4 EMPIRICAL DESIGN - DETECTING REFERRAL EFFECTS
Given the structure of the dataset just described, it is straightforward to characterize our
general research design. Our primary analysis explores the propensity for two individuals to work
in the same location, comparing this propensity for a pair that lives in the same block with that of
a pair that lives in the same block group but not the same block. The implementation of this
design is straightforward and can be summarized in the following equation:
(1) Wijb=ρg+α0Ribj+εij
where i and j denote two individuals that reside in the same Census block group but not in the
same household, Wijb is a dummy variable that is equal to one if i and j work in the same Census
block, Rijb is a dummy variable that is equal to one if i and j reside in the same Census block, and
ρg denotes the residential block group fixed effect - this is the baseline probability of working in
the same block for individuals residing in the same block group. The statistical test of the null
hypothesis that no local social interaction effect exists is simply a test of whether the estimated
coefficient α0 equals zero.
The inclusion of block group fixed effects in equation (1) is designed to control for any
correlation in unobserved attributes among individuals residing in the same neighborhood. Such
correlation can arise because of positive sorting into neighborhoods or because of unobserved
factors present in those neighborhoods (e.g. similar access to the urban transportation network).18
In interpreting α0 as a social interaction effect, therefore, we are implicitly making two
key identification assumptions. First, that while individuals are able to choose their residential
neighborhood (block group), there is no correlation in unobserved factors affecting work location
among individuals residing on the same block within a block group. The plausibility of this
assumption is motivated by two considerations. First, that the thinness of the housing market at
such small geographic scales - the vast majority of block groups in our sample are less than 0.10
square miles in area - restricts an individual’s ability to choose a specific block versus
18 See Manski (1993) or Moffitt (2001) for a detailed discussion of these issues. It is also worth noting that
due to the unique design of this analysis, the “reflection problem” studied by Manski (1993) does not have
an obvious analogue for this portion of our analysis. Manski shows that it is generally impossible to
distinguish the impact of group average outcomes from group average characteristics on individual
outcomes because of the simultaneity in the determination of the individual outcomes. Because the
dependent variable in our framework is a joint outcome for a pair of individuals and the identification of
10
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