A RATIONAL EXPECTATIONS THEORY OF TECHNOLOGY ADOPTION:
EVIDENCE FROM THE ELECTRONIC BILLING INDUSTRY
Yoris A. Au
Assistant Professor, Information Systems and Technology Management
College of Business, University of Texas at San Antonio
yoris.au@utsa.edu
Robert J. Kauffman
Director, MIS Research Center, and Professor and Chair
Frederick J. Riggins
Assistant Professor
Information and Decision Sciences
Carlson School of Management, University of Minnesota
{rkauffman, friggins}@csom.umn.edu
Last revised: April 19, 2006
______________________________________________________________________
ABSTRACT
In this paper, we draw on concepts from the rational expectations hypothesis (REH) and
adaptive learning theory to introduce a new rational expectations theory of technology adoption.
Although the REH and adaptive learning theory have been applied in many non-technology
contexts, this research is among the first that applies rational expectations and adaptive learning
theory to issues related to technology adoption. The proposed theory allows us to examine
technology adoption settings where multiple parties seek to align their expectations of future
value prior to making a decision to adopt. It also takes into account the learning and information
sharing that generally occurs in the marketplace between multiple parties that can further
influence clustered adoption and the overall adoption rate. In our effort to test our new theory,
we construct several hypotheses that allow us to examine issues associated with information
technology adoption that involves multiple parties (multi-partite technology adoption) and strong
network externalities. We test for the existence of clustered adoption and the effects of
information transmission in the electronic bill presentment and payment (EBPP) industry. We
hypothesize that clustered adoption by firms will be influenced by their geographical collocation,
the reach of their consumer bases, their industry sector associations, and their consensus choices
of the technology vendor. Our results show preliminary evidence to support the proposed theory.
KEYWORDS: Clustered adoption, economic analysis, electronic bill payment, information
transmission, rational expectations theory, technology adoption
_____________________________________________________________________________
ACKNOWLEDGEMENTS. The authors are grateful to Neveen Awad, Indranil Bardhan, Sanjeev Dewan, Chris
Forman, Vijay Gurbaxani, Rahul Telang, Kevin Zhu, and other participants of the 2005 Workshop on Information
Systems and Economics at the University of California, Irvine, where an earlier version of this paper was presented.
We also thank Gordon Davis and Paul Glewwe for their helpful comments and feedback. The authors also
acknowledge support from the University of Texas at San Antonio, the Management Information Systems Research
Center (MISRC) at the University of Minnesota, and the third author acknowledges financial support from the 3M
Corporation.
i
INTRODUCTION
In this paper, we will do a general test of a proposed theory that is based on the rational
expectations hypothesis (REH) and adaptive learning theory. We call the proposed theory the
rational expectations theory of technology adoption. We will discuss how the theory allows us to
look into the issues in the technology adoption that involves multiple parties (multi-partite
technology adoption). We set up our discussion and test for the existence of clustered adoptions
and the effect of information transmission in the context of electronic bill presentment and
payment (EBPP).
Much of the adoption decision depends on a firm’s expectations about the benefits and costs
of the technology. In this research, we use the REH and adaptive learning theory and apply
them in the adoption of IT with network externalities decision making settings that require
managers (as economic agents) to have the ability to form certain levels of expectations about
the value of the technology. The REH has been applied in many non-IS/IT contexts, where
decision makers must estimate the benefits associated with different courses of managerial
action related to their perceptions about how beliefs in the economy are shaping up. Such
contexts include interest rate policy formation, financial market forecasting and money market
trading, manufacturing industry investments for the production of durable goods, and policies in
labor market wage-setting.
Our discussion and test will center on EBPP technology, which is a relatively new
technology that exhibits strong network externalities. EBPP also is an excellent example of a
technology that involves multiple parties—in this case, billers, banks, technology suppliers, and
customers—in its adoption process. In this kind of technology adoption context, there are needs
for sharing expectations of value among these disparate parties, making EBPP representative of a
1
class of technology adoption problems that are more complex in nature than what occurs with
single firm technology adoption decision making in isolation.
Despite the touted benefits of ease and convenience, surveys show that the adoption of EBPP
by consumers is still relatively low. Studies by the Tower Group [2002], for example,
discovered that the percentage of households using EBPP had increased only modestly between
1998 and 2002, from 2% to 13.7%. Many analysts argue that the adoption of EBPP has been
plagued by the “chicken and egg” syndrome. Billers are not willing to adopt EBPP until a
significant portion of customers are willing to use it. However, customers are unwilling to use
EBPP until they can pay most of their bills online, that is, until most billers have already adopted
the technology [Au and Kauffman, 2001]. This points to the multi-partite adoption dependency
that exists in the market, for which we theorize that alignment in expectations of value and
willingness-to-adopt must occur.
From the perspective of the billers, there are indirect network effects with regards to the
adoption of EBPP. Indirect network effects arise when the value of a product increases as the
number or the variety of the complementary goods or services increases [Katz and Shapiro,
1985; Economides, 1996]. In the context of EBPP, indirect network externalities occur as
market-mediated effects. The more billers that adopt the technology, the more consumers are
willing to use the service. This allows each biller to realize higher benefits. One of the most
compelling reasons for adopting EBPP is the cost-savings that are available for billers (from the
ability to greatly reduce their cost for mailing paper bills). So it follows naturally that billers are
the ones that must take the initiative to adopt the technology and create the “network of billers”
to attract customers. Many billers seem to have taken this stance, evidenced by the result of an
2
energy industry survey in 2000 showing that more than 90% of respondents at least had
considered offering EBPP to their customers [Brown, 2001].
EBPP systems cost billers about $1.1 million on the average. At a typical recurring cost rate
of 20% to 30% of the base investment annually, we can see why billers should not adopt EBPP
before there are enough customers who ready to use it. If they do this, then it must be because
the billers see some other convincing non-cost reasons to adopt [Gonsalves, 2003].
However, the question becomes: When should each biller adopt the technology? In the next
section, we propose that each biller should wait until the other billers are ready and so that they
all adopt the technology together—clustered in time. IT adopters may be clustered based on
geographical regions, firm size, industry, and so on. In the EBPP case, an electric utility firm in
a major city may observe a telecommunications company that serves customers in the same
geographical area to see if the company is ready to adopt the technology. By adopting together,
both firms reinforce one another’s evaluation of the market and increase the likelihood that
more customers are using the EBPP service, an externality benefit.
We have a number of specific research questions in this kind of technology adoption context.
Do we actually observe the kind of clustered adoption in the real world as suggested by our
theory of rational expectations? If so, then what kinds of clustering occur for technologies that
exhibit strong network externalities? What kinds of factors result in variance in adoption time?
What will a theory-driven conceptual model look like for this context? What facilitates
information sharing by firms related to business value and technology adoption expectations for
EBPP? What kind of empirical model can be used to test the theory?
THEORETICAL BACKGROUND
We will next review the rational expectations hypothesis (REH) and adaptive learning theory
3
that constitute the foundation of the rational expectations technology adoption theory that we
propose, as well as the theory of information transmission that serves as a crucial ingredient in
our theory building. Eventually, we discuss the proposed theory that we are going to test in the
remainder of this paper.
The Theory of Rational Expectations and Adaptive Learning
Muth’s [1961] rational expectations hypothesis (REH) suggests that people are able to learn
fast to adapt to changes in economic conditions, and to anticipate what will happen in the
economic system by examining the patterns of economic activity. The REH effectively
maintains that every individual acts as an economic forecaster, using the information he or she
can collect to foretell what economic events are likely to happen. The forecasts are the
individual's rational expectations. The basic assumption of the theory is that people use of all the
information available to them efficiently. Consequently, an individual’s expectations are said to
be "rational" if she makes efficient use of all available information, allowing for the cost of the
information. Since some information can be costly and hard to obtain, expectations can be
rational but still not very accurate. However, even though rational expectations may not be very
accurate, at least they will be unbiased. This unbiasedness forms the basis of the central tenet of
the theory, that is, the average of people’s subjective expectations is equal to the true values of
the economic variables being forecast.
REH’s strong assumptions fail to consider that people have bounded rationality so although
all the information is available to them, they may not be able to process the information quickly
and accurately. Sargent [1993] suggests the theory of adaptive learning to relax some of the
strong assumptions. In adaptive learning, people are allowed some time to learn the about the
economic circumstances and update their expectations about relevant parameter values on the
4
basis of newly-received information. Furthermore, unlike in the REH, in adaptive learning
boundedly-rational agents are allowed to use simple forecasting strategies—perhaps not perfect,
but at least approximately right—for a complex nonlinear world. A boundedly-rational agent
forms expectations based on observable quantities and adapts her forecasting rule as additional
information and observations become available. Adaptive learning may converge to a rational
expectations equilibrium or it may converge to an approximate rational expectations equilibrium
[Jordan and Radner, 1982], where there is at least some degree of consistency between
expectations and realizations [Evans and Honkapohja, 2001; Hommes, 2004].
The Theory of Information Transmission
For the purposes of this research, information transmission is defined as the situation where
the firm in possession of information signals or transmits the information to another firm. This is
also known as signaling [Spence, 1973; Kreps, 1990]. In other technology adoption decision
making research, the role of information transmission has been discussed mainly in the context
of information asymmetry, which refers to the situation where one firm has more information
than others [Zhu and Weyant, 2003]. In this case, information asymmetry exists and persists due
to the lack of information transmission.
As we have discussed above, information transmission is crucial to the alignment of
expectations in adaptive learning. The ability to learn what the other firms expect with regard to
the value of a new technology will allow each firm to adjust its own expectations and, possibly,
eventually reach an agreement with other firms about the business value of a technology.
Crawford and Sobel [1982] maintain that many of the difficulties associated with reaching
agreements are informational. They further suggest that sharing information makes better
agreements possible. In some cases, however, revealing all of a firm’s decision-relevant
5
information to an opponent may not be the most advantageous policy [Clarke, 1983; Gal-Or,
1985]. For example, although it has been shown that information transmission among supply
chain partners may be beneficial [Mukhopadhyay et al., 1995], its effects among competitors
appear to be more tentative [Zhu, 2004]. These studies suggest that information sharing may not
always be beneficial to a firm, as has also been noted by Han et al. [2004] for the case of
Internet-based financial risk management systems; and Kauffman and Mohtadi [2004] for the
case of Internet-based supply chain management.
In the case of adoption of technologies with strong network externalities, however,
information transmission and sharing will almost certainly benefit each firm. Why? Because
their common objective is to maximize the benefit of using the technology and most of the
benefit comes from network externalities. With potential adopters in a group sharing
information over multiple periods, we can expect that they all will reach an informal consensus
about the cost and benefit of the technology, leading to an adoption decision. This idea has been
suggested by the rational expectations model discussed in Au and Kauffman [2005].
The literature on cooperative game theory and inter-firm coordination seems to support this
view as well. For example, Cooper et al. [1997] present experimental evidence that pre-play
communication resolves coordination problems in a “battle of the sexes” game. Allowing
players to communicate prior to selecting an action almost completely resolved the coordination
problems that were observed in the experimental game without pre-play communication. This
permitted them to select a desired outcome. In a similar vein, Farrell [1987] presents a model in
which the performance of two-way communication is improved if players are allowed additional
rounds in which to communicate.
