Estimation of spillover effects with matched data or longitudinal network data

Social interactions often play a key role in determining the impact of policies, but measuring the magnitude of spillover effects empirically is notoriously challenging because, in most applications, a person’s relationships are likely to reflect her own characteristics (homophily), and people who are connected are likely to be affected by the same shocks (common factors). In addition, a significant share of social interactions is likely to occur through variables that are not observed by the researcher. When matched data are used, observations corresponding to the same cross-sectional units (e.g., workers or students) can be linked over time, and a cross-sectional unit’s relationships (e.g., co-workers or classmates) are indexed in each time period. We show that comparisons over time in the outcomes of individuals whose relationships changed can be used to measure the importance of social interactions in the presence of flexible patterns of selection on unobservables and common factors, even if social interactions only occur through unobservables. We apply our results to estimate the importance of peer effects in student learning in elementary school.