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

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.