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The Rational Expectations Theory of Technology Adoption
Our rational expectations theory of technology adoption suggests that under certain
conditions we can expect to observe clustered adoption, defined as the adoption of a technology
by multiple firms at about the same time. Suppose there is a group of N potential adopting
firms having to decide whether to adopt a new technology or wait until another, possibly better
technology becomes available. The technology exhibits strong network externalities. To realize
the expectations about the benefits from network externalities, a firm in the subgroup will adopt
the technology only when it has learned that the other N – 1 firms are also ready to adopt the
same technology. This is to prevent the firm from getting stranded with a technology that no
other firm would choose. As a result, we can expect that each firm in the subgroup will adopt
the technology at about the same time.
Firms may initially have different levels of expectations about the value of the technology
and, consequently, different levels of willingness to pay. A firm’s willingness-to-pay for a
technology determines the maximum price the firm is willing to pay to purchase the technology.
To achieve concurrent adoption decisions, each firm must reach a level of willingness-to-pay that
is at least equal to the price set by the technology supplier. If some firms in the subgroup have a
willingness-to-pay that is below the technology supplier’s price, then all firms will defer
adoption. We assume that potential adopters are willing and able to freely share information
with each other at no cost. The information sharing is essential for the alignment of expectations
which, in turn, facilitates the adoption.
HYPOTHESES
Based on the REH and adaptive learning theory, Au and Kauffman [2005] suggest that IT
adoption decision makers will observe the environment and try to align their expectations with
7
those of the other decision makers before making an IT adoption decision. This alignment is
necessary to confirm each decision maker’s own expectations about the value of the IT being
considered, due to the inherent uncertainty.
Benchmarking, information sharing and clustered adoption. In their effort to align their
expectations, decision makers “benchmark” against each other and share information within a
targeted group. Here benchmarking refers to the process in which firms evaluate various aspects
of their business processes in relation to the best practice within their own group, which consists
of firms that share similar characteristics and objectives (e.g., belong to the same industry,
competing in or serving the same market). In the case of the adoption process of a new
technology, however, it is unlikely that the so-called “best practice” exists due to the
uncertainties inherent in the new technology. Therefore, we presume that in this particular
“benchmarking” process members will learn from each other by sharing information among
themselves about their perception of the expected value of the technology prior to making an IT
adoption decision. They may eventually reach a tacit consensus, resulting in what we would
observe as time-clustered adoption in the marketplace.
The information sharing will occur in the form of informal communications through email,
telephone calls, conference presentations and panel discussions, and other informal individual
communication. This kind of communication meets the criterion that we noted earlier for cheap
talk. Although it may seem insignificant, Kim [1996] suggests that repeated interaction among
firms can enhance the credibility of cheap talk and improve the efficiency in outcomes that
would be infeasible otherwise. Furthermore, Jordan and Radner [1982] maintain that repeated
observations of the market can smooth the process by which agents construct expectations.
8
We will directly consider the role of information transmission, and develop hypotheses on
how it is likely to affect the patterns of technology adoption. We will also argue that timeclustering of adoption may occur among firms based on four critical dimensions: geographical
collocation, geographical reach, industry sector, and technology vendor. We now will develop
hypotheses around each of these as a means to test the conditions under which time-clustered
technology adoption is likely to occur. We will also consider the role of other drivers of
clustered adoption that are adapted from other theories related to technology adoption, as a
means to gauge the relative strength of the different explanations of EBBP adoption.
Direct effects of information sharing on clustered adoption. A central component of our
theoretical argument is that expectations about the appropriate time to adopt a technology will be
driven by how effectively information is transmitted and sharing among players in the
technology adoption marketplace. Although it is rarely easy to identify the extent to which
cheap talk is occurring in the marketplace, it nevertheless is possible to consider aspects of
information transmission that are likely to support cheap talk. In particular, based on the existing
theory [Seidmann and Sundararajan, 1997; Lee and Whang, 2000], we believe that the frequency
of information sharing is likely to be relevant for identifying the effectiveness of information
transmission. Moreover, it should relate to subsequent observations of adoption.
One approach to capturing this kind of information is to measure the number of conferences
that are held in the marketplace that relate to the technology under consideration. A second
possible way is to identify the number of white papers and industry surveys and studies that
relate to the given technology. There are other means to proxy for the unobservable cheap talk
and communication. Although they are imperfect, they may nevertheless provide a useful
reading on underlying conditions that support information transmission.
9
Regarding conferences, in particular, the rationale is that a conference is a good opportunity
for senior managers from different firms to exchange information and ideas in an inexpensive
way. Although some information transmissions are likely to incur significant costs, we consider
conferences to be costless, relative to the other available means. This is because firms normally
set a certain budget for conference and seminar attendance, to keep up on industry and
technology developments, and so this kind of spending is probably viewed by them as a routine
cost. In addition, for EBPP at least, the conference attendance costs are insignificant relative to
the costs for acquiring and maintaining EBPP technology. Thus, in the EBPP case, we can use
the number of EBPP-related conferences conducted in the past as a proxy of information sharing
activities that occurred among potential adopters of the technology.
Our first hypothesis
follows from this discussion:
•
Hypothesis 1 (The Information Transmission Hypothesis). More information
transmission in the marketplace will be positively associated with the observation of
more clustered adoption.
A related argument that can be made, which also can be developed in the context of the
empirical model that we plan to estimate, is related to the observed rate of adoption over time. In
some cases, technology adoption that is observed may not meet our requirement for clustered
adoption: the time-clustering may not be tight enough, for example. Still, it may be possible to
test a weak form hypothesis for clustered adoption that examines the rate of adoption. We
indicate this in the second hypothesis:
•
Hypothesis 2 (The Information Transmission Technology Adoption Rate
Hypothesis). More information transmission in the marketplace will be positively
associated with faster observed rates of technology adoption.
10
Information transmission allows each firm to share its expectations about the value of the
new technology with other firms. More information transmission leads to greater information
sharing among the firms, which in turns leads to a faster learning process [Morishima, 1991;
Creane, 1995]. With faster learning, we can expect that firms will be able to align their
expectations and make an adoption decision sooner.
Geographical collocation effects. Geographical collocation is a key factor that may
increase the level of interaction among the firms, leading to time-clustered technology adoption.
The degree of interaction and information sharing among firms can be expected to be the highest
locally. This is because the transmission of new information becomes more complex and costly
with increased geographical distance. As a result, the economic activity based on technology
innovations is likely to be clustered geographically [Audretsch and Feldman, 1996]. Geographic
proximity facilitates interaction, information exchange and technological learning [Soete 1985;
Ganesh et al., 1997]. This leads us to assert our hypothesis:
•
Hypothesis 3 (The Geographical Collocation Clustered Technology Adoption
Hypothesis). Firms in the same geographical region are likely to adopt at about the
same time, resulting in clustered adoption.
Geographical reach effects. Keen [1991] uses the term reach to refer to the geographical
locations and the people that a firm’s IT infrastructure is capable of connecting. Similarly, the
term geographical reach has been used to refer to the extent to which a firm has its presence and
markets its services or products [Radecki et al., 1996].
In our case, we can group the firms into two categories based on their geographical reach:
local and regional. We define local firms as firms that serve a customer base in only one state,
and regional firms as firms that serve customer bases in multiple states. We maintain that local
11
firms should adopt a new technology earlier than regional firms because the latter typically go
through a more complicated decision making process due to their larger operations, causing the
learning process to take longer too. Our fourth hypothesis is as follows:
•
Hypothesis 4 (The Geographical Reach Hypothesis). Similar geographical reach is
likely to result in similar underlying conditions for technology adoption, including
similar dynamics for information transmission and learning, with the result that cluster
adoption will be observed.
Industry sector effects. The rate of technology adoption varies between industries. Some
industries may find a given technological innovation more useful in their productions processes
or product lines than others [Hannan and McDowell, 1984b]. Mansfeld [1968] and Romeo
[1975] provide evidence supporting the hypothesis that the more competitive the market or
industry, the greater the rate of technology adoption and diffusion. Kamien and Schwartz [1982]
review the empirical evidence and note that technology adoption and diffusion tend to be faster
in an industry where there are fewer firms in the region and where there are similarities among
firm sizes. Forman et al. [2003] find that industries differ in their rates of adoption in Internet
technology because they differ in their use of other kinds of IT, labor costs, and industry growth
rates.
The economics literature commonly identifies information transmission and sharing among
firms as occurring mostly within the same industry [e.g., Doyle and Snyder, 1999; Christensen
and Caves, 1997] and done through mechanisms such as industry consortia, industry
conferences, and trade associations [e.g., Kirby, 1988; Vives, 1990]. Our fifth hypothesis is
based on the foregoing analysis:
12
•
Hypothesis 5 (The Common Industry Sector Technology Adoption Hypothesis).
Since information transmission and sharing among firms in a common industry will be
earlier to accomplish, clustered adoption by industry sector will be observed.
Technology vendor effects. In the adaptive learning process, firms may initially have only a
general idea about a new technology (e.g., the main functions of the technology, the potential
benefits the technology may offer to the firms). Over time, however, these firms add, update and
process information about many aspects of the technology, including information about specific
vendor(s). As firms share information with each other, they will narrow their focus to a certain
vendor. This will help them to be more effective in reaching a consensus on the value of the
technology being considered, which will drive the outcomes to the equilibrium point suggested
by rational expectations theory [Fryman, 1982]. This suggests that when a group of firms
reaches a consensus to adopt the technology, they are likely to have a specific vendor in mind.
Our sixth hypothesis is derived from this logic.
•
Hypothesis 6 (The Competing Vendor Hypothesis). Since information transmission
and sharing among a group of firms typically focuses on a particular technology vendor,
clustered adoption by technology vendor will be observed.
Firm size effects. It is generally held that firm size is positively correlated with technology
adoption. Large firms or firms with larger market shares are more likely to adopt because they
are more likely to have the financial resources required for purchasing and installing a new
technology. In addition, they may be better able to attract the necessary human capital and other
resources. Larger firms are also more capable of spreading the potential risks associated with
new projects because they are able to be more diversified in their technology choice and are in a
position to try out a new technology while keeping the old one operating at the same time in case
13
of unexpected problems. Larger firms tend to adopt new technologies sooner because they have
the “critical mass” and are able to capture economies of scale from production via the learning
curve more quickly and can spread the other fixed costs associated with adoption across a larger
number of units. The positive relationship between firm size and technology adoption has been
found to occur with reasonable consistency in a variety of empirical research settings [e.g., Link,
1980, in the chemicals and allied products industry; Kimberly and Evanisko, 1981, in the health
sector; Hannan and McDowell, 1984a, in electronic banking; Damanpour, 1992, in
manufacturing organizations; and Karshenas and Stoneman, 1993 and 1995, in the engineering
industry].
Some other literature suggests, however, that large size and market power may slow down
the rate of technology adoption. Larger firms may have multiple levels of bureaucracy that can
slow down technology adoption decision making processes. Furthermore, it may be relatively
more expensive for larger firms to adopt a new technology because they have many resources
and human capital sunk in the old technology and its architecture [Henderson and Clark, 1990].
Brynjolfsson et al. [1994] found that increases in the level of IT capital in an economic sector
were associated with a decline in average firm size in that sector. This may lead to the notion
that smaller firms are more likely to adopt a new technology earlier.
Despite the seemingly opposing views on the effects of firm size on technology adoption, we
argue that if firms of similar size display consistent technology adoption behaviors, then we
should observe clustered adoption by firm size. Our seventh hypothesis is:
•
Hypothesis 7 (The Firm Size Hypothesis). Since firm size affects technology adoption,
clustered adoption by firm size will be observed.
