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Data Envelopment Analysis as Nonparametric Least-Squares Regression

Author

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  • Timo Kuosmanen

    (Economic Research Unit, MTT Agrifood Research Finland, 00410 Helsinki, Finland, and Department of Business Technology, Helsinki School of Economics, 00101 Helsinki, Finland)

  • Andrew L. Johnson

    (Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843)

Abstract

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.

Suggested Citation

  • Timo Kuosmanen & Andrew L. Johnson, 2010. "Data Envelopment Analysis as Nonparametric Least-Squares Regression," Operations Research, INFORMS, vol. 58(1), pages 149-160, February.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:1:p:149-160
    DOI: 10.1287/opre.1090.0722
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    References listed on IDEAS

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