together. In this way, one would have to believe that slight differences (i.e., one- or two-block
distances) in access to mass transportation stations or highways, for example, could cause a large
increase in the propensity of individuals to work together at the block versus block group level.
A second way to gauge whether the increased proximity of individuals at the block level
is a concern is to compare the coefficient estimates for the matched pair's covariates Xij, in levels
and as interactions with the block dummy Rijb (i.e., β and α1, respectively). Assuming that the
same factors that affect the propensity to work together at the neighborhood level are simply
stronger at the block level, then one would expect to see a result at the block level (namely, in α1)
that is qualitatively similar and slightly larger (overall) in magnitude. As we discuss below, this is
clearly not the case in our empirical analysis; in many cases β and α1 have the opposite sign 26
Additional Specifications and Robustness. As described above, our empirical design relies
critically on the assumption that social interactions are especially strong at the block level, while
households are only able to choose a block group at the time of the location decision, due perhaps
to the thinness of the housing market. While the analysis of correlation between observable
neighbor characteristics described above provides assurance that this assumption is reasonable,
we also consider the robustness of our results to alternative samples designed to isolate those
block groups that are most homogenous along a number of dimensions including: race, education,
the presence of children in the household, and immigration status. In particular, in each case, we
select the 50 percent of block groups that display the least amount of within-block group
correlation between the corresponding individual and neighbor characteristics and re-estimate the
baseline model for the restricted sample in order to see if our results are robust across samples.27
A separate confounding issue is the possibility that the estimated social interaction effect
may be due to reverse causation: workers could receive tips and referrals about residential
locations from their co-workers at a given firm. We address this issue in several ways. First, the
empirical focus on the difference between block group- and block-level propensities again
mitigates this problem because residential referrals are unlikely to result in people residing in
exactly the same block, due to the thinness of the housing market at the block level.
26 The limitation of this argument should also be clear. When there are several biases that work in different
directions, the relative magnitudes of the biases may change as we shift the level of geography and as a
result the sign of the bias might reverse. For example, at the block group level, most of the results may be
driven by individual observable heterogeneity, but at the block level residential sorting on unobservable
might become more important.
27 While the resulting analysis obviously changes the nature of the sample, the results described below do
provide some re-assurance that our baseline results are not sensitive to sorting.
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