DOES ONE STANDARD PROMOTE FASTER GROWTH?
AN ECONOMETRIC ANALYSIS OF THE INTERNATIONAL DIFFUSION
OF WIRELESS TECHNOLOGY
Robert J. Kauffman
Professor and Co-Director, MIS Research Center
rkauffman@csom.umn.edu
Angsana A. Techatassanasoontorn
Doctoral Program
angsana@csom.umn.edu
Information and Decision Sciences
Carlson School of Management
University of Minnesota
Minneapolis, MN 55455
Last revised: September 22, 2003
____________________________________________________________________________________
ABSTRACT
International diffusion of wireless telecommunication and mobile e-commerce has increased since
the height of the Internet economy, however, there are a number of different managerial,
technological and interpretative issues that still require a more careful look by Marketing Science and
Information Systems researchers. In this research, we put forward a new theoretical perspective to
enable policy makers to better understand the states of digital wireless phone diffusion and factors
that affect their diffusion rates. We use a modified Bass model and a coupled-hazard survival model
to test the effects of country environmental factors, digital and analog wireless phone industry
environmental factors, and technology policy factors on the speed of diffusion. The results show that
multiple standards and high prices slow down the digital wireless phone diffusion process from the
Introduction state to the Partial Diffusion state. Competition in both analog and digital wireless phone
industry also shape the growth of digital wireless phone diffusion. In addition, different practices of
technology policies influence the digital wireless phone diffusion speed especially during the take-off.
KEYWORDS: Bass model, coupled-hazard model, empirical research, diffusion, digital wireless
technology, international diffusion, survival analysis
_________________________________________________________________________________
ACKNOWLEDGEMENTS. The authors wish to thank three anonymous reviewers, as well as
participants in the Fall 2002 INFORMS CIST Conference, for comments on this and related work.
Special thanks go to Gary Koehler for inspiring us to undertake this research. We are grateful to the
MIS Research Center for financial support.
_________________________________________________________________________________
1. INTRODUCTION
In recent years, the pressures of global competition have prompted governments of developed and
developing countries to explore the means to use emerging networking technologies to achieve
economic and social benefits. Evidence from country policy reports in the past decade has shown that
countries around the world have embraced the new opportunities offered by the Internet and ecommerce (Analysys, 2000). More recently, attention has been focused on digital wireless
technology. Current predictions suggest that more than two billion human beings will be linked by
mobile communications devices by the end of 2005 (Kirkman et al., 2001). Digital wireless has great
potential for developed and developing countries alike, giving the latter the chance to leapfrog and
bypass fixed network solutions that involve high maintenance costs, low reliability, and long
installation delays. Similarly, developed nations can utilize this powerful technology to increase their
wealth and improve social welfare.
Nevertheless, technology diffusion poses some challenges for policy makers. For example,
regulatory agencies are concerned about appropriate policies or interventions to get the diffusion
process going, but they are also equally interested in the appropriate timing of their actions.
Unfortunately, prior diffusion research does not offer much help to address their concerns. This is
because most diffusion research in Marketing Science and Information Systems (IS) disciplines (e.g.,
Gurbaxani, 1990; Takada and Jain, 1991; Talukdar et al., 2002) focuses on examining variables that
affect the entire diffusion process. As a result, little is known about salient factors in the various states
of diffusion.
There are unique issues associated with digital wireless technology, particularly the digital
wireless phone industry, which offers a rich environment to study the diffusion process. First, there
are multiple standards in the digital wireless phone environment. Some of the widely used ones are
2
Global Systems for Mobile Communications (GSM), Code Division Multiple Access (CDMA),
Personal Digital Cellular (PDC), and Personal Communications Service (PCS). Second, countries do
not necessarily adopt the same standards. For example, integrated pan-European telecommunications
regulatory policy prescribes uniform adoption of the GSM standard among members of the European
Union. On the other hand, the United States has opted for open competition among the multiple
standards in the market. This leads us to ask an important question reflected in the title of our paper:
“Does one standard promote faster growth?” Does prescribed standardization regime increase the
long-term adoption payoff? Finally, the diffusion of digital wireless technology is complicated by an
existing installed base of analog wireless technology that may enable or hinder the diffusion of digital
technology.
We will use two diffusion modeling approaches, each with a different theoretical perspective, to
investigate digital wireless phone diffusion. The first model is a modification of the Bass model
(Bass, 1969), which has been proposed by Dekimpe, et al. (1998). The two parameters that
characterize the growth of diffusion in the Bass model are the coefficient of external influence, and
the coefficient of internal influence. The modified Bass model parameterizes variables that may affect
the diffusion growth. Our second model uses a coupled-hazard survival model, as discussed by
Dekimpe, et al. (2000). This model establishes critical diffusion states and empirically tests variables
that affect in-state diffusion speeds using survival analysis.
The research questions that we address are as follows. What factors influence diffusion rates for
digital wireless phones in various countries? What are the key drivers in different states of the digital
wireless phone diffusion process? What kind of modeling and empirical techniques are appropriate to
characterize different states of diffusion and help understand the dynamics of the process? What
kinds of insights do the modified Bass diffusion and coupled-hazard models generate?
