers in Segments Cell-PC isderived by multiplying the potential and actual PC subscribers in the segment and the probabilityof the conditional PC subscription.
Similarly, the cell phone subscriptions of the initial segment in Equation 2 is:
(8)









.

SCell
t  mCell FCInitial t   C  FCInitial t   C 1 C

The ubiquitous Cell-PC and PC-Cell segments are as follows:
(9)
(10)

SCCell-PC  t   mCell-PC  FCInitial  t   C   FCInitial  t   C  1 
SCPC -Cell  t   m PC -Cell FPInitial  t   P  1  FCConditional  t   C   FCConditional  t   C  1 

15

The total number of subscribers of PC and cellular subscribers expressed in Equations 1
and 2 can be further specified through substitution of the segment specific terms which we havepreviously derived in the segment models.
Model Specification and Parameterization
Specification of the cumulative distribution functions of the initial and conditional
subscription follows the Bass model with its parameters p and q:



F t 
r
i

(11)





1 exp  pir  q ir t 
1

r
i
r
i

q
exp  pir  q ir t pwhere r denotes initial or conditional subscription,pir =the coefficient of innovation for initial or conditional subscription with the device
i which captures an external influence, andq ir =

the coefficient of imitation for initial or conditional subscription with the device i
which reflects an internal influence.

InitialTherefore, the proposed model includes twelve coefficients: the innovation coefficients ( p PC,

Initial
Initial
Initial, pCell, and pConditional), the imitation coefficients ( q PC
, q Conditional, q Cell, andpConditional
PC
Cell
PC

), and the market potentials (mPC, mCell, mPC-Cell, and mCell-PC). As shown in Figure 1,
q Conditional
Cell
the market potential for PC subscribers is mPC + mPC-Cell + mCell-PC , and for cellular subscribers
are mCell + mCell-PC + mPC-Cell , respectively, and the total sum of potential subscribers is mPC +mCell + mPC-Cell + mCell-PC where the latter two terms correspond to the ubiquitous segments.
Proposed Model vs Previous Models

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Previous models, such as the models by Kim, Chang, and Shocker (2000) and Petersonand Mahajan (1978), did not explicitly consider various adoption patterns, and the ubiquitoussegment was not yet considered in their models, and an identification of the ubiquitous segments(Segments PC-Cell and Cell-PC) is the first attempt in the literature to our best of knowledge.
Second, the proposed model is capable of identifying and measuring the initial andconditional subscription rates separately. The former is captured by the unconditional
probabilities with pi and qi as in the traditional Bass model, whereas the latter is captured by theconditional probabilities.
Third, the proposed model can overcome the problems associated with the previous
attempt made by Kim, Chang, and Shocker (2000). The market potential of their model for
category i is expressed as m i t   m i S j t r , where mi represents a base factor for the market
ijpotential for category i, Sj(t) as the number of subscribers to category j (j ≠ i), and rij as acoefficient which captures the impact of the subscriptions to category j on the market potential ofcategory i. Although such a formulation of the market potential is capable of identifying
intercategory relationships, it also results in the following problems, as acknowledged byauthors: First, the base factor needs to be provided a priori. Thus, fixing the base factor with aninappropriate value may not correctly capture intercategory relationships. Second, in order toforecast the category subscription, the observed subscription data of the other category are
required, because the market potential for the category is defined in terms of the subscribers to
the other category. Third, since the market potential is defined as a multiplicative form, theinitial subscription must be zero as long as the other category has not yet appeared on the market.
Authors obtained parameter estimates by setting the number of subscriptions before introduction
equal to 1.

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Hierarchical Bayesian Estimation for the New Product Growth ModelingAn estimation of the Bass model confronts researchers due to the limited data, and thisproblem becomes more prevalent when the comprehensive nonlinear model is developed, since
the number of parameters increases despite that the data availability remains the same. We
experienced an inestimable situation with econometric maximum likelihood estimation in our
preliminary analysis, since the number of parameters exceeds the data points.
The hierarchical Bayesian (HB) estimation is proven to be very effective to cope with thistype of problem. Since Lenk and Rao (1990) and Sultan, Farley, and Lehmann (1990) applied
the Bayesian estimation to their diffusion studies,Talukdar et al (2002) and Lee, Boatwright, andKamakura (2003) are able to obtain reliable estimates with the Bayesian estimation for theirextended diffusion studies. As Putsis and Srinivasan (2000) point out, when little data are
available, bringing in auxiliary information is effective to provide sufficient data to estimate
reliably. This auxiliary information could include using data on multiple segments or countries,
multiple product categories, or incorporating priors on the model parameters.
The use of predictive density for diffusion model shows the additional advantages of
employing Bayesian approach. The forecasting with uncertainty expressed as predictive interval
by using predictive density adds important managerial benefits for managers facing marketing
decisions. In contrast, most previous studies reported only point forecasts. We delineate thisadvantageous feature in details in the section of predictive performance of estimation results.
Empirical Analysis
Annual data of Internet users via PC and cellular phone in the U.S. and Japan were used
for the empirical analysis. The U.S. data compiled by the International Telecommunication
Union (ITU) include 14 observations (1990 - 2003) for PC subscribers, and 9 observations (199518

to 2003) for the cellular phone subscribers, respectively.

