This paper formalizes a listed [Guryan et al., 2009] but unproven source of estimation bias in social interaction models. This bias is driven by the systematic exclusion of an individual from her peer group in the computation of average peer group outcomes. After deriving an exact formula for the magnitude of the bias in models using non-overlapping peer groups, we discuss its underlying parameters. We demonstrate that when the true peer effect is small or zero, the negative exclusion bias dominates the positive reflection bias yielding an overall negative bias on the peer effect estimate. We discuss the conditions under
which the exclusion bias is aggravated when adding cluster fixed effects. Simulation results confirm all the theoretical predictions derived in this paper and illustrate how the bias affects inference and the interpretation of estimation results. To achieve consistent inference, we suggest correcting p-values using permutation methods. We provide a characterization of a generalized data generating process that can be used to consistently estimate all structural parameters in the model, both for models using peer groups and models using social network
data. We also show the conditions under which two-stage least squares strategies do not suffer from exclusion bias. This may explain the counter-intuitive observation in the social interaction literature that OLS estimates of endogenous peer effects are often larger than their 2SLS counterparts. |
