as products move through the stages of the product life-cycle Kotler, 1997. He argues that this is the result of different adopter types, with different characteristics,
entering the market at different times Oliva, 1994. Initially, ‘innovative adopters’
1
pay a premium to be first and help firms recover their development costs. But innovators often use different versions of the formats offered. Given their small
numbers, they do not determine the standard by themselves. Also, complementary goods and post-purchase support is limited, since vendors have no real incentive to
join the technological community given the small installed base Teece, 1986; Rosenkopf and Tushman, 1994; Wade, 1995. However, as the product life-cycle
progresses, subsequently larger adopter segments enter the market picking the product that is perceived to be better. Over time a standard is settled on by the
newly evolving technological community
2
. At this point new adopters will join the network, thereby strengthening the hold of the standard.
In time, a challenger may emerge that promises better benefits. The decision to stay with the current standard or switch to a new standard will become inherently
risky for firms. This choice introduces chaos into the structure of the technological community because it creates a dilemma for organizations as they struggle to
answer two crucial questions identified by Rosenkopf and Tushman 1994. They argue that adopting firms must worry about the following: 1 ‘What if we adopt
or switch to a new standard and no one else does?’; and, 2 ‘What if we do not adopt or switch to the new standard and everyone else does?’ Hence, when
externalities are large, the competing standard choice becomes a sort of zero-sum game. This produces an instability in the market that can result in a sudden
bandwagon shift to the new standard if the benefits for making the switch are significant enough.
Using the firm adoptions, costbenefits to switch, and network externalities, it is possible to conceptualize the situation in the form of a catastrophe model of firms’
adoption behavior market behavior. In the sections that follow we present the description of the model, the approach used to estimate the model, a description of
the data, how the variables were operationalized, and an analysis of the findings with conclusions.
2. The catastrophe model
We assume that catastrophe modeling is not new to this audience. We note that economists have used catastrophe theory to examine the following topics, to name
1
The concept of an ‘innovative adopter’ is taken from the marketing literature which categorizes buyers i.e. product adopters by category depending on their characteristics. For example, Innovators
purchase first as opposed to Laggards who enter last in terms of the product’s life-cycle Kotler, 1997.
2
This view is also supported by organizational theorists who describe technological change evolving over time as a process of variation, selection, and retention Tushman and Anderson, 1986; Rosenkopf
and Tushman, 1994.
a few: the business cycle Varian, 1979; an extension of the Phillips Curve Fischer and Jammernegg, 1986; the stability of stock exchange behavior Zeeman, 1974;
and a model of bank failures Ho and Saunders, 1980. In this paper, the use of the cusp model is suggested as one way to examine jump behavior from a different
perspective. This effort is an attempt to get around the more standard modeling assumption that the underlying economic behavior results from smooth decision
rules. Hence, we recognize difficulty of modeling jump behavior, while recognizing there are endogenous decision rules vis-a´-via´ the process. In short, we present the
canonical form of the cusp model in Eq. 1 below as a reasonable way to view the market, because the observed behavior meets the expected qualitative requirements
for the use of such models. As such, the equation represents another way to view market behavior, rather than a definitive description of the underlying economic
processes. To the degree our results are consistent with the existing literature, we are adding one more view of a very complex process.
Fig. 1 presents a description of a catastrophe model using the aforementioned three variables Oliva, 1994. Movement occurs on the curved portion of the model
shown in Fig. 1. Changes in the control or independent variables X — rightleft movement, and Y — backfront movement cause changes in the behavior or
dependent variable Z — vertical movement. If Y is low, smooth changes in Z occur in proportion to changes in X as shown by examining the travel of points A
and B in Fig. 1. When Y is high past the singularity changes in X produce
Fig. 1. A catastrophe model of completing high-technology standards.
relatively small changes in Z until a threshold is reached when there is a sudden discontinuous shift in Z. This is depicted by the path from points C to D in Fig. 1.
Note, that a reversal in X back to the point of the shift in Z, will not cause Z to return back to its original position, since X will have to move well past to cause Z
to shift back. This is shown by the movement from point D to E. The locus of shift points is defined by the cusp points in the figure. The various moves on the surface
are characterized by five qualities that Thom 1975 described as: divergence, catastrophe, hysteresis, bimodality, and inaccessibility, which are briefly reviewed in
the appendix. The canonical form of the basic model in Fig. 1 is given by Eq. 1 below,
Z
3
− X − YZ = 0,
1 where the dependent variable is Z, and the independent variables are X, Y. While
the cubic is basically simple, the model’s implicit term provides difficulties from an estimation standpoint Oliva et al., 1987 since it generates an area of overlap which
is both multivalued and discontinuous.
