Estimating Technical and Allocative Efficiency Using Stochastic Frontier Analysis and Cost Frontier: an Application to Railway

Estimating Technical and Allocative Efficiency Using Stochastic Frontier Analysis and Cost Frontier: an Application to Railway


BOUGNA TCHOFO EMMANUEL, Laboratory Of Transport Economics, Professor YVES CROZET, Laboratory Of Transport Economics


The aim of this article is to present a statistical methodology that allows us to estimate a stochastic production function and measure dirrived efficiencies. The originality of the method is that it lets of simultaneously measuring technical efficiency, allocative efficiency, associated costs and the different factors of effectiveness. As estimation method we got the ordinary least squares and maximum likelihood. The feasibility of this approach is illustrated by an application to the analysis of technical and allocative efficiency of the railway networks of some European countries namely France, Germany and Switzerland


European commission adopted on 30 January 2013 the fourth railway package whose mission is to complete the unification of the railway market. This fourth package, as the previous packages, aims to improve the technical and economic efficiency of railway industry.
To estimate technical effectiveness and productivity of a given sector, the econometricians use stochastic production frontier models, which have been proposed by Aigner, Lovell & Schmidt (1977), and Meeusen and Van den Broeck (1977). These models related physical quantities of output and input. The idea is to define a functional link between the output and the different inputs. The aim of the model is to measure productivity and technical efficiency of the sector. A literature review shows that some authors have tried to measure the productivity and efficiency of the railway system. For example, using data of the International Railways Union (IRU), A. J. Smith (2011) shows a 40% gap between the performance of the better infrastructure European Infrastructure manager (IM) and the British’s IM. This result fits in the sequel to that which occurs in the McNulty report (2011). Based on data for 2008, this report underlined a 34% gap between the top-performing European IM and Network Rail. In this model, performance is measured by the cost of production. Cantos and Maudis (2000) used frontier models to estimate the productivity and efficiency of 15 systems European rail. These authors show that firms that have high performance are those that have a high degree of autonomy. Estimating the frontier cost of the Japanese railway companies, F. Mizutani et al. show that introduction of yardstick regulation and competition tend to decrease a rail company's variable cost. The positive effect of yardstick regulation where also shown by Bouf and Peguy (2001).
This paper uses German, French and Switzerland data to compare the effeciency of the railway systems of these countries. Like Bouf and Peguy (2001), this analysis is limited to railway and passenger transport. As a model to estimate we used Stochastic frontier analysic model, which allows us to measure simultaneously technical efficiency and allocative efficiency of rail systems in Germany, France and Switzerland. This model brings together the production, factors of production and the costs. In this model cost function and production function are approximated by a translog function. Like Bouf and Péguy (2001), we took into account two dimensions of production : Numbers of train-kilometers as proxy for the supply and number of traffic unit (ton-kilometer plus passengers-kilometer) as proxy for traffic. Three dimensions are needed to measure the performance of a railway system namely: costs efficiency, effectiveness and marketing efficiency(Bouf and Peguy, 2001). In these paper we will only use cost efficiency and effectiveness as a performance indicator. As estimation technique we use ordinary least squares method and maximum likelihood method. The goal of the model is to measure the performance of the rail systems but also lists the main factors that affect this performance.


Association for European Transport