A comparison of parametric and non-parametric distance functions: With application to European railways

In this paper we use multi-output distance functions to investigate technical inefficiency in European railways. The principal aim of the paper is to compare the results obtained from the three alternative methods of estimating multi-output distance functions. Namely, the construction of a parametric frontier using linear programming: data envelopment analysis and corrected ordinary least squares (COLS). Input-orientated, output-orientated and constant returns to scale distance functions are estimated and compared. The results indicate a strong degree of correlation between the input- and output-orientated results for each of the three methods. There are also significant correlations observed between the results obtained using the alternative estimation methods, the strongest correlations being between the parametric linear programming and the COLS methods. Finally, the paper concludes with the suggestion that a combination of the technical efficiency scores, obtained from the three different methods, be used as the preferred set of scores. This idea is borrowed from the time series forcasting literature.