3
2. LITERATURE
We review three related streams of theoretical perspectives and literature as a basis to develop our
conceptual framework for modeling the international diffusion of digital wireless phones. We start by
looking at diffusion of innovation theory as a lens to conceptualize the diffusion process and establish
a set of factors that are expected to influence the diffusion process. Then we look at the standards and
standardization in the Economics literature to provide a basis for understanding the technology
diffusion environment when multiple standards coexist and the influence of standards-making on
markets, competition, and innovation. Finally, we discuss theoretical perspectives and empirical
findings from the technology policy literature and relate them to how diffusion is influenced by those
policies and interventions.
2.1. Diffusion of Innovation, Network Externalities
Rogers’ (1995) diffusion of innovation theory suggests that the diffusion of a new technology
generally follows an S-shaped pattern, where the adoption rate is slow at first, but then rises quickly
during a take-off period, and eventually levels off as the market gets saturated. Rogers further
suggests that adopters should be classified based on their adoption timing into five categories.
Innovators (2.5%) are the earliest adopters, followed by early adopters (13.5%), the early majority
(34.0%), the late majority (34%), and finally laggards (16.0%). This classification suggests the
natural states of the diffusion process and it also implies that since some individuals choose to adopt
at later times than others, there may be different factors at play in their adoption decisions. In other
words, we may find different drivers across diffusion states.
Network externalities involve additional perceived business value from a system that has an
increasing number of users (Katz and Shapiro, 1986). Some products and services that experience
stronger network externalities influences possess recognizable complementarities (e.g., hardware and
4
software) and networking products and services (e.g., telephones, fax and digital wireless telecom).
Other products (e.g., food, clothes, and gas) have weaker network effects.
The variable growth rate throughout the diffusion process is the result of varying degrees of
network externalities effects (Gurbaxani, 1990; Rai et al., 1998). In particular, the influence of
network externalities is weak during the technology Introduction state. But, an increase in the number
of adopters over time will create a critical mass, thus generating stronger network externalities
effects. Eventually, the growth rate declines as a saturation number of adopters is reached
In the Marketing Science literature, international product diffusion has been widely investigated
using the Bass diffusion model (Bass, 1969). The emphasis has been on finding constructs that can
help management to forecast future product sales and predict diffusion trajectories of products even
before their launch. These empirical studies have reported the influence of country characteristics
(Dekimpe et al., 2000; Gruber and Verboven, 2001a; Takada and Jain, 1991), the timing of product
information (Takada and Jain, 1991), the installed base and prices of an earlier generation product
(Danaher et al., 2001; Islam and Meade, 1997), and word-of-mouth effects (Talukdar et al., 2002) on
the speed of product diffusion across countries.
Although IS researchers have studied adoption and diffusion since the 1980s, most of the work
has focused at individual, group, and organizational level of analysis. More recently, several IS
researchers have pursued an understanding of the significant factors at play throughout the diffusion
process across countries (e.g., Gurbaxani, 1990; Kraemer and Dedrick, 2000; Kraemer, Gibbs, and
Dedrick, 2002; Rai et al., 1998; Wolcott et al., 2001). For example, Kraemer et al. (2002) and Wolcott
et al. (2001) reported that economic and financial resources, regulatory and legal policy and
framework, and information infrastructure influence cross-country diffusion of e-commerce and the
Internet respectively. However, most of the studies are conceptual frameworks with supporting case
5
studies and country and regional reports. As a result, there is a need for evidence from empirical
studies to help develop a theory for technology diffusion at the international level. Overall, the
studies do not recognize that some factors may be more influential at certain diffusion states than
others, so this is an important area for new innovations in theory development and empirical analysis.
2.2. Technology Standards
Standards are important in IT systems because they are necessary to ensure that complimentary
products (e.g., operating system and application software) can work together. The standards and the
related implications on markets, competition, and innovation have been extensively investigated in
the Economics literature. A standard refers to a set of technical specifications that producers adopt
voluntarily or in accordance with formal agreements or regulatory authority (David and
Steinmueller, 1994). Standards related to IT systems are referred to as compatibility or interface
standards in the economics literature (Antonelli, 1994).
Standardization process can be broadly classified into de facto standards and de jure standards.
De facto standards emerge from market-mediated processes that involve interactions among agents
(David, 1987). In other words, network externalities and inertia induce new users to adopt a standard
chosen by previous adopters, making that standard a dominant one over time. An ongoing battle for
supremacy among the GSM, CDMA, and PCS standards is an illustrative example of marketmediated standardization process in the United States. Meanwhile, Microsoft’s Windows operating
system is an illustrative example of a de facto standard. De jure standards are enforced by agreements
or mandated by standard-setting agencies. The GSM digital wireless standards mandated by European
Union for member countries to adopt is a case in point.
The influence of standards and standardization on competition and innovation is a complex issue.
On the one hand, standards increase competition by reducing entry barriers and lower market prices.
