RATIONAL EXPECTATIONS AND INFORMATION TECHNOLOGY ADOPTION
Yoris A. Au (contact author)
Doctoral Program
yau@csom.umn.edu
Robert J. Kauffman
Co-Director, MIS Research Center and
Professor and Chair
rkauffman@csom.umn.edu
Information and Decision Sciences
Carlson School of Management
University of Minnesota
Minneapolis, MN 55455
Last revised: November 11, 2002
_____________________________________________________________________________________
ABSTRACT
The Economics and Information Systems literature on technology adoption often considers network
externalities as one of the main factors that affect adoption decisions. The existing work assumes that
potential adopters have a certain level of expectations about network externalities when they have to
decide whether to adopt a particular technology. However, there has been little discussion on how the
potential adopters reach their expectations. This paper attempts to address this issue by offering a new
perspective motivated by the rational expectations hypothesis (REH). We show why different firms that
initially have heterogeneous expectations about the potential value of an information technology
eventually able to arrive at contemporaneous decisions to adopt the same technology, creating the desired
network externalities and allowing the firms to become catalysts that facilitate processes that lead to
market-wide adoption. We also discuss the conditions under which adoption inertia will take over in the
marketplace, as well as the managerial implications of the model.
KEYWORDS: Adoption, bounded rationality, economic theory, network externalities, rational
expectations hypothesis, technology adoption.
_____________________________________________________________________________________
ACKNOWLEDGEMENTS
The authors wish to thank the participants in the Information and Decision Sciences Workshop at Carlson
School of Management of University of Minnesota, and the anonymous reviewers of this paper and a
related paper at the 2003 Hawaii International Conference on Systems Science for helpful suggestions.
We also appreciate input on this research offered by Norm Chervany, Eric Clemons, Rajiv Dewan, Paul
Johnson, Rajiv Sabherwal, Jan Stallaert and Chuck Wood. A companion piece to this paper is found in
Au, Y. A., and Kauffman, R. J., “Information Technology Investment and Adoption:
a Rational Expectations Perspective,” in R. Sprague (ed.), Proceedings of the 36th Annual Hawaii
International Conference on System Sciences, Hawaii, HI, January 2003, IEEE Computing Society Press,
Los Alamitos, CA, 2003.
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1
INTRODUCTION
The Economics literature considers such aspects as post-adoption benefits [e.g., Jensen, 1982],
technology costs [e.g., Stoneman and Ireland, 1983], and network externalities [e.g., Farrell and Saloner,
1985; Katz and Shapiro, 1985, 1986; Choi and Thum, 1998] in analyzing the timing of new technology
adoption by firms. However, in most cases, these factors are assumed to be known based on certain
expectations of the economic agents (i.e., firms). Unfortunately, there has been little discussion on how
firms reach their expectations about the value of an economic variable such that they are motivated to
make a particular technology adoption decision.
Information systems (IS) researchers have focused on the role of network externalities, among other
issues, in the adoption of information technology (IT). Using a hedonic price model, Brynjolfsson and
Kemerer [1996] examine the market of microcomputer spreadsheet software and find that network
externalities significantly increased the price of spreadsheet products. This indicated that the adopters
and users were willing to pay more because they expected an increase in the value of the product as the
number of users increased. Kauffman et al. [2000] present a finding in an empirical study on shared
electronic banking networks and suggest that—due to the network externalities—firm adoption
decisionmaking is influenced by the expected size of the shared network. In addition, due to individual
strategic positions, bounded rationality regarding the potential of the technology in the changing
marketplace and different levels of capacity to process information, firms typically have heterogeneous
perceptions of the business value of a given technology that they are considering adopting. More
recently, Au and Kauffman [2001] examine the adoption of electronic bill presentment and payment
(EBPP) technologies in financial services. The authors show that depending upon the expected level of
network externalities, billers may decide to adopt the existing technology now rather than wait for the
next technology to come to market, even though most adopters expect that the next technology will be
superior to the current one.
Taken together, this research shows the importance of expectations, in addition to network
externalities, in the development of theories of technology adoption. This is in line with Shapiro and
Varian [1999, p.181], who maintain that “…success and failure [of a technology product] are driven as
much by consumer expectations and luck as by the underlying value of the product.” However, how
potential technology adopters (including firms and consumers) reach a certain level of expectations has
not been fully understood.
This paper attempts to fill this gap by offering a perspective motivated by the rational expectations
hypothesis (REH), which was first formulated by Muth [1961]. Although REH has since been widely
used in other areas of microeconomics and macroeconomics, and notwithstanding the fact that rationality
is commonly assumed in IS/IT economic analyses, we have not yet seen this particular theory used in
2
technology—particularly IT—investment and adoption research. Our approach can therefore be seen as a
first attempt to bring rational expectations economics to the IS field and use the theory for understanding
the complex issues of IT adoption. With this central perspective in mind, we examine three research
questions in this paper. First, why are different firms that initially have heterogeneous expectations about
the potential value of an information technology eventually able to arrive at contemporaneous decisions to
adopt the same technology, creating the desired network externalities? Second, what sort of model might
be required to represent such settings, and provide a more complete understanding of the inner workings
of the process that eventually leads to the bandwagon adoption? Third, under what conditions will
observed adoption behavior materialize that is consistent with our rational expectations theory? Being
able to understand will also shed light on the conditions that adoption inertia will take over in the
marketplace.
Our analysis will be based on an important assumption: that homogeneous firms tend to prefer to
adopt the technology in the same period (up to the limit of their bounded rationality), in order to be sure
that they will enjoy the resulting network benefits. To this end, we develop a model in which all potential
adopters as well as the technology supplier—as economic agents—perform adaptive learning, and adjust
their forecast rules as new data become available over time. Our analysis of the resulting equilibria is
motivated by the works of Bray and Savin [1986], Fourgeaud et al. [1986], and Evans and Honkapohja
[2001], and suggests the kinds of outcomes that may be observed in the marketplace.
Our adaptation of the REH to the IT adoption context will allow us to treat the technology adoption
issues using a perspective that is based on a longer time horizon. The inclusion of the bounded rationality
notion represents well what we know: that IT adoptions are generally complex in nature due to the
continuous development of the technology and, as a result, managers need some time before they can
really decide what to do with any new technology. Many IT adoption decisionmaking processes therefore
can be seen as an ongoing process that involves long observation in the marketplace rather a quick profitmaximizing decision. We believe this represents the actual challenge that managers face in their IT
adoption decision process in the real world. Consequently, we offer a new approach to the better
understanding of the IT adoption issues.