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A conceptual model for EBPP technology adoption. Based on the foregoing development
of hypotheses, we now are in a position to offer a more general conceptual model for EBPP
technology adoption. To test our clustered adoption hypotheses, we will employ a set of crosssectional models with deviation from mean time-to-adopt as the dependent variable and a set of
independent variables. The values of the dependent variable are calculated based on the mean
time-to-adopt of all firms in the sample. In the other models, the values of the dependent
variable are derived based on the mean time-to-adopt of each group, stratified by region, firm
size, industry, reach, and vendor. In addition, we will use a duration model for survival analysis
involving panel data to identify the instantaneous likelihood to adopt for each firm. This
conceptual model is summarized in the following diagram. (See Figure 1.)
One of the key issues with respect to this general conceptual model will be how we handle time
related to the observation of clustered adoption. Our operational definition for clustering of
technology adoption is based on an analysis of the empirical regularities adoption of technology
in a variety of settings [Fichman, 1992; Hoppe, 2002]. We note that in the context of XML and
Web services standards [Au and Kauffman, 2003; Chen et al., 2003], technologies with similar
multi-partite adoption complexity issues, that adoption occurred in large measure over the course
of one to two years. Other examples include DVDs, Wi-Fi and camera-phones. In the case of
Wi-Fi, research firm IDC predicts that the total number of public Wi-Fi users is expected to grow
from 2.4 million in 2003 to 10.4 million in 2005, a 324% growth over a period of two years
[Infonet, 2003].
In addition, we also have seen this kind of time horizon for the main elements
of technology adoption occurring in mobile telecommunications in Europe. Gruber and
Verboven [2001] report that technology adoption was rather swift in this context also. We
further note that the multi-partite adoption issues that are likely to be present here will require a
15
similar rational expectations theory interpretation of adoption-related information transmission
and sharing.
Figure 1. Conceptual Model to Test Rational Expectations-Based EBPP Adoption
Cross-sectional Models
Overall
Dependent
Variables
Independent
Variables
•DevMeanTimeToAdopt
•TimeToEvent
•Northeast
•Midwest
•South
•FirmReach
•Telecom
•Metavante
•FirmSize
•∆Lag2QConfDensity
•∆Lag2QDJIA
•∆Lag2QVendorStockPrice
•Northeast
•Midwest
•South
•FirmReach
•Telecom
•Metavante
•FirmSize
•∆Lag2QConfDensity
•∆Lag2QDJIA
•∆Lag2QVendorStockPrice
By Region
By FirmReach
•Northeast
•Midwest
•South
•FirmReach
•Telecom
•Metavante
•FirmSize
•∆Lag2QConfDensity
•∆Lag2QDJIA
•∆Lag2QVendorStockPrice
By Industry
•Northeast
•Midwest
•South
•FirmReach
•Telecom
•Metavante
•FirmSize
•∆Lag2QConfDensity
•∆Lag2QDJIA
•∆Lag2QVendorStockPrice
•Northeast
•Midwest
•South
•FirmReach
•Telecom
•Metavante
•FirmSize
•∆Lag2QConfDensity
•∆Lag2QDJIA
•∆Lag2QVendorStockPrice
By Vendor
•Northeast
•Midwest
•South
•FirmReach
•Telecom
•Metavante
•FirmSize
•∆Lag2QConfDensity
•∆Lag2QDJIA
•∆Lag2QVendorStockPrice
Panel Data Model / Duration Model
Based on our brief assessment of adoption patterns for other technologies likely to have had
adoption issues caused by value flows being constrained by the adoption of different kinds of
players in the same time frame, we will argue that a one-year window of time is a reasonable
period within which to observed clustered adoption. We further note that this is consistent with
the manner in which capital budgeting for large capital projects is done in firms: they normally
must plan ahead for big investments such as EBPP, and their budgeting plans typically are done
once a year. There is no requirement that their budgets all be developed over the same set of
16
months, however. Thus, we think a window of time—rather than a smaller specific period of
time—ought to make the most sense for this study.
DATA AND MEASURES
Data Sources
In this section, we will provide a description of the data set and how we collected the data as
well as the descriptive statistics for the variables in the study that we will use to test the
hypotheses discussed earlier.
Description of the Data Set
Our sample consists of EBPP adopting firms in the utilities and telecommunications industries
in the United States. We focused our analysis on two major EBPP vendors: CheckFree and
Metavante. To compile the sample, we used the list of corporate customers that CheckFree
posted on its website, as well as a list of corporate customers that we obtained directly from
Metavante. Due to the unavailability of financial information for privately-held firms, we chose
to include only public firms in our base sample set. However, in our extended sample set we
included all these private firms to perform a comparison analysis without any firm-specific
financial information. In addition, we considered companies that had the same parent company
as one company.
Since CheckFree’s list did not include the adoption dates of any of the companies, we
searched for the information on the Internet using multiple data sources, including Google,
LexisNexis, and the annual report of each company. In this case, we defined the adoption date as
the date when a company signed an EBPP agreement with the technology vendor.
Furthermore, we collected information about each company including company location (city,
state, and zip code), company size (in terms of the number of customers in the year adopted
17
EBPP), and company financial performance as measured in annual sales and earnings before
interest and tax (EBIT). While information about company location and company size could be
found on each company’s web site, we used the COMPUSTAT database to obtain the company
financial performance data. For the number of EBPP conferences per quarter, we searched the
Web, LexisNexis, and conference organizer web sites. We confirmed our data by contacting
several major conference organizers.
To determine the location of regional firms whose operations span multiple states that might
fall into different regions, we used the location of the headquarters and the region where most of
the operations were taking place. Our coding of regions follows the designations specified by
the United States Census Bureau. (See Appendix 1.)
Specification of measures for the variables included in this study
Our analysis will employ two different models. The first model is cross-sectional and will
be the primary means for testing the clustered adoption hypotheses. The second is a duration
model involving panel data with time-varying covariates for identifying the instantaneous
likelihood of adoption of a particular firm at a specific point in time. Consequently, we will
specify two different sets of dependent variables to reflect the use of two different models. The
sets of independent variables are almost the same between the two models. However, as the
names imply, the first model uses cross-sectional data, whereas the second model employs panel
data. Both models include lagged variables as explanatory variables.
Table 4 summarizes the measures and definitions for the variables that are used in this
empirical study. The use of the lagged value in some of the variables is based on the idea that it
will take some time before conference activities are seen to affect any adoption decision by a
firm. Furthermore, the use of the difference in the numbers of conferences between periods
18
captures the idea about how firm adoption decisions in certain periods were affected by the
increase or decrease in the frequency of the related conference activities. Table 5 shows
descriptive statistics for variables in our data set.
EMPIRICAL MODELING
The empirical analysis in this chapter will involve two separate models. The first is a crosssectional model set that offers a primary test of the cluster adoption hypothesis through
econometric analysis of models that represent the five different clustering strata. The goal of the
analysis is to estimate the extent to which the different theorized effects arise for different
subgroup codings for the dependent variables, relative to deviations in time from the central
tendency of firms to adopt EBPP.
The second empirical analysis involves the specification of an accelerated failure time panel
data model, whose structure is developed to make it possible to identify the instantaneous
likelihood of adoption of a given firm in time. This analysis does not focus on deviations from
time to adopt. Nor does it include sub-sample stratifications that affect the definition of the
dependent variable. Instead, the dependent variable is the occurrence of EBPP adoption by a
firm at a specific point in time, such that the general model can capture information about the
temporal likelihood of adoption for all firms. We introduce the stratifying variables from the
first model into this panel data model, as the size of the data set allows, as categorical fixed
effects. However, we should note at the outset that it is not possible for us to include all of the
hypothesized clustered adoption conditions; the size of the data size is insufficient in statistical
power terms.
19
Table 4. Summary of Variable Definitions and Measures for This Study
VARIABLE
DEFINITION
ISSUES
Dependent Variables
DevMeanTime
ToAdopt
The deviation from group average time-to-adopt (in
quarters from the beginning of the adoption timeline).
TimeToAdopt
The duration of time from the start of the observation
period to the event. For each firm in each time period,
the event is coded with a “1” if the firm made an
adoption decision, and with a “0” if otherwise.
Theory-Bearing Independent Variables
The difference between the number of EBPP-related
∆Lag2QConf
Density
FirmSize
FirmReach
Metavante
Regional
dummy
variables
conferences held two quarters prior to the adoption
period of each firm and the number of similar
conferences held four quarters prior in the region.
Size of each firm, measured in terms of number of
customers.
Dummy variable that codes for the operational span of
an EBPP adopter, with 1=regional span and 0=local
span only. Local span is the base case.
Dummy variable that codes for a vendor, with
1=Metavante, 0=CheckFree. Checkfree is the base
case.
A set of dummy variables that code for four geographic
regions of the U.S. and proxies for demographic
similarities in the operational environment of an EBPP
adopter:
• Northeast: 1=Northeast, 0=otherwise.
• Midwest: 1=Midwest, 0=otherwise.
• South: 1=South, 0=otherwise.
The base case is the West region.
Emphasis is on differences in
groups, leading to different
deviations for similar
observations.
Requires information about
duration, but acts only as a
technical parameter in the
model.
A number of different lag
specifications were examined.
This two-quarter lag variable
was most appropriate.
Proxy for firm size, since
employees were not available.
Span was coded based on a
single state (local) or a
number of states (regional).
Other span definitions were
possible too.
No other vendors were
included in this study for a
lack of public information.
Coding is based on regional
definitions of the U.S. Census
Bureau. Using the west region
as the base case reflects our
belief that this is the region
whose EBPP growth
dynamics are most well
understood.
Control Variables
Change in quarterly average of DJIA indices compared
∆Lag2QDJIA
Values computed on the basis
of daily market indices.
Choice of lag intended to
match ConfDensity variable.
Change
in
quarterly
average
of
vendor
stock
price
Values computed on the basis
∆Lag2QVendor
(CKFR for CheckFree adopters and MI for Metavante
of daily stock market prices.
StockPrice
adopters) compared to the previous quarter, measured
Choice of lag intended to
two quarters prior to the time-to-adopt.
match ConfDensity variable.
Change of a firm’s annual EBIT in the year prior to the Single-year lag used due to
∆LagFirm
year-of-adoption compared with the previous year.
financial reporting limitations,
Profit
based on annual report info.
Notes: The specifications of the variables that are used in this study reflect a blend of ideal measures and
pragmatic measures. The variable that codes vendor, Metavante, is an example of the former. The lag
measures typically were pragmatic choices, when there were many possible measures to choose from.
to the previous quarter, measured two quarters prior to
the time of adoption.
20
Table 5. Descriptive Statistics
VARIABLE
N
MEAN
DevMeanTimeToAdopt
Northeast
Midwest
South
FirmReach
Telecom
Metavante
∆Lag2QConfDensity
∆Lag2QDJIA
∆Lag2QVendorStockPrice
80
80
80
80
80
80
80
80
80
80
0
0.275
0.225
0.275
0.663
0.188
0.113
0.150
0.019
0.330
STD.
DEV
3.586
0.449
0.420
0.449
0.476
0.393
0.318
1.801
0.067
0.759
MIN
MAX
-6.025
0
0
0
0
0
0
-4.000
-0.060
-0.664
10.975
1
1
1
1
1
1
3.000
0.453
1.541
Note: Northeast, Midwest, South, FirmReach, Telecom, and Metavante are dummy
variables and therefore have a value of either 0 or 1 only.
