assumptions concerning how Xi enters labor market outcomes and, consequently, such an exercise
is unlikely to provide reliable insights into the effect of match quality on labor market outcomes.
Finally, it is important to point out a limitation of this exercise. In particular, what is
actually identified by the first-stage analysis are types of pairs that are more likely to work
together due to the strength of the referral effect between the pair. As discussed above, we expect
this effect to be large in two cases: (i) when a pair is more likely to interact within their
residential neighborhood and (ii) when one person is well attached to the labor market and the
other likely to need a referral. In this way, for a person that is not well attached to the labor
market, the measure of match quality described here should do a good job of characterizing the
quality of matches in a neighborhood. For a person better attached to the labor market, however,
our match quality variable may actually measure neighborhoods in which such a person provides
rather than receives referrals. In this way, to the extent that our estimated social interaction effects
in the first stage of our analysis are driven by the asymmetry in labor market attachment rather
than by the strength of neighborhood interactions, our analysis of the effect of match quality on
labor market outcomes is likely to understate the benefits of improved matches.
Measurement Error. An important issue that arises in the estimation of equation (4) results
because the Census contains only a 1-in-7 sample of households rather than the full set of
households on each block. This means that the constructed average block neighbor attributes
(including our constructed match quality variable) included in equation (4) are measured with
error. Assuming that the Census sampling design ensures that the measurement error is
uncorrelated with the true underlying average block attributes, this measurement error would not
pose much of a problem for our analysis if average match quality Qi were the only variable
measured with error included in the analysis. In this case, letting σQ* represent the true variation
in match quality and σQ the measured variation, the probability limit of the estimated coefficient
would be equal to the true coefficient times the ratio of σQ* to σQ:
(5) plim (β )= β-— ⇒ plim (β )ctq = /.>σQ *
σQ
In this way, one can obtain a consistent estimate of the effect of a one standard deviation increase
in the true measure of match quality on labor market outcomes by multiplying the estimated
coefficient by the standard deviation of our constructed measure of average match quality. When
20