The Translog Costs Function Applied to European Railways.

This paper expands the exploratory analysis undertaken by Vigoroux-Steck (1990), who used statistical cost techniques, in conjunction with UIC published data, to estimate cost functions for 13 Western European railway operations. Four improvements have been made to Steck's work. Firstly, the data has been up-dated from 1987 to 1990 and re-indexed to incorporate the most recent information on international prices. Secondly, consistency is introduced into the Returns to Scale and Density measures by including all relevant estimated parameter values. Thirdly, we constrain the repssion model to insure linear homogeneity of degree one in factor prices. Fourthly, we attempt to reduce statistical problems by redefining variables around the sample mean (although there is further work to be undertaken in this respect). Three further amendments were undertaken with limited success. Attempts to introduce a more complex treatment of technological change led to implausible returns to scale. Attempts to re-define the returns to density measure by using a length of line variable rather than a density (train kilometres divided by length of line) variable also led to some implausible results. A re-definition of Steck's returns to density measure gave more plausible results. Despite these statistical problems, some common results do come hmgh. In particular, it appears that Western Europe's largest railways exhibit decreasing returns to scale and increasing returns to density. This does suggest that some European railways are operating beyond the point of maximum efficient scale and re-organisation into smaller units may be sensible. Our findings are less robust on how small these units should be. Railways with less than 3,000 km of route may be below the minimum efficient scale. Another important finding is that some Western Europe railways do exhibit diseconomies of density most notably those of Switzerland and the Netherlands. Proposed expansion of infrastructure in these countries may be sensible. Lastly, in terms of an index of managerial efficiency, we find that the railway of Sweden is a consistently high performer and those of Austria and Belgium poor performers.