Identification and Estimation in Fuzzy Regression Discontinuity Designs with Covariates

We study fuzzy regression discontinuity designs with covariates and characterize the weighted averages of conditional local average treatment effects (WLATEs) that are point identified. Any identified WLATE equals a Wald ratio of conditional reduced-form and first-stage discontinuities. We highlight the Compliance-Weighted LATE (CWLATE), which weights cells by squared first-stage discontinuities and maximizes first-stage strength. For discrete covariates, we provide simple estimators and robust bias-corrected inference. In simulations calibrated to common designs, CWLATE improves stability and reduces mean squared error relative to standard fuzzy RDD estimators when compliance varies. An application to Uruguayan cash transfers during pregnancy yields precise RDD-based effects on low birthweight.

💡 Research Summary

This paper addresses a fundamental gap in the fuzzy regression discontinuity design (RDD) literature: when covariates are available, which causal parameters are point‑identified and which of those make the most use of the design’s informational strength. The authors formalize a broad class of weighted local average treatment effects (WLA TEs), defined as weighted averages of covariate‑specific local average treatment effects (LATEs) at the cutoff. Under a set of assumptions that are essentially the standard RDD conditions applied conditionally on covariates—continuity of potential outcomes in the running variable, conditional independence of potential outcomes and treatment from the running variable, a weak monotonicity condition (for each covariate value, either compliers or defiers but not both exist near the cutoff), overlap (each covariate value with positive weight appears on both sides of the cutoff), and a non‑zero conditional first‑stage discontinuity—the paper proves that a WLA TE is point‑identified if and only if every covariate value receiving positive weight satisfies the latter two conditions. Moreover, any identified WLA TE can be expressed as a Wald ratio
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