Identity, Structure, and Causal Representation in Scientific Models - Mechanism and Causality in Biology and Economics - page 38

3 0 Þ

C ( α CA A þ α CB B : ð 3 :

Cartwright ( 2007 , p. 16, passim ) refers to such equations as “causal laws” - that
is, laws that connect specific causes to specific effects. Woodward ( 2003 ), as well as
most of the literature on graphical causal models, considers one-way causation
only. Economists refer to such systems as recursive , while the graphical
representations are often known as directed acyclical graphs ( DAG s). Cyclical
graphs (e.g., A ! B ! C ! A ) are sometimes entertained, but the tight cycle of

the simultaneous system ( A B ), a bread-and-butter system in

economics, is encountered far less frequently. The equations themselves are gener-
ally taken to be linear - especially linear in parameters. While these restrictions are
by no means necessary, they highlight the inadequacy of the graphs fully to
represent various levels of causal complexity. Economists avoiding graphs ( pace
Pearl) are perhaps partly motivated by an appreciation of the subtlety of causal
representation and not some intuitive revulsion toward graphical gimmickry.

! B ! A or A $

2.2 Simon on Causal Order

Following Haavelmo's “The Probability Approach in Econometrics” ( 1944 ),
econometricians focused on what Frisch had called the “inversion problem” -
namely, how to infer the original structure from passive observation of the data
that it generates (Lou¸˜ 2007 , p. 95). Later dubbed the “identification problem,” a
detailed account of the mathematics was for a time the central focus of the Cowles
Commission (Koopmans 1950 ; Hood and Koopmans 1953 ). Identification naturally
requires something to identify. Simon's contribution to the 1953 Cowles Commis-
sion volume sought to characterize the causal order of a system of equations.
Simon started with a complete system of equations - that is, a system that could
be represented as a multivariate function with a well-defined solution. He then
focused on self-contained subsystems of the complete system. To illustrate,
Eqs. ( 3.1 ), ( 3.2 ), and ( 3.3 ) form a complete system. Equation ( 3.1 ) is a self-
contained subsystem in that it determines the value of A without reference to any
other equation. Equations ( 3.2 ) and ( 3.3 ) considered separately are not self-
contained subsystems as they do not contain enough information to determine B
or C. In contrast, Eqs. ( 3.1 ) and ( 3.2 ) together are a self-contained subsystem, since
they determine the values of A and B without reference to Eq. ( 3.3 ).
Simon's conception is closely related to his later work on hierarchies of systems
(Simon 1996 ; see also Hoover 2012c ). Causes are the outputs of lower-level
systems and the inputs to higher-level systems. The relationship is closely
connected to the solution algorithms for systems of equations. In system ( 3.1 ),
( 3.2 ), and ( 3.3 ), A is determined entirely by ( 3.1 ) and can be regarded as an output.
If we know A , we do not need to know ( 3.1 ) to determine B ; a specific value for A
forms an input that, in effect, turns the non-self-contained subsystem ( 3.2 ) into a