Data Envelopment Analysis as Nonparametric Least-Squares Regression

• Published in: Operations research Vol. 58; no. 1; pp. 149 - 160
• Main Authors: Kuosmanen, Timo, Johnson, Andrew L.
• Format: Journal Article
• Language: English
• Published: Hanover, MD INFORMS 01.01.2010; Institute for Operations Research and the Management Sciences
• Subjects: Applied sciences; Bankers; benchmarking; Benchmarks; Consistent estimators; Data envelopment analysis; Decision analysis; Estimating techniques; Estimation bias; Estimation methods; Estimators; Exact sciences and technology; frontier estimation; Information retrieval noise; Inventory control, production control. Distribution; Least squares; Mathematical programming; Mathematics; nonparametric estimation; Nonparametric inference; Nonparametric models; Nonparametric statistics; Operational research and scientific management; Operational research. Management science; performance measurement; Probability and statistics; Production estimates; Production functions; Regression analysis; Sciences and techniques of general use; Statistics; Studies; United States; Performance evaluation; Integration; Parametric programming; Benchmarking; Non parametric estimation; Regression analysis; Production function; Modeling; Axiomatic; frontier estimation; performance measurement; Unbiased estimation; Least squares method; nonparametric estimation; Square shape; Competitive intelligence; Asymptotic approximation; Econometrics; Data envelopment analysis; Mathematical programming
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1090.0722

Data envelopment analysis (DEA) is known as a nonparametric mathematical programming approach to productive efficiency analysis. In this paper, we show that DEA can be alternatively interpreted as nonparametric least-squares regression subject to shape constraints on the frontier and sign constraints on residuals. This reinterpretation reveals the classic parametric programming model by Aigner and Chu [Aigner, D., S. Chu. 1968. On estimating the industry production function. Amer. Econom. Rev. 58 826-839] as a constrained special case of DEA. Applying these insights, we develop a nonparametric variant of the corrected ordinary least-squares (COLS) method. We show that this new method, referred to as corrected concave nonparametric least squares (C 2 NLS), is consistent and asymptotically unbiased. The linkages established in this paper contribute to further integration of the econometric and axiomatic approaches to efficiency analysis.