A Regression Discontinuity Stochastic Frontier Model with an Application to Educational Attainment

Johnes, Geraint and Tsionas, Mike (2019) A Regression Discontinuity Stochastic Frontier Model with an Application to Educational Attainment. Stat, 8 (1): e242. ISSN 2049-1573

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Abstract

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. In the tradition of Battese and Coelli (1995), the inefficiency scores are modelled as part of the system but we follow a novel non-parametric 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 authors of earlier studies in identifying a class size effect.