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Data Envelopment Analysis as Nonparametric Least-Squares Regression

Economic Research Unit, MTT Agrifood Research Finland, 00410 Helsinki, Finland, and Department of Business Technology, Helsinki School of Economics, 00101 Helsinki, Finland
Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843
timo.kuosmanen{at}hse.fi
ajohnson{at}tamu.edu

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 (C²NLS), is consistent and asymptotically unbiased. The linkages established in this paper contribute to further integration of the econometric and axiomatic approaches to efficiency analysis.

Subject classifications: frontier estimation; mathematical programming; nonparametric estimation; performance measurement; benchmarking.
History: Received May 2008; revision received November 2008; accepted April 2009.