We provide new results regarding the identification of peer effects. We consider an extended version of the linear-in-means model where each individual has his own specific reference group. Interactions are thus structured through a social network. We assume that correlated unobservables are either absent, or treated as fixed effects at the component level. In both cases, we provide easy-to-check necessary and sufficient conditions for identification. We show that endogenous and exogenous effects are generally identified under network interaction, although identification may fail for some particular structures. Monte Carlo simulations provide an analysis of the effects of some crucial characteristics of a network (i.e., density, intransitivity) on the estimates of social effects. Our approach generalizes a number of previous results due

Bill & Melinda Gates Foundation.

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Heterogeneous Impacts in PROGRESAHabiba Djebbari Jeffrey Smith D I S C U S S I O N P A P E R S E R I E S ABSTRACT Heterogeneous Impacts in PROGRESA *The "common effect" model in program evaluation assumes that all treated individuals have the same impact from a program. Our paper contributes to the recent literature that tests and goes beyond the common effect model by investigating impact heterogeneity using data from the experimental evaluation of the Mexican conditional cash transfer program PROGRESA. Our analysis builds upon and extends that in Heckman, Smith and Clements (1997) and more recent studies of quantile treatment effects and random coefficient models. We find strong evidence of systematic (i.e. subgroup) variation in impacts in PROGRESA and modest evidence of heterogeneous impacts conditional on the systematic impacts. We find evidence against the perfect positive dependence assumption that underlies the interpretation of quantile treatment effects as impacts at quantiles of the untreated outcome distribution. Our paper concludes with a discussion of the policy relevance of our findings and of heterogeneous impacts more generally.JEL Classification: C21, C14, I38

SUMMARY We provide the first empirical application of a new approach proposed by Lee (Journal of Econometrics 2007; 140(2), 333–374) to estimate peer effects in a linear‐in‐means model when individuals interact in groups. Assumingsufficient group size variation, this approach allows to control for correlated effects at the group level and to solve the simultaneity (reflection) problem. We clarify the intuition behind identification of peer effects in the model. We investigate peer effects in student achievement in French, Science, Mathematics and History in secondary schools in the Province of Québec (Canada). We estimate the model using conditional maximum likelihood and instrumental variables methods. We find some evidence of peer effects. The endogenous peer effect is large and significant in Mathematics but imprecisely estimated in the other subjects. Some contextual peer effects are also significant. In particular, for most subjects, the average age of peers has a negative effect on own test score. Using calibrated Monte Carlo simulations, we find that high dispersion in group sizes helps with potential issues of weak identification. Copyright © 2012 John Wiley & Sons, Ltd.

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We survey the recent, fast-growing literature on peer effects in networks. An important recurring theme is that the causal identification of peer effects depends on the structure of the network itself. In the absence of correlated effects, the reflection problem is generally solved by network interactions even in nonlinear, heterogeneous models. By contrast, microfoundations are generally not identified. We discuss and assess the various approaches developed by economists to account for correlated effects and network endogeneity in particular. We classify these approaches in four broad categories: random peers, random shocks, structural endogeneity, and panel data. We review an emerging literature relaxing the assumption that the network is perfectly known. Throughout, we provide a critical reading of the existing literature and identify important gaps and directions for future research. Expected final online publication date for the Annual Review of Economics, Volume 12 is August 3, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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