LITERATURE
The Rational Expectations Hypothesis (REH) has attracted as many supporters as critics since it was
first formulated by Muth in his 1961 seminal article [Muth, 1961]. Its most well-known applications are
found in the works of Lucas, Sargent, and others in the early 1970s (e.g., Lucas [1972, 1973, 1975],
Sargent and Wallace [1976]) on the new classical explanations of output and inflation. The REH makes
some rather strong assumptions and, as a result, is very different from another popular concept called
3
“adaptive expectations”. In this section, we present the contrast between the two concepts to highlight
the key assumptions in the REH. We then introduce the notion of “adaptive learning,” which is based on
REH but considers economic agents’ bounded rationality. (To support our readers’ understanding of the
new concepts that we are introducing from an area of economic theory that is new in IS research, we
include a table of definitions for the primary terms and concepts that are drawn from rational expectations
economics theory. See Table 1.)
Table 1. Definitions of Key Terms from Rational Expectations Economics Theory
CONCEPT /
TERM
Rational
Expectations
Hypothesis
(REH)
Adaptive
Expectations
Bounded
Rationality
Adaptive
Learning
Perceived Law of
Motion (PLM)
Actual Law of
Motion (ALM)
Rational
Expectations
Equilibrium
(REE)
DEFINITION
A theory formulated by Muth [1961] that suggests that economic agents form their
expectations on the basis of the “true” structural model of the economy in which
their decisions are made, and that on average, these expectations are essentially the
same as the predictions of the relevant economic theory.
A hypothesis that states that in any one period, expectations are revised (linearly)
in light of past errors in expectations [Pesaran, 1987].
Recognizes the limited cognitive capacity of humans in decisionmaking when they
face problem complexity under the constraints of time and lacking information.
A framework that is based on the rational expectations hypothesis, which assumes
that economic agents know the true equilibrium structural relations of the economy
but—due to bounded rationality considerations—are allowed to learn the actual
values of the parameters in the equilibrium relations. Adaptive learning is also
known by the term “boundedly rational learning” [Pesaran, 1987].
The working model of the stochastic process that generates the equilibrium
condition that economic agents believe will occur. This reflects their perception
of the dynamics that govern and lead to the relevant economic outcome. The
working model may not have the correct parameter values, which agents must
learn.
The actual stochastic process that governs and leads to the economic outcome (in
this case, technology adoption) that is under consideration. To know the actual
stochastic process, agents must learn the values of the model parameters.
An equilibrium condition characterized by three main features: (1) all markets
clear at equilibrium prices; (2) every agent knows the relationship between
equilibrium prices and private information of all other agents; and (3) the
information contained in equilibrium prices is fully exploited by all agents in
making inferences about the private information of others [Pesaran, 1987].
Adaptive Expectations versus Rational Expectations: Basic Concepts
Expectations are typically related to past information available to economic agents or firms. A
classic example is a problem that involves a lag of production, where a farmer must estimate the price of
corn “tomorrow”—at which time the corn will be harvested—in order to decide how much to plant
“today.” Nerlove (1958) uses an “adaptive expectations” model to show that farmers’ planting decisions
depend upon and are adapted to the prices they expect to receive when the crop is marketed. In turn, the
actual price for the crop depends on the amount finally harvested and the current level of demand. A
4
a
basic model is formulated with respect to period t, in which the corn price anticipated by a farmer p t is
given by:
p ta = p ta−1 + η ( p t −1 − p ta−1 )
(1)
where pta−1 is the anticipated price in period t −1 (as of period t − 2 ), p t −1 is the actual spot price in
period t −1, and 0 < η < 1 .
Grossman [1981] reminds us that this is a distributed lag model with the form:
∞
pta = η ∑ (1 − η ) j pt − j −1
(2)
j =0
He further maintains that it is essential to put some a priori restrictions on the form of the lag structure.
One restriction, as suggested by Muth [1961], is that the distributed lag should be “rational.” This means
that if a particular stochastic process generates a sequence of actual prices {pt }t = −∞ , then the anticipated
t = +∞
price in period t (i.e., pt ), as of period t − 1, should be given by pta = E [ pt | pt −1 , pt −2 ,] . Therefore, if
a
the farmer knows the stochastic process, he should be able to determine the expected price for period t
based on the conditional expectation of pt given all past prices. The farmer is considered “rational”
because he utilizes all the price information to correctly compute the true conditional expectation.
Grossman [1981] provides this example to show how Muth’s rational expectations notion differs
from Nerlove’s adaptive expectations model. Suppose that the stochastic process generating {pt} is given
by:
1
pt = 
2
for t ≤ 1
for t ≥ 2
(3)
Then, following the distributed lag model in Equation 2, under adaptive expectations:
p 2a = 1,
p3a = 1(1 − η ) + 2η ,
p 4a = (1 + η )(1 − η ) + 2η , , lim pta = 2 ;
t →∞
(4)
However, under a rational expectations structure,
p2a = E[ p2 | p1, p2 ,] = 2 since p 2 ≡ 2 .
(5)
The above example illustrates that under adaptive expectations, agents will need some time before
they learn that the price has changed from 1 to 2 since all they do is look at past prices. On the other
hand, the rational expectations notion assumes that people know the stochastic price process in (3) so
they know that after t = 1 , price will have changed permanently from 1 to 2.
The Rational Expectations Hypothesis
The essence of Muth’s [1961] rational expectations is that economic agents form their expectations
on the basis of the “true” structural model of the economy in which their decisions are made. So,
5
expectations are essentially the same as predictions of the relevant economic theory: their expectations
are informed predictions of future events.
The REH equates economic agents’ subjective, psychological expectations of economic variables to
the mathematical conditional expectation of those variables. In other words, subjective expectations are,
on average, equal to the true values of the variable. Based on this, Muth suggests that we should expect
economic actors to change the way they form their expectations if the underlying economic system
changes and, therefore, should not be satisfied with adoption evaluation functions and models with fixed
expectations that do not allow for change.
Lucas [1975] interprets the REH as a hypothesis that assumes that every economic agent optimally
utilizes available information in forming expectations. He proposes the minimum mean square error
criterion for assessing the optimality of individual expectations. Using this optimality criterion,
individual agents are assumed to form their forecasts by minimizing the expectation (based on the
equilibrium probability distribution) of the forecast error conditional on the information available to them.
