Do we estimate an input or an output distance function? An application of the mixture approach to European railways

In this paper, we estimate parametric input and output distance functions and discuss how to estimate a mixture/latent class model (LCM) involving the output and input distance functions in the context of multi-input and multi-output production technology. The proposed technique is applied to a panel data on European Railways (1971–1994). This model allows us to identify determinants of the efficiency orientation, thereby providing useful information that can help researchers to choose between the input and the output-oriented approaches. In addition, we develop cross-indices that can be used to compute input (output) technical inefficiency from the estimates of output (input) distance function. Copyright Springer Science+Business Media, LLC 2007