On the suitability of ratio variables in data envelopment analysis: An application to education with methodological extensions

2026-07-19

AI Summary

This study addresses the limitation of traditional data envelopment analysis (DEA) in handling ratio-type variables, which has hindered its application in international educational assessments such as PISA. The authors propose a novel DEA framework tailored for fully ratio-based inputs and outputs, establishing equivalence between the variable returns-to-scale ratio model and the constant returns-to-scale volumetric model to enable fair efficiency measurement across OECD countries. Innovatively incorporating the index of economic, social, and cultural status as an input, the framework extends both radial and directional distance functions and integrates advanced techniques—including adaptive convex envelope splines (ACES), stochastic chance constraints, and fuzzy DEA—to enhance model robustness and usability. Empirical application to PISA data facilitates equitable cross-socioeconomic comparisons of educational performance, offering a generalizable and reproducible analytical tool for international assessments.

Abstract

It is well known that the use of ratio variables is inconsistent with the fundamental assumptions of convex Data Envelopment Analysis (DEA). However, in this paper, we establish a general result demonstrating the equivalence between DEA models with ratio variables under variable returns to scale and DEA models with volume (non-ratio) variables under constant returns to scale, provided that all variables are ratio variables sharing a common denominator. This significant result enables the development of a framework for evaluating the efficiency of the Organisation for Economic Co-operation and Development (OECD) countries based on the results of the Programme for International Student Assessment (PISA) report, using mean performance scores as outputs. In this framework, we give some methodological innovations, such as the incorporation of the index of economic social and cultural status (ESCS) as an input, thereby enabling fairer comparisons with countries with a lower socio-economic level. Furthermore, we introduce different methods for estimating directions of improvement and calculating targets appropriate to the difficulty of improving each performance score. Finally, we review and introduce several novel contributions to emerging methodologies that can complement classical radial and directional models, such as efficient frontier estimation with adaptive constrained enveloping splines (ACES), stochastic chance-constrained models, and fuzzy models. All these methodologies can be used to analyse data from other PISA or similar reports, allowing non-specialists to implement DEA appropriately.

Problem

• ratio variables
• Data Envelopment Analysis
• efficiency evaluation
• PISA
• OECD countries

Innovation

• ratio variables
• data envelopment analysis
• variable returns to scale
• adaptive constrained enveloping splines
• stochastic chance-constrained models