Social Interactions and Endogenous Association - Department of ...

and then estimates that include the neighborhood variables. The substantial reduction in
the sample reduces the precision of the estimates, but neither the change in sample, nor
the inclusion of the neighborhood variables substantially affects the point estimates.
V. B. Macro-Group Composition
Under the assumption that people prefer to associate with others who are similar
to themselves, the model implies that for people who have a particular (binary)
characteristic, there should be a concave relationship between the share of their
associates that have that characteristic and the share of the group that has that
characteristic. For people who do not have that characteristic, the model implies that
there should be a convex relationship between the share of their associates that have that
characteristic and the share of group that does. The difference in the share of associates
who have the characteristic between people with and without it will be hump-shaped.
Intuitively, once a small number of people with a characteristic are introduced, the people
who also have that characteristic will be able to have associates who are similar to
themselves; people without the characteristic will not be forced to associate with people
with it until most of the group has the characteristic.
We test this hypothesis by regressing the share of peoples’ associates who have
some exogenous binary characteristic,
the characteristic,
G
x
i
A
x
i
, on cubics in the share of the group who have
, and these cubics interacted with the person’s value for the
characteristic, x
i
. We focus on race and ethnicity because of the strength of sorting on
them (as shown in Table 3). 13 Formally, we estimate,
13 Results are not reported for Indians because less than 3% of school-grades are 15% or more Indian.
25