Data Envelopment Analysis as Least-Squares Regression

Data envelopment analysis (DEA) is an axiomatic, mathematical programming approach to productive efficiency analysis and performance measurement. This paper shows that DEA can be interpreted as a nonparametric least squares regression subject to shape constraints on production frontier and sign constraints on residuals. Thus, DEA can be seen as a nonparametric counter-part of the corrected ordinary least squares (COLS) model. This result bridges the conceptual and philosophical gap between DEA and regression methods to frontier estimation, and paves a way to a stochastic nonparametric methodology for frontier estimation.