6
From the demand perspectives, standards help reduce consumers’ uncertainty and risks, hence
speeding up the diffusion process. On the other hand, standards, especially in the case of de facto
standards, can make it more difficult for rival firms or new entrants to compete with firms that control
a dominant standard. In addition, this may subsequently lead to stagnant innovation in the
marketplace because firms with a dominant standard and a large installed base may not have enough
pressure to innovate. To address this issue, others suggest that multiple standards in the marketplace
help increase competition and force technology providers to constantly improve the technology, thus
resulting in lower product and service prices for consumers, which will lead to increased adoption.
Empirical evidence of the effects of standards on a technology diffusion process is reported in Gruber
and Verboven (2001a), where competing standards tend to slow diffusion of mobile
telecommunications. In other words, the diffusion process appears to be faster in markets with a
single standard.
2.3. Technology Policy
Government policies and interventions play an important role in the diffusion of a new
technology, especially those networking technologies such as the Internet, and the emerging digital
wireless telecommunications (Hargittai, 1999; Kraemer et al., 2002; Montealegre, 1999; Wolcott et
al., 2001). Unlike stand-alone computing technology, networking technology requires large-scale
network services and infrastructures to be in place before any provision of services can take place. In
addition, digital wireless services operators require designated spectrums from the pooled resources
of a country, and these need to be appropriated through mechanisms chosen by a government. As a
result, government actions such as licensing of service operators, preventive mechanisms of anticompetitive behavior, and price regulation are inevitable in the digital wireless environment. In this
vein, Gruber and Verboven (2001b) report that regulatory practices governing competition through
7
licensing, among other things, seem to help increase the diffusion of wireless communications in
fifteen European countries.
There are two related streams of research on technology policy and IT innovations in the IS
literature. The first stream includes King et al.’s (1994) framework of institutional intervention in IT
innovation and studies that validate the framework. The second includes studies that use researchers’
own models to investigate the link between government policy and IT diffusion.
King et al. (1994) propose a theoretical framework of the role of governments, and institutions, in
general, in IT innovation through their influence and regulatory powers on both the production and
use of innovation. In particular, they categorized institutional actions into six classifications:
knowledge building, knowledge deployment, subsidies, mobilization, standard setting, and innovation
directives. Later, Montealegre (1999) empirically validated the framework in his study of Internet
adoption in four Latin American countries. He found that not only institutional actions facilitate
Internet adoption, but appropriate interventions during different phases of the adoption process are
essential for successful results. For example, standard setting that prescribes certain ways of doing
things contributes the most in the early phase of the adoption process while the dissemination of new
knowledge about the innovation contributes the most in the later phase of the process.
Similarly, the second stream of research on government policy and IT diffusion also finds support
for the influence of government policy on the diffusion process. For example, Kraemer et al. (2002)
reported that national policy in the forms of telecommunication liberalization, promotion, and
legislation has been significant in promoting the use of e-commerce in ten developed and developing
nations. Wolcott et al. (2001) also found that government policy in the form of regulations and laws is
one of the important determinants of Internet diffusion in the twenty five countries in their data set.
Taken together, the two streams of research strongly suggest that government policy has
8
implications on the IT diffusion process. In addition, they also imply that we should expect to observe
different policies at play depending on the study context (i.e. a set of countries or a type of IT).
However, it is important to take note that all of the studies cited here use detailed case studies to
establish the relation between technology policy and the diffusion process. And so it would be useful
to obtain stronger evidence from empirical studies to further delineate the influence of technology
policy on IT diffusion.
3. CONSTRUCTS, MEASURES, HYPOTHESES
Based on the variables suggested from the theories and past studies that we reviewed, we propose
a model of digital wireless technology diffusion that posits that the international diffusion of digital
wireless phones is influenced by the effects of country environmental factors, digital wireless phone
industry environmental factors, analog wireless phone industry environmental factors, and
technology policy factors.
Country environmental factors. National wealth is correlated to country’s diffusion rates and
patterns (Dekimpe, et al., 1998; Gruber and Verboven, 2001a, 2001b; Kiiski and Pohjola, 2002;
Kraemer, et al., 2002). We use GNP per capita in 1995 U.S. dollars (GNP) to measure national
wealth, and expect it to have a positive relationship with diffusion rates. In addition, diffusion rates of
advanced ITs, such as the Internet, are correlated with the adequacy and maturity of infrastructure
development (Wolcott et al., 2001). Thus, we expect that countries with a higher number of fixed-line
telephone installations (PHONE) are likely to have higher diffusion rates. A workable proxy is
number of fixed-line phones per 1000 population.
Digital and analog wireless phone industry environmental factors. Our rationale to include
both the digital and analog variables in our model is from the theory of diffusion of successive
generations of a technology. Norton and Bass (1992) have noted that a subsequent generation of
9
technology will eventually replace an earlier technology over time. Thus, the interrelationship
between generations of technology suggests that diffusion studies will not be complete if variables
associated with prior generation technology are ignored. Four variables related to these constructs are
the number of existing digital (analog) wireless phone users in terms of a percentage penetration rate
(DIGITAL_PEN, ANALOG_PEN), number of digital (analog) wireless phone operators
(DIGITAL_OPR, ANALOG_OPR), number of digital (analog) wireless phone standards
(DIGITAL_STD, ANALOG_STD), and digital (analog) wireless phone service prices
(DIGITAL_PRC, ANALOG_PRC) also stated in 1995 U.S. dollars. Consistent with the network
externalities literature, we expect a positive relationship between the number of existing analog and
digital wireless phone users and the digital wireless phone diffusion rate.
