© Jesse Rothstein 2024
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Annals of Applied Statistics 17 (4).
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In a pilot program during the 2016–17 admissions cycle, the University of California, Berkeley invited many applicants for freshman admission to submit letters of recommendation. This proved controversial within the university, with concerns that this change would further disadvantage applicants from disadvantaged groups. To inform this debate, we use this pilot as the basis for an observational study of the impact of submitting letters of recommendation on subsequent admission, with the goal of estimating how impacts vary across predefined subgroups. Understanding this variation is challenging in an observational setting because estimated impacts reflect both actual treatment effect variation and differences in covariate balance across groups. To address this, we develop balancing weights that directly optimize for “local balance” within subgroups while maintaining global covariate balance between treated and control units. Applying this approach to the UC Berkeley pilot study 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 applicant strength. However, we find little average difference for applicants from disadvantaged groups, although this result is more mixed. In the end we conclude that soliciting letters of recommendation from a broader pool of applicants would not meaningfully change the composition of admitted undergraduates
Journal of the Royal Statistical Society, Series B 84 (2).
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N.B.: An earlier version of this paper circulated under the title “Synthetic Controls and Weighted Event Studies with Staggered Adoption.”
Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units that closely balances the treated unit’s pre-treatment outcomes. In this paper, we generalize SCM, originally designed to study a single treated unit, to the staggered adoption setting. We first bound the error for the average effect and show that it depends on both the imbalance for each treated unit separately and the imbalance for the average of the treated units. We then propose ‘partially pooled’ SCM weights to minimize a weighted combination of these measures; approaches that focus only on balancing one of the two components can lead to bias. We extend this approach to incorporate unit-level intercept shifts and auxiliary covariates. We assess the performance of the proposed method via extensive simulations and apply our results to the question of whether teacher collective bargaining leads to higher school spending, finding minimal impacts. We implement the proposed method in the augsynth R package.
Journal of the American Statistical Association 116 (536).
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The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The “synthetic control” is a weighted average of control units that balances the treated unit’s pretreatment outcomes and other covariates as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pretreatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pretreatment fit is infeasible. Analogous to bias correction for inexact matching, augmented SCM uses an outcome model to estimate the bias due to imperfect pretreatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pretreatment fit while minimizing extrapolation from the convex hull. This estimator can also be expressed as a solution to a modified synthetic controls problem that allows negative weights on some donor units. We bound the estimation error of this approach under different data-generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to estimate the impact of the 2012 Kansas tax cuts on economic growth. We implement the proposed method in the new augsynth R package.
Journal of Economic Perspectives 30(3).
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Economics of Education Review 28(3).
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Data from college admissions tests can provide a valuable measure of student achievement, but the non-representativeness of test-takers is an important concern. We examine selectivity bias in both state-level and school-level SAT and ACT averages. The degree of selectivity may differ importantly across and within schools, and across and within states. To identify within-state selectivity, we use a control function approach that conditions on scores from a representative test. Estimates indicate strong selectivity of test-takers in “ACT states,” where most college-bound students take the ACT, and much less selectivity in SAT states. To identify within- and between-school selectivity, we take advantage of a policy reform in Illinois that made taking the ACT a graduation requirement. Estimates based on this policy change indicate substantial positive selection into test participation both across and within schools. Despite this, school-level averages of observed scores are extremely highly correlated with average latent scores, as across-school variation in sample selectivity is small relative to the underlying signal. As a result, in most contexts the use of observed school mean test scores in place of latent means understates the degree of between-school variation in achievement but is otherwise unlikely to lead to misleading conclusions.
© Jesse Rothstein 2024
UC Berkeley Privacy Policy
Website design & development by MIGHTYminnow.