Measuring and decomposing firm׳s revenue and cost efficiency: The Russell measures revisited

Overall inefficiency measurement and decomposition are important for firms facing a world of changing prices since the resultant loss has implications on managers׳ decision making. In this paper, we draw attention to some problems within existing approaches to decompose overall inefficiency into its sources and propose new revenue and cost inefficiency measures based on the well-known Russell measures. Specifically, the technical inefficiency component is calculated by the Russell output (input) measure, which is able to incorporate all sources of inefficiency corresponding to the output (input) side, specifically output (input) slacks, whereas allocative inefficiency is retrieved residually. All our results are derived from a new Fenchel-Mahler inequality using the theory of convex conjugates. This paper has several implications in theory and practice. From a theoretical point of view, we establish a natural dual relationship between the revenue (cost) function and the Russell output (input) measure; despite the previous unsuccessful attempts in the literature to provide such duality result. From a practical point of view, we provide a way of decomposing revenue (cost) inefficiency into allocative inefficiency and a component that measures technical inefficiency in the sense of Pareto, contrasting with the usual approaches for decomposing revenue (cost) inefficiency, such as those based on Shephard׳s output (input) distance function and the directional output (input) distance function.