Drawing on the standards literature and prior studies, we argue that the intensity of competition
and the number of standards are expected to influence the diffusion rates. In particular, we anticipate
a positive (negative) relationship between number of digital (analog) wireless phone operators and
the digital wireless phone diffusion rate, and a negative (positive) relationship between number of
digital (analog) wireless phone standards and the digital wireless phone diffusion rate. Finally,
willingness to adopt a technology is generally correlated to its pricing in the market (Danaher et al.,
2001). Consequently, we hypothesize a negative (positive) relationship between digital (analog)
wireless phone service prices and the diffusion rate of digital wireless phones.
Technology policy factors. Drawing on the standards and technology policy literature, we argue
that standardization (STD_POL) and licensing policies (LICENSE1, LICENSE2) affect the
diffusion of digital wireless phones. Our preliminary data collection indicates two practices of
standardization, market-mediated policy, and regulated regimes. We expect a faster pace of adoption
among countries that employ regulatory initiatives over those that permit market-mediated policies to
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develop. We classify competition policies based on a country’s government decision on geographical
service coverage of digital wireless phone operators into national licensing policy, regional licensing
policy, and hybrid (national and regional) licensing policy. We expect countries with either national
or hybrid licensing policy to outperform those with regional licensing in terms of diffusion rates. 1
4. MODEL ESTIMATION AND DATA
We next discuss how we conceptualize “diffusion states,” and then explain the models and
estimation methods we use, as well as the data to be analyzed.
4.1. Modeling Preliminaries
We define diffusion states as different periods in time for which there are likely to be different
factors influencing the diffusion rates of a technology. According to the diffusion of innovation
theory (Rogers, 1995), diffusion increases gradually before the critical mass of adopters decides to
adopt and then rises quickly after that. This suggests that we should take a closer look at factors that
affect diffusion rates before and after critical mass is reached. This suggests a natural partitioning of
diffusion states: Introduction, Partial Diffusion, and Maturity. The Introduction state is the time when
a country begins its digital wireless phone adoption. We define Partial Diffusion state as the time
when critical mass in the market has been reached. Adoption rates that reflect a critical mass of
adopters vary from one innovation to another. Rogers (1995) suggests that critical mass typically
occurs when approximately 10% to 20% of adopters have adopted. As a result, we have set the
critical mass of digital wireless phone adoption at 15% of all adopters. Finally, the Maturity state is
defined as the time when the penetration potential or market saturation point has been reached
(Dekimpe et al., 2000). Since digital wireless phone is introduced in 1990s, it is still considered a
1
We code standardization policy in terms of a dummy variable with the base case, 0, representing marketmediated standards, and 1 representing the regulatory regime approach. In addition, we code licensing
competition policy with two dummy variables, so that (0,0) represents the base case of regional licensing, (0,1)
indicates a national licensing policy, and (1,0) indicates a hybrid policy.
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relatively young technology. It will take some time before digital wireless phone diffusion reaches the
Maturity state. So, we estimate factors that affect diffusion speed from Introduction to Partial
Diffusion.
We use a modified Bass model (Dekimpe et al., 1998) and a coupled-hazard survival model
(Dekimpe et al., 2000) to model state-wise digital wireless phone diffusion. (See Table 1 and Figure 1
for comparisons.) The former model provides an appropriate point of comparison to validate the
results that we have obtained from the coupled-hazard model, a new model that offers a different
estimation structure for the theory and somewhat different managerial insights.
4.2. Modified Bass Model
The Bass diffusion model (Bass, 1969) suggests that a new product adoption decision is driven by
two factors: coefficient of external influence, the influence that is independent of the existing number
of adopters, and coefficient of internal influence, the social influence of the existing number of
adopters. The model specifies that the likelihood that an individual will adopt a new product at time t,
given that he has not yet adopted, is a linear function of the number of existing adopters:
h (t ) =
f (t )
= p + qF (t ) .
1 − F (t )
h(t) is the hazard rate or the likelihood to adopt at time t given that no
adoption has occurred in the time interval (0, t). f(t) and F(t) denote the probability density and
cumulative density function at time t. p and q are the coefficient of external and internal influence
respectively (0 < p, q < 1). Since we often observe an aggregate number of adopters, not an
individual’s adoption behavior, the hazard model can be specified in terms of the number of adopters
as n(t ) =  p +

q

N (t ) (m − N (t ) ) , where n(t) = mf(t) is the number of adopters at time t, N(t) is the
m

cumulative number of adopters at time t, and m is market potential.
