Efficiency measurement, multiple-output technologie and distance functions: With application to European Railways

The single-output production function has long been regarded as one of the principle limitations of the econometric approach to technical efficiency measurement. If one wished to investigate efficiency in a multiple-output industry using econometric methods one would usually either: (a) aggregate outputs into a single index of output (e.g., total revenue or a multilateral Tornqvist output index); or (b) attempt to model the technology using a dual cost function. The first of these methods require that output prices be observable (and reflect revenue maximising behaviour), while the latter approach requires an assumption of cost-minimising behaviour. There are a number of instances, however, when neither of these requirements are met (the public sector contains many examples). In this study we outline the recently developed distance function solution to the multi-output problem. The method is illustrated using data on European railways. Output-orientated, input-orientated and constant returns to scale distance functions are estimated using corrected ordinary least squares. The distance function estimates are also compared with production function estimates involving aggregate output measures. These comparisons indicate that, for the case of European railways, a production function involving a multilateral Tornqvist output index exhibits substantially less aggregation bias relative to a production function that uses total revenue as a measure of aggregate output.