The Japanese data cover 16

observations (1990-2005) for the PC subscribers and 7 observations (1999-2005) for the cellularsubscribers.

The Japanese data are compiled by the Ministry of Internal Affairs andCommunications and the New Media Development Association.
It is a challenge to match international data across countries such that empirical results
can be compared one to one across countries. This requires that the data be collected in acomparable manner across countries with respect to data collection methods, measurement, andother criteria (Craig and Douglas 2005). In our data set, the PC subscription data deem to be
sufficiently comparable between the U.S. and Japan to make inferences. As for the cellular
phone subscription data, the Japanese data directly measure the Internet access subscription,
since separate monthly access fee is required for the Internet service, e.g., NTT DoCoMo’s
highly successful and popular i-mode service. The U.S. data, on the other hand, reflect monthly
charges for cellular phone service by wireless carriers such as Verizon Wireless, AT&T, Sprint,
T-Mobile, among others, which are assumed to include voice communication, emails, and accessto the Internet. Some carriers may impose additional one-time fee for extra service, however thedataset does not explicitly cover these costs.
In the following section, we present the estimation equations of the proposed model,
estimation results, followed by the comparative analysis between the U.S. and Japan based on
the estimation results, the temporal pattern analysis of segment sizes, and predictive validity ofthe model using the hold-out samples. We then present the theoretical perspective and empiricalresults with respect to the network externalities within the framework of Bass diffusion model.
Model Estimation

19

The proposed theoretical model in equations of (1) and (2) can be canonically expressedas the set of nonlinear equations, where each equation shares the common parameters in
respective equations. By adding the error terms to theoretical model, we derive the econometricmodel for country k as follows: SkP  t   f kP  t |  k    kP (t ) SkC  t   f kC  t |  k    kC (t )(12)where  k denotes the vector of parameters for k=US, Japan, formally defined as
Initial
Initial
Initial
Initial, q kPC, p kCell, q kCell k   kInitial ', kConditional ',  km ' ' , where  kInitial   p kPC' kConditional   p Conditional , q Conditional , p Conditional , q Conditional  ' and
kPC

kPC

kCell

kCell

 km   m PC , mCell , mCell  PC , m PC Cell  ' . We assume independent normal distributions on the error
k

k

k

k

terms  kP (t ) and  kC (t ) .

The prior distribution is set for parameters after logit transformations for p, q with zeroone restriction and log transformation for m with positive restrictions, i.e.,
Initial k*   logit  pkP
 , logit  qkCConditional  ; log  mkPC  , , log  mkPC-Cell  ' . Then the standard random

effect model k ~ N  , V is used for HB estimation. The data set includes a small number of*observations (the U.S. data contain 7 observations for PC, 14 observations for Cell, respectively,
while Japanese data include 8 for PC and 17 for cell, respectively) for the model with 12
parameters to be estimated. Thus, pooling data of two countries is a viable solution for obtaining
stable estimates from the hierarchical Bayesian model. We rely on the effect of “borrowing thestrength of power from neighbors,” an intrinsic nature of HB modeling.

20

The MCMC method under noninfomative proper prior distributions is applied to estimate
the posterior density of parameters. The specification of likelihood function and prior density
are provided in Appendix A. The joint posterior density is evaluated by MCMC MetropolisHasting sampling algorithm by using WinBUGS. 100,000 samples are generated and first
60,000 samples are discarded as burn-in period to confirm the convergence.
Posterior Distribution

The posterior density of parameters in Figure 3 shows that the majority of posterior
densities are skewed and fat or long tailed. Most of the mean and median estimates yield similarvalues, whereas a large deviance between mean and median occurs for some parameters. Thus
we report the median estimates along with means for interpreting the estimation results in thefollowing section.
[Insert Figure 3 about here]
What do Estimation Results Imply and Suggest?

