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propose an approach (PC-algorithm) to distinguish spurious associations induced by a common cause
from genuine causation:
Theorem 2 (Controlling for third variables):
One can assume a relation X → Y to be causal if and
only if the time series of the potential effect Y incorporates not only patterns of its potential cause X
but also those of the predecessors P (i.e. causes) of X in the cause-and-effect model. If X and Y as well
as P and X are informationally redundant but P and Y are not, an unknown third variable U rather than
a causal relation must be assumed to induce the informational redundancy between X and Y.
As a consequence the patterns of
P
are reflected within the time series of
X
but they are not passed
on to
Y
due to the absence of a genuine cause-and-effect relation
X
→
Y
.
A basic tool for the analysis of these assumptions within causal graphs is the concept of conditional
independence: Two variables
A
and
B
are conditionally independent given a set of variables
S
AB
- written
as
(A
⊥
B | S
AB
)
- if
A
and
B
are informationally redundant but if the impacts of
S
AB
on
B
are eliminated,
this property vanishes. Therefore
S
AB
is said to “block” the causal path between
A
and
B
.
Applying this concept to the above theory, spurious associations between a potential cause
X
and a
potential effect
Y
can be ruled out by the following observations:
• There exists a minimal set of blocking variables
S
PY
causing conditional independence between
any predecessor
P
of
X
and the effect
Y
, denoted as
(P
⊥
Y | S
PY
)
.
•
X
is part of the set
S
PY
.
The theory to detect third variable effects as outlined in this chapter is implemented by the IC
4
or PC-
algorithm. For reasons of lucidity, this chapter dispenses with a detailed discussion of these procedures
but refers to the appropriate literature (Pearl & Verma, 1991; Hillbrand, 2003, p. 198).
Summarizing this approach, the mapping of nomothetic cause-and-effect hypotheses by decision
makers represents a prerequisite for their proof as well as the first causality criterion. The second and
third condition for causality - informational redundancy and temporal sequence - are tested by analyz-
ing the cross correlations between the prewhitened time series of the respective variables connected by
a cause-and-effect hypothesis. To rule out a third variable inducing informational redundancy between
two lagged variables, this analysis is completed by the application of the IC-Algorithm as outlined above.
Only relations which pass all these tests satisfy the necessary causality conditions and are therefore
said to be genuinely causal.
aPPro XiMation of unknown causal f unctions
The proof of causality as proposed in the previous section is the main prerequisite for the approximation
of the unknown causal function affecting the values of any arbitrary business variable within a cause-
and-effect structure. This provides the necessary numeric properties for the causal model base of a DSS
to run simulations as well as how-to-achieve or what-if analyses. One crucial issue of this task is that
the form of these cause-and-effect functions cannot be assessed a priori. Therefore three alternative
approaches are to be considered in this context:
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