current quarter. This provides a measure of an indirect network externality because the larger the total number of complementary goods available, the greater the
opportunity to purchase compatible software. Techtel’s data provides a measure of the percentage of members who adopted complementary goods for Windows or
DOS operating systems. Both of these measures were based on the average percentages for the two standards DOS and Windows. For instance, if 25 and
35 of the panel adopted complementary goods for the DOS and Windows operations systems, respectively, then the total indirect network externality for that
quarter would be at the average of 30.
Keep in mind that we are measuring externalities at the product market not operating system level. By doing this, the variable provides a measure of how
important compatibility is as a whole. The trade-off is that we are not distinguish- ing between the relative degrees of externality for each operating system. However,
this approach is consistent with other research Gandal, 1994; Saloner and Shepard, 1995; Brynjolfsson and Kemerer, 1996. We have operationalized the independent
Y-variable measures as follows:
Complementary goods average of firms who adopted complementary Y
1
goods for either Windows or DOS during the current quarter Installed base average of firms who adopted either Windows or DOS
Y
2
in the previous quarter.
6. Analysis and findings
Data on 128 organizations covering 25 quarters of Lotus Freelance software adoptions were analyzed using the GEMCAT II procedure. Preprocessing of the
data was necessary to prepare it for use by the GEMCAT II program. First the data were standardized so that estimated construct parameters could be compared
Oliva, 1991. Since the data are measured over time, a linear constant was added to each score so all numbers would have positive values. The standard practice of
taking log transforms to deal with time related effects in the data Burns and Wholey, 1993 was also performed. Finally, a standard correlation analysis on the
prepared data set was run to examine colinearity among the indicators.
Given that within measure colinearity was relatively high, we tested several different models fully expecting to use a reduced set of the original variables
identified. Ultimately, we found that the best model used the following three indicators X
1
1 = relative awareness, Y
1
1 = complementary goods, Z
1
1 = rela- tive adoption with a Z offset. In order to provide a more rigorous test of the cusp
model, we also ran compared the results against linear regression and fold catastro- phe models using the same indicators. The data were fitted using version 1.3 of
GEMCAT II Lang et al. 1999, yielding the average squared difference FN =
45 R
. Lange
et al
. Structural
Change and
Economic Dynamics
12 2001
29 –
57
Table 1 GEMCAT II results for the cusp model
Z-Mean SE
Bias P\0
Indicator measures Z-Coefficient
Estimated coefficient Mean
0.8547 0.0068
− 0.0015
0.8600 0.0073
X
1
1.0705 0.0058
− 0.0100
1.0000 0.0461
3.7621 Y
1
0.1733 3.9782
0.1833 –
0.0000 0.0000
1.0000 –
Z
1 a
1.0000 1.0000
− 0.0161
0.0000 0.0465
− 8.0538
− 0.3747
Constant −
0.3586 −
7.7068 df1
df2 Pseudo-F
Pseudo-R
2
0.99967 22
2 33294.354
a
Z
1
parameter fixed At 1.000 as per discussion in: Oliva et al. 1987.
Table 2 Wilcoxon Friedman tests
Cusp model Linear model
Fold model 1.56
Average rank sum 2.00
2.44 Friedman tests = 9.680
Kend. Coefficient = 0.194
0.0000236 between the actual and the predicted Z. Note that a perfect fit implies that F in Eq. 6 equals 0. The corresponding Pseudo-R
2
index of fit for the cusp was 0.99967, while the residuals were approximately normally distributed. It would
seem difficult to improve on this fit and indeed the linear model and the fold catastrophe each containing the same number of parameters as the cusp showed
lower R
2
values. Specifically, the linear regression model produced an R
2
value of 0.985. However, observations 1 and 13 were outliers and observation 1 had large
leverage. Also, the fold catastrophe produced a Pseudo-R
2
of 0.99752, but again two outlying observations were evident.
Because all three formulations provided high fit indices, we wanted to know if the differences across the three models were statistically significant. If not, it is arguable
that using catastrophe theory is not worth the effort. Therefore we analyzed the squared residuals of the three models using Friedman’s non-parametric test for
multiple groups as available in SPSS V7.0. The models show significantly different fit x
2 2
= 9.680, P B 0.008, 2 sided and the average ranks shown in this Table 2
confirm the ordering of the R
2
values. Additional pairwise Wilcoxon’s tests over
Fig. 3. Streco 190
Fig. 4. YZ Planar view of organizational adoptions.
the squared residuals not shown indicated that the cusp significantly outperformed the linear model Z = 4.671, P B 0.001 as well as the fold catastrophe Z = 5.086,
P B 0.001. Finally, Fig. 3 provides compelling evidence for arriving at the same conclusion as the cusp has no outlying residual values, but, as pointed out earlier,
the other models do. In other words, the cusp fits all observations whereas the linear model and the fold cannot deal with at least two of the 25 data points. This
is a significant point in favor of our cusp catastrophe formulation that becomes even more compelling when the market adoption tracks are examined in Fig. 4, Fig.
5, and Fig. 6 below.
Given the relative merit of the cusp model in this case, we now look at Table 1 for the GEMCAT II estimates. Note that the indicators are listed in the first
column, followed by their weights in the second column ‘Estimated Coefficient’. Substitution of these weights into Eq. 5 yields the following cusp: Z
1
− 0.3586
3
− 0.0073X
1
− 0.1833Y
1
Z
1
− 0.3586 = 0.