In this case, the rational expectations solution is based on the assumption that individuals behave
optimally, something that is consistent on the whole with traditional economic theory [Fryman, 1982].
Information Requirements and Assumptions in REH
The information requirements in REH are not unique: other theories often impose the same kind of
requirements. For example, the rational choice theory as discussed by Elster (1985) emphasizes that a
decision is not rational unless there is optimality in all of the following three criteria: (1) the choice of
action, (2) the formation of beliefs for a given set of information, and (3) the collection of information
that is relevant for the decision. Instead, what makes the REH unique is the assumption that economic
agents know the stochastic process generating the equilibrium condition. This implies that they know a
great deal about the economy. Indeed, the application of these ideas came in the context of the
development of a formal theory for agent reactions to adjustments in macroeconomic and monetary policy
variables that have been characterized by such noted economic theorists as Lucas [1972, 1975], Sargent
and Wallace [1976], and Sims [1980], among others, in the rational expectations economics literature
[Lucas and Sargent, 1981; Pesaran, 1987; Sheffrin, 1996].
However, this assumption often is considered as too strong. Why? Because it requires that economic
agents have full knowledge of the structure of the relevant models and their parameter values. It also
requires that random shocks that may affect agent expectations are independent and identically
distributed. As a result, empirical economists typically will admit that they do not know the parameter
values and must estimate them econometrically.
A somewhat weaker assumption may be more appropriate: that agents act like econometricians when
they make forecasts about the future state of the economy, in the sense that they are willing and able to
6
update their expectations about relevant parameter values on the basis of newly-received information.
This perspective introduces a specific form of “bounded rationality” which Evans and Honkapohja [2001]
call adaptive learning. When bounded rationality is considered, economic actors are assumed to learn to
use reasonable model specifications (and choose meaningful model parameters), which are often
appropriate in the resulting observed outcomes but misspecified when there is learning.
In the context of technology adoption that we discuss in this paper, we assume that the technology
supplier and potential adopters know about the economic structure (i.e., the supply and demand functions)
of the technology but must learn the parameter values that reflect each potential adopter’s willingness-topay for the technology. As we will see in the next section, the willingness-to-pay is represented by a
certain price level that the technology supplier and potential adopters must estimate.
MODELING AND ANALYSIS
Our modeling is based on the equilibrium concept, wherein we assume each of the entities (i.e.,
technology-adopting firms and technology supplier firm) in the model knows about the true equilibrium
relations of the economy that pertains to a technology that exhibits network externalities, but must learn
about the true values of the parameters in the relations. This assumption is consistent with that of
adaptive learning that is based on the rational expectations hypothesis (REH).
Figure 1 shows N potential adopters, who may initially have many different levels of price
expectations. Later, they may eventually reach the same level of expectations with respect to price. We
call this the rational expectations equilibrium (REE). These price expectations represent the willingnessto-pay of the potential adopting firms for the technology. (See Figure 1.) Figure 2 shows that the
technology supplier will learn the collective price expectations—which is indicative of their willingnessto-pay—of the potential adopters. The supplier will then adjust its own expectation accordingly in order
to reach the REE that allows the adoption of its technology. (See Figure 2). In our models, we will first
look at how the technology supplier reaches the REE. We will then discuss in the second model how the
heterogeneous price expectations of N potential technology-adopting firms converge to the REE.
Our emphasis in this paper is on the economic principle of equilibrium, and not optimization, with the
understanding that each potential adopting firm is looking at maximizing the network benefits in the
process. But they are also trying to make sure that this can actually be achieved by reaching the rational
expectations equilibrium, which is a point where all firms can be observed to have a consensus about
willingness-to-pay.
7
Figure 1. Different Price Expectations of Potential Technology Adopters in Different Time Periods
Converge to the Rational Expectations Equilibrium
Price
The “accuracywithin-an-error” due
to bounded
rationality may cause
firms to adopt in this
period despite the
fact that the REE has
not been reached.
p1,t
p2,t
A higher
precision in
market
observation
among firms
will lead to
adoption at
the REE.
p3,t
p4,t
p5,t
Rational
Expectations
Equilibrium
(REE)
p6,t
Legend:
pi,t = price for firm i in period t
p7,t
t=1
Note:
Period t
t=2
t=3
t=4
t=5
t=6
t=7
t=8
Prices reflect what firms in the marketplace are willing to pay to adopt a new technology. They may
converge to the REE from both above and below. A firm may start with a high willingness-to-pay but later
adjust it lower, based on new information it receives, and vice versa.
Modeling Preliminaries
Our model consists of N potential technology-adopting firms of the same size and one technology
supplier firm. We should emphasize that although there is only one supplier in the model, there will be
other suppliers coming into play with newer, and possibly better, technologies. As a result, the supplier in
our model cannot exercise monopoly power since the potential adopting firms will have choices. The
technology we consider exhibits the network externalities characteristics, which promise an increased
value to each adopter as the number of adopters increases. Due to their desire to maximize the value from
the network externalities, each adopter wants to be certain that the other N–1 adopters will also adopt the
same technology. This leads to our main assumption that all N potential adopters will make the adoption
decision at about the same time, i.e., when they learn that the other adopters are also ready to adopt. We
will see that this is a key assumption because the model will not reach an equilibrium until all N potential
adopters hold the same willingness-to-pay for the technology.
8
Although the above assumption may look quite strong, we should emphasize that the value N
represents only a subset of potential adopting firms that share similar interests in the technology. This
subset may contain only a few firms that would like to benchmark against each other, by learning each
other’s willingness-to-pay, to make sure that they adopt the technology roughly in unison, at about the
same time, to realize the network benefits. It may take some time before each of them reaches a “comfort
level” to make a decision. This “comfort level” is characteristic of the equilibrium in which all N
potential adopters reach the same willingness-to-pay (with the assumption that they are of roughly the
same size).
Figure 2.
