Mechanisms and Extrapolation in the Abortion-Crime Controversy - Mechanism and Causality in Biology and Economics - page 195

rely on harder-to-justify assumptions. This point was illustrated by the Donohue
and Levitt study, wherein extrapolating a qualitative claim about positive causal
relevance rested on much firmer ground than extrapolating a quantitative claim
about the strength of that impact. The second theme had to do with the connection
between extrapolation and distinct levels of inquiry. Studies of causal relationships
in social systems can focus on mechanisms linking individual people or take a
bird's-eye statistical view of the population as a whole. Since the causal processes
at these levels are not independent, claims about the one can have implications for
the other. This idea is illustrated by the role of Donohue and Levitt's scale-up model
in linking an extrapolated claim that being born unwanted doubles the chance of
criminal conviction to statistical estimates of the impact of legalized abortion on
crime. The correspondence of the results from these two lines of reasoning provides
indirect support for the adequacy of that extrapolation as a rough approximation.
The interplay between levels of inquiry leads to the third philosophical theme that
extrapolation is normally one interwoven component of a complex and interdepen-
dent collection of arguments and, hence, is rarely a knockdown proof in its own
right. Consequently, critiques which observe that extrapolations rarely if ever
constitute definitive evidence sail wide of the mark. Building a case based on the
coherence of multiple lines of imperfect evidence is the norm for social science and
other sciences that study complex systems that are widely diffused across space and
time. To insist otherwise is to misconstrue the nature of science and to obstruct
applications of scientific knowledge to many pressing real-world problems.
Appendices
Appendix 1: Definition of d-separation
For completeness, I include the definition of d-separation, cited from Pearl ( 2000 ,
pp. 16-17).
A path p is said to be d- separated (or blocked ) by a set of nodes Z if and only if
1. p contains a chain i ! m ! j or a fork i m ! j such that the middle node m is in Z,
or
2. p contains an inverted fork (or collider )i! m j such that the middle node m is not in
Z and such that no descendant of m is in Z.
A set Z is said to d-separate X from Y if and only if Z blocks every path from a node in X to a
node in Y.
D-separation is important because it indicates all and only those probabilistic
independence relationships entailed by the Markov condition. That is, the Markov
conditions entails that X and Y are probabilistically independent conditional on Z in
a DAG G if and only if Z d-separates X and Y in G .