Experimental Design Details
The methodology of the project corresponds to a Randomized Control Trial (RCT) that varies peer characteristics in two variables: cognitive and social skills. Cognitive skills are measured by the score in the written test during the admission process. Social skills correspond to measures of centrality in social networks for 4th and 5th graders (the centrality measures were calculated using network surveys performed in November of 2016. Students were asked to list their friends, study partners, social partners and those they would like to have as roommates.) and the social-fit score (a group of psychologists who observe how do applicants interact with each other assigns an individual score for social behaviors such as cooperation, teamwork, and empathy.) for 3rd graders. In order to avoid weak variation in peers characteristics , students are categorized into four different types: (i) type HH: high cognitive and high social, (ii) type HL: high cognitive and low social, (iii) type LH: low cognitive and high social, and (iv) type LL: low cognitive and low social.
Conditional on the student type, they were randomly assigned to one of ten potential groups. Each one of these groups is composed of students of one or two different types. The following chart shows the ten possible combinations that can be formed using the four types. Group 1, for example, is composed only by students of type HH, while group 3 is composed by students of types HL and LH. During the 2017 school year, 21 out of 25 schools in the COAR network followed these groups to assign students to dorms (3rd, 4th, and 5th grade) and classrooms (3rd grade).
Given the composition of these groups, and that conditional on the student type they were randomly assigned to certain type of peers, the experimental design allows to identify the causal effect of being exposed to HH, HL, and LH peers relative to LL peers with the following equation:
\begin{equation}
y_{it} = \beta_{0} + \beta_{1} HH_{it} + \beta_{2} HL_{it} + \beta_{3} LH_{it} + \gamma_{t} + \varepsilon_{it} \;,
\label{eq: main}
\end{equation}
where $y_{it}$ corresponds to the outcome of student $i$ categorized with type $t$; $HH_{it}$, $HL_{it}$, $LH_{it}$ correspond to dummy variables of being assigned to peers of high cognitive and high social skills, high cognitive and low social skills, and low cognitive and high social skills, respectively; $\gamma_{t}$ corresponds to type fixed effects since the likelihood of being assigned to peers of each type vary by this variable\footnote{Students of each type $t$ are twice as likely of being assigned to peers of type $t$ than of being assigned to type $\tilde{t}$ with $\tilde{t} \neq t$. }; finally, $\varepsilon_{it}$ corresponds to an error term.