The Allocative Efficiency Measure by Means of a Distance Function : The Case of Spanish Public Railways

This paper is an empirical application of the distance function to study the allocative efficiency of a regulated railway firm, RENFE, where the cost minimising hypothesis may be questioned. The distance function, which is the dual of the cost function, completely describes the technology and, like the cost function, it allows a multiproduct analysis. However, unlike the cost function, the input prices are not needed for its calculation and it does not imply cost minimisation. We have obtained the shadow prices of the productive factors, which satisfy the condition of minimum cost. These shadow prices are used to calculate the degree of allocative inefficiency of the firm and the origin of this inefficiency by using a parametric correction of prices (kij). The procedure followed has consisted of estimating a system of equations for the input distance function and cost share equations, employing the iterative seemingly unrelated regressions method (ITSUR). Moreover, in contrast with other studies which have used this method, we assume that the employment of an input in a proportion different from that which would minimise cost could be systematic, and incorporate this possibility into our empirical model. The model was estimated using annual data over the period 1955-95. In order to achieve a distribution and the confidence intervals of the proportionality terms estimated, kij, we have used a standard bootstrap technique