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Figure 1. Models of international diffusion of digital wireless technology
Table 1. Contrasting Empirical Models
MODEL
ELEMENTS
Dependent
variable
Independent
variable
Parameters
Estimation
method
MODIFIED BASS MODEL
Number of adopters
from Introduction to
Partial Diffusion state
or end of observation
Social system size,
long-run ceiling, and
cumulative adopters
Intercept and growth
rate of diffusion curve
Intercept and growth
rate of diffusion curve
Non-linear least
squares
Non-linear least
squares
Proposed independent
variables
Regression parameters
COUPLED-HAZARD
MODEL
Duration of times from Introduction to
Partial Diffusion or end of observation,
and indicator of Partial Diffusion
(0=no, 1=yes)
Proposed independent variables
Weibull shape (α) and scale (λ)
parameters, and parameters of
independent variables
Survival analysis
Dekimpe, et al. (1998) point out that the Bass model limits comparison of diffusion parameters
across countries. Why? First, the Bass model uses a time series of number of adopters to estimate the
diffusion parameters. As a result, a small and a large country that have the exact same number of
adopters over time will have the same diffusion parameters. This implies that the two countries,
without considering their sizes, share the same diffusion pattern, which may not necessarily be
correct. Second, by using fixed time periods for all countries in a data set, there is higher risk of lefthand truncation bias where the estimates of the intercept of the diffusion curve are inflated for those
countries that start their adoption process earlier than the time frame represented by the data.
13
To address these limitations, they proposed a modified Bass model for a country i as
 n i ,1
ni ,t = 
 C i S i

N

 + Bi  i ,t −1  C i S i − N i ,t −1

CS 

 i i 
[
] , where ni,t is the number of adopters at time t, Ni,t-1 is the
cumulative number of adopters up to time t-1, Si is the social system size, Ci is the long-run
 ni ,1 


 Ci S i 
penetration ceiling, and Bi is the diffusion growth rate. The diffusion curve intercept 
is also
referred to as parameter Ai1. The social systems are populations in a country and the long-run
penetration ceiling is defined as the maximum proportion of the population that will adopt.. Factors
that govern the dynamics of social systems and long-run penetration ceiling are exogenous to a
technology.
The model requires matched sampling of the first two parameters (C,S) and the alignment of
introduction timing of an innovation across countries for valid comparisons of the cross-country
diffusion parameters. It should be noted that parameters Ai1, Bi, and CiSi are similar to parameters p, q,
and m in the Bass model. Although the modified Bass model was designed to examine overall
diffusion process, it is flexible enough to estimate state-based diffusion parameters by limiting
observations to those defined by diffusion states of interests. Also two logistic models test covariates
that affect the first year adoption and diffusion growth rates: Ai1 =
1
1+ e
− d1 X i
, Bi =
1
1 + e −d2 X i
, where d1
and d2 are vectors of parameters and Xi is a vector of covariates.
4.3. Coupled-Hazard Survival Model
Diffusion states along the diffusion curve of the same technology are not independent from each
other. There is a natural order embedded in the diffusion process. For example, a country has to start
from the Introduction state, and then proceed to the Partial Diffusion state, before it can finally reach
14
the Maturity state at some later time. We use a coupled-hazard survival model (Dekimpe et al., 2000)
to set up such interdependencies across the diffusion states.
The coupled-hazard model characterizes transitions that a country has to traverse from state-tostate leading to the full adoption of a technology. Diffusion states and transition rates are the two key
elements in the model. We model time until Partial Diffusion, and time until Maturity as two
interdependent failure-time processes. Each process has two possible values: 0 which means that
neither Partial Diffusion nor Maturity has been achieved; 1 means either Partial Diffusion or
Maturity has been reached. As a result, we have State[0,0]—no Partial Diffusion or Maturity has
been reached, State[0,1]—no partial diffusion has been reached but maturity has been achieved,
State[1,0]—partial diffusion has been reached but not Maturity, and finally State[1,1]—both Partial
Diffusion and Maturity have been reached. To maintain logical consistency of the diffusion process
for our econometrics, we drop State[0,1] because it is impossible for a country to reach Maturity
without going through Partial Diffusion. This leaves three states, which we call Introduction [0,0],
Partial Diffusion[0,1], and Maturity[1,1].
The dynamics of the diffusion process are depicted with transition rates, the likelihood at any
point in time that a country will move from one diffusion state to another. Since there are three
diffusion states, there are six possible transition rates based on R(R-1), where R is the number of
states, as shown in Figure 2.
Figure 2. A Fully-Specified Coupled-Hazard System (3 States, 6 Transition Rates)
15
The reduced coupled-hazard system for the international diffusion of digital wireless phones with
three diffusion states and two transition rates is illustrated in Figure 3.
Figure 3. A Reduced Coupled-Hazard System (3 States, 2 Transition Rates)
Since an empirical regularity in the observed data is that a country never falls back to an earlier
state on the diffusion curve, we can eliminate the dashed-line transitions in Figure 2. We can also
remove the dotted-line transition that jumps from Introduction to Maturity.
