Regression discontinuity design: estimating the treatment effect with standard parametric rate

Regression discontinuity design models are widely used for the assessment of treatment effects in psychology, econometrics and biomedicine, specifically in situations where treatment is assigned to an individual based on their characteristics (e.g. scholarship is allocated based on merit) instead of being allocated randomly, as is the case, for example, in randomized clinical trials. Popular methods that have been largely employed till date for estimation of such treatment effects suffer from slow rates of convergence (i.e. slower than $\sqrt{n}$). In this paper, we present a new model and method that allows estimation of the treatment effect at $\sqrt{n}$ rate in the presence of fairly general forms of confoundedness. Moreover, we show that our estimator is also semi-parametrically efficient in certain situations. We analyze two real datasets via our method and compare our results with those obtained by using previous approaches. We conclude this paper with a discussion on some possible extensions of our method.