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negative causal relevance and claims about causal structure. For instance, suppose
our concern was to extrapolate the claim that there is a causal chain from U to C .In
this situation, we would not need to suppose that A mediates all selection variables
impacting the effect of U upon C , nor would we have to assume that all causal paths
from U to C pass through E . Extrapolating the claim that U has an effect on C only
requires the premise that no circumstances are present in the target population that
could completely eliminate this effect. Although it is easy to think of factors that
could modulate the effect of U upon E , plausible circumstances that obliterate this
effect entirely, if it exists, are much more difficult to come by. So, directly
extrapolating a causal chain from U to C may be reasonable in this case. Such
reasoning could be naturally extended into an extrapolation of positive causal
relevance. The takeaway point of this example is that extrapolating claims about
causal structure or positive causal relevance depend on much less stringent
assumptions about the selection diagram. That makes such extrapolations more
robust, though less informative.
This section has illustrated two central points concerning extrapolation. First, it
is not necessary that the causal relationship to be extrapolated is the same in the
model as in the target. Given knowledge of the probability distributions for the
model and target along with the selection diagram, it can be possible to make
adjustments to account for differences. Secondly, the conditions needed for extrap-
olation vary with the type of claim to extrapolated. In general, the more informative
the causal claim, the more stringent the background assumptions needed to justify
its transfer. This second point is very important for explaining how extrapolation
can remain possible even when substantial uncertainty exists about the selection
diagram. In the next, section I consider, in relation to the Donohue and Levitt study,
how distinct levels of analysis can be helpful for assessing assumptions about the
similarity of model and target.
4 Levels and Evidence
Extrapolation depends on background knowledge about ways in which the model
and target are and are not likely to differ, knowledge that can be represented by a
selection diagram. One obvious question, therefore, is where this knowledge comes
from. Some similarities might be known only as a result of studies performed
separately on the two populations. In other cases, the assumed similarity may be
grounded in the acceptance of a common fundamental mechanism concerning, say,
human psychology. For instance, it is natural to suppose that negative psychologi-
cal impacts on a child of, say, insensitive and unconcerned parents are likely to be
fairly stable across populations. In this type of situation, one might infer a causal
relationship in the target on the grounds that it is found in the model and that model
and target are unlikely to differ in that respect. However, it would be difficult to
justify extrapolating a quantitative causal claim on the basis of such general
theoretical considerations. Such background psychological knowledge might, for
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