Nonparametric Bayes Analysis of the Sharp and Fuzzy Regression Discontinuity Designs

We develop a Bayesian analysis of the sharp and fuzzy RD designs in which the unknown functions of the forcing variable are modeled by penalized natural cubic splines, and the error is distributed as student-t. Several novel ideas are employed. First, in estimating the functions of the forcing variable, we include a knot at the threshold, which is not in general an observed value of the forcing variable, to allow for curvature in the estimated functions from the breakpoint to the nearest values on either side of the breakpoint. Second, we cluster knots close to the threshold with the aim of controlling the approximation bias. Third, we introduce a new second-difference prior on the spline coefficients that can deal with unequally spaced knots. The number of knots and other features of the model are compared through marginal likelihoods, which are easily computed by the method of Chib (1995). Fourth, we develop an analysis of the fuzzy design based on a new model that utilizes the principal stratification framework, adapted to the RD design. Posterior computations for both designs are straightforward and are implemented in two R-packages that may be downloaded. The excellent performance of the proposed Bayes ATE and (complier) ATE estimates is documented in simulation experiments.