Identity, Structure, and Causal Representation in Scientific Models - Mechanism and Causality in Biology and Economics - page 41

parameters is only a representational convention. Any situation in which it appears
that putative parameters are mutually constraining can always be rewritten so that
the constraints are moved into the functional forms that connect variables to each
other.
For example, in the system

X ¼ a ð : Þ

3 9

Y ¼ bX ; b a ð : Þ

3 10

the parameters are not variation-free, since the choice of a constrains the value of b .
However, this system can be reformulated into a related (nonlinear) system with the
same solutions in which the parameters are variation-free:

X ¼ a ð 3 : 11 Þ

bX ; if a b

Y ¼ ð 3 : 12 Þ

undefined ; if a < b :

Because of its analogy with the Principle of the Common Cause, we refer to the
stipulation that parameters be variation-free as the Reichenbach Convention .
Except for the system of Eqs. ( 3.11 ) and ( 3.12 ), we have considered only linear
equations. But the structural account can accommodate nonlinearity quite gener-
ally. The key step is that parameters are not defined as coefficients uniquely
associated with particular variables, as they are, for example, in path analysis, in
which the parameters are merely the regression weights associated with each causal
arrow.
To see the role of nonlinearity, consider a simplified example of a two-equation
system from a macroeconomic model with rational expectations 3 :

m t ¼ λ þ m t 1 þ ε t ; ð 3 : 13 Þ

p t ¼ m t þ αλ δ þ ν t : ð : Þ

3 14

The subscripts are time indices. Our concern is only with the causal relationship
between m t and p t , so the lagged value of m can be regarded as a constant. While it is
not vital for our purposes, ( 3.13 ) is interpreted as a rule for fixing the money supply,
while ( 3.14 ) determines the price level.
It is obvious that in Simon's framework m t directly causes p t . In our earlier
examples, there was a simple, natural association of individual parameters with
individual variables in equations written in a canonical form (causes on the right-
hand side; the effect on the left-hand side; the two sides connected by an

3 The model is drawn from Hamilton ( 1995 ).