4.4. Coupled-Hazard Estimation Method
Since the diffusion states and transition rates are analogous to events and hazard rates, this
naturally suggests survival analysis methods as the appropriate choice for the empirical test. We use
parametric survival methods to empirically evaluate the factors that may affect the proposed
transition rates. In particular, we use a proportional hazard model (Cox and Oakes, 1984) to estimate
the effects of covariates on the diffusion rates. The proportional hazard model specifies the hazard for
technology diffusion for country i at time t as the product of a baseline hazard function and a linear
function of a row vector of covariates, X: hi(t) = δ0(t)eXβ. In this expression, h(t) is the hazard
function, δ0(t) is the baseline hazard function, and β represents the column vector of covariate
parameters. By taking the logarithm of the hazard function, we get a familiar regression model, log
hi(t) = δ(t) + X . We selected the Weibull specification with two parameters, α and λ, for our
16
baseline hazard function: δ0(t) = αλtα-1.
2
This makes sense because unlike other functions (e.g.,
exponential, log-logistic), a Weibull baseline hazard matches the monotonically increasing function
of the diffusion curve. The model permits us to explain why adoption is occurring and how its
conditional probability changes over time via eXß.
4.5. Data
We collected annual data for the dependent variables and covariates. The implementation years
varied from 1992 to 1997. Countries started their digital wireless phone implementation in different
years. All of the observations ended in 1999. The data cover the diffusion of digital wireless phones
and corresponding covariates in forty six developed and developing countries in Europe, Asia, Africa,
and North America. 3
5. RESULTS AND DISCUSSION
We next describe the estimation results from the models, and interpret their common and
contrasting insights. We also discuss their broader implications.
5.1. Results of the Modified Bass Model
To estimate the models, we set the social system size (S) to the total population of the year when
the countries started their digital wireless phone diffusion. The long-term penetration ceiling (C) is
Estimating the model yields maximum likelihood estimates for the explanatory variable, so we can determine
whether the observed effects are consistent with the hypothesized effects.
Such estimation also yields a
reading on the proportional hazard of country's conditional probability of transition from state-to-state in the
diffusion process for digital wireless phones. The estimates of the parameters tell us the percent changes in
the hazard rate for a one unit change in a covariate.
3
The countries covered are Australia, Austria, Belgium, Canada, China, Cyprus, Denmark, Egypt, Finland,
France, Germany, Greece, Hong Kong, Hungary, Iceland, India, Indonesia, Ireland, Italy, Japan, Jordan,
Korea, Kuwait, Luxembourg, Malaysia, Morocco, Netherlands, New Zealand, Nicaragua, Norway, Pakistan,
Philippines, Portugal, Russia, Saudi Arabia, Singapore, South Africa, Spain, Sweden, Switzerland, Thailand,
Turkey, United Arab Emirates, United Kingdom, United States, and Vietnam. Data sources include
international organizations such as International Telecommunication Union (ITU), World Bank and the United
Nations (UN). We also obtained data from private databases and publications such as Gartner Group, Wireless
Week magazine, Global System for Mobile Communications (GSM) web site (www.gsmworld.com), and
Code Division Multiple Access (CDMA) development group web site (www.cdg.org).
2
17
defined as a proportion of the population aged fifteen or older. We used the logistic model to estimate
the effect of covariates on the first year adoption level. We parameterized the logistic transformation
of a growth rate into the modified Bass model to estimate the parameters of the proposed covariates.
Table 2 summarizes the factors that affect the first year adoption level and growth rate parameters
in the modified Bass model. The results show a higher number of significant variables for the first
year adoption level than the growth rate. We discuss the results of the first year adoption level. GNP
per capita (GNP) is positive and significant (p<.05). Since its coefficient is close to zero (0.0002), its
effect on the first year adoption level is relatively small. Two of the digital wireless phone variables
(DIGITAL_STD, DIGITAL_PRC) are significant (p<.01, and p<.05 respectively). Consistent with
our expectation, the number of digital wireless phone standards has a negative effect on the first year
adoption level. However, contrary to our hypothesis, digital wireless phone prices have a positive
influence on the first year adoption level. This may be because those early adopters are innovators
who will adopt a technology regardless of its high prices.
Similarly, two of the analog wireless phone variables (ANALOG_STD, ANALOG_PRC) are
significant (p<.05). The higher the number of the analog wireless phone standards, the higher the first
year adoption level of digital wireless phones. Analog wireless phone prices show a negative effect
on the first year adoption level of digital wireless phones. Perhaps high analog wireless phone prices
delay the adoption decisions of some potential adopters who may associate high analog wireless
phone prices with high digital wireless phone prices.
18
Table 2. Modified Bass Model Results
VARIABLES
GNP
DIGITAL_PEN
DIGITAL_OPR
DIGITAL_STD
DIGITAL_PRC
ANALOG_PEN
ANALOG_OPR
ANALOG_STD
ANALOG_PRC
STD_POL
LICENSE1
LICENSE2
1ST YEAR ADOPTION (AI1)
COEFFICIENT
STANDARD
ERROR
0.0002**
0.0001
NA
NA
-0.69
0.61
***
-26.06
8.84
**
0.71
0.27
0.17
0.48
0.29
2.18
**
5.48
2.14
**
-0.54
0.23
**
-4.12
1.60
**
7.43
2.97
*
4.96
2.70
GROWTH RATE (BI)
COEFFICIENT
STANDARD
ERROR
-0.0003
0.0002
NA
NA
*
3.87
2.33
-7.63
4.82
0.17
0.15
-0.26
0.27
*
-6.43
3.78
*
9.97
6.03
0.53
0.32
-0.37
2.43
0.78
3.14
2.44
3.04
Note: 4R2 of the intercept model is 0.92. R2 of the growth rate model is 0.70. The significance levels for the covariates
are: * = p<.10, ** = p<.05, and *** = p<.01. The cumulative digital wireless phone penetration (DIGITAL_PEN) is not
applicable in the first year adoption level model (NA) because there is no cumulative number of adopters in the first
year. Since the growth rate logistic model is nested in the modified Bass model, which already has a cumulative
number of adopters as one of the independent variables, we exclude DIGITAL_PEN from this model. GNP per capita
(GNP) and the number of fixed line phones per 1000 inhabitants (PHONE) are highly correlated (ρ =0.8571), so we
dropped PHONE from the model.
