Using multi-level frontiers in DEA models to grade countries/territories

Several investigations to and approaches for categorizing academic journals/institutions/countries into different grades have been published in the past. To the best of our knowledge, most existing grading methods use either a weighted sum of quantitative indicators (including the case of one properly defined quantitative indicator) or quantified peer review results. Performance measurement is an important issue of concern for science and technology (S&T) management. In this paper we address this issue, leading to multi-level frontiers resulting from data envelopment analysis (DEA) models to grade selected countries/territories. We use research funding and researchers as input indicators, and take papers, citations and patents as output indicators. Our research results show that using DEA frontiers we can unite countries/territories by different grades. These grades reflect the corresponding countries' levels of performance with respect to multiple inputs and outputs. Furthermore, we use papers, citations and patents as single output (with research funding and researchers as inputs), respectively, to show country/territory grade changes. In order to increase the insight in this approach, we also incorporate a simple value judgment (that the number of citations is more important than the number of papers) as prior information into the DEA models to study the resulting changes of these Countries/Territories' performance grades.