N Potential Technology-Adopting Firms and One Technology Supplier Firm Converge
on the Rational Expectations Equilibrium
Price
Supplier’s Price Expectations
p1,t
p2,t
Rational
Expectations
Equilibrium
(REE)
p3,t
p4,t
Potential Adopters’
Collective Price
Expectations
p5,t
p6,t
Legend:
pi,t = price for firm i in period t
p7,t
Period t
t=1
t=2
t=3
t=4
t=5
t=6
t=7
t=8
Note: The potential adopters’ collective price expectations in each period are assumed to be the average of all price
expectations of the potential adopters in the period. The technology supplier may start by setting a price
higher than the price expectations (or the willingness-to-pay) of any of the potential adopters. However, the
supplier will learn more about the collective price expectations of the technology adopters in each period and
adjust its own expectations about the price at which it can sell its technology. A given potential adopter, on
the other hand, will also learn how much the other potential adopters are willing to pay and at what price the
technology supplier wants to sell its technology. Combined with other newly-available information, this
price expectations information will allow each of the potential adopters to adjust its price expectations in each
period accordingly. Notice that a potential adopter still may have a willingness-to-pay that is higher than the
price the supplier asks for, due to the potential adopter’s perception of the benefits of the technology.
However, this alone will not make the potential adopter adopt the technology. The contemporaneous
adoption requirement increases the likelihood that the adopter will wait until the REE is reached.
9
An alternative way of looking at the willingness-to-pay issue is to think of firms actually having
unique levels of willingness-to-pay that may be perceived in the market as being “accurate-within-anerror.” The error results from the information processing limitations that most firms have: as a result,
they may not know enough to know how to make the best estimate. This is in line with other related
economic theories for decisionmaking that discuss the problem of infinite regress [Kelly, 2000]. This
refers to the situation where economic agents start collecting information that they believe will inform a
specific decision, but then find themselves unable to stop because there is always additional information
to collect that may be relevant to the problem in hand. As a result of not having a stopping rule for
collecting information, it becomes difficult for the decisionmaker to identify when they “know” enough to
know whether to decide. Melberg [1999] points out that decisionmakers often think that they have to
recursively collect information about how much information to collect about how much information to
collect, and so on. Unfortunately, there is no limit to the number of times this kind of retroductive
reasoning can be applied. So some tolerance of error in decisionmaking is needed to avoid this problem.
Another important point we would like to stress is that all of these N potential adopting firms actually
share the same interest, in the sense that each of them would like to see the others adopt to realize the
network benefit. In this regard, the assumption that there is a free flow of information actually makes
sense. However, since each firm may have different information processing capabilities, it will take some
time before all of them will reach an equilibrium.
In our first model, we consider a multi-period scenario in which the technology supplier must predict
the price at which all potential adopters are willing to pay for the technology. The predicted price
represents the expectations on the technology supplier side. We use the market-clearing condition for
supply and demand to show that, under certain conditions, the technology supplier will be able to
eventually arrive at the correct prediction of the price that represents the willingness-to-pay of all the
potential adopters. Our second model shows how potential adopters eventually arrive at the same price
expectations under learning, despite the heterogeneous levels of willingness-to-pay they initially have.
Model 1: The Rational Expectations of the Technology Supplier
In this model, we consider a technology supplier firm that must predict the willingness-to-pay of the
potential adopters of its technology in every period t −1 in order to plan in advance for the resources (e.g.,
people, equipment) that it needs to serve the market in period t. In this context, the planned level of
supply of the technology will depend on the technology supplier’s expectation of the price at which it will
be able to sell its technology. In the period when the adoption occurs, this price is the actual price that
each of the adopters will pay for the technology. However, in the periods before the adoption actually
occurs, we assume that this price represents the average willingness-to-pay of the potential adopters. As
10
previously discussed, there can be heterogeneous levels of willingness-to-pay until an equilibrium is
reached among potential adopters. (This equilibrium will be discussed in Model 2 later in this section).
We further assume that all potential adopters—as well as the technology supplier—will be able to
observe others’ willingness-to-pay.1 In addition, we assume that the average level of the willingness-topay of all potential adopters reflects the price that each potential adopter would be willing to pay, if each
were able discover in advance the willingness-to-pay of the other potential adopters. In other words, if
each of the potential adopters (through whatever means are available in the marketplace) were able to
reveal willingness-to-pay (i.e., price) to the others, all of them will reach a consensus to purchase the
technology at the average price.
These prices will only become known to each of the agents at the end of period, by which time more
information will become available and cause each potential adopter to adjust its price. This process will
repeat until an equilibrium is reached, and willingness-to-pay levels across firms in the market converge
to a value that reflects similar value assessments. Our assumption of the ability of each potential adopter
to learn the others’ willingness to pay is quite realistic, in view of the extensive contacts that occur among
firms whose senior managers, strategic planners and IT professionals seek to get a sense of the market’s
attitude relative to the adoption of a technological innovation.
For our readers’ convenience, we list the notation that we use in Model 1, together with their
definitions in Table 2. (See Table 2. A similar table of notation for Model 2 will be presented later.)
Let us denote ptp as the pseudo-price in period t. With our use of pseudo-price, we intend to direct
the reader’s attention to the contrast between demand that will be based on the actual price that potential
adopters will pay if each eventually decides to purchase the technology, as opposed to the demand that is
revealed prior to actual adoption. In other words, the pseudo-price for a period indicates the price that
would prevail if adoptions (i.e., transactions) occurred in that period. Recall that one of our main
assumptions is that information flows freely due to the interests that potential adopting firms share,
creating the willingness to send their signals to each other either directly or indirectly, and in turn
enabling each to know others’ willingness-to-pay for the technology and therefore the “pseudo-price” in
every period prior to the adoption. However, this “pseudo-price” changes from period to period as firms
adjust their willingness-to-pay based on newly available information.
1
Realistically, the willingness-to-pay, per se, is difficult to observe. However, we assume that each of the potential
adopters will be able to utilize as a proxy some of the observable economic indicators at the firm, industry, and/or
macro level.
11
Table 2. Definitions for Notation -- Model 1
NOTATION
DEFINITION
ptp
Pseudo price in period t.
pts
Technology supplier’s price expectations estimated in period t − 1 that determines the
supply function in period t.
The intercept of the supply function
β 0s
β 0d
st
dt
X t −1
βs
δ
σ
m
n
ε td
The intercept of the demand function.
Supply for technology in period t.
Demand for technology in period t.
K-dimensional vector of observable variables in period t − 1 . X t −1 = ( X 1t −1 , ... , X K t −1 )'
Row vector of parameters ( β1s , ... , β Ks ) of exogenous variables that affect supply.
The slope of the demand function. This parameter enables us to model the demand
for the technology as decreasing in price, and vice versa.
The slope of the supply function. This parameter allows us to represent the supply for
the technology as increasing in price, and vice versa.
