Mechanisms and Extrapolation in the Abortion-Crime Controversy - Mechanism and Causality in Biology and Economics - page 192

instance, support extrapolating the claim that being born unwanted increases the
risk of criminality, but it would be unlikely to justify the claim that unwantedness
doubles that risk. It would be desirable, therefore, to have some means of testing
assumptions about similarities between model and target. In this section, I consider
how distinct levels of analysis can be helpful here.
Recall the connection between the concepts of extrapolation and integration as
defined in Sect. 3.1 . In extrapolation, a causal relationship R in the model is used,
possibly with some adjustments, as a basis for inferring R in the target. Integration,
by contrast, involves the extrapolation of R as part of a larger inference whose
object is to infer another causal relationship, R 0 . Donohue and Levitt's reasoning fits
this pattern because it extrapolates a claim about the effects of unwantedness on
criminal convictions in order to draw an inference about the impact of abortion
legalization in 1973 on crime rates in the 1990s. These observations suggest an
approach for testing assumptions that underlie an extrapolation. Suppose that the
causal relation R is directly extrapolated from model to target. Suppose, moreover,
that R together with other background knowledge entails a further causal relation-
ship R 0 . Then tests of R 0 will be indirect tests of the correctness of the direct
extrapolation of R . In the Donohue and Levitt study, R is the claim that being
born unwanted doubles the chance of criminal conviction later in life, while R 0 is
the result of the scale-up model (or “back-of-the-envelope” calculations) described
in Sect. 2 . The results of the scale-up model, then, can be compared to estimates of
the effect of abortion from Donohue and Levitt's state-level comparisons
concerning abortion and crime rates. Donohue and Levitt characterize their statisti-
cal estimates of the impact of legalized abortion on crime as “roughly consistent,
but somewhat larger than” their back-of-the-envelope result ( 2001 , p. 391, p. 405).
This rough consistency, then, is presumably taken as a reason for thinking that the
scale-up model—including the extrapolated claim that being born unwanted
doubles the chance of criminal conviction later

in life—is a decent first

approximation.
This example illustrates how differing levels of analysis can provide a means for
testing assumptions about similarity and difference between model and target.
Extrapolation at the level of a mechanism can be integrated with other information
to generate an estimate of a macro-level causal effect, which then can in turn be
compared with estimates directly made on the basis of macro-level data. The result
of this process is an inference in which distinct lines of evidence, each with its own
inevitable uncertainties, may mutually support or conflict with one another. The
effect in the case of mutual support is, naturally, to strengthen the overall inference.
Let us briefly consider the uncertainties in the present example. The uncertainties in
the scale-up model are fairly easy to see. First, extrapolations rest on background
assumptions concerning similarities and differences between model and target,
assumptions which are often difficult to directly test. For instance, it is plausible
that being born unwanted approximately doubles the chance of criminal conviction
later in life in the USA just as found in the European studies described in Sect. 1 .
But it would be difficult to decisively eliminate the possibility that some divergence
between the two populations exists that undermines this assumption, especially as