mapping of friendship networks collected in the baseline survey.<sup>20</sup> Our design provides both an explicit mapping of children’s friendship networks and random assignment of the fraction of a student’s friends who are treated. This allows us to compare directly students who have more treated friends to those who have less, using Equation 3. As in the family regressions, the possible endogeneity arising from the fact that registration is likely to have followed friendship ties is controlled by instrumenting for the faction of registered friends actually receiving the treatment.

The friendship question in the baseline survey asked the children to name up to five of their closest friends who were in the same school and grade. All of the children provided at least 1 friend and three quarters provided five. The names of these friends were then matched with the results of the random assignment lottery to determine which friends were treated by the program. Half of the students had no treated friends and about 92 percent had up to 40 percent of their friends treated. On average 15 percent of a students’ friends were treated (about 1 friend). This provides significant variation in treatment density, but also means that our results cannot be generalized to conditions in which more than 40 percent of a child’s friends are treated. All of the results are presented in Table 11.

Column 1 contains the OLS regression between our verified attendance measure and the fraction of a students’ friends that are treated. Already the positive but declining contribution of treated friends is apparent with the coefficient on the linear term of 0.03 and the quadratic term of -0.04. However, both point estimates are statistically insignificant.

The first stage regression is presented in Column 2. The estimates confirm that the outcome of the random assignment process (the fraction of registered friends who are treated) does, in fact, generate significant variance in the overall fraction of a student’s friends who are treated. It in fact, explains 70 percent of the variance in the fraction of the friends treated.

> 20 Such externalities have been previously estimated for conditional cash transfers by exploiting the fact that the original PROGRESA program only provided subsidies for the poorest families in a village.  Both Bobonis and Finan (2006) and Lalive and Cattaneo (2006) compare the school attendance patterns of children whose families were too rich to receive the subsidy between treated and untreated villages.  This comparison allows them to experimentally identify the effects of the externality by looking for changes in the children who would not have been directly treated in both treatment and control villages.  However, the relative percentage of treated and untreated children in each village (the treatment density) is determined by the distribution of wealth in each village, making it difficult to causally associate the magnitude of the effect with the density of treatment in a village.  In unpublished results, we estimate a similar measure (the fraction of treated children within a students’ school-grade-gender cohort) and find no effects suggesting that this indirect measure may underestimate the effects of peers.

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