Results summarized in Table 2 show the mean and median estimates along with the 95%
confidence intervals for each parameters. (We note that “HPD-highest probability density- region”
is correct in Bayesian terminology, however, we use “confidence interval” hereafter for
convenience.) Coefficient p estimates range from the smallest value of 0.0014 for the initial PC
subscription to the largest value of 0.097 for the initial cell subscription, both of these in Japan.
These estimates are consistent with the meta-analysis results (Sultan, Farley, and Lehmann1990).
The U.S. values show the smaller range varying from the smallest value of 0.0046 for the initial
PC subscription to the largest value of 0.007 for the conditional cell subscription.
[Insert Table 2 about here]21

Coefficient q estimates, larger values than p estimates, would be the major interest forunderstanding the dynamics of diffusion processes. The results show the largest estimate of
0.899 for the initial cell phone subscription in Japan, whereas the smallest of 0.523 for the initial
PC subscription in the U.S.
Conditional Diffusion and the Learning and Time Effect Hypotheses

We expect that the initial subscription estimates of the q coefficient tend to be smaller than theconditional ones, based on the hypothesis that the learning effect would accelerate the adoption
rate for the conditional adoption. The same phenomenon is expected due to the time effect,
because newer and better technology with a lower cost would accelerate the adoption rate.
This holds for PC subscription in the U.S. (0.523 for initial subscription < 0.734 for conditional
subscription) and Japan (0.586 for initial subscription < 0.745 for conditional subscription).
This does not hold for cellular phones either in U.S. (0.836 > 0.737) or in Japan (0.899 > 0.701)
Thus, the same pattern emerges in both U.S. and Japan.
Product EffectWe further analyze q estimates from the perspective of the device employed for access to
the Internet, i.e., diffusion rate of pc subscriptions versus cellular subscriptions. The hypothesisof this product effect is that the diffusion rate of pc subscription is expected to be slower than thecellular subscription. Primary rationale for this hypothesis is that the subscription by the newtechnology device tends to accelerate the diffusion rate. The estimation results are that this holds
true for the U.S. where the range of PC subscriptions vary from 0.523 for initial subscription to
0.734 for conditional subscription is smaller than that of cellular subscription which varies from
0.836 for initial subscription to 0.737 for conditional subscription. Japan’s initial subscription
results support the hypothesis that pc subscription diffusion (0.586) is lower than the cellular22

subscription diffusion (0.899). However, the conditional subscription results show much smallerdifference where PC subscription diffusion rate (0.715) and cellular diffusion rate (0.701).
These very interesting and intriguing results may imply that the different results for PC and cell
subscriptions could be related to the old versus new innovations. The diffusion process of theold technology tends to last longer with smaller q values as opposed to the shorter diffusion
process of the newer technology with larger q values. Therefore seemingly contradictory results
are not anomaly but very plausible outcome.
Implications

In summary, PC subscription is considered to be a traditional diffusion which is characterized as
slow diffusion at the initial stage and accelerating diffusion which is represented by the higher
conditional subscription rate. Cellular subscription, on the other hand, is more modern
technology which often entails the fast initial diffusion. Due to its newness, the conditional
cellular subscription rate could be mitigated after the explosive initial diffusion. Even though
we have a very intriguing results emanated both from two countries and two innovations as animportant findings, we must be cautious not stretching its implications too much. We need morecases to draw any generalizable results.
Country Effect and the Flattening Hypothesis

The flattening hypothesis as opposed to the lead-lag hypothesis implies that there is not muchdifference in diffusion process among countries, more subtle for the access by the newer
generation device. The estimation results support the hypothesis where diffusion rates of pc
subscription are very similar for initial and conditional subscriptions (U.S. (0.523-0.734) ≈ Japan(0.586-0.745)). The difference of initial and conditional subscriptions between the U.S. andJapan is very small (0.211-0.159 = 0.052). Cellular subscription diffusion also shows a smaller23difference between the two countries. [US (0.836-0.737) ≈ Japan (0.899-0.701), Δ(0.099-0.198)= 0.099].
In summary, the results support the flattening hypothesis.
Parameter m

The aggregate estimates for the U.S. and Japan (265980 and 135515 subscriptions, respectively)
as shown in Figure 4 are plausible, considering the populations of these two countries (317million and 127 million people, respectively). The penetration in the Japanese market isrelatively higher. This seems to be consistent with the geophysical characteristics of thesecountries where the population density in Japan is vastly higher in the much smaller market thanthe U.S. market.
[Insert Figure 4 about here]
We analyze the results with respect to the specific segment estimates. The largest among four
segments in the U.S. are two conditional segments. The conditional “PC -> Cell” segment isdominant, and adopters in this segment initiate their access to the Internet by PC, and later on,
add the cellular access. The next large segment, another conditional “Cell ->PC” segment,shows the opposite sequence of adoption, the segment most likely corresponding to the younger
generations who tend to start their access with their cell phones. These conditional segments
dominate the independent segments of “Only PC” and “Only Cell”. Considering the subscribers’desire for the ubiquitous access to the Internet from home, workplace, and outdoors, theemergence of these two conditional segments as the major ones in the market place is quiteplausible.
The Japanese market shows somewhat different outcome. The largest segment is theindependent PC subscribers segment (38245), followed by the conditional “Cell->PC” segment24

