Varying impacts of letters of recommendation on college admissions: Approximate balancing weights for subgroup effects in observational studies
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In a pilot study during the 2016-17 admissions cycle, the University of California, Berkeley invited many applicants for freshman admission to submit letters of recommendation. We are interested in estimating how impacts vary for under-represented applicants and applicants with differing a priori probability of admission. Assessing treatment effect variation in observational studies is challenging, however, because differences in estimated impacts across subgroups reflect both differences in impacts and differences in covariate balance. To address this, we develop balancing weights that directly optimize for “local balance” within subgroups while maintaining global covariate balance between treated and control populations. We then show that this approach has a dual representation as a form of inverse propensity score weighting with a hierarchical propensity score model. In the UC Berkeley pilot study, our proposed approach yields excellent local and global balance, unlike more traditional weighting methods, which fail to balance covariates within subgroups. We find that the impact of letters of recommendation increases with the predicted probability of admission, with mixed evidence of differences for under-represented minority applicants.
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