Identity, Structure, and Causal Representation in Scientific Models - Mechanism and Causality in Biology and Economics - page 42

”)). 4 But here we cannot associate the asymmetrical assignment operator (“ (

parameter exclusively with either equation. Indeed, the notion of a canonical

form of equations is merely heuristic and must be abandoned in this case.
Equations displaying this sort of nonlinearity in parameters are referred to in the
macroeconometrics literature as subject to “cross-equation restrictions.” Suppose
that the monetary authority wants to loosen monetary policy; it would increase

λ

λ

.
Because of the cross-equation restriction, in addition to the direct causal effect of m t
on p t , there is a change in the functional relationship between p t and m t .Ina
stochastic version of the model, the conditional probability distribution of p t on
m t would not be invariant to changes in m t . This striking conclusion is well known
to economists as the “Lucas critique” (Lucas 1976 ). 5 Economists often discuss it in
terms of “deep parameters” (here

α and λ ) versus empirically observable

coefficients (say, a regression coefficient , but

which is estimated as a unit). In terms of our account of causal representation, the
deep parameters are just the parameters that define causal order.
While the Lucas critique is not unknown to philosophers, it is not always
appreciated that it undermines any necessary connection between a well-defined
causal relationship and the invariance of the probability of an effect conditional on
its causes. Indeed, our account of causal order suggests that it is the invariance of
the probability distribution of the cause (the marginal probability distribution) to
independent changes of other causes of the effect that is the empirical hallmark of a
causal relation (see Hoover 2001 , Chap. 8). This claim amounts to saying that it is
not the conservation of the functional relationship of causes to effect as causes vary
that is most characteristic of causal relations; rather it is that effects do not flow
backward against the causal arrow.

, which in fact equals αλ δ

Π

2.4 Causal Identity

Implicit in our discussion so far is the notion that variables in causal relationships
must be causally distinct. Let us make this notion more explicit. Variables are
distinguishable when we have some independent means of measuring, observing, or
characterizing them. Yet variables that are distinguishable in this general way need
not be causally distinct.
To take an economic example, prices ( P ) are distinguishable from quantities ( Q ),
but consider the simple supply and demand model in which quantities and prices are
mutually determined:

4 Which in fact suggested the scheme of distinguishing parameters by subscripts: for example,

α BC

was the parameter multiplying the variable C in the canonical equation for B.
5 For expositions of the Lucas critique, see Hoover ( 1988 , Chap. 8, section 8.3; 2001 , Chap. 7,
section 7.4).