Exclusion Bias in the Estimation of Peer Effects
We formalize a noted [Guryan et al., 2009] but unexplored source of bias in peer effect estimation, arising because people cannot be their own peer. We derive, for linear-in-means models with non-overlapping peer groups, an exact formula of the bias in a test of random peer assignment. We demonstrate that, when estimating endogenous peer effects, the negative exclusion bias dominates the positive reflection bias when the true peer effect is small. We discuss conditions under which exclusion bias is aggravated by adding cluster fixed effects. By imposing restrictions on the error term, we show how to consistently estimate, without the need for instruments, all the structural parameters of an endogenous peer effect model with an arbitrary peer-group or network structure. We show that, under certain conditions, 2SLS do not suffer from exclusion bias. This may explain the counter-intuitive observation that OLS estimates of peer effects are often larger than their 2SLS counterpart.
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Document Object Identifier (DOI): 10.3386/w22565