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This complementary methodology can also be illustrated by the debate between
Das Gupta and Oster. According to Das Gupta, the change of sex ratio at birth is so
closely correlated with the sex composition of the existing children in the family
that it is very unlikely that biological factors could play any significant role in
determining that ratio; she therefore concluded that the cultural explanation should
replace the biological one. In response, Oster provided a miniature formal model to
show that, regardless of the naturally occurring average, resource-constrained
utility-maximizing parents would still behave in a way that has the marginal effect
of changing the sex ratios (Oster 2006 , pp. 326-327). In addition to the formal
presentation of the difference between the average and marginal effects, Oster gave
an example to illustrate her main point. Consider that there are two countries:
country A is in the desert, and country B is in the Arctic. On average, due to its
location, country A is hotter than country B. Imagine that we also observe that
country A is cooler when the weather is cloudy, and country B is hotter when the
weather is sunny. It is obvious that we won't therefore conclude that the entire
difference between the weather of country A and that of country B is cloud cover;
instead, we would say that “there is a naturally occurring difference in the average
temperature but on the margin the temperature in both places can move” (Oster
2006 , p. 325; emphasis added).
Thus, we can interpret Oster's example in terms of Cartwright's notions of
causal structure and capacity. HBV can be regarded as a factor possessing the
capacity to produce a naturally occurring difference—that is, a change in sex ratio
at birth—if unimpeded. In the actual world, economists surely know that no factor
can operate in an undisturbed environment. They, however, can assume that the
various effects of these disturbances can be averaged out so that the phenomenon of
interest—normally a relation between two targeted factors—can be observed as if
the observed phenomenon were undisturbed. By using the ideas of capacity and
causal structure, we can thus describe the positive relation between HBV (targeted
factor 1) and sex ratio at birth (targeted factor 2) as a net result produced by HBV's
capacity under a stable causal structure; the various effects of the relevant factors
are all averaged out except the two targeted factors. According to such thinking, we
can thus suppose that HBV, on average, can have a positive effect on the sex ratio.
Next, by following the logic illustrated in Oster's weather analogy, let's suppose
that there are two countries: country A, which has a high percentage of HBV-
infected population, and country B, which has low rate of HBV infection. And let's
further suppose that we observe that people in country A have no tendency for son
preference, but people in country B, for local reasons (such as the need to have more
males to do hard agricultural work), prefer having more male births. We can then
expect that when the families in country B already have two girls, they will try their
best—for example, they may try fetal sex-determination technology—to have a boy
in their third birth. As a result, in country B, we can observe a high correlation
between the sex of the previous children in a family and the sex ratio of subsequent
births. Therefore, just as we may perceive in the weather example that “there is a
naturally occurring difference in the average temperature but on the margin the
temperature in both places can move,” we can also observe in the HBV case that
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