The dummy variable (STD_POL) that measures standardization policy is significant (p<.05). The
values “0” and “1” denote market-mediated and regulated policy respectively. Since the estimated
parameter is negative, this means that, all other things equal, those countries that use regulated policy
observe lower first year adoption level than countries that use market-mediated policy. The dummy
variables (LICENSE1, LICENSE2) that measure licensing policy are significant (p<.05 and .10,
respectively). Since both coefficients are positive, this means that, all other things equal, countries
that use hybrid licensing policy (LICENSE1=1, LICENSE2=0) and national licensing policy
A concern is whether the binary variables are highly associated. Cramer’s V, a χ2-based measure of
association ranging from 0 to 1, between STD_POL and the two licensing policy variables (LICENSE1,
LICENSE2) is 0.402—not a high association. This is sensitive to sample size and number of levels of
variables. We looked at Goodman-Kruskal lambda (also in 0 to 1 range), the percentage reduction in errors in
predicting values of one variable given knowledge of the other. Its value is 0.115, indicating low association
between STD_POL and licensing policy (LICENSE1, LICENSE2).
4
19
(LICENSE1=0, LICENSE2=1) have higher first year adoption level than countries that use regional
licensing policy (LICENSE1=0, LICENSE2=0).
There are three significant variables for the growth rate. The number of digital wireless phone
operators (DIGITAL_OPR) is positive and significant (p<.10). This suggests that the diffusion
growth rate appears to be faster in a higher competitive market. In contrast, the number of analog
wireless phone operators (ANALOG_OPR) is negative and significant (p<.10). Higher competition in
the analog wireless phone industry slows down the growth of digital wireless phone diffusion.
Finally, similar to the result of the first year adoption level, the number of analog wireless phone
standards (ANALOG_STD) is positive and significant (p<.10). This supports our hypothesis that the
higher number of analog wireless phone standards speed up the growth of digital wireless phone
diffusion.
5.2. Results of the Coupled-Hazard Survival Model
Table 3 summarizes the coupled-hazard Weibull survival model estimation. The model has a
likelihood ratio of 64.48 (p=0.00). (See Table 3.) All digital wireless phone industry environment
variables except the number of digital operators (DIGITAL_OPR) are significant. Digital mobile
phone penetration (DIGITAL_PEN) is highly significant (p<.01) with a hazard ratio of 1.358. This
means that a 1% increase in digital wireless phone penetration will increase the hazard rate of
reaching Partial Diffusion by 35.8%.
20
Table 3. Coupled-Hazard Model Results
VARIABLES
GNP
DIGITAL_PEN
DIGITAL_OPR
DIGITAL_STD
DIGITAL_PRC
ANALOG_PEN
ANALOG_OPR
ANALOG_STD
ANALOG_PRC
STD_POL
LICENSE1
LICENSE2
α
λ
COEFFICIENT
STANDARD
ERROR
0.00002
0.070
0.325
1.153
0.056
0.072
0.654
0.888
0.055
0.776
1.470
1.395
1.204
-0.00001
0.306***
0.247
-2.081*
-0.130**
0.020
-0.355
-1.579*
0.111**
-1.790**
-3.524**
-3.353**
8.412***
0.00002***
4
2.382
HAZARD RATIO
0.999
1.358
1.280
0.125
0.878
1.020
0.701
0.206
1.117
0.167
0.029
0.035
NA
NA
***
Note: Likelihood ratio, model significance = 64.48 . The significance levels for the covariates are
given by: * = p<.10, ** = p<.05, and *** = p<.01. “NA” means “not applicable.” GNP per capita
(GNP) and the number of fixed line phones per 1000 inhabitants (PHONE) are highly correlated (ρ
=0.8571), so we dropped PHONE from the model. All variance inflation factors (VIFs) of the rest of
covariates are lower than 10, showing no presence of multicollinearity.
The number of digital standards (DIGITAL_STD) is negative and significant (p<.10) with a
hazard ratio of 0.125. An additional standard reduces the hazard rate by 87.5%. Digital wireless
phone service price (DIGITAL_PRC) also is negative and significant (p<.05) with a hazard ratio of
0.878, so a unit price increase decreases the hazard rate by 12.2%. Two analog wireless phone
industry variables are significant. Number of analog wireless standards (ANALOG_STD) is negative
and significant (p<.10) with a hazard ratio of 0.206. An additional analog wireless phone standard
reduces the hazard rate by 79.4%. Analog wireless phone service price (ANALOG_PRC) is
significant (p<.05) with a hazard ratio of 1.117. So a unit increase in price increases the hazard rate by
11.7%.
