Data Envelopment Analysis as Nonparametric Least-Squares Regression

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 frontier and sign constraints on residuals. This reinterpretation reveals the classic parametric programming model by Aigner and Chu (1968) 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 and benchmarking. Area of review: Decision Analysis