The intercept in the perceived law of motion relation; m=w /(1-v).
The parameter in the perceived law of motion relation; n = u / (1-v).
Factors that are unobservable or unexpected but still affect demand for technology.
ε ts
εt
Factors that are unobservable or unexpected but still affect supply for the technology.
u
u=−
v
w
εt =
1 d
(ε t − ε ts )
δ
v=−
w=
1 s
(β )
δ
σ
δ
1 d
( β 0 − β 0s )
δ
We will denote d t and st as the technology demand and supply functions in period t. Demand for the
technology in the market in period t is given by: 2
d t = β 0d − δ ptp + ε td
(6)
where δ > 0 , β 0d is the intercept of the demand function, and ε td represents factors that are unobservable
or unexpected but still affect demand for the technology. The parameter δ enables us to model the
demand for the technology as decreasing in price, and vice versa.
Just like the potential adopters, the supplier will be able to observe the pseudo-price in period t − 1 .
Moreover, the supplier can use it to estimate the expected price pts that determines the supply function in
2
The analytical derivation of our models is an adaptation of Evans and Honkapohja [2001].
12
period t. As we will see in Equation 9 shortly, the expected price pts that the supplier estimates in period
t − 1 will determine the pseudo price in period t ( ptp ). The supply function in period t is as follows:
s t = β 0s + β s X t −1 + σ p ts + ε ts
(7)
where σ > 0 . In addition, X t −1 is a vector of variables which are observable in period t − 1 and which
affect the level of supply. In addition, β 0s is the intercept of the supply function, β s is a row vector of
parameters ( β1s , ... , β Ks ) of the exogenous variables that affect supply, and ε ts represents the factors that
are unobservable or unexpected but affect the supply of the technology. The parameter σ represents the
fact that the supply for the technology is increasing in price, and vice versa.
Another interpretation of the pseudo-price discussed above is the market equilibrium price of the
technology under consideration for adoption. In market equilibrium, each potential adopter is willing to
pay this price for the technology, and the supplier is willing to sell the technology at the same price. The
market equilibrium price itself is determined by the intersection of the supply and demand curves,
represented by d t and st , respectively:
d t = st
(8)
Substituting Equations 6 and 7 (that characterize supply and demand) into Equation 8, and
rearranging terms yields following expressions:
β 0d − δ ptp + ε td = β 0s + β s X t −1 + σ pts + ε ts ,
p tp =
σ
1 d
1
1
( β 0 − β 0s ) − p ts − ( β s X t −1 ) + (ε td − ε ts ) , and
δ
δ
δ
δ
ptp = w + v pts + u X t −1 + ε t
where w =
(9)
1
1 d
1
σ
( β 0 − β 0s ) ; v = −
; u = − ( β s ) ; and ε t = (ε td − ε ts ) .
δ
δ
δ
δ
As described previously, the parameter δ enables us to model the demand for the technology as
decreasing in price, and vice versa. Likewise, the parameter σ allows us to represent the supply for the
technology as increasing in price, and vice versa.
The parameter w represents the proportional difference between the intercept of the demand curve
and that of the supply curve. The greater w is, the higher the market clearing price and quantity will be
(holding all other parameters constant). The parameter v is the ratio of the slope of the supply curve to
that of the demand curve. Any plausible economic demand and supply situation will have an absolute
value of v that is less than 1. The parameter u represents the magnitude to which the exogenous variables
will negatively affect the price. The parameter ε t , which incorporates ε td and ε ts (the unobservable factors
13
in the demand and supply functions, respectively), represents the effect of unobservable or unexpected
factors on the market-clearing price.
Analysis of the Technology Supplier’s Model
The objective of the following analysis is to show that the technology supplier will be able to learn
the potential adopters’ expectations and adjust its own expectation accordingly in order to reach a
condition that allows the adoption of its technology. We will start by recalling that pts is the supplier’s
expected price determined in period t − 1 . The rational expectations hypothesis (REH), maintains that
the expected value of pts is the optimal prediction—the best linear predictor which minimizes the expected
square prediction error—made in period t − 1 based on a set of information I t −1 , which is a Kdimensional vector of observable variables X t −1 = ( X 1t −1 , ... , X K t −1 )' , some of which may be random.
Following Fourgeaud et al. [1986], we define the optimal prediction pts as the theoretical linear regression
of ptp on I t −1 . The term I t −1 is a K-dimensional vector of observable variables, some of which may be
random. The random variables reflect the characteristics (i.e., the unpredictability) of the some of the
observed real world events that may affect willingness-to-pay on the part of firms, and hence, the
observed pattern of technology adoption decision. If we denote the optimal prediction by E ( ptp | I t −1 ) ,
then Equation 9 becomes:
ptp = w + v E ( ptp | I t −1 ) + u X t −1 + ε t
(10)
Taking the optimal linear prediction of both sides of the Equation 10 gives the following result:
E ( ptp | I t −1 ) = w + v E ( ptp | I t −1 ) + u X t −1 or
E ( ptp | I t −1 ) =
w
u X t −1
+
1− v 1− v
(11)
Substituting Equation 11 into Equation 10 gives the following:
ptp =
w
u
+
X t −1 + ε t ,
1− v 1− v
ptp = m + n X t −1 + ε t
with m =
v≠0
(12)
w
u
and n =
.
1− v
1− v
Note that Equation 12 gives a unique rational expectations equilibrium (REE): ptp does not depend
on any expected future prices. REE refers to a state in the marketplace where all acts of “learning” are
complete, in the sense that there is no incentive on the part of agents to change the beliefs they hold about
their economic environment. (In the above case there is actually no learning; therefore, it gives a unique
14
REE right away.) Pesaran [1987, p.33] maintains that a rational expectations equilibrium can be
characterized by three main features:
all markets clear at equilibrium prices;
every agent knows the relationship between equilibrium prices and private information of all
other agents; and,
the information contained in equilibrium prices is fully exploited by all agents in making
inferences about the private information of others.
