This paper from the National Bureau of Economic Research (NBER) provides an outline of some of the practical issues around the implementation of Regression Discontinuity (RD) designs whilst reviewing some of the new developments in the area.
"After reviewing some basic concepts in Section 2, the paper focuses on five specific issues in the implementation of RD designs. In Section 3 we stress graphical analyses as powerful options for illustrating the design. In Section 4 we discuss estimation and suggest using local linear regression options using only the observations close to the discontinuity point. In Section 5 we propose choosing the bandwidth using cross validation. In Section 6 we provide a simple plug-in estimator for the asymptotic variance and a second estimator that exploits the link with instrumental variables options derived by HTV. In Section 7 we discuss a number of specification tests and sensitivity analyses based on tests for (a) discontinuities in the average values for covariates, (b) discontinuities in the conditional density of the forcing variable, as suggested by McCrary, and (c) discontinuities in the average outcome at other values of the forcing variable." (Imbens & Lemieux, 2007)
Imbens, G., & Lemieux, T. (2007). Regression discontinuity designs: A guide to practice. Journal of Econometrics, Retrieved from http://www.nber.org/papers/w13039.pdf?new_window=1