International efficiency evaluation of education and impacts of bullying: a value inversion–data envelopment analysis approach

Education plays a vital role in the development of any country or region, making it imperative to address obstacles that hinder educational quality such as school bullying. This is an under-researched topic in the social sciences. Bullying is a form of social mistreatment that may have detrimental effects, because students who experience frequent bullying tend to perform poorer compared to their peers who do not report such incidents. Given this evidence, it is crucial to assess the educational performance of countries by considering the overall well-being, including mental well-being, of students. In this context, data envelopment analysis (DEA) is a valuable method for evaluating the performance of decision-making units in education. In our paper, we discuss various approaches to apply DEA when dealing with "undesirable" outputs like bullying. Common techniques involve transforming undesirable outputs using reciprocal transformations and employing a "bad-output" model. However, these methods have several drawbacks, such as altering the nature of the selected output items, loss of linearity, reduced robustness of the efficiency frontier, and limited versatility. To address these concerns, our paper proposes and tests a value inversion–DEA model that can consistently transform "undesirable" data into a reverse measurement scale, while preserving linearity. We demonstrate the high versatility of this model across different types of DEA models with undesirable outputs. Furthermore, we apply this proposed method to assess the educational efficiency of OECD countries, focusing on bullying as an undesirable output. Our findings show that significant improvements in performance are possible in many countries by addressing school bullying.