A Cross-Sectional Clustered Adoption Model for EBPP Technology Adoption
Our main premise is that in the presence of information transmission a group of firms sharing
similar characteristics will adopt EBPP at about the same time, resulting in clustered adoption.
In practice, some of the firms will adopt either a little earlier or a little later. In other words,
clustered adoption may occur with an error term for timing, since firms with similar
characteristics will not be identical, may process information differently, and so on.
Nevertheless, we posit that the average time of adoption reflects the group’s rational expectations
about how to maximize the value associated with technology adoption by adopting at the valuemaximizing time. A firm that adopts either earlier or later than the average time shows a
deviation from the central tendency for adoption timing by members of the group. This may
diminish the firm’s ability to obtain network externality-led benefits (when adoption is too early)
or cause the firm to miss out on capturing value that is available in the marketplace (when
21
adoption occurs too late). The objective of our cross-sectional model is to explain the deviations
for operationally-defined dependent variables that reflect different possible subgroups of firms.
We base our model on the multiplicative model which takes the form of:
yi = β 0 x1β, i1 x2β,2i K xKβ K, i ε
where
k = counter for k = 1 to K independent variables
yi = deviation from mean time-to-adopt for EBPP adopter firm i among
i = 1 to I firms in the sample
x1,i, x2,i, …, xK,i = explanatory variable k for firm i
ε = normally-distributed error term with 0 mean
The multiplicative model represents interactions among the independent variables. For
example, the deviation from mean time-to-adopt might be a combination effect of the location of
the firm and its size.
The above multiplicative form can be rewritten in the log-linear form using the variable
names specified in the previous section:
ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South
+ β 4 Firm Re ach + β 5Telecom + β 6 Metavante
+ β 7 ln( FirmSize) + β 8 ln(∆LagFirm Pr ofit )
+ β 9 ln(∆Lag 2QConfDensity ) + β10 ln(∆Lag 2QDJIA)
+ β11 ln(∆Lag 2QVendorStock Pr ice) + ln ε
(The Basic Cross-Sectional Model) (1)
This basic cross-sectional model includes all the independent variables. The value of the
dependent variable for each observation (in other words, each row in the regression) is calculated
based on the deviation from the mean time-to-adopt of all observations in the sample.
22
For computational purposes, to avoid an invalid operation with the logarithmic function in
the model because of a negative or zero value, we add a constant (10) to each of the dependent
variable DevMeanTimeToAdopt value as well as each ∆Lag2QConfDensity value. Similarly, we
add 1 to ∆LagFirmProfit, ∆Lag2QDJIA as well as ∆Lag2QVendorStockPrice. These constants
will be taken care of when we calculate the marginal effect of the respective coefficients later on.
In addition, we also estimate four other models based on four different clustering strata:
region, reach, vendor, and industry. The model based on the region stratifier excludes the
Northeast, Midwest, and South dummy variables, with the Western United States region as the
base case. This is because the values of those variables are reflected in the values of dependent
variable, which is calculated based on the difference in mean time-to-adopt of observations per
region.
ln( DevMeanTimeToAdopt ) = ln β 0 + β 4 Firm Re ach + β 5Telecom + β 6 Metavante
+ β 7 ln( FirmSize) + β 8 ln(∆LagFirm Pr ofit )
+ β 9 ln(∆Lag 2QConfDensity ) + β10 ln(∆Lag 2QDJIA)
+ β11 ln(∆Lag 2QVendorStock Pr ice) + ln ε
(The Regional Stratification Model) (2)
Similarly, we have a model based on the firm reach stratifier that will exclude the FirmReach
variable and whose dependent variable values are calculated based on the difference in the mean
time-to-adopt per reach group (regional and local).
ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South +
+ β 5Telecom + β 6 Metavante + β 8 ln( FirmSize)
+ β 7 ln(∆Lag 2QConfDensity ) + β 9 ln(∆LagFirm Pr ofit )
+ β10 ln( Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice)
(The Firm Geographical Reach Stratification Model) (3)
The next model is based on the industry stratifier and it will exclude the Telecom variable.
23
The dependent variable values are calculated based on the difference in mean time-to-adopt per
industry group (utilities and telecommunications).
ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South
+ β 4 Firm Re ach + β 6 Metavante + β 7 ln( FirmSize)
+ β 8 ln(∆Lag 2QConfDensity ) + β 9 ln(∆LagFirm Pr ofit )
+ β10 ln(∆Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice)
(The Industry Stratification Model) (4)
The last cross-sectional model is based on the vendor stratifier and it will exclude the
Metavante variable. The dependent variable values are calculated based on the difference in
mean time-to-adopt for firms by vendor group for Metavante and CheckFree.
ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South
+ β 4 Firm Re ach + β 5Telecom + β 7 ln( FirmSize)
+ β 8 ln(∆Lag 2QConfDensity ) + β 9 ln(∆LagFirm Pr ofit )
+ β10 ln(∆Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice)
(The Vendor Stratification Model) (5)
A Panel Data Model for EBPP Technology Adoption Likelihood
We analyze our data using a duration model for survival analysis (Greene, 2002; Hosmer and
Lemeshow, 1999; Hougaard, 2000). The data consist of a response variable that measures the
duration of time until a specified event occurs, as well as a set of independent variables
associated with the adoption time variable. The response variable is also known as the event
time, failure time, or survival time variable. The purpose of survival analysis is to model the
underlying distribution of the event time variable and to assess the dependence of the event time
variable on the independent variable.
We analyze our panel data using an accelerated failure time (AFT) model, also known as the
accelerated time model or the ln(time) model [Cleves et al., 2002; Lee and Wang, 2003]. The
24
typical form of the model is ln(t i ) = xi β x + ln(τ i ) , where ti is time-to-adopt of firm i and τ i is the
residual. The word “accelerated” refers to the fact that in such a model, the effect of a change in
one of the independent variables increases with time. This is something we expect to see in
many technology adoption scenarios, including EBPP adoption. This is especially true in the
context of our theory, where we expect the potential adopters to go through a learning process
for a while to reinforce their understanding and expectations about the technology. In addition,
technologies have underlying elements that exogenously improve. As a result, as EBPP matures
over time, we should observe a more profound effect of the independent variables, leading to the
greater likelihood of adoption of the technology by firms.
Our basic panel data model is as follows:
ln(t i ) = β 0 + β1 Northeast + β 2 Midwest + β 3 South + β 4 Firm Re ach + β 5Telcom
+ β 6 Metavante + β 7 Firm Re ach + β 8 ∆LagFirm Pr ofit
+ β 9 ∆Lag 2QConfDensity + β10 ∆Lag 2QDJIA + β11∆Lag 2QVendorStock Pr ice
+ ln(τ i )
(The Basic Panel Data Model) (6)
In the AFT model, exponentiated coefficients have the interpretation of time ratios for a oneunit change in the corresponding covariate. For an EBPP adopting firm i with covariate
values xi = ( x1 , x2 ,K, xk ) , t i = exp( β1 x1 + β 2 x 2 + K + β k xk )τ i . If the value of x1 for the firm
increases by 1, then t i* = exp{β1 ( x1 + 1) + β 2 x2 + K + β k xk }τ i , and the ratio of t i* to t i will be
exp( β 1 ) .
Results of the Basic Cross-Sectional Model
The estimation results from our basic cross-sectional model are summarized in the following
table. (See Table 6.) We check for the presence of multicollinearity by calculating the variance
inflation factor (VIF). Each VIF value in the table is less than two, suggesting there is no
25
multicollinearity issue with our data. The values of R2 and adjusted R2 (60.4% and 54.0%,
respectively) both indicate a relatively good model fit. The value of F-statistic (9.44) is highly
significant (p-value < 0.0001), suggesting that we can reject the hypothesis that all coefficients of
the explanatory variables all equal to zero.
Table 6. Results of the Basic Model
VARIABLES
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Telecom (β5)
Metavante (β6)
FirmSize (β7)
∆LagFirmProfit (β8)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVendorStockPrice (β11)
R2 (Adj. R2)
F-statistic
White’s Test
COEFFICIENT
(STD. ERROR)
4.521*** (0.660)
0.199* (0.101)
0.176* (0.100)
0.250** (0.097)
0.182** (0.081)
-0.075 (0.109)
0.228* (0.121)
0.007 (0.030)
0.029 (0.247)
-1.168*** (0.197)
-2.151*** (0.638)
0.094* (0.056)
60.4% (54.0%)
9.44***
57.89 (p-value = 0.72)
P-VALUE
0.000
0.053
0.083
0.012
0.028
0.491
0.064
0.816
0.908
0.000
0.001
0.102
Notes: Model: Basic Cross-Sectional Model (Equation 1). Dependent variable is
ln(DevMeanToAdopt). Sample size N = 80. The estimated parameter significance levels are:
*
= p < .10, ** = p < .05, and *** = p < .01. Each VIF value is less than 2, suggesting there is
no multicollinearity issue with our data.
By observing the p-value of each coefficient, we can see that the majority of the variables are
statistically significant. Three variables—Telecom, FirmSize, and ∆LagFirmProfit—are clearly
insignificant. Another variable, ∆Lag2QVendorStockPrice, is marginally significant. This gives
us some idea about which variables to exclude in our revised models, taking into account the key
variables needed for testing our theory.
26
To provide us with a better idea about our data, we next performed the estimations based on
the stratification models. The results, which are summarized in Table 7, show that the three
variables—Telecom, FirmSize, and ∆LagFirmProfit—are not statistically significant in any of
the models. Our revised models will exclude these three variables.
Table 7. Results of the Basic and Stratification Models
VARIABLES
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Telecom (β5)
Metavante (β6)
FirmSize (β7)
∆LagFirmProfit
(β8 )
∆Lag2QConf
Density (β9)
∆Lag2QDJIA
(β10)
∆Lag2QVendorS
tockPrice (β11)
R2
Adjusted R2
F-statistic
White’s Test
BASIC
MODEL
Regional
Coefficient Coefficient
(Std.
(Std.
Error)
Error)
4.230***
4.521***
(0.619)
(0.660)
**
N/A
0.199
(0.101)
N/A
0.176*
(0.100)
N/A
0.250***
(0.097)
0.159**
0.182**
(0.081)
(0.078)
-0.075
-0.104
(0.109)
(0.101)
0.249**
0.228**
(0.121)
(0.115)
0.007
0.027
(0.030)
(0.028)
0.029
0.026
(0.247)
(0.229)
***
-1.168
-1.082***
(0.197)
(0.183)
***
-2.151
-2.064***
(0.638)
(0.603)
*
0.094
0.101*
(0.056)
(0.053)
60.4%
56.0%
54.0%
51.1%
***
9.44
11.31***
57.89
45.30
(p = 0.72)
(p = 0.26)
STRATIFICATION MODEL
FirmReach
Industry
Vendor
Coefficient Coefficient Coefficient
(Std.
(Std.
(Std.
