Estimation of a score-explained non-randomized treatment effect in fixed and high dimensions

In non-randomized treatment allocation models, treatment is assigned to a unit based on a score, e.g., scholarship is allocated based on the score obtained in a merit test, while antihypertensive treatments are allocated based on blood pressure level. In this paper, we present a new model coined SCENTS: Score Explained Non-Randomized Treatment Systems that utilizes the dependency of the score on the explanatory variables to permit efficient estimation. We derive an estimator of the treatment effect which is n consistent, asymptotically normal, and achieves semiparametric efficiency under normal errors. The analysis is extended to ultra-high dimensional vectors of covariates, where a n consistent and asymptotically normal debiased estimator is proposed. We analyze two real data sets via our method and compare our results with those obtained by using previous approaches like regression discontinuity design. Some possible extensions are discussed.