2
.
1
. Dependent 6ariable In the present conceptualization, the dependent variable Z represents the percent
of firms choosing one of two standards, where one choice is the old or current standard and the second choice is the new or competing standard. The number of
firms adopting either choice depends on the X-level of costbenefits resulting from abandoning the old standard for the new standard, when Y-level of compatibility
is required or desired in the market by firms. Unlike more standard approaches, the model has an area where bimodal response is possible from a given independent
variable pair i.e. a given X,Y pair can have two different Z-values associated with it. One of the Z-values representing the distribution of firms at the old technology
standard, and the other Z-value representing the number of firms at the new standard which is represented by the overlap area of Fig. 1. It is also this area of
the model that gives it the ability to describe a wide variety of interesting behaviors like bandwagons, hysteresis lags in adoption, first mover advantages, or a
predispositions towards a give standard. Determination of which value of Z is the appropriate one to use in a given situation is made by examining the history or
trajectory of the market Zeeman, 1976. Hence, once you have a identified a historical point for the market, knowledge of the time series from that point
forward enables you to resolve any ambiguity about which of two competing standards the market adopted or will adopt
3
. There is no restriction on the movement of firms, though in practice there is a tendency to move only in one
direction with regard to technology. They may move back and forth between the old technology standard and new technology standard depending on changes in
benefits and network externality level. An example of a situation where there has
3
We arbitrarily define the market as having ‘no standard’ when the distribution of firms is at 5050, the market is at the ‘new standard’ if X \ 0.50, and the market is at the ‘old standard’ if X B 0.50.
been a retreat of sorts is with packaging in fast-food establishments. For environ- mental reasons McDonalds, Wendy’s, Burger King and other major vendors have
replaced plastic food containers with paper moving back to the old packaging standard. In the approach used in paper, there would not be a problem with such
a switch back as there would be with other modeling techniques.
2
.
2
. Independent 6ariables The X-variable represents the costbenefits that accrue from switching to the new
or competing technology standard. In situations where no externalities are present and costbenefits are accrued from switching are zero, firms are equally divided
across the two technology choices. Like previous studies that have applied a benefit approach to the competing technology-product standards issue, we assume that all
adopting firms have similar benefit functions over time Farrell and Saloner, 1985. For high-technology product standards, adoption benefits are usually framed in
terms of perceived technical superiority, ease of use, and manufacturers reputation Farrell and Saloner, 1985; Katz and Shapiro, 1985, 1985; Arthur, 1989.
The Y-variable represents the degree of externality in the marketplace. Small values of Y indicate low levels of network externalities exist or are desired, while
large vales of Y indicate high levels of network externalities exist or are desired. The Y-variable is called the splitting factor, because as Y moves out from the origin, a
critical point is reached where the surface bifurcates. Prior to this point, no adoption bandwagons are expected to occur, while after this point, only adoption
bandwagons are expected to occur. One implication of the model is that the size of any potential bandwagon is directly associated with the level of network externali-
ties desired or existing in the market.
2
.
3
. The response surface The response surface is the curved portion of Fig. 1. Vertical and horizontal lines
have been added for the purpose of helping orient the reader to the location and direction of the three axes. Location of the origin is at the back middle of the
surface. Values of Y increase from back to front, with low-externality represented at the back of the diagram, and high externality represented at the front. Changes
in X values are represented by horizontal movement, such that ‘negative’ benefits costs for switching to the new technology are on the left and ‘positive’ benefits are
on the right. The percent of firms adopting the technology standard is represented by vertical movement in the figure. At the bottom left front part of the surface
bottom sheet no firms are adopting the new technology standard, while at the right front part of the surface top sheet all firms have adopted the new standard.
Beyond the threshold value, firms will only adopt the competing standard. The locus of bandwagon threshold points is identified by a cusp which has been
projected onto the XY-plane for easier visualization. This is the set of points at which bandwagons will occur for given X,Y combinations. By restricting Y-values
to high values, the model produces behavior described in the literature see, e.g.
Fig. 2. Planar views Slices of the ctaatrophe model.
Farrell and Saloner, 1985. That is, network externalities are high and firms will only shift to the new standard in bandwagons when benefits are sufficiently high
enough.
2
.
