Identity, Structure, and Causal Representation in Scientific Models - Mechanism and Causality in Biology and Economics - page 40

of equations are causally ambiguous, which is the rationale for supplementing them
with graphs.
Simon does not appeal to graphs. Instead, he considers a higher-order relation of
direct control over parameters (Simon 1953 , pp. 24-27). He invites us (and nature)
to experiment on a system by directly controlling the value of its parameters (the
coefficients now being thought of as parameters that can take different values). The
privileged parameterization is the one in which such experiments can be conducted
independently. Thus, if one represents a causal system by Eqs. ( 3.1 ) and ( 3.2 ) and
can control A directly by choosing α A and thereby control B indirectly without
altering the functional form of Eq. ( 3.2 ), then the parameter set { α A , α BA }is
privileged. No other functionally equivalent system shares this property.
If, for example, ( 3.1 ) and ( 3.2 ) represented the true causal order, but we instead
modeled the causal relationships with ( 3.4 ) and ( 3.5 ), our control of A and B would
not show the same sort of functional invariance. In fact, the only way to achieve the
same values for A and B would be for the coefficient values of { β AB } to shift

according to the restrictions ( 3.6 ), ( 3.7 ), and ( 3.8 ). In effect, the decision that {

β A , β B ,

α A ,

α BA }is the parameter set - and that any other set of coefficients (e.g., { β AB })

are simply functions of those parameters - determines the causal direction among
the variables: it puts the arrowheads on the shafts.

β A , β B ,

2.3 The Structural Account of Causal Order

I refer to an account of causal order based on Simon's seminal analysis as the
structural account . 2 It is structural in the sense that what matters for determining
the causal order is the relationship among the parameters and the variables and
among the variables themselves. The parameterization - that is, the identification of
privileged set of parameters that govern the functional relationships - is the source
of the causal asymmetries that define the causal order. The idea of a privilege
parameterization can be made more precise, by noting that a set of parameters is
privileged when its members are, in the terminology of the econometricians,
variation-free. A parameter is variation-free if, and only if, the fact that other
parameters take some particular values in their ranges does not restrict the range
of admissible values for that parameter.
Defining parameters as variation-free variables has a similar flavor to Hans
Reichenbach's ( 1956 ) Principle of the Common Cause : any genuine correlation
among variables has a causal explanation - either one causes the other, they are
mutual causes, or they have a common cause. Since we represent causal connections
as obtaining only between variables simpliciter , we insist that parameters not display
any mutual constraints. Whereas, the Principle of the Common Cause is a metaphys-
ical or methodological presupposition with significant bite, the variation-freeness of

2 A more formal presentation of the structural account is given in Hoover ( 2001 , Chap. 3).