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Decomposing DEA self-efficiency: A cross-efficiency-based quantity-price framework
Yanjun Liu1, Zanfu Ma2, Hao Zhan1
1School of Transport and Logistics, Guangzhou Railway Polytechnic, Guangzhou, China.
Plos One
|August 10, 2026
Summary
This study introduces a new framework to decompose Data Envelopment Analysis (DEA) self-efficiency into quantity and price components. It reveals how production technology and endogenous weights jointly shape performance metrics.
Area of Science:
- Operations Research
- Econometrics
- Management Science
Background:
- Data Envelopment Analysis (DEA) self-efficiency scores are crucial for performance measurement.
- Understanding the joint impact of endogenous weights and production technology on DEA efficiency remains challenging.
- Existing cross-efficiency studies often overlook the rich information within cross-efficiency matrices.
Purpose of the Study:
- To develop a quantity-price decomposition framework for DEA self-efficiency.
- To quantify the contributions of production-position and endogenous valuation information to efficiency scores.
- To provide an interpretive lens for understanding DEA self-efficiency formation.
Main Methods:
- Exploiting the dual informational structure of cross-efficiency matrices.
- Developing a reciprocal Quantity Index (QI) and Price Index (PI).
- Decomposing self-efficiency differences into quantity-related and valuation-related components using four cross-efficiency elements.
Main Results:
- A novel framework for decomposing DEA self-efficiency into quantity and price elements is proposed.
- The framework reveals how production-position and endogenous valuation information are embedded in cross-efficiency matrices.
- Empirical analysis demonstrates the reshaping of quantity and valuation structures under alternative technological assumptions.
Conclusions:
- The proposed framework offers an exact algebraic representation for self-efficiency differences.
- It provides a method to quantify the influence of endogenous weights and technological assumptions on DEA efficiency.
- This study shifts focus to the informational structure of DEA, enhancing understanding of model dependence and efficiency formation.
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