Randomization Method
At the school level, randomization occurs across two dimensions simultaneously: (1) treatment saturation as schools are assigned to one of four saturation arms (0%, 20%, 50%, 80%), determining the share of students within each school eligible to receive the information intervention; and (2) default enrollment condition, where schools are assigned to either an opt-in or opt-out framing, crossed with saturation to yield eight school-level treatment groups. Target allocation across saturation levels is 30%, 20%, 30%, and 20% of schools respectively, split equally between opt-in and opt-out schools within each saturation level. School randomization is stratified by school size (above vs. below median enrollment). Within schools, individual students are randomly assigned to treatment or control (for the information intervention) consistent with their school's saturation target, with treatment status harmonized among siblings.
A rerandomization procedure was implemented computationally using Python. Following school assignment, students within each school were randomly assigned to treatment or control consistent with their school's saturation target. A post-processing step then unified treatment status among siblings sharing the same parent within a school, with ties broken randomly. Across 50,000 iterations, the procedure selected the assignment minimizing the maximum deviation between realized and target shares of schools and students across saturation arms, subject to a tolerance of 2 percentage points.