fixed effects. Since we rely only on administrative data on nonenrolled students, spillover results are limited to school grades and behavior reports.

Table 4 shows the results of spillover effects. We find evidence that the interaction of students with a greater share of ASP participants generates positive effects on their reading, math and science grades, and reduces their bad behavior at school. Estimations indicate that adding 3 treated students in a classroom of 22 (almost a 1 standard deviation increase in treated students, 13.4% on average) increases academic achievement up to 0.095 standard deviations, (e.g., on math grades: 13 _._ 4% _×_ 0 _._ 007 = 0 _._ 095), and reduces bad behavior reports by 0.15 standard deviations (13 _._ 4% _×_ 0 _._ 011).<sup>21</sup> These results have similar signs to some evidence previously found in the literature. For example, Carrel and Hoekstra (2010) use the share of classmates coming from troubled families—that is, the share of children exposed to domestic violence—to measure its effect on grades and classroom misbehavior. They found that making 5% of a class troubled students (1 standard deviation) significantly decreases reading and math test scores by 0.69 percentage points, and increases misbehavior in the classroom by 0.09 more infractions.

To sum up, the spillover results yield two findings. First, these positive spillovers on nonenrolled students indicate that the ASP’s direct effects described in subsection 4.1-A are lower bounds of the total effect of the intervention in the context of these highly violent schools. Second, combining these results with those from Carrel and Hoekstra (2010), we can conclude that it is possible to outweigh the negative effects of misbehaving children by incorporating students with improved or positive behavior in their classrooms. This result particularly contributes to the evidence of optimal class design, indicating that finding the optimal share of bad-to-good peers can maximize the total effect of a program (Krueger, 2003; Lazear, 2001).

In Appendix 4 we present a more complete analysis of the structure and characteristics of these spillover effects, such as optimal combination of treated with high and low violence level, intensity of exposure, and proximity on misbehavior between enrolled and nonenrolled children within classrooms. What do we find?

First, from the results in Table 4 we learn that exposure to a greater share of treated children increases nonenrolled student performance. However, that group of treated classmates can have different levels of violence before the intervention. Therefore, an important missing factor in these results is whether the high- or the low-violence group is causing the main spillover effects. In other

> 21After adding individual controls, estimated coefficients are similar in magnitude and statistical significance except for bad behavior reports, which are no longer statistically significant due to the increase in the standard errors. Despite this, the sign of the effect is negative, indicating that a higher share of treated classmates reduces the effect on bad behavior reports and provides additional evidence of reduction in the formation of violence networks or disruption during classes.

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