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The indirect treatment effect on non-remedial students remaining in smaller, more homogeneous classrooms was 0.133 standard deviations (statistically insignificant, with a 95% confidence interval ranging from -0.076 to 0.189).
Fully treated friendship networks produced a 0.46 standard deviation increase in knowledge (versus 0.28 SD for students with zero treated friends) and a 0.24 standard deviation increase in positive sexual attitudes (versus 0.04 SD for students with zero treated friends).
Demonstrates that under heterogeneous student preferences across curricula (such as commercial versus academic/industrial tracks), student sorting increases average aggregate utility without imposing negative peer externalities on non-participants.
The theoretical framework demonstrates that under linear-in-means peer assumptions, student re-sorting does not alter aggregate population test scores ($\bar{Y} = \beta_0 \bar{X} + \beta_1 \bar{X}$); individual gains are strictly offset by losses to non-participants unless $\beta_2 > 0$.
Among vocational applicants, voucher winners attended schools where peers were 25% less likely to attend college and 33% more likely to drop out. Despite worse peer characteristics, voucher winners experienced a 25% increase in high school graduation likelihood and a 0.33 to 0.66 standard deviation increase in college entrance exam (ICFES) scores.
Assigned teacher effectiveness showed no statistically significant relationship with peer baseline math scores (coefficient = 0.246, SE = 0.164) or other peer traits; joint hypothesis p-values were 0.405 for grades 4–8 and 0.321 for high school, proving post-randomization peer stability.
The component removed by peer effect controls predicted student achievement after random assignment with a coefficient of 1.150 (p < 0.01, SE = 0.336), proving it contains causal teacher effectiveness. In contrast, the component removed by individual baseline score controls yielded a coefficient of 0.047 (SE = 0.042), showing baseline score controls successfully remove non-teacher sorting noise.
Aggregate interaction flows between peers across business-weighted and sentiment-weighted networks exhibit a high positive correlation ($r = 0.699$), and both correlate strongly with the unweighted benchmark network ($r = 0.821$ and $r = 0.951$, respectively). Virtual-within peer effects on proposal submission remain virtually identical across benchmark ($\beta = 0.533, p < 0.01$), business ($\beta = 0.521, p < 0.01$), and sentiment ($\beta = 0.530, p < 0.01$) networks.