We now introduce the learning aspect into the process that occurs as buyers form their willingness-topay levels for adoption the technology. When there is learning, the supplier’s prediction of price pts is
not optimal; instead it is expected to improve over time. Here we assume that the supplier believes that
pts follows the process described in Equation 11 and corresponding to the REE, but must estimate m and
n. This signifies that in forecasting the price, the technology supplier acts like an econometrician:
ptp = m + n X t −1 + ε t
(13)
Equation 13 depicts the perceived law of motion (PLM) of the firm [Evans and Honkapohja, 2001],
suggesting that the firm attempts to estimate the parameters m and n. PLM refers to the stochastic process
generating the equilibrium condition that economic agents believe in. This is the key bounded rationality
assumption. In forecasting the price, the decisionmakers in the firm act in aggregate like an
econometrician who believes that the economy has reached equilibrium. They use all available data to
estimate the parameters of Equation 13. We further assume that the supplier firm estimates m and n using
an ordinary least squares (OLS) regression of pip on X i , ( i = 1, ..., t − 1 ). At period t − 1 , the forecast is
made using the following least squares regression equation:
ptp = mt −1 + nt' −1 X t −1
(14)
The parameters mt −1 and nt −1 are given by the following formula, which is the standard formula
for least squares regression solutions:
 mt −1   t −1
 t −1


 =  ∑ Yi −1Yi '−1  ∑ Yi −1 pip 
 i =1

 nt −1   i =1
(
where Yi ' = 1
X i'
)
(15)
Convergence and Stability
Next we will see that the parameters m and n indeed converge to certain values over time and that the
convergence is stable, indicating that the supplier’s price estimate (or expected price) will eventually
match the potential adopters’ average willingness-to-pay. Recall that this is one of the important
assumptions that we made for technology adoption to occur in the first place: all potential adopters must
15
eventually arrive at the same willingness-to-pay and the technology supplier must be willing to sell its
technology at the price that all the potential adopters are willing to pay.
Bray and Savin [1986] have shown that the convergence of least squares learning (i.e., mt → m and
nt → n as t → ∞ , where m and n are the convergence values of mt and nt , respectively), will be
obtained if and only if v < 1 . To show that the convergence that characterizes the rational expectations
equilibrium is stable, we use the “expectational stability” principle (hereafter referred to as “e-stability”)
[Evans and Honkapohja, 2001]. A rational expectations equilibrium is said to be e-stable if, given a
small deviation of expectations functions from rationality, the system returns to the equilibrium under a
natural revision rule. Imposing e-stability can narrow the number of acceptable solutions, and in some,
but not all, cases there is a unique locally stable equilibrium [Evans, 1985].
The basic required concept is the mapping from the perceived law of motion (PLM) to the actual law
of motion (ALM). ALM describes the stochastic process followed by the economy if forecasts are made
under the fixed rule given by the PLM. One can think about the ALM as the actual dynamics that govern
the economic condition that is under consideration, and the PLM as the economic agents’ perception of
the dynamics. The economic agents’ perception and the actual dynamics may initially be different;
however, under adaptive learning, over time the two will get closer and eventually become the same. In
our model, we assume that the economic agents know the structure of the actual dynamics but need to
estimate the true parameters of the structure. This estimate is done through the mapping from the PLM to
the ALM. The e-stability principle states that the mapping from the PLM to the ALM governs the
stability of equilibria under learning. The e-stability conditions obtained from this mapping provide the
conditions for asymptotic stability of an REE under least squares learning. As in Equation 13, the PLM
is:
ptp = m + n X t −1 + ε t
(16)
Note that ptp in this case is the same as pts because they both denote the forecast for period t price
for the technology that the supplier makes in period t – 1.
For m = m and n = n , the PLM also will be the REE, but since we allow agents to learn, they can
have “non-rational” expectations along the way. Thus, for any value of m and n, the period t – 1 forecast
of ptp is given by:
ptp = m + n X t −1
(17)
Inserting Equation 17 into Equation 9, we obtain the actual law of motion implied by the PLM:
ptp = (w + v n ) + (u + v m ) X t −1 + ε t
(18)
16
Our interpretation of ALM is that it describes the stochastic process for willingness-to-pay levels (as
prices) followed by the marketplace, if forecasts are made under the fixed rule given PLM. Equation 18
also implicitly defines the mapping from the PLM to the ALM:
 m  w + v m

T   = 
 n  u + v n 
(19)
An e-stability condition can then be defined to determine the stability of the REE for technology
adoption under the least squares learning model. The unique REE for our model is the unique fixed point
of the mapping for T in Equation 19. The differential equation in Equation 20 represents the
“displacements” from the REE point (m, n)' over a small “notional” or “artificial” period of time τ .
d
dτ
 m  m
m
  = T   −  
n  n 
n 
(20)
The REE is e-stable if it is locally asymptotically stable under Equation 20. This means that the PLM
parameters m and n are adjusted slowly in the direction of the implied ALM parameters. The REE is estable if small displacements from (m, n)' are returned to (m, n)' under the learning rule.
To determine e-stability, we combine the two equations, Equations 19 and 20, and write the
differential equation component by component:
dm
= w + (v − 1) m
dτ
(21)
dni
= ui + (v − 1) ni , for i = 1, ... , K
dτ
(22)
The above results show that the REE is e-stable if and only if v < 1 , which is also the condition for
convergence of least squares learning obtained by Bray and Savin [1986].
These results show that under least squares learning, the technology supplier in our model will be able
to learn the potential adopters’ expectations and adjust its own expectation accordingly to reach a
condition where adoption of the technology actually occurs. The managerial implication is that in order
to be successful, a supplier that enters the market with a technology that shows the appropriate network
externalities characteristics should try to continually learn about the market and keep adjusting its strategy
based on signals from and perceptions by the potential adopters’ (i.e., the market) and other relevant
developments. The model reveals that it is possible for the technology supplier to eventually take the
adoption to occur despite the initial differences in expectations among potential adopters.
Model 2: The Heterogeneous Rational Expectations of the Potential Adopters
We will now show how the potential adopters eventually reach the same willingness-to-pay, despite
the initially different expectations they may have. Since there are N potential adopters, there can initially
17
be as many as N different levels of willingness-to-pay (represented by N different price expectations.
(See Figure 2.) Furthermore, based on the idea that price expectations of firms tend to be distributed even
for the same information set—as suggested by Muth [1961], we can presume that some sort of a
distribution of willingness-to-pay will be observed. The distribution will change as each firm adjusts its
expectations based on the newly-revealed information in each period. Such stochastic changes are
allowed by the dynamic system in our model. These different expectations are also due to bounded
rationality as each firm may have a different level of ability to access and process information. However,
all firms learn asymptotically over time to reach the rational expectations equilibrium.
