Mechanisms and Extrapolation in the Abortion-Crime Controversy - Mechanism and Causality in Biology and Economics - page 183

commit crimes. 5 For homicide, this rough model predicts an 11 % reduction due to
legalized abortion by 1997, when homicide rates had fallen from their peak by
30-40 % (Donohue and Levitt 2001 , p. 390).
This scale-up model is relevant to the present discussion in several respects. It
explicitly involves an across-population extrapolation, as the estimate for the
impact of unwantedness on criminal behavior is directly borrowed from the Euro-
pean studies described above. In addition, the scale-up model is important for
understanding the relation of extrapolation to multiple levels of aggregation in
making an overall case for a causal claim. In particular, the scale-up model provides
an indirect way to test the claim that the populations are sufficiently similar to
justify the extrapolation. This point is discussed in greater detail below in Sect. 4 .
3 A Conceptual Framework for Extrapolation
Transferring or extrapolating results across populations is essential for making
scientific inquiry relevant to practical problems. Reasoned answers to questions
about the causes of the decline in crime rates in the 1990s, or about the health
impacts of a pesticide, and many other issues must consider a variety of studies
whose data sets are not all drawn from the same population. The role of the
European studies on the impacts of unwantedness is the most obvious but not
sole example of this in the Donohue and Levitt study. In tracing the mechanism
they propose, Donohue and Levitt cite studies—for example, about the effects of
teenage motherhood on the life outcomes of the child—that use distinct US data
sets. In this section, I synthesize and further develop approaches to extrapolation
proposed by myself (Steel 2008 ) and Pearl and Bareinboim ( 2011 ).
3.1 Selection Diagrams and a Definition of Extrapolation
I will use the term model to refer to the population that is the basis of the
extrapolation and the term target for the population that is the object of the
extrapolation. In the Donohue and Levitt study, the European women in Sweden
and Czechoslovakia during times in which terminations of pregnancies required
legal approval are the models and the USA is the target. As this example illustrates,
there may be more than one model. Extrapolating (or transporting, to use the term
favored by Pearl and Bareinboim) depends on some background knowledge about
ways in which the model and target are likely to differ and ways in which they are
5 Note that this last assumption is consistent with the results of the Prague cohort study described
above. However, Donohue and Levitt cite a study concerning a Finnish data set here (Rasanen
et al. 1999 ).