Efficiency Measurement in Network Industries: Application to the Swiss Railway Companies

Abstract

This paper examines the performance of several panel data models to measure cost and scale efficiency in network industries. Network industries are characterized by a high degree of heterogeneity, much of which is network-specific and unobserved. The unaccounted-for heterogeneity can create bias in the inefficiency estimates. The stochastic frontier models that include additional firm-specific effects, such as the random-constant frontier model proposed by Greene (2004), can control for unobserved network effects that are random but time-invariant. In cases like railway networks the unobserved heterogeneity is potentially correlated with other exogenous, but observed, factors such as network size and density. In such cases the correlation with explanatory variables may bias the coefficients of the cost function in a random-effects specification. However, these correlations can be integrated into the model using Mundlak’s (1978) formulation. The unobserved network effects and the resulting biases are studied through a comparative study of a series of stochastic frontier models. These models are applied to a panel of 50 railway companies operating over a 13-year period in Switzerland. Different specifications are compared regarding the estimation of both cost frontier coefficients and inefficiency scores.