Identity, Structure, and Causal Representation in Scientific Models - Mechanism and Causality in Biology and Economics - page 48

Cartwright's account of its working. The rough sketch of a structural causal
representation of the carburetor supports Cartwright's view that in this case, as in
many others, a causally unambiguous system need not be modular.
Where Cartwright goes astray is in her belief that the failure of a well-defined
causal system to be modular in Woodward's sense threatens an interventionist
account and not just Woodward's particular formulation of it (the manipulability
account). The structural account is a type of interventionist account that relies
on a different sort of modularity - that is, modularity at the level of parameters.
By definition, parameters can change independently of each other. Cartwright
might object to the assumption that parameters are necessarily independent (or
variation-free). But as I previously argued, this is a matter of convention;
representations can always be formulated with variation-free parameters,
constraints having been moved into the functional relationship of variables. As a
conventional restriction on causal representation, however, modularity of the
parameters does not pack any punch: it does not tell us that a causal mechanism
can be disassembled into parts that operate independently of each other. Indeed,
modularity of that sort is not conventional but substantial and highly special. The
modularity of parameters is, nonetheless, the sort of modularity that we need to
define causal structure. The structural account allows us to see that Woodward's
definition of direct cause is too strong; it rules out too many relationships that are
clearly causal in an obvious and practical sense.
Woodward may object to Cartwright's implicit, and the structural account's
explicit, characterization of an intervention. For Woodward, an intervention is
setting a variable to a value come what may - a severing of its relations to its
own causes. In the structural account, an intervention is a more delicate matter of
influencing a variable in some particular way by changing one or more parameters
in a context in which multiple parameters connected to the variable under some
functional constraints are the rule.
The failure of modularity does not depend on which notion of intervention we
employ. Wiping out a causal arrow (or equation) does not necessarily leave other
causal arrows intact. Consider the monetary-policy system ( 3.13 ) and ( 3.14 )
referred to in our earlier discussion of the Lucas critique. The cross-equation
restriction (i.e., the appearance of in both equations) arises because of the

assumption that agents form expectations of the path of the money supply ( m t )
based on knowledge of the policy rule. Woodward's type of intervention would
amount to setting m t to a definite value independent of its past value - essentially
wiping out the causal arrow from m t 1 to m t . Eliminating that causal arrow does not
merely imply a change in the values of the parameters of ( 3.14 ), which would be a
failure of invariance of the sort highlighted by the Lucas critique and implicit in
Cartwright's carburetor example, it would in fact render the parameter

λ

meaning-
less as it would undercut any basis for forming a rational expectation of the path of
m t . In effect, the wiping out of the causal arrow from m t 1 to m t does not merely
alter the causal arrow from m t to p t ; it smashes it. There are plenty of real-world
examples of devices in which one part cannot be removed without breaking others,
which nonetheless possess well-defined causal structure.

λ