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In a pilot program during the 2016-17 admissions cycle, the University ofCalifornia, Berkeley invited many applicants for freshman admission to submitletters of recommendation. We use this pilot as the basis for an observationalstudy of the impact of submitting letters of recommendation on subsequentadmission, with the goal of estimating how impacts vary across pre-definedsubgroups. Understanding this variation is challenging in observationalstudies, however, because estimated impacts reflect both actual treatmenteffect variation and differences in covariate balance across groups. To addressthis, we develop balancing weights that directly optimize for ``local balance''within subgroups while maintaining global covariate balance between treated andcontrol units. We then show that this approach has a dual representation as aform of inverse propensity score weighting with a hierarchical propensity scoremodel. In the UC Berkeley pilot study, our proposed approach yields excellentlocal and global balance, unlike more traditional weighting methods, which failto balance covariates within subgroups. We find that the impact of letters ofrecommendation increases with the predicted probability of admission, withmixed evidence of differences for under-represented minority applicants.

Varying impacts of letters of recommendation on college admissions: Approximate balancing weights for subgroup effects in observational studies