4
. Model dynamics Fig. 2, panels A, B, and C, respectively, show three slices of the ZX-plane for
low, moderate, and high Y levels, while panel D presents a top down projection of the surface onto the XY-plane. When the market prefers choice over compatibility
low Y-values, the adoption function is relative flat as shown in Fig. 2A. In this case the market is relatively indifferent and we would expect the distribution of
firms to be in the neighborhood of the median i.e. near 5050. Points A and B in Fig. 1 trace changes in costbenefits X-values for low Y-values, which corresponds
with Fig. 2 panel A.
If the market wants compatibility, network externality increases, and both the shape and vertical dimensions of the adoption function change. Fig. 2B depicts the
situation at moderate network externality levels. The emerging S-shape implies that as Y increases, the firm adoption distribution moves increasingly away from the
median, as firms favor one standard over the other. In the typical situation switching from old to new, when benefits increase past the benefit-neutral posi-
tion, increasingly more firms are willing to switch to the new standard for smaller additional benefits.
When the market desires high compatibility, then most of the firms will be at one standard or the other. This phenomenon is depicted by the pronounced S-shape
more like Z-shaped bifurcation of the surface. At this point the firm adoption ratio approaches 0, 1 or 1, 0 in favor of either the old or new standard Fig. 2C
depending on which provides the better benefits. The S-shape has now become very pronounced as has the area of overlap. Depending on which standard is dominant,
movement to the benefit-neutral position from a benefit-extreme does not cause firms to switch to the alternative standard. In the typical situation, firms will not
switch from the old standard to the new until x ] x. In cases where switching back to the old is possible, this will not occur unless benefits are significant in the reverse
direction i.e. x 0 x. The locus of x and x forms the benefit thresholds identifying where bandwagons will occur for given combinations of network
externalities and costbenefits as shown in Fig. 2D. Points C, D, E in the Fig. 1, illustrate such movement when externality levels are high. At point C, there is little
willingness to switch from the old standard. If X continues to increase, eventually a point is reached x ] x where benefits to switching are significant and a
bandwagon occurs as a group of firms shifts to the new standard at point D. The number of firms that switched is measured by the vertical distance between the
bottom and top sheets of the surface. However, in order to return to the old standard, the costbenefit value must go back past x to x for the system return to
E. This will only occur when there are high negative benefits costs from being away form the old standard. The lag in switching represents the hysteresis effects
inherent in the process and reasonably represents the kind of inertia found in actual markets.
Firms can be located at one of two states in the overlap area. In part, this captures the stickiness in the market and reflects the unwillingness of firms to leave
the standard they are currently at when network externalities are high. This is also consistent with the nature of bandwagons discussed in Farrell and Saloner 1985,
p. 76. Boundaries width of the bandwagon zone defined by the cusp vary in size with the level of network externality in the market as depicted in Fig. 1 and Fig.
2D. When network externality increases in the market, the width of the bandwagon zone increases, as does the vertical distance between the sheets. The large number
of adoptions helps the new standard by providing a ready-made network of sorts. It also helps insure that a minimum critical mass exists to cover the degree of
network externality needed in the market to establish the standard.
The expected track of firm adoptions in nascent markets is shown by the dotted line in Appendix Fig. 7 and Fig. 8. The two figures show the same trajectory from
different perspectives. Both depict how one product, which has a small costbenefit advantage, emerges as the standard, then subsequently loses it to a competitor after
the market has developed. In Fig. 1 and Figs. 6 and 7 in the appendix, the emerging dominant standard F provides slightly different costbenefits vis-a´-vis G. That is, F
is at x \
Dx and G is at x
B Dx, where Dx is a small change in benefits. Assuming
that firms favor F over G, this slight initial difference in position between F and G gets magnified as network externalities grow. This drives F and G farther apart as
shown in Figs. 1, 6 and 7. Interesting market examples of this behavior are provided by the AppleATARI competition in the early 1980’s, and the VHSBETA
competition in VCR’s. While the AppleATARI battle is more interesting, the VHSBETA competition is the most often cited. Conventional wisdom argues that
in the VCR’s the VHS versus BETA format ‘war,’ the small initial advantage of a 3 versus 2.5 h recording capability ultimately resulted in more consumers picking
VHS over BETA. Since American football games run around 3 h, only VHS allowed them to be taped in their entirety. This led to more software rental movies
being available in VHS format; which, in turn, led new consumers to pick VHS over BETA as they came into the market.
In time a better competitor may enter the market G to challenge F in the now
developed market. Since the market now has high network externalities, it must provide benefits in excess of the threshold value x, for firms to switch. If it does,
then the firms will shift in a bandwagon to the new competitor G, as shown in Figs. 6 and 7.
3. Estimation issues