Error)
Error)
Error)
4.643***
4.752***
4.947***
(0.659)
(0.620)
(0.622)
0.131
0.142
0.202**
(0.095)
(0.103)
(0.100)
**
0.100
0.202
0.173*
(0.094)
(0.101)
(0.098)
**
**
0.179
0.212
0.266***
(0.091)
(0.099)
(0.093)
N/A
0.123
0.150**
(0.082)
(0.076)
-0.085
N/A
-0.041
(0.101)
(0.104)
0.212**
0.133
N/A
(1.109)
(0.120)
0.003
-0.027
-0.004
(0.231)
(0.028)
(0.028)
0.097
-0.061
0.069
(0.231)
(0.249)
(0.242)
***
***
-1.134
-1.081
-1.191***
(0.184)
(0.199)
(0.192)
***
***
-1.713
-2.086
-2.016***
(0.595)
(0.664)
(0.623)
0.070
0.059
0.086
(0.053)
(0.057)
(0.055)
54.5%
54.1%
59.5%
47.9%
47.4%
53.6%
***
***
8.28
8.13
10.12***
56.95
48.08
51.40
(p = 0.44)
(p = 0.77)
(p = 0.68)
27
Notes. Model: Basic Cross-Sectional Model (Equation 1); Regional Stratification Model
(Equation 2); Firm Reach Stratification Model (Equation 3); Industry Stratification Model
(Equation 4); Vendor Stratification Model (Equation 5). Dependent variable in each model is
ln(DevMeanToAdopt). Sample size in each model is N = 80. The estimated parameter
significance levels are: * = p < .10, ** = p < .05, and *** = p < .01.
Revised Estimation Models
The results of the basic cross-sectional models presented earlier show that three variables—
Telecom, FirmSize, and ∆LagFirmProfit—are not statistically significant although we have
initially expected the opposite. This suggests that adoption times are not clustered by industry.
In addition, firm characteristics (especially firm size and profitability) appear not to affect the
time of adoption in the EBPP context.
We will estimate the following revised econometric models by excluding those three
variables:
ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South
+ β 4 Firm Re ach + β 6 Metavante + β 9 ln(∆Lag 2QConfDensity )
+ β10 ln(∆Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice) + ln ε
(The Revised Cross-Sectional Model) (7)
Similarly, our revised panel data model will also exclude the three variables.
ln(t i ) = β 0 + β1 Northeast + β 2 Midwest + β 3 South + β 4 Firm Re ach
+ β 6 Metavante + β 9 ∆Lag 2QConfDensity + β10 ∆Lag 2QDJIA
+ β11∆Lag 2QVendorStock Pr ice + ln(τ i )
(The Revised Panel Data Model) (8)
In the following sections we will present the results of these models.
Results of the Revised Models
The results from the revised basic model are shown in Table 8 below. Now all coefficients
are statistically significant and the adjusted R2 value is slightly higher compared with that of the
28
original basic model (55.7% versus 54.0%). The F-statistic is highly significant (13.40, p <
0.0001). All of the VIF values are below two, suggesting that there is no indication of
multicollinearity.
Table 8. Results of the Revised Basic Model
VARIABLES
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVendorStockPrice (β11)
R2 (Adjusted R2)
F-statistic
COEFFICIENT
(STD. ERROR)
4.585*** (0.444)
0.187** (0.093)
0.186* (0.096)
0.249*** (0.093)
0.170** (0.074)
0.208* (0.111)
-1.143*** (0.188)
-2.163*** (0.604)
0.088 (0.054)
60.2% (55.7%)
13.40 (0.000)
P-VALUE
0.000
0.048
0.057
0.009
0.026
0.064
0.000
0.001
0.105
Notes. Model: Revised Cross-Sectional Model (Equation 7). Dependent variable is
ln(DevMeanToAdopt). Sample size is N = 80. The estimated parameter significance levels are:
*
= p < .10, ** = p < .05, and *** = p < .01. Each VIF value is less than 1.8, suggesting there is no
multicollinearity issue with our data.
In addition to the revised basic model, we performed estimations for the revised stratification
models. The results are summarized in Table 9. Notice that industry is not one of the stratifiers
any more since we now exclude the Telecom variable. The results show generally consistent
estimates in terms of the sign and the significance level of each coefficient across the different
models. For example, ∆Lag2QConfDensity and ∆Lag2QDJIA are all negative and highly
significant, and FirmReach is positive and significant.
29
Table 9. Results of the Revised Basic and Stratification Models
VARIABLES
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConf
Density (β9)
∆Lag2QDJIA
(β10)
∆Lag2QVendor
StockPrice (β11)
R2
Adj. R2
F-statistic
OVERALL
MODEL
Coefficient
(Std. Error)
4.585***
(0.444)
0.187**
(0.093)
0.186**
(0.096)
0.249***
(0.093)
0.170**
(0.074)
0.208*
(0.111)
-1.143***
(0.188)
-2.163***
(0.604)
0.088*
(0.054)
60.2%
55.7%
13.40***
STRATIFICATION MODELS
Regional
FirmReach
By Vendor
Coefficient
Coefficient
Coefficient
(Std. Error) (Std. Error)
(Std. Error)
4.575***
4.646***
4.682***
(0.421)
(0.399)
(0.428)
N/A
0.123
0.200**
(0.088)
(0.090)
N/A
0.111
0.178*
(0.090)
(0.095)
**
N/A
0.174
0.261***
(0.088)
(0.090)
**
0.156
N/A
0.139**
(0.072)
(0.069)
0.199***
0.206**
N/A
(0.104)
(0.099)
-1.063***
-1.094***
-1.168***
(0.178)
(0.174)
(0.183)
***
***
-1.942
-1.756
-2.078***
(0.575)
(0.569)
(0.593)
*
0.092
0.066
0.087
(0.051)
(0.051)
(0.053)
55.2%
53.4%
59.3%
52.1%
49.5%
55.3%
***
***
18.21
12.05
14.97***
Notes. Model: Revised Cross-Sectional Model (Equation 7). The other three models are
stratification models similar to Equations 2, 3, and 5 but without the Telecom, FirmSize, and
∆LagFirmProfit variables on the right-hand side. Sample size is N = 80. Dependent variable
is ln(DevMeanToAdopt). The estimated parameter significance levels are: * = p < .10, ** = p
< .05, and *** = p < .01.
The following Table 10 shows the size of the marginal effect of each coefficient and its
actual impact on the dependent variable. The marginal effect of the Northeast dummy variable
can be calculated as follows. Let y Base be the value of the dependent variable in the base case
(i.e., West region), and y Northeast be that of the Northeast region. If y Base = e (where B
B
represents the sum of the values on the right-hand side of the cross-sectional model for the base
30
case), then y Northeast = e
B + β1
. The marginal effect of the coefficient β1 on the dependent
variable is given by: y Northeast − y Base = e
of e
β1
B + β1
− e B = e B (e β1 − 1) . Table 10 shows the value
− 1 for each model. We can derive a similar marginal effect for the other dummy variable
coefficients (Midwest-β2, South-β3, FirmReach-β4, and Metavante-β6).
Table 10. Coefficient marginal effects on the dependent variable
VARIABLES
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConf
Density (β9)
∆Lag2QDJIA
(β10)
∆Lag2QVendor
StockPrice (β11)
OVERALL
MODEL
Coefficient
Marginal
Effect
0.206
0.204
0.283
0.185
0.231
STRATIFICATION MODELS
Regional
FirmReach
By Vendor
Coefficient
Coefficient
Coefficient
Marginal
Marginal
Marginal
Effect
Effect
Effect
N/A
0.131
0.221
N/A
0.117
0.195
N/A
0.190
0.298
N/A
0.149
0.169
0.220
0.229
N/A
-0.007
-0.008
-0.008
-0.007
-0.021
-0.019
-0.017
-0.020
0.001
0.001
0.001
0.001
Note: To avoid an invalid operation with the logarithmic function in the model because of a
negative or zero value, we added a constant (10) to each ∆Lag2QConfDensity value, and 1
to ∆Lag2QDJIA as well as ∆Lag2QVendorStockPrice. As a result, each constant shows
up in the marginal effect for the respective coefficient as shown above in this table. The
β
β
β
marginal effects of β1, β2, β3, β4, and β6 are calculated using e 1 − 1 , e 2 − 1 , e 3 − 1 ,
e β 4 − 1 , and e β 6 − 1 respectively. The marginal effect of β9 is determined using
e β 9 ln(10 + ∆ ) − e β 9 ln(10 ) , with ∆ = 1. The marginal effects of β10 and β11 are calculated using
e β10 ln(1+ ∆ ) − 1 and e β11 ln(1+ ∆ ) − 1 , respectively, with ∆ = 1%.
The results in Table 9 show that both ∆Lag2QConfDensity and ∆Lag2QDJIA have a negative
coefficient and they are both significant at 0.01 level. This suggests that an increase in
conference activities and a positive change in the economy in general have accelerated the
31
adoption of EBPP. This supports the Information Transmission Technology Adoption Rate
Hypothesis (H2). The difference in the values of the dependent variable caused by a change in
the number of conferences of ∆ is given by
y * − y Base = e B+β9 ln(10+∆ ) − e B+ β9 ln10 = e B e β9 ln(10+∆ ) − e B e β9 ln10
= e B (e β9 ln(10+∆ ) − e β9 ln10 )
Therefore, the marginal effect is given by e β9 ln(10+ ∆ ) − e β9 ln 10 , where ∆ is the actual difference in
the number of EBPP conferences as defined for ∆Lag2QConfDensity. (Note: The constant 10
appears in the calculation above since we added the number 10 to every ∆ prior to estimating our
cross-sectional model to avoid an invalid operation with the logarithmic function in the model
because of a negative or zero value.) Since β9 is negative, a positive ∆ will result in a negative
marginal effect, which means earlier adoption. For example, in the overall model case, if ∆ = 1,
then the marginal effect is e −1.143 ln(10+1) − e −1.143 ln 10 = −0.007 .
For ∆Lag2QDJIA (β10), the difference in the values of the dependent variable caused by a
change in the DJIA stock market index ∆ is given by:
y * − y Base = e B+β10 ln(1+∆ ) − e B+ β10 ln1 = e B e β10 ln(1+∆ ) − e B e 0
= e B (e β10 ln(1+∆ ) − 1)
Therefore, the marginal effect is given by coefficient of ∆Lag2QDJIA (β10) is given by
e β10 ln(1+ ∆ ) − 1 , which also means earlier adoption for a positive change in the stock index. (Note:
Similar to the number of conferences case, we added the constant 1 to every ∆ prior to estimating
our cross-sectional model to avoid an invalid operation with the logarithmic function in the
model because of a negative or zero value.) For example, in the overall model case, if ∆ = 0.01
32
(which means the stock market index increases by 1%, then the marginal effect
is e −2.163 ln(1+ 0.01) − 1 = −0.021 .
The other variables have a positive coefficient and are statistically significant at various
levels. The ∆Lag2QVendorStockPrice variable has a positive coefficient and is statistically
significant in two of the revised models. The positive sign is counter-intuitive since we would
expect that a positive change in the vendor stock performance should accelerate the adoption of
the technology; instead, the result shows the opposite.
The FirmReach variable has a positive coefficient and is statistically significant at 0.05 level.
FirmReach is set to “1” if a firm is a regional firm. The fact that the coefficient is significant
suggests that there is a relative clustering of regional firms in terms of time of adoption because
holding all other things equal, each regional firm will adopt at the same time. The positive
coefficient suggests that regional firms adopted later than the base case (i.e., the local firms).
