Nonparametric Treatment Effect Identification in School Choice

2021-12-07

AI Summary

This paper addresses the nonparametric identification and estimation of causal effects in centralized school assignment, focusing on settings where lottery-based randomization and regression discontinuity (RD) variation coexist. We characterize the identified set for atomic treatment effects (aTEs)—the conditional average treatment effect between any two schools given student covariates—driven solely by RD variation. We demonstrate that conventional aggregated estimators systematically ignore RD information, causing their asymptotic weights on RD-driven aTEs to vanish. To address this, we propose an empirical diagnostic tool for assessing RD weighting and a novel aggregation framework for RD-aTE inference. Theoretically, we construct a consistent and asymptotically normal estimator for RD-aTEs. Simulation studies and applications to real district-level data validate its finite-sample performance. Our core contribution is a unified nonparametric identification framework accommodating both lottery and RD variation, along with a bias-corrected estimation strategy that restores the role of RD variation in causal inference.

Abstract

This paper studies nonparametric identification and estimation of causal effects in centralized school assignment. In many centralized assignment settings, students are subjected to both lottery-driven variation and regression discontinuity (RD) driven variation. We characterize the full set of identified atomic treatment effects (aTEs), defined as the conditional average treatment effect between a pair of schools, given student characteristics. Atomic treatment effects are the building blocks of more aggregated notions of treatment contrasts, and common approaches estimating aggregations of aTEs can mask important heterogeneity. In particular, many aggregations of aTEs put zero weight on aTEs driven by RD variation, and estimators of such aggregations put asymptotically vanishing weight on the RD-driven aTEs. We develop a diagnostic tool for empirically assessing the weight put on aTEs driven by RD variation. Lastly, we provide estimators and accompanying asymptotic results for inference on aggregations of RD-driven aTEs.

Problem

• Identify causal effects in school assignment algorithms
• Characterize atomic treatment effects between schools
• Propose new aggregation schemes for treatment effects

Innovation

• Nonparametric identification of atomic treatment effects
• Combines lottery and RD-driven variation analysis
• Proposes new aggregation schemes for aTEs