Identity, Structure, and Causal Representation in Scientific Models - Mechanism and Causality in Biology and Economics - page 37

Fig. 3.1 Causal graph of the
system (3.1)-(3.3)

C

A B

B ¼ α BA A ; ð 3 : 2 Þ

C ¼ α CA A þ α CB B ; ð 3 : 3 Þ

where, for the moment, we regard the α ij as fixed coefficients.

Systems of equations are causally ambiguous. In stochastic cases, we generally
recognize that correlation is not causation; in nonstochastic cases, the analogue is
that functional relations are not causation. The arrows in the graph represent the
primitive notion of the asymmetry of causation.
Graphs and equations interpreted causally both have a long history in economics
(see Hoover 2004 ). But it is fair to say that equations have gained the upper hand
and that, for many years, causation itself was rarely referred to directly, but at best
was implicit in distinctions between dependent and independent (or endogenous
and exogenous) variables and in synonyms and circumlocutions: instead of “ A
causes B ,” A produces , influences , engenders , affects ,or brings about B ,or B
reflects , is a consequence of, is a result of ,or is an effect of A (see Hoover 2009 ).
A growing wariness of causal language went hand in hand with a wariness of
graphical representation. As Pearl puts it:
Early econometricians were very careful mathematicians; they fought hard to keep their
algebra clean and formal, and they could not agree to have it contaminated by gimmicks
such as diagrams. (Pearl 2000 , p. 347)

Equations alone are causally ambiguous, since in themselves they do not repre-
sent causal asymmetry. But graphs are themselves causally ambiguous, because
quite different functional relationships can be represented by the same graph
(Woodward 2003 , p. 44). Just as economists found circumlocutions to express
“cause,” they have typically - although not necessarily consistently - represented
causal asymmetry by the convention of writing causes on the right-hand side and
effects on the left-hand side of equations. Various devices have been suggested for
explicitly combining the functional detail of systems of equations with the
asymmetries of the graph. In lieu of the equal sign, Cartwright ( 2007 , p. 13)
suggests a causal equality ( c ¼ ) which Hoover ( 2001 , p. 40) writes as ( ). With a

new notational device, the graph in Fig. 3.1 could be omitted and the system ( 3.1 ),
( 3.2 ), and ( 3.3 ) could, then, be rewritten as

(

1 0 Þ

A ( α A ; ð 3 :

2 0 Þ B ( α BA A ; ð 3 :