  Treatment effects in regression discontinuity designs (RDDs) are often
estimated using local regression methods. However, global approximation methods
are generally deemed inefficient. In this paper, we propose a semiparametric
framework tailored for estimating treatment effects in RDDs. Our global
approach conceptualizes the identification of treatment effects within RDDs as
a partially linear modeling problem, with the linear component capturing the
treatment effect. Furthermore, we utilize the P-spline method to approximate
the nonparametric function and develop procedures for inferring treatment
effects within this framework. We demonstrate through Monte Carlo simulations
that the proposed method performs well across various scenarios. Furthermore,
we illustrate using real-world datasets that our global approach may result in
more reliable inference.