Standardization policy (STD_POL) is significant (p<.05) with a hazard ratio of 0.167. This is a
dummy variable where 0 and 1 denote market-mediated and regulated policy, respectively. This
21
means that the hazard rate of countries using regulated policy is 16.7% of those that use marketmediated policy. The dummies that measure licensing policy (LICENSE1, LICENSE2) are negative
and significant (p<.05) with a hazard ratio of 0.029 and 0.035. The base case is regional licensing
policy (LICENSE1=0, LICENSE2=0). So, the hazard rate of countries that use national licensing
(LICENSE1=0, LICENSE2=1) is 3.5% of those that use regional licensing. Also, the hazard rate of
countries that use hybrid licensing (LICENSE1= 1, LICENSE2=0) is 2.9% of those that use regional
licensing.
5.3. Discussion
We used modified Bass and coupled-hazard survival models to test effects of country
environmental factors, digital and analog wireless phone environmental factors, and technology
policy factors on the speed of diffusion from the Introduction to the Partial Diffusion state. First year
adoption rate and a further growth rate characterize a diffusion speed in a modified Bass model. A
hazard rate illustrates the likelihood of reaching Partial Diffusion in a coupled-hazard survival model.
In addition to using the results from the two models to confirm the effect of covariates on the
diffusion speed, we also differentiate the influence of covariates in the first diffusion year and the
following years.
Our results show that GNP per capita is positive and significant during the first diffusion year.
Rich countries may have a slight head start with diffusion. But later, countries with lower GNP per
capita can catch up quickly. The number of digital operators shows a positive effect on a growth rate
in the modified Bass model, but has no effect on the hazard rate in the coupled-hazard model. Taken
together, these results suggest that competition does not affect overall diffusion speed from
Introduction to Partial Diffusion, but has an effect after the first year of diffusion. The number of
digital wireless phone standards shows a negative effect in both models, confirming our expectation
22
that multiple standards slow down the diffusion speed. Overall, digital wireless phone prices
marginally reduce the likelihood of reaching Partial Diffusion. During the first year of diffusion, high
prices appear to induce more adoption. This may be because early adopters adopt new higher-priced
digital wireless phones to stay ahead of the game, setting them apart.
The number of analog wireless phone operators appears to slow down the growth rate after the
first year of adoption. This makes sense because digital wireless phones at that time were new
technology. So competition from a more stable analog wireless technology may slow down its
diffusion process. The impact of number of analog wireless phone standards runs somewhat counter
to our intuition, however. It positively affects the first year adoption level and the growth rate in the
modified Bass model, but it reduces the hazard rate of reaching Partial Diffusion in the coupledhazard model. Finally, higher analog wireless phone prices speed up overall diffusion of digital
wireless phones. However, a unit increase in analog wireless phone prices reduces the first year
adoption level of digital wireless phones by roughly 11%.
The results of standardization are consistent across the models. Countries that use marketmediated policy have a higher adoption level than countries that use regulations during the first year
of diffusion. This may be because countries that use market-mediated policy have 6% higher number
of operators than countries that use regulations. The high competition may help raise awareness of
technology value, resulting in more adoption. Finally, countries that use national and hybrid licensing
policy have lower likelihood of achieving partial diffusion than countries that use regional licensing
policy. However, the reverse (hybrid, national, and regional licensing) is the case during the first
diffusion year. This may be because regional operators are closer to customers and provide better
services.
23
6. CONCLUSION
We tested the effects of country environmental factors, digital and analog wireless phone industry
environmental factors, and technology policy factors on diffusion speed of digital wireless phones
from Introduction to Partial Diffusion state (15% penetration) using a modified Bass model and a
coupled-hazard survival model. One of the significant findings across the two models is that multiple
digital wireless standards significantly slow down the diffusion growth. One standard appears to
promote faster growth in the international diffusion of digital wireless phones. Also our results
indicate that high prices slow down digital wireless phone diffusion. Competition in the analog and
digital wireless phone industry also shape the growth of digital wireless phone diffusion. Also
different policies influence diffusion speed, especially during the initiation.
This study broadens our understanding of salient factors at critical states of international diffusion
of digital wireless phone technologies. It also represents an attempt to develop a theory of
international diffusion of a technology, where multiple standards and various practices of technology
policies coexist. In addition to these theoretical contributions, the results of this study have policy
implications for governments to develop interventions at appropriate times to induce faster diffusion
of digital wireless phones.
There are some limitations to our findings. First, due to the unavailability of international data,
we have only forty six countries in our data set. In addition, our observations end in 1999. However,
we plan to add more countries and expand the observation period to include recent years to our data
set. Second, all variables are annual data. This may be imprecise as a basis for establishing a time
point when a country reaches partial diffusion. To get more accurate parameter estimates in a statewise diffusion process, monthly or quarterly data are needed, but the currently available sources do
not permit that in this research.
24
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