Therefore, the Geographical Reach Hypothesis (H4) is supported. The marginal effect of the
FirmReach coefficient for the overall model is 0.185. (See Table 10.) This means that holding
all other things equal, regional firms’ deviation from the overall mean time-to-adopt is smaller
than local firms’ by 0.185 times. Since the deviation from the overall mean time-to-adopt of the
base case is negative, we conclude that on the average regional firms adopted later than the local
firms.
The Metavante variable has a positive coefficient and is statistically significant at 0.01, 0.05,
or 0.10 level, depending on which model we look at. Metavante is set to “1” if a firm is a
Metavante adopter. Again, the fact that the coefficient is significant suggests that there is a
relative clustering of Metavante adopting firms in terms of time of adoption. The positive
coefficient suggests that Metavante adopters adopted later than the base case (i.e., the CheckFree
33
adopters). This supports the Competing Vendor Hypothesis (H6). The marginal effect of the
Metavante coefficient for the overall model is 0.231. (See Table 10.) This means that holding all
other things equal, Metavante firms’ deviation from the overall mean time-to-adopt is smaller
than Checkfree firms’ by 0.231 times. Since the deviation from the overall mean time-to-adopt
of the base case is negative, we conclude that on the average Metavante firms adopted later than
Checkfree firms.
The Northeast, Midwest, and South variables all have a positive coefficient and are
statistically significant at different levels (except in the FirmReach stratification model where
Northeast and Midwest are not significant). This suggests that there is clustered adoption in each
region, supporting the Geographical Collocation Clustered Technology Adoption Hypothesis
(H3). The positive sign suggests that firms in each of these regions adopted later than the base
case, which is the Western firms. The marginal effect of the Northeast coefficient for the overall
model is 0.206. (See Table 10.) This means that holding all other things equal, Northeast firms’
deviation from the overall mean time-to-adopt is smaller than West firms’ (the base case) by
0.206 times. Since the deviation from the overall mean time-to-adopt of the base case is
negative, we conclude that on the average Northeast firms adopted later than West firms.
Similar arguments hold for Midwest as well as South, which marginal effects are 0.204 and
0.283, respectively. Again, the fact that each of these coefficients is significant shows that there
is a relative clustering of adoption time per region.
Estimations with an Extended Sample Size
Since we have removed all firm-specific variables (i.e., FirmSize and ∆LagFirmProfit), we
can now include all the non-public firms that were initially taken out of the original sample set.
This is because we no longer have the need to include values of variables that would only be
34
typically reported by publicly-held firms. This will allow us to work with a larger sample set
(118 firms versus 80 originally). Our extended sample set consists of 92 utilities and 26 telecom
firms. There are now 26 Metavante firms (versus 9 in the original sample set), and 92 Checkfree
firms (versus 71 in the original sample set).
Although there are more observations, the results of the estimations using the extended
sample set do not give us better support for our hypotheses. (See Table 11). Although there are
more telecommunications firms in the extended sample set, we still do not have a statistically
significant coefficient for the Telecom variable. Indeed, all three regional variables (Northeast,
Midwest, and South) are now statistically insignificant. We suspect that non-public firms may
behave differently than public firms in terms of deciding when to adopt a technology.
Table 11. Results of the Revised and Stratification Models with Extended Data Set
VARIABLES
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Telecom (β5)
Metavante (β6)
∆Lag2QConf
Density (β9)
∆Lag2QDJIA
(β10)
BASIC
STRATIFICATION MODELS
MODEL
Regional
FirmReach
Industry
Vendor
Coefficient Coefficient Coefficient Coefficient Coefficient
(Std.
(Std.
(Std.
(Std.
(Std.
Error)
Error)
Error)
Error)
Error)
4.800***
4.538***
4.670***
4.696***
4.747***
(0.386)
(0.392)
(0.397)
(0.359)
(0.357)
0.108
N/A
0.145
0.076
0.091
(0.097)
(0.097)
(0.092)
(0.090)
0.029
N/A
0.077
0.058
0.026
(0.101)
(0.100)
(0.096)
(0.094)
0.105
N/A
0.112
0.074
0.086
(0.084)
(0.085)
(0.080)
(0.076)
**
**
0.187
N/A
0.105
0.152**
0.158
(0.075)
(0.075)
(0.070)
(0.064)
-0.028
-0.036
0.014
N/A
-0.032
(0.084)
(0.086)
(0.083)
(0.074)
0.043
0.053
N/A
0.121
0.155**
(0.095)
(0.088)
(0.084)
(0.094)
-1.193***
-1.199***
-1.130***
-1.074***
-1.148***
(0.175)
(0.178)
(0.176)
(0.163)
(0.163)
***
***
***
***
-2.165
-1.839
-2.451
-2.286
-2.080**
(0.683)
(0.692)
(0.682)
(0.648)
(0.637)
35
∆Lag2QVendorS
tockPrice (β11)
R2
Adj. R2
F-statistic
0.033
(0.055)
52.9%
49.0%
13.49***
0.033
(0.056)
48.6%
45.8%
17.45***
0.039
(0.056)
50.9%
47.3%
14.13***
0.016
(0.052)
50.9%
47.3%
14.13***
0.028
(0.051)
52.8%
49.3%
15.22***
Notes: Model: Basic Cross-Sectional Model (Equation 1); Regional Stratification Model
(Equation 2); Firm Reach Stratification Model (Equation 3); Industry Stratification Model
(Equation 4); Vendor Stratification Model (Equation 5); all without FirmSize and
∆LagFirmProfit. Dependent variable in each model is DevMeanToAdopt. Extended sample size
in each model is N = 118. The estimated parameter significance levels are: * = p < .10, ** = p <
.05, and *** = p < .01.
Panel Data Model Results
We used Stata 8.0’s STREG command to estimate our panel data model. The STREG
command allows the analysis of the panel data using the accelerated failure time model.
Alternate Parametric Functional Forms for the AFT Model
There are five parametric models that can be used: exponential, Weibull, generalized gamma,
log-normal, and log-logistic. Briefly, the different parametric models permit the representation
of somewhat different assumptions about τ i = exp(− xi β x ) t i in applied settings involving the
adoption of IT. With an exponential parametric model, it is assumed that
τ i ~ Exponential{exp( β 0 )} , i.e., τ i is distributed as exponential with mean exp( β 0 ) . With a
Weibull parametric form, it is assumed that τ i ~ Weibull ( β 0 , p) , i.e., τ i is distributed as Weibull
with parameter ( β 0 , p) . The generalized gamma parametric form implies that
τ i ~ Gamma( β 0 , κ , σ ) , i.e., τ i is distributed as generalized gamma with parameter ( β 0 , κ , σ ) .
Finally, the assumption for the log-normal regression model is that that τ i ~ Lognormal ( β 0 , σ ) ,
i.e., τ i is distributed as log-normal with parameter ( β 0 , σ ) . In contrast, with the log-logistic
regression model, the assumption is that τ i ~ Log log istic ( β 0 , γ ) , i.e., τ i is distributed as log-
36
logistic with parameter ( β 0 , γ ) . The log-normal and the log-logistic parametric forms differ in
that they increase and decrease (in this case, the log-logistic hazard increases and decreases
if γ < 1 ). As a result, they may be more appropriate to represent settings in which the hazard rate
is going up and then going down, a phenomenon that we would observe in many technology
adoption settings where adoption is initially slow then going at a faster rate but eventually
slowing down after some time. Taken together the empirical modeling choices offered by the
parametric forms of the accelerated failure time model constitute a strong basis for studying a
variety of IT adoption phenomena.
The time option of the STREG command specifies that the model is to be estimated in the
accelerated failure-time metric rather than in the log relative-hazard metric. This option is only
valid for the exponential and Weibull models since they have both a hazard ratio and an
accelerated failure-time parameterization. For the other three models, the STREG command
always estimates the accelerated failure time model.
Empirical Model Selection Procedure
To determine which model to use, we followed the recommendation made by Akaike [1974].
This paper suggests penalizing each model’s log-likelihood to reflect the number of parameters
being estimated and then comparing them. Although the best-fitting model is the one with the
largest log-likelihood, the preferred model is the one with the lowest value of the Akaike
information criterion (AIC). For parametric survival models, the AIC is defined as:
AIC = −2 ln L + 2( k + c )
where k is the number of model covariates and c the number of model-specific distributional
parameters [Cleves et al., 2002]. The values of c for the different distributions are shown in
Table 12.
37
Table 12. AIC’s c Value for Various Distributions
DISTRIBUTION
C
Exponential
Weibull
Generalized gamma
Log-normal
Log-logistic
1
2
3
2
2
We first performed the accelerated failure time estimation using the basic panel data model.
Table 13 shows the log-likelihood and AIC values of each distribution model. We can see that
the log-logistic model has the lowest AIC value. The Weibull and generalized gamma functional
forms were roughly tied for second place, with some distance in terms of the AIC score that
separated the log-logistic form. As a result, we selected the log-logistic model. These results
practically conform with what the different parametric forms have to offer. As discussed earlier,
only the log-normal and log-logistic forms are non-monotonic, which is more in line with our
EBPP adoption pattern. And despite the similarities between log-normal and log-logistic, the
latter allows it to increase at a slower rate initially with the appropriate value of γ (in this case,
STATA reported using a value of γ of 0.138).
Table 13. The AIC’s c Value for Various Distributions (Basic Panel Data Model)
DISTRIBUTION
Exponential
Weibull
Generalized gamma
Log-normal
Log-logistic
LOG
K
C
AIC
LIKELIHOOD
-233.24943
-99.06118
-98.717149
-101.67105
-98.379405
11
11
11
11
11
1
2
3
2
2
490.49886
224.12236
225.43430
229.34210
222.75881
38
Full and Revised Panel Data Model Results for the Log-Logistic AFT Model
Table 14 shows the estimation results of the basic panel data model using the log-logistic
model.
Table 14. Results of the Basic Panel Data Model
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Telecom (β5)
Metavante (β6)
FirmSize (β7)
∆LagFirmProfit (β8)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVendorStockPrice (β11)
Log-likelihood
LR(χ2)
Prob > χ2
COEFFICIENT
(STD. ERROR)
2.757*** (0.062)
0.030 (0.057)
-0.051 (0.057)
-0.006 (0.056)
0.101** (0.050)
-0.010 (0.066)
0.004 (0.068)
3.18e-09 (0.000)
0.021 (0.045)
-0.030*** (0.011)
-0.887** (0.376)
-0.057** (0.028)
-98.379
33.15
0.0005***
Z
44.43
0.53
-0.90
-0.10
2.03
-0.16
0.06
1.05
0.48
-2.61
-2.36
-2.08
Notes: Model: Basic Panel Data Model (Equation 6). Dependent variable in each
model is Time-to-Adopt (t). Sample size in each model is N = 80. The estimated
parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. LR(χ2)
is the likelihood ratio χ2.
Several variables have a statistically significant coefficient. They are FirmReach,
∆Lag2QConfDensity, ∆Lag2QDJIA, ∆Lag2QVendorStockPrice. In the revised panel data
model, we eliminated the insignificant variables from the model. However, we still retained
Northeast, Midwest, South, and Metavante to enable us to compare the results with the revised
cross-sectional model. Table 17 lists the AIC value of each distribution of the revised panel data
model. Again, log-logistic is the preferred distribution based on the AIC criterion. In addition,
the Weibull functional form performs almost as well.
