where θg are standard block group fixed effects, Xi is the vector of individual attributes that are
the same set of attributes used in the workplace clustering specification, and X i is the vector of
block averages on the same attributes. The latter are included in order to control for overall or
non-individual specific effects of neighborhood on employment.
It is useful to consider the reflection problem again in the context of the labor market
outcome regressions in equation (4). As noted above, Manski shows that it is generally
impossible to distinguish the impact of group average outcomes from group average
characteristics on the outcome of interest. Ignoring the presence of block-level match quality Qi
in equation (4) for a moment, this implies that it is generally impossible to distinguish the effect
of average neighborhood labor market outcomes from average neighborhood sociodemographic
characteristics and, for this reason, we do not include a measure of average neighborhood labor
market outcomes in equation (4). As Manski points out, δ2 continues to provide a test for the
presence of social interactions more generally but does not distinguish between these
mechanisms.
In the presence of this general concern, the match quality variable constructed from our
first stage analysis is intriguing because its basis on the propensity of individuals to work together
implies that this effect comes about through labor market referrals. In this way, we argue that this
effect is informative about a particular channel through which the employment of neighbors
might affect an individual’s outcomes. The magnitude of the impact of neighbor employment
levels on outcomes, however, remains a function of the match between individual and neighbor
characteristics (e.g., the likelihood that the two interact) and, consequently, it is important to keep
in mind that this effect does not operate directly through a group average labor market outcome.
In principle, this model is identified with block fixed effects because Qi varies across
individuals in a block. In our opinion, however, it would not be appropriate to include block fixed
effects in this model. The current specification with block group fixed effects is identified
because similar individuals reside in different blocks within the same block group and therefore
have different match quality. In other words, the conceptual experiment considered is to change
the match quality for a generic individual with observables Xi by moving them from one block to
another block in the same block group, which we believe is the appropriate comparison or
exercise. A specification that included block fixed effects would be identified by a comparison of
individuals with different match quality in the same block. But individuals with the same Xi have
exactly the same Qi if they are in the same block and, consequently, the associated, and in our
opinion undesirable, conceptual experiment would involve changes in an individual's observable
attributes. Clearly, the results of this second exercise would be very sensitive to parametric
19