(35660). The “PC->Cell” segment, the largest one in the U.S., turns out to be the smallest inJapan. According to the report compiled by the Japanese Government (Japan Tourism Agency2011), the free Wi-Fi access in Japan needs an improvement for foreign tourists who haveexpressed the troubling experience with limited Wi-Fi access and the strict security protocol,
compared with other developed countries. This turns out to be a major concern for Japan who
will host the summer Olympic Games in 2020 expecting the surge of foreign travelers.
Considering the Internet access environment unique to Japan, the emergence of the large
independent PC segment is plausible, and may imply that traditional access by PC is stillcommon. The conditional cell-PC segment, similar to the U.S., may correspond to the younger
generation who started their access by their cell phones and add the PC access to achieve more
ubiquitous access.
Temporal Dynamic Segment Shift

The subscribers consist of three segments, namely one independent and two ubiquitoussegments, as illustrated in Figure 1. Estimation results in Table 2 provide market potentials forthese segments. The model is capable of unfolding the temporal shift among the segments sothat we can better understand, not just the composition of the segments, but gain valuable
insights into dynamic shift, if any, among segments. The results are summarized in Figure 5
where each bar consists of an independent segment labeled “only” and two ubiquitous segments.
[Insert Figure 5 about here]
Overall plots clearly illustrate the diffusion processes of conditional ubiquitous
subscribers over time for the U.S. and cell phone subscribers in Japan, and supporting theubiquitous hypothesis in Table 1. For the Japanese PC subscribers, the independent andconditional ubiquitous segments appear to coexist over time.

25

Notable differences in the diffusion processes between PC and cellphone subscribers areevident in Figure 5, across U.S. and Japan. Diffusion processes of pc subscribers tend to bemodest and slow, in comparison to the cellular diffusion which shows faster diffusion dominatedby the ubiquitous segments. The temporal plots reconfirm the empirical findings that q values
for cell subscribers are higher than those for pc subscribers as reported in Table 2. The results
thus support the accelerating diffusion and learning effect hypothesis presented in the theoreticalframework in Table 1.
The emergence of similar diffusion patterns within the device, but the lack of significant
differences in the diffusion processes across countries, support the flattening hypothesis.
Model Validations

The proposed model is validated by conducting the following analyses: (1) comparison against
alternative model formulation, (2) “in sample fit analysis” of the proposed model versus actual
data, and (3) predictive performance and the advantage of the unconditional predictive density.
Those analyses show that the proposed model outperforms the alternative model, and that themodel has a very good fit to the data. We showcase that on top of the excellent predictive
performance, the unconditional predictive density can provide more valuable information forforecasting than the traditional point estimates.
Model Comparison

The proposed ubiquitous HB model is compared against a nested HB model. The nested
model uses the subscription data by a single device, either cell phone or PC, whereas the data
used for the proposed model include both devices, thus the pooling for these models varies. The
alternative model is labeled as the “non-ubiquitous HB model,” because subscription to theInternet relies upon a single device.

26

ModelUbiquitous HB
Non-Ubiquitous HB

DIC
867.9
894.4

Log ML-447.8-453.2

The above results clearly indicate that the proposed model performs better than thealternative model based on two goodness fit of measures, commonly used for Bayesian modeling,
the deviance information criteria (DIC) and the log of marginal likelihood (log ML). The
proposed model shows the smaller DIC and the larger log ML values. In addition, thepredictions by the ubiquitous HB model, as is discussed soon below, perform significantly better
than other comparable models.
In Sample Fit

An overall fit of the proposed model is very well as illustrated in Figure 6 where theactual data is indicated in red while the predicted mean values indicated as a bar in the interquarter range box plot. The majority of predicted values lie within 95% confidence interval
which is shown as an outer range around the box plot, except for just three cases (US-PC, obs. 7
and 14, and Japan-cellphone, obs. 10). It is notable that the proposed HB model can provide
more reliable information for its prediction by generating the posterior density around theestimated values, on top of the traditional point estimates. The posterior density distribution via
interpolation was constructed by using the algorithm for s-step predictive density with thenegative predictive step ( s  0 ), i.e., retrospective prediction, as is shown in the following
section.
[Insert Figure 6 about here]
Predictive Validity

The advantageous feature of using Bayesian approach is that we can obtain the predictive
density, and that forecasting with uncertainty can be expressed with predictive interval, in27

comparison to the econometric approach which usually only provides the point forecast. This isimportant for marketing managers who need to make decisions under uncertainty, because they
can foresee the distribution around the forecast. The predictive density has been introduced in
the early period of modern Bayesian inference (cf. Zellner 1970, pp.29-30), and the recent
application includes the study by Terui and Ban (2013). Neelamegham and Chintagunta (1999)
applied predictive distribution to the diffusion study of new movies viewership forecast by using
the generalized linear model. Their model is static and therefore the predictive density is
conditional upon the possible scenarios for future covariates. Our dynamic model, on the other
hand, generates the unconditional predictive density as explained below.
The unconditional predictive density The predictive density for s-step ahead forecast isformally defined as(13)

p YT  s | Data    p YT  s |   p  | Data  d

where YT  s stands for s step ahead forecast of dependent variable and  means the parameter
vector. The integration in (13) can be numerically evaluated by efficient Monte Carlo methods,i.e., by generating samples YT  s ( i ) in addition to MCMC iterations for posterior densityp  | Data  . The algorithm in detail is described in Appendix B. For diffusion models with an





