  In many contexts, particularly when study subjects are adolescents, peer
effects can invalidate typical statistical requirements in the data. For
instance, it is plausible that a student's academic performance is influenced
both by their own mother's educational level as well as that of their peers.
Since the underlying social network is measured, the Add Health study provides
a unique opportunity to examine the impact of maternal college education on
adolescent school performance, both direct and indirect. However, causal
inference on populations embedded in social networks poses technical
challenges, since the typical no interference assumption no longer holds. While
inverse probability-of-treatment weighted (IPW) estimators have been developed
for this setting, they are often highly unstable. Motivated by the question of
maternal education, we propose doubly robust (DR) estimators combining models
for treatment and outcome that are consistent and asymptotically normal if
either model is correctly specified. We present empirical results that
illustrate the DR property and the efficiency gain of DR over IPW estimators
even when the treatment model is misspecified. Contrary to previous studies,
our robust analysis does not provide evidence of an indirect effect of maternal
education on academic performance within adolescents' social circles in Add
Health.
