Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods

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 $\mathit{\text{Boundary}}\mathit{\text{Average}}\mathit{\text{Treatment}}\mathit{\text{Effect}}\mathit{\text{Curve}}$ (BATEC), as well as for two aggregated causal parameters: the $\mathit{\text{Weighted}}\mathit{\text{Boundary}}\mathit{\text{Average}}\mathit{\text{Treatment}}\mathit{\text{Effect}}$ (WBATE) and the $\mathit{\text{Largest}}\mathit{\text{Boundary}}\mathit{\text{Average}}\mathit{\text{Treatment}}\mathit{\text{Effect}}$ (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.