Fixed Bandwidth Asymptotics for Regression Discontinuity Designs
In this paper, the authors analyze the asymptotic distribution of local polynomial estimators in the context of regression discontinuity designs. The standard "Small-h" approach in the literature (Hahn Todd and van der Klaauw 2001, Porter 2003, Imbens and Lemieux 2008 and Lee and Lemieux 2009) is to assume the bandwidth, h, around the discontinuity shrinks towards zero as the sample size increases. However, in practice, the researcher has to choose an h > 0 to implement the estimator. This paper derives the fixed-h asymptotic distribution that allows for the bandwidth to be positive, providing refined approximations for the estimator's behavior.