Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods
Abstract
Boundary discontinuity designs are used to learn about causal treatment effects along a continuous assignment boundary that splits units into control and treatment groups according to a bivariate location score. We analyze location-based local polynomial treatment effect estimators that directly employ the bivariate score of each unit. We develop pointwise and uniform estimation and inference methods for the Boundary Average Treatment Effect Curve (BATEC), as well as for two aggregated causal parameters: the Weighted Boundary Average Treatment Effect (WBATE) and the Largest Boundary Average Treatment Effect (LBATE). Our results cover both sharp and fuzzy (imperfect compliance) designs. We illustrate the methods with an empirical application, and provide companion general-purpose software. The supplemental appendix includes additional substantive theoretical results, methodological details, and simulation evidence.
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