On endogenizing direction vectors in parametric directional distance function-based models

• Published in: European journal of operational research Vol. 262; no. 1; pp. 361 - 369
• Main Authors: Färe, Rolf, Pasurka, Carl, Vardanyan, Michael
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2017; Elsevier
• Subjects: Directional distance function; Economics and Finance; Humanities and Social Sciences; Nonlinear programming; OR in energy; OR in energy; Directional distance function; Nonlinear programming
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2017.03.040

•We show how to select directional distance functions’ direction vectors optimally.•The algorithm is based on parametric nonlinear optimization methods.•Empirical illustration using the U.S. electric power plant data is provided.•Optimally selected vectors and commonly used ad hoc vectors yield different results. Empirical studies of production technologies using directional distance functions have traditionally resorted to ad hoc ways of choosing direction vectors for these functions. Yet it is well known that the assumptions placed on the direction vector can have a non-negligible impact on the estimation results. Several recent studies have attempted to address this issue using econometric estimation and Data Envelopment Analysis. We demonstrate the use of parametric nonlinear programming to select the direction vector optimally. Data on the US electric power plants from early 2000s are used to show the difference between results obtained with endogenously determined direction vectors and ad hoc vectors.