(i )
(i )
explanatory variable of “time”, the structural equation p YT s | 
is easily updated byshifting T to T+s, without assuming scenarios for future explanatory variables. Moreover, we

can evaluate the joint predictive density for consecutive predictors p YT s , YT s* | Data , and thisallows us to makes joint predictive interval when necessary.
Based on the predictive density, we could state with 95% confidence that the numbers of
PC subscribers in both countries in the period of T+k will fall within the predictive interval.
28

Figure 7 shows the predictive density of two step ahead forecasting for respective products inboth countries. The 95% predictive interval is provided at the bottom of each graph in 7. We
observe that most predictive densities are well defined, and predictive intervals contain the actual
holdout samples for all the cases.
[Insert Figure 7 about here]
The predictive interval is constructed based on finite number of sample. The counterpart
is possible in case of maximum likelihood estimation by using asymptotic theory, which assumes
that large number of samples are available. Obviously, it would not work well, if the number ofobservations is limited, and if the model is highly nonlinear, like ours.
The root mean squared errors (RMSE) of forecast are provided in Table 3. The proposed
Bass model has the smallest RMSE marginally in most cases, and it has smaller total RMSE
value than other models, including the ubiquitous model estimated by nonlinear LS(leastsquares) method[Insert Table 3 about here]
Network Effects

We measure the direct network externalities following the study by Nagard-Assayag andManceau (2001) in which their indirect network externality model is specified as the number ofusers of a product at time t, S(t), based on a binary logit framework as follows:(14)St   m

1,
1  exp  U t 

where U(t) is the utility that a consumer derives from subscription. In order to measure the direct
network externality, we specify U(t) as:(15)

Ut     St  1 ,29

where S(t-1) is the lagged number of subscribers, or the network size,  is to capture the network
independent, or the “stand-alone” utility of the subscription, and  measures the direct network
effects. The formulation and its variants of Equation 14 have been widely employed in thetheoretical and empirical studies (e.g., Katz and Shapiro 1992; Goolsbee and Klenow 2002;
Padmanabhan, Rajiv, and Srinivasan 1997) to operationalize to measure the direct network
effects where a positive estimate of  would indicate the network externality.
Estimation results employing the HB estimation summarized in Table 4 show that thedirect network externalities are present for the diffusion of PC and cellular subscriptions in the
U.S. and Japan, since estimates of PC, US and Cell, US, PC, JPN, and Cell, JPN are positive andsignificant. Thus, digital convergence as discussed in the theoretical framework and summarizedin Table 1 is evident.
[Table 4 about here]
Two more significant results call for further analysis within the theoretical framework.
First, the empirical results show that cellular subscription exhibits the stronger network
externality than PC subscription. This confirms the existence of the accelerating diffusion andsupport of the learning effect hypothesis. More importantly, stronger network effect emanatedfrom the cellular subscription is in concordance with higher conditional adoption by theubiquitous segment as conjectured in the theoretical framework (1.3). Second, Japan exhibits
higher level of the network externality than the U.S. This may be attributable to the substantial
difference in the macro environment, such as geographic environment in which Japan is a highdensity country with very limited land area which is roughly equivalent to the state of Montana,and this consequently contributes to a much higher level of physical proximity among
subscribers.
30

Conclusions

The major theme of this study is to study the diffusion processes of the ubiquitous IT
innovation. The empirical results appear to support the majority of hypotheses as summarized inTable 1. We organize this section into three sections. First, we review contributions of thisstudy to diffusion research, specifically three areas of contributions, namely, theoretical,
methodological, and empirical contributions. Second, we discuss managerial contributions to be
derived from empirical findings. Third, we conclude this section by reviewing limitations of thisstudy, and directions for future studies.
First, we attempt to highlight theoretical contributions to the diffusion research emanatedfrom the formulation of the comprehensive ubiquitous diffusion model. The basic Bass model
under the homogenous market assumption is not appropriate for grasping the highly complex
diffusion mechanism of the ubiquitous diffusion. First, the realization of the existence ofheterogeneous market segments defined by the sequential adoption processes of innovation isnecessary to properly account for the heterogeneous diffusion processes. Our modelingapproach could be characterized as a bottom-up process, starting from building the segment
specific diffusion models and aggregating the models across segments, in contrast to a top-down
approach which may start with formulating a single equation model and add extra parameters toaccount for heterogeneity. We chose the former strategy because diffusion process of theubiquitous segments involve far more complex mechanism, and cannot be explained by merely
throwing in extra parameters. Second, the objective of developing the conditional diffusion
model was to properly represent the adoption process within the ubiquitous segment. Third, theubiquitous nature of IT innovation requires more comprehensive and recursive model than the31