Table 1 further shows the average bootstrap values ‘Mean’ and standard error ‘SE’, which can be used to obtain standard i.e. parametric tests of significance of
the indicator weights ‘Z-Coefficient’ and ‘Z-Mean’. Although such tests are sometimes appropriate, we prefer the bootstrap values listed in the last column
‘P \ 0’ as these provide non-parametric tests of significance Note: 500 replica- tions were used. According to this criterion, the weight of the Y
1
indicator Complementary Goods is statistically significant P B 0.01, whereas that of X
1
Relative Awareness is not P \ 0.13. Thus, networks externalities have the greatest impact on the adoption process, a result that is consistent with economic
theory Farrell and Saloner, 1985; Katz and Shapiro, 1985. The latent constructs calculated by the GEMCAT II procedure are given in
Table 3 and their plots are shown graphically Fig. 4, Fig. 5 and Fig. 6. Each of the three possible planar combinations of the latent dependent and independent
variables is shown. Fig. 4 and Fig. 5 depict the YZ and XY variable planes,
respectively
4
The points in the adoption trajectory are labeled in historical sequence by quarter from 1 to 25 for convenience.
Fig. 4 shows the movement in the independent variable YZ-plane with a parabolic projection superimposed for reference i.e. a sideways view. DOS has a
small advantage in the first quarter, but it is not until after the fourth quarter that it starts to get established. During this early period network externalities are low
and the surface is relatively flat. As network externalities increase, the surface bifurcates, and the trajectory moves downward locking DOS in as the standard.
Between the 13th and 14th quarter there is a major discontinuous shift in the market, and a bandwagon of some 60 firms adopt Windows version of the software
in the 14th period. In order to make this purchase the Firms must have already converted to Windows or done so at the same time. Note that externalities continue
to increase through the remaining periods as shown in Fig. 4. The shift of 60 firms represents about 47 of the sample firms. While 60 firms is not directly translatable
into total U.S. organizational sales of Freelance for Windows, it is a substantial
Fig. 5. XY Planar view of organizational adoptions.
4
Note how well the trajectories match the expected movement described by the dotted lines in Figs. 6 and 7. The lines show the a priori adoption path expected for a new market, where a given standard
evolves, dominates, and is eventually supplanted by a competitor.
one-time shift that reasonably mirrors historical information regarding Lotus’ decision to ultimately move forward with a Windows-only version and abandon the
DOS version. Fig. 5 presents the same data from a different perspective. In Fig. 5 DOS develops an initial benefit advantage which tends to get locked in as network
externalities increase user base expands. However, there is a shift in benefits between periods 13 and 14 in favor of Windows, and there is a sudden shift to the right, which
crosses the right-cusp boundary signaling the switch away from DOS. The behavior shown is consistent with the sales information at the time Windows 3.0 and 3.1 were
taking over the market. Note that after the switch both benefits and network externalities increase, but that the increases in network externalities are significant
in comparison to the rather small gains in benefits. This would be expected in a market where network externalities are growing in importance.
Fig. 6 shows movement from the perspective of the ZX-plane. It shows why the fold model did so well in fitting the data. The figure shows a fold catastrophe, which
is not surprising given the underlying structure of the basic catastrophe models described in the literature Thom, 1975; Zeeman, 1976. Taken together, Fig. 4, Fig.
5 and Fig. 6 present a consistent theoretical and empirical picture of the market as we know it at that time.
Turning to the impact coefficients we see that the coefficients of X
1
and Y
1
had values of 0.0073 and 0.1833, respectively. Since the data were standardized, we can
compare the impacts of these two coefficients as is shown in Oliva et al. 1987. It is not surprising that the network externality measure dominates the benefit measure.
In markets where compatibility is important, the firms are better off if they are on the same standard, even if there are only modest benefits. When network externalities
matter, it changes the shape of the diffusion curve, and we expect that the impact coefficient of the network externality measure would dominate other measures. Of
the various variable combinations tested, it is not surprising that awareness turned out to be the best measure of costbenefits. This makes sense since awareness can
be a proxy for external influence as mentioned earlier. Norton and Bass 1987 note that technological generations can differ in susceptibility to external influence, which
can affect the speed and breadth of diffusion. Additionally, the result is consistent with the marketing literature on diffusion, and more broadly with marketing’s
hierarchy-of-effects assumptions see, e.g. Kotler, 1997. It appears that in this study as awareness increases it provides a sense of security regarding the adoption of the
new standard. Finally, the result supports Farrell and Saloner 1985 assumption that whatever a firm’s decision is, it wants other firms to make the same choice.
Similarly, we are not surprised that of the variables tried Y
1
complementary goods provided the best results. For software products operating system software compat-
ibility is the critical issue. Apple Computers has suffered in the market because of a lack of software titles relative to the vast numbers of DOS, and subsequently,
Window compatible products that were available.
The forgoing results clearly illustrate the efficacy of using the catastrophe theory models for examining firm adoptions in situations where competing standards are
at issue. We believe that they add to the literature by providing a more detailed look at the dynamics involved in such processes.
7. Conclusions
