关于比率变量在数据包络分析中的适用性：在教育中的应用及方法扩展
Data envelopment analysis with common-denominator ratio variables: An application to education with methodological extensions
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中文总结 AI 辅助
研究比率变量在数据包络分析中的适用性，通过建立等价性结果开发评估OECD国家效率的框架，有方法创新，还介绍了估计改进方向等方法及对新兴方法的贡献，可用于分析相关报告数据。
中文摘要 AI 辅助
众所周知，比率变量的使用与凸性数据包络分析（DEA）的基本假设不一致。本文建立了一个一般性结果，表明在规模报酬可变下具有比率变量的DEA模型与在规模报酬不变下具有数量（非比率）变量的DEA模型之间的等价性，前提是所有变量都是具有共同分母的比率变量。这一结果使得能够基于国际学生评估项目（PISA）报告的结果，以平均成绩分数为产出，开发一个评估经济合作与发展组织（OECD）国家效率的框架。在此框架中，给出了一些方法创新，如纳入经济社会和文化地位指数（ESCS）作为输入，从而能与社会经济水平较低的国家进行更公平的比较。还介绍了估计改进方向和计算适合提高每个成绩分数难度的目标的不同方法。最后，回顾并引入了对新兴方法的一些新贡献，如自适应约束包络样条（ACES）的有效前沿估计、随机机会约束模型和模糊模型。所有这些方法可用于分析来自其他PISA或类似报告的数据，让非专业人员能正确实施DEA。
英文摘要
The use of ratio variables in convex Data Envelopment Analysis (DEA) models has long been recognized as a methodological issue, as ratios may be incompatible with the convexity assumptions underlying standard DEA. However, in this paper, we prove that if all variables are ratio variables sharing a common denominator, then convex combinations of feasible activities are also feasible. Moreover, we establish a result demonstrating the equivalence between DEA models with common-denominator ratio variables under variable returns to scale and DEA models with volume (non-ratio) variables under constant returns to scale. These significant results enable 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 extensions, 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.
发表机构
- University of Valencia（瓦伦西亚大学）
- UNED（西班牙国立远程教育大学）
机构由 AI 辅助整理，请以论文原文为准。
