Mechanisms and Extrapolation in the Abortion-Crime Controversy - Mechanism and Causality in Biology and Economics - page 185

Fig. 10.2 A selection
diagram with an unmeasured
common cause

U E C

S

A

hypothesis about the causal relationship between unwantedness and crime. The
variable U indicates whether or not the person was born from an unwanted
pregnancy, E is a variable indicating harmful psychological effects (e.g., an
impaired ability to adapt to frustration), A indicates whether or not the child was
adopted, and C indicates whether the person has been convicted of a crime. In
contrast, S is a variable that represent unmeasured factors that may create
differences between the two populations. In Steel ( 2008 , pp. 58-62) these are called
disrupting factors , while in Pearl and Bareinboim ( 2011 , p. 6) they are called
selection variables . I follow Pearl and Bareinboim's terminology here, as the
term “disruption” suggests factors that entirely block a causal relationship, while
the differences between model and target could come in other forms. To understand
selection variables, it is important to realize that two causes may interact with one
another in bringing about an effect. For example, by altering the adoption rate, S
may change the impact of U upon E . That is, a child born from an unwanted
pregnancy but adopted into a loving family shortly after birth would presumably be
spared the deleterious psychological effects of unwantedness. In the extreme case,
if every child born unwanted were adopted, the harmful effects of unwantedness
might be eliminated entirely. That extreme scenario seems rather improbable—a
survey of studies concerning children born from unwanted pregnancies found a
maximum adoption rate of around 20 % (Dagg 1991 , p. 582)—but the important
point is differences in the selection variable S could mitigate the deleterious
psychological effects of unwantedness. Note that the absence of selection variables
pointing into variables other than A in Fig. 10.2 is also significant. For instance, the
diagram in Fig. 10.2 says that E impacts C in the target exactly as in the model.
Pearl and Bareinboim ( 2011 ) refer to graphs like the one in Fig. 10.2 as selection
diagrams. Selection diagrams, then, represent judgments about similarities and
differences between model and target populations. A selection variable indicates
a source of potential difference between the model and target. For example, the
selection diagram alerts us to the possibility that the effect of unwantedness upon
psychological difficulties in the target may differ from that in the model due to
differences in adoption rates between the two populations. A selection diagram,
then, represents the causal structure in the target, namely, the DAG that results from
removing the selection variables. In addition, the selection diagram indicates ways
in which the causal structure in the target may differ from the model. For example,
in Fig. 10.2 , it is possible that the selection variable changes the distribution of A in
such a way as to eliminate all influence of U upon E in the target. Even if the causal
structure represented by the DAG is the same for model and target, the quantitative