Exclusion Bias in the Estimation of Peer Effects

Abstract

We examine a largely unexplored source of downward bias in peer effect estimation, namely, exclusion bias. We derive formulas for the magnitude of the bias in tests of random peer assignment, and for the combined reflection and exclusion bias in peer effect estimation. We show how to consistently test random peer assignment and how to estimate and conduct consistent inference on peer effects without instruments. The method corrects for the presence of reflection and exclusion bias but imposes restrictions on correlated effects. It allows the joint estimation of endogenous and exogenous peer effects in situations where instruments are not available and cannot be constructed from the network matrix. We estimate endogenous and exogenous peer effects in two datasets where instrumental approaches fail because peer assignment is to mutually exclusive groups of identical size. We find significant evidence of positive peer effects in one, negative peer effects in the other. In both cases, ignoring exclusion bias would have led to incorrect inference. We also demonstrate how the same approach applies to autoregressive models.

The Use of Instrumental Variables in Peer Effects Models

“… The latter also holds for the ‘exclusion bias’, which Caeyers and Fafchamps () show converges to zero when tends to infinite while remains bounded. …”

“…IV approach 1 provides a consistent estimation for the peer effect , while IV approach 0 is inconsistent. 11 The latter also holds for the 'exclusion bias', which Caeyers and Fafchamps (2016) show converges to zero when n c tends to infinite while n p remains bounded.…”

“…As the existing literature mainly considers additively separable specifications, we characterize the bias for this case only in section 'Asymptotic bias'. 10 In addition to avoiding the bias discussed here, it also corrects for the 'exclusion bias' defined by Caeyers and Fafchamps (2016).…”

“… In addition to avoiding the bias discussed here, it also corrects for the ‘exclusion bias’ defined by Caeyers and Fafchamps (). …”

More than Just Friends? School Peers and Adult Interracial Relationships

“…As noted by Guryan, Kroft and Notowidigdo (2009), however, one cannot test for this by simply regressing an individual's race on that of their peers, because each individual is present in many others peer groups but necessarily not their own. We therefore undertake a number of tests designed to avoid this problem, including those proposed by Guryan et al (2009), Stevenson (2015 and Caeyers and Fafchamps (2016). Details of these tests and results can be found in Appendix B.…”