A regression discontinuity stochastic frontier model with an application to educational attainment

We extend the regression discontinuity design model to the case in which the line of best fit is replaced by a stochastic frontier. The method allows causality issues to be examined in a context where the performance measure is subject to inefficiency and where, in addition to the relationship between dependent and explanatory variables, there may be a discontinuity in the inefficiency measure at the break. The inefficiency scores are modelled as part of the system, but we follow a novel nonparametric approach. We illustrate the method with an application to data from Texas on class size and pupil performance, exploiting a Maimonides' rule discontinuity. We find that class size affects performance in the expected direction but that there is a corresponding effect in the opposite direction on efficiency. This may contribute to the difficulty experienced by the authors of earlier studies in identifying a class size effect.