successive substitution model by Norton and Bass (1987), and the simultaneous recursive model
is developed.
Methodological contributions are associated with the formulation of hierarchical
Bayesian estimation model of simultaneous econometric equations. We showcase the effective
use of posterior density around the parameter estimates, which can provide the predictions withmore reliable information than the traditional point estimates. Analysis of the predictive density
is still at infancy in diffusion research, in spite that studies in econometric time series analysis
demonstrate the utility of predictive density, and that marketing studies, even though limited,show its usefulness (Neelanmegham and Chintagunta 1999). Our study illustrates that thepredictive density is valuable information for managers, since they are eager to assess future
sales potential. Needless to state, the HB estimation for diffusion research is proven to be morethan efficient and effected than the traditional econometric modeling of the Bass model due tothe limited data available for estimation.
The empirical findings indicate that the ubiquitous segments are significant, in particular
for cellular subscribers segments for both the U.S. and Japan. This lends support for the validityof the ubiquitous diffusion model and the conditional diffusion processes. Further, the quite
similar diffusion processes are emerging in both countries, which supports the flattening
hypothesis. As summarized in Table 1, the accelerating diffusion effect is evident, and thelearning effect hypothesis is supported. An existence of the network effect is confirmed, and alarge magnitude of its effect is in concordance with the ubiquitous segment hypothesis and theaccelerating hypothesis. In summary, it appears to be fair to state that theoretical testing with theempirical evidence of this study yields the plausible results.

32

Managerial implications derived from the empirical results are as follows: First,
managers need to properly understand the complex diffusion processes of heterogeneous markets.
Relying on the homogeneous assumption and using the single equation diffusion model leads tomisleading understanding of the market place. This calls for a comprehensive modeling andaccurate data. Second, managers need to understand the dynamic interactive behavior of theubiquitous subscribers who employ various devices in a variety of sequences to gain access to
the Internet. Third, potential market size for separate segments derived from the proposed model
provides managers with capability to assess sales potentials for each segment. Properly
understanding and assessing the importance and significance of the ubiquitous segment is vitalfor determining the target segment and formulating the marketing strategy.
There are some limitations of this study. We used data on digital cellular phone subscribers
in the U.S., considering them as the good approximation of Internet users via cellular phone.
However, the U.S. data may be inflated because digital cellular phone subscribers include not
only cellular phone Internet users but also regular talk only users. It is desirable to have the data
which can isolate the Internet subscription from other functions.
As for future studies are concerned, for better generalization, we need to accumulate
empirical evidence by applying the proposed model to data on other countries. Second, tofurther examine the model performance, the proposed model needs to be applied to data on other
innovations.
In summary, the demand for ubiquitous access is expected to accelerate further in the future,
and we are already observing such evidence with the added capability of the Internet access to awide variety of devices, such as game machines (Nintendo Wii), Apple Touch, and HDTVs. The
gaining popularity of large screen smartphones and mini tables such as mini iPad and Android

33

tables are expected to further accelerate the diffusion of ubiquitous access to the Internet. We
believe that the proposed model can be expanded to cope with these future developments.

34

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38

Table 1
Theoretical and Modeling Framework and Empirical Results

1

2

Theoretical constructs andhypotheses
Consumer heterogeneity andmarket segmentation
H1. The ubiquitous market
segment hypothesis
Successive and more
Comprehensive model.

3

The conditional diffusion
model

4

Accelerating diffusion
H2. The learning effecthypothesis

5

Cross-country research
H3. The flattening hypothesis

6

Network externalities
H4. The direct network
externalities

Previous studies

Empirical results

Implications

The majority of studies use
the homogeneous assumption
with single market segment*

Heterogeneous market segment
model is developed.

The diffusion model under the heterogeneous
market assumption is necessary to properly
identify and measure the diffusion processes ofvarying market segments.

H1. The dominant segment isthe ubiquitous segment.
Successive substitution model Subscribers using newer(Norton and Bass 1987)
generation of devices also
adopt older devices.
None for ubiquitous
Ubiquitous adoption is evident.
diffusion, and the majority of Non-ubiquitous diffusion is
studies are limited to nonprevalent for PC subscription,ubiquitous diffusion of thewhile ubiquitous conditional
initial adoption model
adoption is more prevalent forcell subscription.
International diffusion
Accelerating diffusion occurs
research confirms thefor cell subscription.
accelerating and learning
effect.
H2. The learning effecthypothesis is supported
for PC subscription.
International diffusion
Cellular subscriptions show
research found the lead andhomogeneous diffusion pattern.
lag effect.
H3. Supported
Extensively studied
The direct network externalities
exist for the data.
H4. Supported.

