Triadic Closure Reframes Student Group Assignment Effects

Random group assignment is often used to estimate how classrooms, dorms, or orientation groups shape social networks. The usual dyadic design asks whether two assigned-together people become connected. This paper argues that the dyadic question misses a policy-relevant channel: group assignment may create mutual friends, and those mutual friends may then create additional links through triadic closure.

The setting is first-year students at the Technical University of Denmark in 2013. Students were randomly assigned within study programs to teaching-assistant classrooms of roughly 30 students and, separately, to introductory social groups of about seven students. The authors link those assignments to phone-call metadata, SMS records, Bluetooth-based physical co-location, Facebook friendships, and administrative records from the Copenhagen Network Study.

Core Contribution

The paper’s main contribution is to move the estimation target from pairwise connection alone to a model that can distinguish direct dyadic link formation from triangle formation. That distinction changes the interpretation of the intervention. In a dyadic 2SLS design, social-group assignment looks like a strong treatment on later interaction: assigned-together students communicate more, meet more, and are much more likely to cross a composite friendship threshold. But the SUGM estimates suggest that, for social groups, the direct pairwise channel is small and statistically imprecise; most of the network effect is carried by the formation of closed triads.

Figure 1 gives the dyadic result before the higher-order decomposition: social groups shift several interaction margins, while classroom assignment has weaker and narrower effects.

Technical Approach

The authors first estimate a standard instrumental-variable dyadic model. The realized same-group indicator is instrumented with a recentered version of random assignment, following the logic that raw assignment probabilities differ by study program size, sex composition, dietary restrictions, and late assignment changes. They compute 1,000 counterfactual assignments to recenter the instrument, then use 2SLS to estimate effects on Facebook friendship, weekly call duration, SMS count, physical meetings, and a PCA-based binary friendship measure.

The second step adapts a subgraph generated model. In the SUGM, the observed network is the union of links formed directly between pairs and links induced by triangles among triples. For a pair $ij$, the model includes a direct-link equation; for a triad $ijk$, it includes a triangle equation whose treatment term counts how many pairs in the triad share the relevant group. Estimation uses a two-step control-function approach: first recover residuals from the same-group first stage, then estimate link and triangle parameters by nonlinear least squares over pairs and triads. Standard errors come from 100 bootstrap samples that resample study programs.

Results and Analysis

The dyadic estimates are large for social groups. In Table 3, same social-group membership raises Facebook friendship by 0.696 over a 0.207 baseline, weekly call duration by 0.290 minutes over 0.022, weekly SMS count by 1.334 over 0.083, weekly physical meetings by 2.928 over 1.775, and the binary friendship indicator by 0.317 over 0.085. In prose, the authors summarize this as a 32 percentage-point increase in link formation, about 3.8× the 8% baseline. Classroom effects are smaller: the binary friendship effect is 0.026 over a 0.083 baseline, and the clearest interaction effects are on call duration and SMS count rather than Facebook or physical meetings.

The SUGM estimates change the causal story. Table 4 reports that social-group membership has a negative and insignificant direct pair effect on link formation, -0.027 with standard error 0.110, but a positive triangle effect of 0.037 with standard error 0.007. Since a triad can contain three same-group pairs, the authors interpret this as an 11.1 percentage-point increase when all three students share the social group. Classroom estimates are noisier: the direct pair estimate is 0.120 with standard error 0.117, while the triangle estimate is -0.005 with standard error 0.005.

The simulation section shows why the decomposition matters for welfare analysis. Using 500 simulated networks per model, the dyadic and SUGM specifications produce similar link counts, about 130 versus 133, but very different clustering: 9.52 average triangles under the dyadic model versus 51.6 under the SUGM. Under a utility model that values direct links and spillovers through mutual friends, the SUGM predicts higher average utility whenever spillovers matter. Figure 3 shows that the difference is near zero when spillover strength is zero, then grows as the value of closed-triad spillovers rises, reaching 3.19 in the highest plotted spillover-strength and closed-triad-weight condition.

Caveats

The evidence is strongest for this institutional setting: one Danish technical university, one 2013 cohort, and students who opted into the Copenhagen Network Study. The paper is careful about this. Participation is voluntary, the network data observe only sampled students, Facebook and SMS use reflect a 2013 communication environment, and the SUGM relies on independence assumptions that abstract from higher-order dependence beyond links and triangles. The result is still useful: for policies intended to shape early social integration, the paper shows that counting extra pairwise links can miss the mechanism that makes small-group assignment work.