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eXPeri Ment al r esul ts and Proof of conce Pt
The concepts to validate corporate cause-and-effect hypotheses and to approximate the underlying
causal function from empirical evidence as proposed in this chapter have been implemented in the
form of a research prototype (Hillbrand, 2003, pp. 288-319). The latter has been implemented based on
a modeling environment—as previously described—provided by the metamodeling platform ADONIS
(Karagiannis & Kühn, 2002). This provides the basis for an in-depth investigation about the admissibility
of the proposed approach for real-world strategic scenarios as well as about its limitations with respect
to several problem classes. Therefore this proof of concept employs a causal system consisting of five
variables each of which is described by artificially generated time series. According to the characteris-
tics of these time series the respective CFKs are assigned to specific problem classes. Starting from a
completely interlinked causal strategy model it has to be tested, if all spuriously inserted associations
are detected and eliminated from the model. Furthermore the correct windows of impact have to be
identified. Based on this reconstructed model the approach should construct appropriate causal function
approximators which are trained subsequently. The superior prediction quality of the trained function
approximator is then tested in comparison with similar techniques.
A generating Causal System for the Proof of Concept
The causal system in Figure 6 is implicitly represented by the following functional associations:
as
=
t
N
(1;0.05)
rm
=
t
N
(1;0.05)
7
⋅
as
−
6
1
1
sr
=
0.95
+
+
−
t
−
1
+
t
U
( 0.15, 0.15)
−
+
30
⋅
as
−
23.5 6.66
⋅
as
−
5
8
t
−
1
t
−
2
(
)
(
)
(
)
(
)
cg
= −
2.5 0.25 4 sin 4 5
+
−
+
sr
+
0.2 4 sin 2 7
−
+
sr
+
1.1
rm
+
0.8
rm
+
t
t
−
1
t
−
2
t
−
2
t
−
3
U
( 0.3, 0.3)
−
+
3
∑
cg
t t
−∆
∆ =
t
1
sp
=
+
t
U
( 0.15, 0.15)
−
+
3
Where
as
t
,
rm
t
,
sr
t
,
cg
t
and
sp
t
stand for the values of the variables
average salary
,
price of raw mate-
rial
,
share of rejects
,
cost of goods manufactured
and
selling price
in period
t
, respectively. The term
ε
U (-0.15,+0.15)
stands for uniformly distributed random number within the interval [-0.15,+0.15] and ε
N (1;0.05)
represents a normally distributed random number with expected value of 1 and a standard deviation
of
0.05
.
Identification of Spuriously Inserted Cause-and-effect hypotheses
Since the generating system of causally related time series as defined above does not exist explicitly
in real-world scenarios, it is the aim of this approach to reconstruct the structure of the causal model
as shown in Figure 6, to identify the appropriate time lags and to approximate the functional depen-
dencies. The basis for the application of this approach is a rudimentary causal strategy model which
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