What explains the performance of students in a heterogeneous environment? Conditional efficiency estimation with continuous and discrete environmental variables

Efficiency estimations which do not account for the operational environment where production units are operating in may have only a limited value. This article presents a fully nonparametric framework to estimate relative performance of production units when accounting for continuous and discrete background variables. Using insights from recent developments in nonparametric econometrics, we show how conditional efficiency scores can be estimated using a tailored mixed kernel function with a data-driven bandwidth selection. The methodology is applied to the sample of dutch pupils from the organization for economic co-operation and development's programme for international student assessment (oecd pisa) data set. We estimate students' performance and the influence of its background characteristics. The results of our application show that several family- and student-specific characteristics have a statistically significant effect on the educational efficiency, while school-level variables do not have impact on performance.