The World Bank Economic Review 15 With this information, a measure of network treatment intensity is naturally defined as the proportion of the student’s network of closest friends who were treated (friends in a treatment classroom/total listed friends).<sup>21</sup> If a student and his or her entire network of close friends were all in the same treatment classroom, then the proportion is equal to one, but if the network of friends includes students from other classrooms or from outside the school, then the proportion is lower. The analysis uses variation in the proportion of close friends that are in the student’s classroom to estimate a heterogeneous treatment effects regression in which the main effects are now interacted with the proportion of friends in the network who were treated ( _Fij_ ). The specification becomes: where in order to control for popularity of a particular student, the regression includes _Nij_ defined as the number of people who mentioned individual _i_ as a friend. Throughout the analysis, standard errors are clustered at the school level. In tables 7, 8, and 9 the interpretation of the main effect ( _Tj_ ) now becomes the effect of assignment to treatment for someone who has zero friends also treated, whereas the coefficient on ( _Fij_ × _Tj_ ) is the additional effect of the course for someone whose full set of friends are also treated (analogously for _S j_ ).

In interpreting these results, the reader should be cognizant that the distribution of a student’s network of friends is not a randomly assigned variable. The identifying variation is coming from whether the student’s friends are in his or her classroom or are rather in another classroom in the school or from outside of the school. This may lead to bias if, for example, more extroverted students have a larger proportion of their best friends in the classroom and this extroversion is related to the outcome beyond the effect stemming from social reinforcement. For this reason, the study conditions on _Nij_ , the number of individuals that mention another student as a best friend.<sup>22</sup> The necessary assumption hence becomes that the proportion of friends in the classroom is related to the treatment response only through the network effects (conditional on the number of friends).

With this assumption in mind, results for network interactions are presented in tables 7, 8, and 9, which report effects six months after finishing the course. Table 7 provides clear evidence of a significant reinforcing interaction effect for students in the treatment group in terms of the overall knowledge index (column 6). The study is able to identify an effect of 0.46 standard deviation in knowledge for wholly treated networks, as opposed to a 0.28 standard deviation effect if the student’s network is not treated. In contrast, there are no statistically significant effects for spillover students, even if their network was fully treated. As noted before, large standard errors are obtained for the spillover estimates due to the small number of spillover students with treated networks. At the bottom of each column, the table reports the _p_ -value from a test of equality of the friendship interaction effects for treatment and spillover students. The reinforcing interaction effect is positive, large, and significant for all five subindices except for those reporting knowledge concerning sexual violence and knowledge about condom use (columns 2 and 5).

Table 8, on attitude indicators, shows an even starker reinforcing interaction effect. In this case, the effects are significant _only_ if the student’s friendship network also took the course. For example, if a student’s full network was treated, the student is predicted to have a 0.24 standard deviation higher attitude index score, whereas the estimated effect is only 0.04 standard deviation if no one in his or her friendship network was treated. Similar outcomes are observed in each of the subcomponents of the index. As in table 7, there is no significant network spillover effect for a student who did not take the course.

> 21 One shortcoming of this network analysis is that the questionnaire did not clearly differentiate between friendship and romantic  relationships.

> 22 When looking at determinants of being more popular in school, the data shows that kids who are more popular are less likely to smoke, drink, and consume drugs at baseline.