39
Table 17. AIC’s c Value for Various Distributions (Revised Panel Data Model)
DISTRIBUTION
Exponential
Weibull
Generalized gamma
Log-normal
Log-logistic
LOG
K
C
AIC
LIKELIHOOD
-233.71317
-100.06237
-99.77483
-102.53552
-99.510098
8
8
8
8
8
1
2
3
2
2
485.42634
220.12474
221.54966
225.07104
219.02020
In Table 18, we report the results of the revised panel data model. We can see that the same
variables are significant.
Table 18. Results of the Revised Panel Data Model
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVendorStockPrice (β11)
Log-likelihood
LR(χ2)
Prob > χ2
COEFFICIENT
(STD. ERROR)
2.757*** (0.061)
0.051 (0.055)
-0.054 (0.057)
-0.002 (0.056)
0.122*** (0.046)
0.003 (0.066)
-0.030*** (0.011)
-0.892** (0.374)
-0.061** (0.028)
-99.510
30.89
0.0001***
Z
44.98
0.92
-0.94
-0.03
2.62
0.04
-2.64
-2.38
-2.21
Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each
model is Time-to-Adopt (t). Sample size in each model is N = 80. The estimated
parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01.
LR(χ2) is the likelihood ratio χ2.
The marginal effects of the coefficients that are statistically significant are as follows:
•
FirmReach (β4):
e0.122 = 1.130
•
∆Lag2QConfDensity (β9):
e–0.030 = 0.970
•
∆Lag2QDJIA (β10):
e–0.892 = 0.410
40
•
∆Lag2QVendorStockPrice (β11):
e–0.061 = 0.941
A marginal effect that is smaller than 1 means that the variable has an accelerating effect,
whereas greater than one means the variable has a decelerating effect on the time-to-adopt.
Assessing Parameter Heterogeneity and Stability via Pseudo-Replicate Data
Sets
To estimate the accuracy of our sample statistics, we perform the jackknifing procedure.
Jackknifing uses a number of pseudo-replicate data sets, each of which contains all but one of
the original data elements [Efron, 1979]. Variations on this approach also permit the analyst to
iteratively drop out one, then two, then three observations, etc., up to the point where it becomes
impossible to establish coefficient estimates due to the lack of data. In our case, we do three
types of jackknifing that we have conceptualized for the purposes of this analysis: backward,
forward, and one-period-at-a-time jackknifing:
•
In backward jackknifing, we start with the full data set, then go backward in time and
iteratively take out observations from the latest period, and estimate the remaining
sample each time, until the sample becomes too small to provide any meaningful
results. With this approach, fewer and fewer more recent observations of technology
adoption will be included. (See Table 19.)
•
Forward jackknifing is the opposite of backward jackknifing. In forward
jackknifing, we start with the full data set, then go forward in time and iteratively
remove observations from the earliest period, and estimate the remaining sample each
time, until the sample becomes too small for further useful analysis. With this
41
approach, fewer and fewer earlier observations of technology adoption will be
included. (See Table 20.)
•
One-period-at-a-time jackknifing involves an analysis process in which we take away
one period of observations from the overall sample each time and iteratively estimate
the model’s coefficients on the remaining parameters. With this approach, we have
an opportunity to remove observations from middle periods in the panel of data, while
preserving data from the other periods with which to run the estimation model. (See
Table 21.)
Table 19. Results of the Panel Data Backward Jackknifing
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVndrStckPrc (β11)
Log-Likelihood
Sub-sample No. of Firms
LR(χ2)
T
2.757***
0.051
-0.054
-0.002
0.122***
0.003
-0.030***
-0.892**
-0.061**
-99.510
80
30.89***
≤ T-1
2.693***
0.109**
0.002
0.052
0.116***
0.016
-0.029***
-0.803**
-0.051*
-93.564
79
28.70***
≤ T-2
2.627***
0.031
0.006
0.020
0.148***
0.090
-0.039***
-0.616*
-0.026
-72.936
76
28.75***
≤ T-3
2.561***
0.090*
0.065
0.075
0.140***
0.105**
-0.039***
-0.539**
-0.015
-66.072
75
29.34***
≤ T-4
2.627***
0.031
0.006
0.020
0.148***
0.090
-0.039***
-0.616*
-0.026
-61.715
74
27.53***
Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is
Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05,
and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is
generally already known. LR(χ2) is the likelihood ratio χ2.
42
Variable
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVndrStckPrc (β11)
Log-Likelihood
Sub-sample No. of Firms
LR(χ2)
≤ T-5
2.564***
0.046
0.035
0.073
0.119***
0.115**
-0.048***
-0.428
-0.002
-56.978
72
25.46***
≤ T-6
2.569***
0.015
0.032
0.049
0.100**
0.130**
-0.054***
-0.298
0.014
-51.252
70
26.07***
≤ T-7
2.458***
0.101*
0.061
0.145**
0.130***
0.102
-0.063***
-0.082
0.031
-41.395
65
28.04***
≤ T-8
2.448***
0.081
0.084
0.123**
0.083*
0.125*
-0.098***
-0.099
0.036
-27.926
57
36.68***
≤ T-9
2.581***
0.045
0.015
0.055
0.054
0.021***
-0.273***
-0.131
0.061*
8.275
43
84.41***
Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is
Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05,
and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is
generally already known. LR(χ2) is the likelihood ratio χ2.
Table 19 above shows that FirmReach (β4), ∆Lag2QConfDensity (β9), ∆Lag2QDJIA (β10)
are consistently significant. Metavante (β6) is also significant but shows some inconsistency.
We suspect that this is due to the unbalanced sample (there are much fewer Metavante than
Checkfree observations).
Table 20. Results of the Panel Data Forward Jackknifing
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVndrStckPrc (β11)
Log-Likelihood
Sub-sample No. of Firms
LR(χ2)
ALL
2.757***
0.051
-0.054
-0.002
0.122***
0.003
-0.030***
-0.892**
-0.061**
-99.510
80
30.89***
≥ T-5
2.780***
0.034
-0.070
-0.019
0.105**
-0.012
-0.028***
-0.876**
-0.064**
-94.186
79
30.24***
≥ T-6
2.804***
0.018
-0.083
-0.036
0.088**
-0.025
-0.026**
-0.981***
-0.068***
-88.984
78
31.26***
≥ T-7
2.871***
-0.017
-0.116**
-0.074
0.038
-0.083
-0.019**
-0.539
-0.083***
-74.824
74
27.74***
≥ T-8
2.882***
-0.023
-0.124**
0.085*
0.033
-0.107**
-0.015
-0.332
-0.089***
-59.844
70
30.26***
Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is
43
Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05,
and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is
generally already known. LR(χ2) is the likelihood ratio χ2.
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVndrStckPrc (β11)
Log-Likelihood
Sub-sample # of Firms
LR(χ2)
≥ T-9
2.893***
-0.031
-0.123**
-0.081*
0.023
-0.113**
-0.011
-0.934***
-0.106***
-43.908
67
45.10***
≥ T-10
2.899***
-0.031
-0.102***
-0.075**
0.005
0.130***
-0.005
-1.469***
-0.108***
-17.025
59
61.32***
≥ T-11
2.890***
-0.018
-0.113***
0.063*
0.017
-0.141***
-0.005
-1.117***
-0.101***
-12.523
55
55.30***
≥ T-12
2.897***
-0.019
-0.099**
-0.067***
0.022
-0.158***
-0.003
-0.662
-0.112***
-11.704
52
49.25***
≥ T -13
2.968***
-0.036
-0.114***
-0.077*
0.001
-0.145***
0.008
-0.129
-0.129***
-0.667
37
43.97***
Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is
Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05,
and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is
generally already known. LR(χ2) is the likelihood ratio χ2.
Table 20 shows results similar to those in Table 19. In addition, Midwest (β2) and South (β3)
are also significant pretty consistently when we take out observations from the earlier periods.
There may be outliers in those two regions that may sway the results.
44
Table 21. Results of the Panel Data One-Period-at-a-Time Jackknifing
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVndrStckPrc (β11)
Log-Likelihood
Sub-sample # of firms
LR(χ2)
ALL
2.757***
0.051
-0.054
-0.002
0.122***
0.003
-0.030***
-0.892**
-0.061**
-99.510
80
30.89***
T=3 OUT
2.780***
0.034
-0.070
-0.019
0.105**
-0.012
-0.028***
-0.876**
-0.064**
-94.186
79
30.24***
T=5 OUT
2.782***
0.034
-0.067
-0.019
0.104**
-0.011
-0.028***
-0.992***
-0.065***
-94.737
79
31.34***
T=7 OUT
2.825***
0.016
-0.087
-0.040
0.071
-0.057
-0.023**
-0.424
-0.077***
-87.651
76
24.67***
T=8 OUT
2.766***
0.046
-0.060
-0.010
0.118***
-0.017
-0.025**
-0.763**
-0.066**
-88.707
76
29.19***
Notes: Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is
Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05,
and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is
generally already known. When a time period is not indicated as having been dropped out, it
means that there were no observations of adoption occurring in that period. LR(χ2) is the
likelihood ratio χ2.
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVndrStckPrc (β11)
Log-Likelihood
Sub-sample # of firms
LR(χ2)
T=9 OUT
2.785***
0.039
-0.060
-0.007
0.104*
-0.020
-0.024**
-1.231***
-0.084***
-88.616
77
39.49***
T=10
OUT
2.782**
0.051
-0.035
0.000
0.100*
-0.022
-0.022**
-1.237***
-0.065**
-86.391
72
30.52***
T=11
OUT
2.734***
0.075
-0.060
0.019
0.144***
-0.002
-0.031***
-0.582
-0.049*
-95.799
76
29.16***
T=12
OUT
2.753***
0.054
-0.039
0.000
0.131***
0.009
-0.029**
-0.689
-0.066**
-99.171
77
27.22***
T=13
OUT
2.771***
0.063
-0.043
-0.011
0.147***
0.081
-0.020
-1.115**
-0.062*
-94.010
65
23.85***
Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is
Time-to-Adopt (t). Sample size in each model is N = 80. The estimated parameter significance
levels are: * = p < .10, ** = p < .05, and *** = p < .01. Information on R2, adjusted R2, and Fstatistic omitted, since model fit is generally already known. LR(χ2) is the likelihood ratio χ2.
45
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVndrStckPrc (β11)
Log-Likelihood
Sub-sample # of firms
LR(χ2)
T=14
T=15
T=16
T=17
T=18
OUT
OUT
OUT
OUT
OUT
2.730***
0.069
-0.055
-0.013
0.170***
0.065
-0.046***
-1.059***
0.018
-92.758
66
30.31***
2.765***
0.062
-0.060
-0.008
0.137***
-0.011
-0.030**
-0.990**
-0.090***
-92.996
72
35.56***
2.701***
0.094
-0.052
0.046
0.158***
-0.010
-0.034***
-0.819**
-0.060**
-93.991
75
34.50***
2.763***
0.044
-0.056
-0.010
0.117**
0.006
-0.034***
-0.837**
-0.061**
-97.580
78
30.13***
2.766***
0.033
-0.080
-0.000
0.110**
0.003
-0.039***
-0.864**
-0.054*
-94.289
77
30.10***
Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is
Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05,
and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is
generally already known. LR(χ2) is the likelihood ratio χ2.
