Estimation and Inference of Regression Discontinuity Design with Ordered or Discrete Duration Outcomes

We consider the regression discontinuity (RD) design with the duration outcome which has discrete support. The parameters of policy interest are treatment effects on unconditional (duration effect) and conditional (hazard effect) exiting probabilities for each discrete level. We find that a flexible separability structure of the underlying continuous-time duration process can be exploited to substantially improve the quality of the fully nonparametric estimator. We propose global sieve-based estimators, and associated marginal and simultaneous inference. Simultaneous inference over discrete levels is nonstandard since the asymptotic variance matrix is singular with unknown rank. The peculiarity is delivered by the nature of the RD estimand, and we provide solutions. Random censoring and competing risks can also be allowed in our framework. The standard practice of applying local linear estimators to a sequence of binary outcomes is in general unsatisfactory, which motivates our semi-nonparametric approach. First, it provides poor hazard estimates near the end of the observation period due to small sizes of risk sets (in the neighborhood of the cutoff). Second, it fits each probability separately and thus does not support joint inference. The estimation and inference methods we advocate in this paper are computationally easy and fast to implement, which is illustrated by numerical examples