Regression Discontinuity with Integer Running Variable and Non-Integer Cutoff: Dental Care Program Effect on Expenditure

In regression discontinuity (RD), the treatment is determined by a continuous running variable G crossing a known cutoff c or not. However, often G is observed only as a rounded-down integer S (e.g., birth year observed instead of birth date), and c is not an integer. In this case, the “cutoff sample†(the observations with the same S value around c) cannot be used, because it is not clear whether their G actually crossed c or not. This paper shows that if the distribution of the measurement error e ≡ G − S is specified, then despite non-integer c, the cutoff sample can be used fruitfully in estimating the treatment effect and in testing for the distributional assumption on e. Particularly, there are good reasons to believe that e is uniform on [0,1], not least because e is close to a popular way how pseudo uniform random numbers are generated in simulation studies. Also, whereas two-step estimation has been proposed in the RD literature, we show that the treatment effect can be estimated with single-step OLS/IVE as in typical RD with G observed. A simulation study and an empirical analysis for effects of a dental care support program on dental expenditure are provided.