Estimating and explaining effciency in a multilevel setting: A robust two-stage approach

Various applications require multilevel settings (e.g., for estimating fixed and random effects). However, due to the curse of dimensionality, the literature on non-parametric efficiency analysis did not yet explore the estimation of performance drivers in highly multilevel settings. As such, it lacks models which are particularly designed for multilevel estimations. This paper suggests a semi-parametric two-stage framework in which, in a first stage, non-parametric α efficiency estimators are determined. As such, we do not require any a priori information on the production possibility set. In a second stage, a semiparametric Generalized Additive Mixed Model (GAMM) examines the sign and significance of both discrete and continuous background characteristics. The proper working of the procedure is illustrated by simulated data. Finally, the model is applied on real life data. In particular, using the proposed robust two-stage approach, we examine a claim by the Dutch Ministry of Education in that three out of the twelve Dutch provinces would provide lower quality education. When properly controlled for abilities, background variables, peer group and ability track effects, we do not observe differences among the provinces in educational attainments.