At the beginning of the period t, each potential adopter i holds its own price, pi, which is formed
based on a set of available information. The price reflects the potential adopter’s willingness-to-pay for
the technology. Since the information available to each potential adopter may vary, the prices that they
hold can be different from each other. As discussed earlier, we assume that due to the desire to
appropriate the value associated with network externalities, adoption will occur only when all adopters
have the same willingness-to-pay. This can be thought of as the price at which the potential adopters are
willing to purchase the technology.
We list the notation that we use in Model 2 together with definitions in Table 3. (See Table 3.)
Table 3. Notation Definitions -- Model 2
NOTATION
DEFINITION
p
Pseudo price in period t.
pie, t
Expected price of potential adopter i for period t, made in period t − 1 .
pte
Average of expected prices of all potential adopters for period t, made in period t – 1.
p
t
ni , t −1
Vector of parameters of potential adopter i for period t − 1 .
ni , t
Vector of parameters of potential adopter i for period t.
X t −1
K-dimensional vector of observable variables in period t − 1 . X t −1 = ( X 1t −1 , ... , X K t −1 )'
u
v
εt
M
N
1 s
(β )
δ
σ
v=−
δ
1
ε t = (ε td − ε ts ) ; where ε td represents factors that are unobservable or unexpected
u=−
δ
but still affect demand for the technology, and ε ts represents factors that are
unobservable or unexpected but still affect supply for the technology.
M = E X t2 .
Number of the potential adopters in the model.
( )
18
Analysis of the Potential Adopters Model
First, we assume that each potential technology adopter is able to forecast according to the linear rule:
pie, t = ni , t −1 X t −1
(23)
Each potential adopter is allowed to arrive at different parameter estimates, however. As in the case of
the technology supplier, all potential adopters also learn from past prices, which are essentially the past
perceptions of the market’s willingness-to-pay (represented by ptp−1 ), and the observable variables X t −1 .
We further assume that the average potential adopters’ expectations in Equation 24 affect the market
price which is given by the model in Equation 25:
p te =
1
N
N
∑p
i =1
e
i, t
(24)
ptp = v pte + u X t −1 + ε t
(25)
Substituting Equations 23 and 24 into Equation 25 results in:
ptp =
N
1
v (∑ ni , t −1 ) X t −1 + uX t −1 + ε t
N i =1
(26)
To compute the coefficient vector ni ,t of the dynamic system in Equation 23, we use the recursive
least squares algorithm as follows:
ni , t = ni , t −1 + λt Ri−, 1t X t −1 ( ptp − ni , t −1 X t −1 )
(27)
The moment matrix Ri ,t is determined using the following formula:
Ri , t = Ri , t −1 + λt ( X t2−1 − Ri , t −1 ) , i = 1, , N
(28)
To generate the least squares values, the initial value for the recursive must be set appropriately.
The analysis of convergence in these algorithms is carried out by deriving the associated ordinary
differential equation as follows:
dni
v

= Ri−1 M u +
dτ
N

N
∑n
i =1
i

− ni 

dRi
= M − Ri
dτ
(29)
(30)
( )
where M = E X t2 .
The system is recursive and the above set of equations is a globally stable system with Ri → M from
any starting point i = 1, ... , N . Therefore, Ri−1 M → I from any starting point (assuming that Ri is
invertible along the path). As a result, the stability of this differential equation system is determined
entirely by the stability of the smaller dimension system in Equation 29:
19
dni
v
=u+
N
dτ
N
∑n − n
i
i
(31)
i =1
In the matrix form, the equivalent formulation is:

 u   1 ... 1

dn    v 

= o  +   o r o  − I N  n
dτ   N 


 u   1 ... 1
(32)
The coefficient matrix of this linear system has one eigenvalue of v − 1 and N − 1 eigenvalues of –1.
Therefore, it is globally asymptotically stable with each ni converging to n , provided v < 1 . The
condition v < 1 occurs when the demand curve crosses the supply curve from above, a situation in the
standard economically plausible case. This indicates that if the potential adopters and the technology
supplier both act normally in the economic sense (i.e., demand increases when price decreases and vice
versa; and by the same token, supply increases when price increases and vice versa), then the rational
expectations will reach an equilibrium that is stable under learning. When v > 1 the supply curve crosses
the demand curve from above, an economically implausible case occurs. This causes the rational
expectations equilibrium to be unstable under learning. When v = 1 the supply curve is parallel to the
demand curve, no rational expectations equilibrium exists.
DISCUSSION
The ability of all of the potential adopters in the model to eventually reach the same estimate of
willingness-to-pay is actually the primary condition that must be satisfied, since the “consensus”
willingness-to-pay is also what the technology supplier continues to observe and use as a basis for
adjusting its strategy in the context of the process that eventually leads to actual adoption. We have
shown here that it is possible for all the potential adopters in the model to reach a consensus, allowing the
technology adoption to occur. In fact, the model we use indicates that as long as the potential adopters
and the technology supplier act “normally” in the economic sense, the equilibrium will be reached with a
probability of one and it will be stable under learning.
There are cases where a potential adopter also will not act “normally” in the economic sense. For
example, a company could ignore the cost factor and adopt a new technology mainly based on strategic
decisions that aim to pre-empt the competition. Another example is when a large company can afford to
make a new technology adoption decision based on its size and market share, basically setting the
standards for the industry it is in. Clearly, as we have seen in the above analysis, the rational expectations
notion does not apply in such cases.
20
The main assumption of the REH is that economic agents know the true equilibrium relations of the
economy [Pesaran, 1987]. The equilibrium is the future state of the economy in which the technology
under consideration reaches its maturity, i.e., when the real-world benefits of the technology are
confirmed and accepted by the market. In our context of adaptive learning, where agents are allowed to
learn the actual values of the parameters in the equilibrium relations, the assumption that the agents know
the true equilibrium also holds.
For any new and emerging technology, there is a phase of over-enthusiasm and unrealistic projections
due to a flurry of well-publicized activity by technology leaders, resulting in some successes, but more
failures, as the technology is pushed to its limits. During this phase, which Gartner Research calls the
“peak of inflated expectations” [Linden et al, 2001], it is possible that self-fulfilling expectations will be
developed when a possibly false model is considered by all market participants as the true economy
relationship. The situation occurs when everyone acts as if the model is correct and knows that everyone
else believes and acts in the same way. It is also possible that only a subset of the market participants
maintains the false model. In either case, our model suggests that the adoption of a technology based on
expectations about network externalities benefits could occur prematurely, depending on how fast the
potential adopters reach the “consensus” willingness-to-pay.