39

Both directions of old-new innovation adoptions
need to be incorporated in the model.
The comprehensive model for both ubiquitousand non-ubiquitous diffusion is required.
Old generation service follows the traditional
diffusion pattern, while new generation service
follows a more complex diffusion pattern.
Younger segments tend to adopt the newgeneration devices faster, and without much
effort to learn.

The standardized strategy may fit for diffusionof the cellular subscriptions across different
countries.
Digital convergence is evident.

Table 2
Estimation Results

US
Parameters
p

PC

Cell

q

PC

p

Median

ini
US,PC

.0048

.0046

.0017

pcond
US,PC

.0178

.0057

.0001

p

Parameters

Mean

Median

.0094

p

ini
JP,PC

.0021

.0014

.0001

.0088

.1088

pcond
JP,PC

.0188

.0066

.0002

.1214

ini
JP,Cell

.0990

.0968

.0608

.1505

.0074

.0065

.0019

.0174

p

pcond
US,Cell

.0096

.0070

.0001

.0376

pcond
JP,Cell

.0201

.0053

.0002

.1489

q ini
US,PC

.531

.523

.406

.710

q ini
JP,PC

.593

.586

.347

.889

cond
JP,PC

.706

.745

.212

.978

cond
US,PC

.696

.734

.202

.979

q

q ini
US,Cell

.792

.836

.408

.986

q ini
JP,Cell

.873

.899

.627

.989

q condUS,Cell

.712

.737

.302

.979

q condJP,Cell

.666

.701

.179

.975

PC

PC
m US

53026

45275

4273

142205

PC
m JP

38615

38245

6458

74860

Cell

mCell
US

51848

46405

5535

124300

mCell
JP

35208

34410

5350

70860

PC-Cell

PC-Cellm US

11304011600022517

183303m JPPC-Cell

29963

27200

5293

68321

Cell-PCm

131600

m

36492

35660

5645

71881

Cell

Cell-PC
US

61207

p
q

0.009
0.73
41415

58300

7255

Cell-PC
JP

0.007
16370
80161
0.742 0.0010 0.0291
39025
0.458
0.936
m
a
Market potential
PC
227273
PC a
Cell b226095Cell bPC
PC-Cell
Cell-PC
a: The potential market size for PC is calculated as m + m+m.
b: The potential market size for cellular phone is calculated as mCell + mCell-PC + mPC-Cell.
Common

95% CI
Lower
Upper

ini
US,Cell

q

m

Mean

Japan
95% CI
Lower
Upper

40

105070101663

Table 3
Root Mean Squared Errors of Forecast

Forecast
Model
Period1 Step Ubiquitous HB
Ahead Non-Ubiquitous HB
Nonlinear LS
2 Steps Ubiquitous HB
Ahead Non-Ubiquitous HB
Nonlinear LS

US,
PC
7793
8463
8467
5020
5334
5349

41

US,
Cell
8495
10735
11199
8373
13237
14320

Japan,
PC
244
687
325
916
1324
356

Japan,
Cell
1293
4486
4366
1005
4861
4692

Total
5801
7202
7353
4928
7567
7997

Table 4
Network EffectParameters
U.S.


m
Japan


m

Mean

PC
MedianMean

Cell
MedianSDSD-2.4780.04
160482-2.4620.039
159900

0.213
0.005
8710

-2.4590.065
130953-2.4120.064
130000

0.37
0.016
9153

-2.9
0.14
62113

-2.82
0.132
61650

0.605
0.046
5988

-2.5320.462
69314-2.396
0.428
67070

0.937
0.352
10707

42

Figure 1
Ubiquitous Model and Market Segments

Segmentation
Access by PC

Segment size

Access by cell phone

Independent
Segment(PC)

Ubiquitous
Segment(PC-Cell)Ubiquitous
Segment(Cell-PC)

Independent
Segment(Cell)

mPC

mPC-CellmCell-PC

mCell

Model for subscription by PC
- PC
t 
SP t   SPPC t   SPPC-Cell t   SCell
P

Initialsubscription

Conditional
subscription

Model for subscription by cell phone









SC t  SCellt  SCell-PCt  SCPC-Cell t
CC
Initialsubscription

43

Conditional
subscription

Figure 2
Initial and Conditional Adoption Processes
Independent Segment PC

Independent Segment Cell

Ubiquitous Segment Cell-PC

Ubiquitous Segment PC-Cell
Case 1Case 2Time tPC Introduction
P = 0Cell Introduction
C

