Plausible values and their use in efficiency analyses with educational data

There is extensive literature focused on the evaluation of efficiency in the education sector, both at the micro level, analyzing the performance of students or schools, and at the macro level, exploring the behavior of regions or countries. This type of studieshas been driven by exploiting data available in international large-scale assessments, where output measures are usually represented by the so-called plausible values, understood as a representation of the range of the abilities of each student. In this study, we analyze the different options available to incorporate these plausible values in applied studies focused on measuring efficiency and how the results obtained can be affected according to the selected criterion. To do this, we assess the efficiency of Spanish schools participating in PISA using the two most common methodologies in this field: data envelopment analysis and stochastic frontier analysis and considering three different proxies for the educational output: (i) a single plausible value; (ii) an aggregate measure calculated from the ten plausible values available; (iii) an average of the estimates made with the ten plausible values separately. The main conclusion derived from our results is that there are hardly any differences between in the estimates made with different strategies.