VARIABLE
Constant (β0)
Northeast (β1)
Midwest (β2)
South (β3)
FirmReach (β4)
Metavante (β6)
∆Lag2QConfDensity (β9)
∆Lag2QDJIA (β10)
∆Lag2QVndrStckPrc (β11)
Log-Likelihood
Number of firms
LR(χ2)
T=19 OUT
2.757***
0.051
-0.054
-0.002
0.122***
0.003
-0.030***
-0.892**
0.061**
-99.510
79
30.89***
T=20 OUT
2.716***
0.090
-0.016
0.036
0.118***
0.012
-0.031***
-0.857**
-0.055**
-96.181
79
29.82***
T=22 OUT
2.695***
-0.027
-0.052
-0.032
0.154***
0.076
-0.042***
-0.728**
-0.036
-79.987
77
34.43***
T=24 OUT
2.693***
0.109**
0.002
0.052
0.116***
0.016
-0.029***
-0.803**
-0.051*
-93.564
79
28.70***
Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is
Time-to-Adopt (t). Sample size in each model is N = 80. The estimated parameter significance
levels are: * = p < .10, ** = p < .05, and *** = p < .01. LR(χ2) is the likelihood ratio χ2.
46
Tables 19, 20, and 21 show relatively consistent results for the coefficients in terms of their
magnitudes, signs, and significance levels. This confirms the model robustness and the
parameter stability of the primary estimate of our sample.
DISCUSSION
We have examined clustered adoption using deviation from group mean time-to-adopt as the
dependent variable in cross-sectional models. We have also employed the accelerated failure
time model using panel data econometrics. In this section, we will discuss the results in greater
detail, and try to wrap up the case for the observation of clustered adoption relative to our
proposed rational expectation theory of technology adoption.
As we hypothesized, conference activities have a significant effect on the adoption timing of
the firms. As the results of the cross-sectional and panel data model show, an increase in the
number of EBPP conferences decreases the time-to-adopt. In this case, we use a two-quarter lag
variable, which measures the difference between the number of EBPP-related conferences held
two quarters prior to the adoption period of each firm and the number of similar conferences held
four quarters prior in the region where the firm is located. The use of lagged values makes sense
because we believe it will take some time before information sharing facilitated by the
conferences would take effect.
The variable FirmReach is significant and has a positive sign, indicating that there is relative
clustering with regard to the geographical reach of the firms, thus supporting our hypothesis. In
this case, regional firms adopted later than local firms. Based on the adaptive learning
perspective, we can argue that regional firms require more learning time due to the fact that they
may need to align their expectations with more firms that serve the many regions in which they
operate. Another possible explanation is that relative to local firms, regional firms probably need
47
to involve more constituents inside their own organization in their technology adoption decision
making, causing the process to take more time.
Contrary to our hypothesis, FirmSize does not affect time-to-adopt. We suspect it is because
EBPP is still within the affordability range of small to medium firms. So firms of any size can
adopt the technology whenever they feel the technology is worth adopting, i.e., whenever they
think the benefits would outweigh the costs. Furthermore, firms of all size categories can be
found in each region. If large and small firms tend to cluster by region, then it will be difficult to
expect that they will also cluster by size.
However, we did not find evidence for clustered adoption by industry. We suspect it is
because there are fewer telecommunications firms (compared with the number of utilities firms)
in our sample set. The reason is that the majority of the telecommunications market nationwide
is served by just a few major companies (e.g., AT&T/SBC, Verizon, Sprint, and MCI). Another
possible explanation is that while most of the telecommunications firms in our sample are
national/regional firms, there are a few that are local, creating an imbalance in the sample.
In addition to the theory-bearing variables, we included several control variables in our
models to help us explain some of the variation in the dependent variables that is not otherwise
explained by the theory-bearing variables. Our results show that the general economic condition
(represented by the change in Dow Jones Industrial Average index) significantly impacts the
adoption times. A positive increase in the DJIA index pulls the deviation away from the group
mean time-to-adopt to the left, meaning that firms adopt earlier in a positive economic condition,
holding all other things equal. It suggests that a positive economic condition eases and
accelerates technology adoption decision making.
48
The variable ∆LagFirmProfit is not statistically significant although we had initially
expected that firms that are profitable will be more likely to adopt a new technology earlier. We
believe that the reason why the profitability of adopting firms does not matter in our case is
because EBPP is considered a strategic necessity by many firms. Our claim is supported by
interviews conducted by Celent [2002] (a Boston-based consulting firm) which revealed that
most firms cite competitive pressures and strategic necessity as their primary motivators for
offering e-services. We argue that because EBPP is a strategic necessity, it will be adopted by the
firms when the other factors tell them to adopt, without really considering whether they have
been profitable recently or not. In fact, we could argue that some firms might consider EBPP as
a means for cutting costs, offering the potential for them to be profitable or become more
profitable. In addition, competitive pressures—cited as the other factor by Celent—prompt firms
to constantly benchmark themselves against each other in their comparison group, thus
conforming to the information sharing and learning process that we have described to support
our theory.
Our results also show that ∆Lag2QVendorStockPrice is not consistently significant, in the
sense that the results of the different models do not consistently show that this particular variable
is statistically significant. We argue that this is because the observation period (1997-2002) is a
period when stock prices were very volatile and it would be difficult for the potential adopting
firms to base their decisions on the ups and downs of the vendor stock prices.
We next discuss the results of the panel data model in the log-logistic regression. Several
variables have statistically significant coefficients. They are FirmReach, ∆Lag2QConfDensity,
∆Lag2QDJIA, ∆Lag2QVendorStockPrice. Although they apply to the time-to-adopt, these
variables have a similar interpretation as in the cross-sectional model. Therefore, the positive
49
coefficient of FirmReach means that regional firms adopted later than the base case (i.e., the
local firms), whereas the negative coefficients of ∆Lag2QConfDensity, ∆Lag2QDJIA,
∆Lag2QVendorStockPrice mean that a positive change in the value of each of these variables
will reduce the time-to-adopt, meaning earlier adoption.
As discussed earlier, the cross-sectional model is the primary means for testing the clustered
adoption hypotheses, whereas the duration model involving panel data is for identifying the
instantaneous likelihood of adoption using a specific parametric model. Although the results are
slightly different due to the different models employed, we see consistencies in some of the
variables such as FirmReach and ∆Lag2QConfDensity.
Overall, our results show some evidence for the rational expectations theory of technology
adoption that we propose in this thesis.
CONCLUSION
In this section we will discuss the main findings and theoretical contributions of this research
related to our application of rational expectations theory and thinking, as well as our
conceptualization of clustered adoption. In addition, we will discuss contributions to practice
and insights for managers.
Main Findings and Theoretical Contributions
This research is among the first that applies rational expectations and adaptive learning
theory and thinking to technology adoption issues. The theory allows us to look into the issues
in technology adoption that involve multiple parties (multi-partite technology adoption) who
seek to align their expectations of value prior to making a decision to adopt. The theory further
enables us to offer an alternative perspective by factoring in the complex interactions among
50
different firms over multiple periods, beyond the typical approach that involves modeling only
two firms in two periods. More specifically, it takes into account the learning and information
sharing that occur between multiple entities over many periods, a phenomenon that generally
occurs in the marketplace. Although the alignment of expectations by multiple firms in the
presence of the same information will never be the same due to bounded rationality and costs
associated with processing information, the theory provides a useful characterization of the
underlying dynamics that occur in the market relative to the time-clustered adoption of a
technology.
The resulting technology adoption theory derived from rational expectations and adaptive
learning suggests that due to network externalities, it is in the best interest of each firm within a
group sharing similar characteristics and/or serving similar markets to adopt simultaneously (up
to the point at which bounded rationality and information processing costs become influential).
This leads to our conceptualization of the clustered adoption hypotheses, which are an alternative
view to those based on the rational herding behavior theory of Bikchandani et al. [1992, 1998].
Our clustered adoption theory differs in the fact that it assumes that decision makers are willing
to collect more information over time and utilize all available information efficiently before
making a technology adoption decision. We believe this is more in line with the basic
assumption of firm value maximization.
The representation of the dependent variable for empirical analysis in the cross-section
models deserves special mention. Although we could have alternatively used the actual period
number of the time-to-adopt of each firm as the dependent variable, we believe that using the
deviation from the mean time-to-adopt allows us to better illustrate clustered adoption, since it is
very easy to see how much each firm has deviated from the group mean time-to-adopt. We also
51
contribute to the IS/IT literature by showing how we can use the forward, backward, and dropone jackknifing methods to assess the robustness and the stability of the estimation models’
results, in view of their relatively small sample size.
We used the multiplicative model in our cross-sectional analysis since we believe there are
interactions among the independent variables, which are comprised of binary/dummy and
continuous variables. The dummy variables allow us to see if there are effects of the categories
on the deviation from the group mean time-to-adopt. For example, if a dummy variable for a
region has a coefficient of a certain magnitude that is statistically significant, then we can argue
that there is a relative clustering in that particular region. This is indeed very similar to the idea
of using dummy variables to identify whether there are relative groupings of incomes of lawyers,
doctors, professors, etc. A statistically significant coefficient of the dummy variable that
represents the lawyer category would indicate that lawyers have a certain level of income and
each lawyer’s income is expected to be clustered around that level.
Contributions to Practice and Insights for Managers
IT adoption is an important responsibility of IS and other managers in a firm and
expectations about the benefit and cost of the technology being considered always play an
essential role in the adoption decision making process. The REH offers a unique perspective by
suggesting that in setting their expectations, managers should not base their decisions on the
results of the past beyond the point where past information serves as an input for forming
expectations about the future. We can see why this perspective is appropriate if we consider the
ever-changing nature of information technologies. Technologies that worked in the past may not
be relevant anymore today, let alone in the future.
52
For the EBPP technology vendors, the findings in this research suggest that it may be useful
for them to identify which firms belong to which groups or subgroups. This is because we
believe that each firm tries to learn about a new technology by communicating with and
observing the other firms within the same group. This creates an opportunity for a vendor to
eventually sign up most, if not all, of the firms in the group in a relatively short period of time.
Our clustered adoption theory can be extended to some other nascent industries in which the
technologies exhibit strong network externalities characteristics similar to EBPP. Such
technologies include voice over Internet protocol (VoIP) and radio frequency identification
(RFID). Relative to each of these cases, we would again point out that before making a decision
to adopt the technology, firm decision makers will collect information over time and utilize all
available information efficiently. And since there are network externalities involved, we should
observe clustered adoption to some extent.
In closing, we believe that this research contributes to the IS/IT literature by offering a new
theoretical perspective on multi-partite technology adoption. Further studies in different
industries and technology settings will enable us to confirm the soundness of the theory we have
proposed.
53
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Appendix 1
United States Census Bureau Regions
REGION 1
(NORTHEAST)
Connecticut
Maine
Massachusetts
New Hampshire
New Jersey
New York
Pennsylvania
Rhode Island
Vermont
REGION 2
(MIDWEST)
Illinois
Indiana
Iowa
Kansas
Michigan
Minnesota
Missouri
Nebraska
North Dakota
Ohio
South Dakota
Wisconsin
REGION 3
(SOUTH)
Alabama
Arkansas
Delaware
District of Columbia
Florida
Georgia
Kentucky
Louisiana
Maryland
Mississippi
North Carolina
Oklahoma
South Carolina
Tennessee
Texas
Virginia
West Virginia
REGION 4
(WEST)
Alaska
Arizona
California
Colorado
Hawaii
Idaho
Montana
New Mexico
Nevada
Oregon
Utah
Washington
Wyoming
Source: U.S. Census Bureau (available at www.census.gov/geo/www/us_regdiv.pdf).
58