Initial PC Adoption

Conditional PC Adoption

Initial Cell Adoption

Conditional Cell Adoption

44

Figure 3
Posterior Distribution of Parameters

45Figure 4
Estimated Market Potential46

Figure 5
New Subscribers Within Each Segment
US, PC

US, Cell

40000

40000

35000

35000

30000

30000

25000

25000

20000

20000

15000

15000

10000

10000

5000

5000

0

0
1

2

3

4

5

6

Only PC

7

8

PC-Cell

9

10

11

12

13

14

1

2

3

Cell-PC

4

5

6

Only Cell

Japan, PC

7

8

Cell-PC

9

10

11

12

13

14

PC-CellJapan, Cell

25000

25000

20000

20000

15000

15000

10000

10000

5000

5000

0

0
1

2

3

4

5

6

Only PC

78

9

PC-Cell

10 11 12 13 14 15 16

1

Cell-PC

2

3

4

5

6

Only Cell

47

7

8

9

Cell-PC

10 11 12 13 14 15 16

PC-CellFigure 6
In Sample Fit:
Actual vs. Predicted

30000
20000
10000
0

0

10000

20000

30000

40000

US, Cell

40000

US, PC

1

2

3

4

5

6

7

8

9

10

11

12

13

14

1

2

3

4

5

6

8

9

10

11

12

13

14

14

15

16

30000
20000
10000
0

0

10000

20000

30000

40000

JP, Cell

40000

JP, PC

7

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

1

48

2

3

4

5

6

7

8

9

10

11

12

13

Figure 7
Predictive Density: Two-Steps Ahead
Subscribers at time period T

5000 10000

20000

10000

20000

30000

40000

Mean = 10977, Median = 9806, SD = 4268,
95% CI = [5902, 22327]

Japan, PC (Actual Value = 1856.56)

Japan, Cell (Actual Value = 4698)

Density

0.00000

0.000100.000150.000200.00030

Mean = 9023, Median = 8663, SD = 2912,
95% CI = [4377, 15744]

0.00000

Density

0.000100.00000

Density

0.00010

U.S., Cell (Actual Value = 20720)

0.00000

Density

U.S., PC (Actual Value = 2632)

0

5000

10000

15000

0

Mean = 2755, Median = 2347, SD = 1764,
95% CI = [583, 7369]

5000

15000

25000

Mean = 4157, Median = 3427, SD = 2782,
95% CI = [1016, 11234]

Subscribers at time period T - 1
U.S., Cell (Actual Value = 20720)

Density
5000

10000

20000

10000

20000

30000

40000

Mean = 18552, Median = 17988, SD = 3775,
95% CI=[12719, 27636]

Japan, PC (Actual Value = 1856.56)

Japan, Cell (Actual Value = 4698)

Density

0.00000

0.000100.000100.000200.00020

Mean = 12610, Median = 12430, SD = 2904,
95% CI=[7468, 18797]

0.00000

Density

0.00006
0.00000

0.00006
0.00000

Density

0.000120.00012

U.S., PC (Actual Value = 2632)

0

5000

10000

15000

5000

Mean = 4013, Median = 3720, SD = 1885,
95% CI=[1219, 8508]

10000

20000

Mean = 5578, Median = 5112, SD = 2316,
95% CI=[2460, 11227]

49

Appendix: The MCMC Algorithms

A: Joint Posterior Density
Under the assumption of independent normal distribution on the error terms  kP (t ) and kC (t ) , we have the Gaussian joint likelihoods from the equation (E1)
(A1)





Japan Cellp Skr  t  , t |  k     k US r  PC

Tkr /2kr

2
 1 Tkr
exp   Skr  t   f kr  t |  k  /  kr2 
 2 t 1where  k denotes the vector of parameters in the equation (E1) for k=US, Japan, and r=P, C. The
prior distribution is set for parameters after logit transformations for p, q with zero-one
restriction and log transformation for m with positive restrictions, i.e.,
Initial k*   logit  pkP
 , logit  qkCConditional  ; log  mkPC  , , log  mkPC-Cell  ' . Then we employ thestandard random effect model  k* ~ N  , V  and this is combined with the likelihood function(E2) , with adjusted by appropriate Jaconbinas to get the joint posterior densityp  k  | Skr  t  , t . The hyper-parameters are set as noninformative  ~ N  0, 100  I  ,V ~ IW  ,   I  and   dim  k   3 . We also set the diffuse prior on the error variance as kr2 ~ IG .001, .001 .
B: Predictive Density
The algorithm for predictive density follows:p  | Data (i)generate a sample  (i )(ii)conditional on  ( i ) , we make YT  s (i ) according to the structural equation p YT  s ( i ) |  ( i )  in
(13).

(iii)

This process is iterated many times to get YT  s ( i ) , i  1,..., M  .
50

Then the empirical distribution of it converges to the predictive density p YT  s | Data  as M goesto infinity.
We note that the structural equation p YT  s ( i ) |  ( i )  is easily updated simply by shifting T
to T+s, not assuming scenarios for future explanatory variables. In addition, we can evaluate thejoint predictive density for consecutive predictors p YT  s , YT  s* | Data  by evaluating

Y

T s

(i )





, YT  s* (i ) , i  1,..., M .

51