This is because our model allows the set of potential adopting firms that “benchmark” against each
other to be of any size. This means, for example, that it is possible to have a small number of firms with
similar characteristics (e.g., firms in the same industry, firms serving the same geographical location
and/or market segment, etc.) sharing similar interests and beliefs in the potential of the technology. Each
of these firms in the small set will then observe the behaviors and actions—that relate to the adoption of
the new technology—of the other firms within the same set and base its own adoption decision on such
observations. The main premise is that all firms in the set desire to capitalize on the network externalities
benefits that the new technology can potentially deliver. With such “market-observing” behavior, all
firms will tend to act rationally, thus making economically plausible adoption decisions. However, as
long as all firms in the set believe in the same model, the convergence to the rational expectations
equilibrium can occur in a relatively short amount of time because of the small number of firms, resulting
in the adoption of the technology. The economic model these firms believe in may, however, be either
true or false.
As assumed, the set of firms in our model is actually just a fraction, or a subset, of the total number of
potential adopting firms. The convergence to the rational expectations equilibrium that leads to the
adoption of a technology among the firms in the subset may subsequently trigger a series of adoption
decisions for the same technology by the rest of the firms in the market. This is because the network
externalities characteristics may tip the market to favor the technology since the market may see the
21
adoption by a few firms (especially if the firms are considered to be the most informed) as a positive
signal that reinforces the private signals that each of the firms in the market has been receiving so far.
Alternatively, the signal from the adoption by a subset of firms may replace the other firms’ own private
information, causing them to ignore their own private signals, which may be dissimilar and simply follow
suit and adopt the same technology. This phenomenon is known as an informational cascade in
technology adoption, and is described in the Economics [Bikhchandani, Hirshleifer and Welch, 1992 and
1998; Zhang, 1997] and Information Systems [Li, 2003; Walden and Browne, 2002] literatures.
Whichever alternative takes place subsequently, the initial decision by the subset of firms under
consideration plays a key role in determining the succeeding outcomes, and we have seen that this initial
decision can be explained by the adaptive learning model based on the REH. Furthermore, each of the
subsequent alternatives can also be explained by the REH. Why? Because in each case the rest of the
firms in the market utilize the newly-available information (i.e., the fact that a subset of firms have
decided to adopt) to update their current formation. This new information either confirms or overrides the
existing information, resulting in one of the two alternatives discussed above. The position that each
firm takes with regard to the adoption of the technology is therefore among the most important
information. As Au and Kauffman [2003] maintain, having rational expectations means knowing about
the position of each potential adopting firm with regard to the various dimensions, and then acting
accordingly. In a dynamic adoption process, a subset of firms that adopt earlier can become catalysts in
the whole system, facilitating bandwagon adoption among the remaining firms.
The above discussion suggests that the ability of a technology supplier to quickly convince as many
potential adopters as possible of the potential of the technology and help them believe in a favorable
model is all it takes to successfully sell the technology to many firms. It will not be necessary to wait
until the technology has actually proven itself by demonstrating that it can indeed deliver the real-world
benefits as promised. In other words, a technology supplier can capitalize on the network externalities
characteristics that its technology possesses. For the prospective adopting firms, it is important to look
carefully into the model they believe in to see if it truly reflects the actual value of the technology.
Network externalities are simply not the only the criteria they should focus on.
CONCLUSION
In this paper we offer a new approach to analyzing the adoption of information technology that
exhibits the network externalities characteristics. We propose an answer to our research questions by
using the rational expectations hypothesis (REH) to explain why different firms that initially have
heterogeneous expectations about the potential value of an information technology are eventually able to
arrive at contemporaneous decisions to adopt the same technology, creating the desired network
22
externalities. We have described how different levels of willingness-to-pay of the potential technology
adopters may eventually converge and reach a consensus. We have also shown that, if the technology
supplier in our model keeps observing the signals and perceptions that the market (i.e., the potential
adopters) provides and adjusts its expected price accordingly, it will eventually reach the same price level
(at the rational expectations equilibrium) as the potential technology adopters will. Based on the
assumption that all potential technology adopters must purchase the technology at the same time, the
ability to reach the same price level is essential for obtaining the network externalities expectations. In
addition, we argue that a technology supplier can capitalize on the network externalities characteristics of
its technology and draw many adopters by making them believe in a certain model that favors the
technology.
The notions of bounded rationality and learning that we consider in our model reflect the real issues
in IT adoption where the potential technology adopters need to continuously learn about newlyintroduced technology and other relevant developments, and the technology supplier must continuously
adjust its selling strategies based on the feedback that it gathers from its potential market. In the learning
phase, the agents (the potential adopters and the technology supplier) are assumed to know the
equilibrium model but may be ignorant of the structural parameter values. They are irrational in the
strong sense of REH but can become asymptotically rational. The potential ignorance is due to bounded
rationality that will be overcome by learning over time, a notion known as adaptive learning.
Our model incorporates commonly used OLS regression expressions. We believe these are
representative of the IT adoption settings that involve the kind of learning that we consider in this paper.
The set-up can be interpreted as a linear regression model with time-varying parameters, for instance.
Other functions—such as univariate/multivariate or linear/non-linear, among others—can also be
considered for other learning situations. However, the estimates may or may not converge. If this
occurs, then the agents should carry out diagnostic checks on the model to see whether it is misspecified,
and also rely upon real world knowledge and interpretation of the applied setting. In such cases, it will
probably be appropriate that the specification of the model will be changed, with the result that the agents
will have to try to learn in the context of the new model.
In the context of the particular case of OLS regression that we use in our model, we show that all the
potential adopters and the technology supplier will eventually reach an equilibrium that is stable under
learning as long as they act “normally” in the economic sense, i.e., all their actions follow the
economically plausible supply and demand mechanism.
Muth [1961] maintains that from a purely theoretical perspective, there are good reasons for assuming
rationality; one of them is because it is a principle applicable to all dynamic problems (if true). However,
the only real test will be to examine the empirical implications of the rational expectations hypothesis in
23
practical situations. Our effort in this paper should therefore be seen as the first step towards applying the
rational expectation economics thinking to further understanding IT adoption issues when network
externalities are present. It will be interesting and important, for example, to understand what economic
variables that the potential technology adopters observe during their learning process. This will enable us
to predict the kinds of outcomes when other new technologies with similar characteristics are introduced
to the market in the future.
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