The standard reverse approach for decomposing economic inefficiency

The traditional approach decomposing profit inefficiency into the sum of its technical and its allocative components identifies first the frontier projection of each firm based on the exogenous choice of a specific technical measure, e.g., based on slacks, directional, etc. However, in real life situations, firms and organizations are interested in benchmarking themselves against competitors representing the largest feasible profit improvement given market prices. Resorting to the recently defined general direct approach decomposition of profit inefficiency, which decomposes profit loss into the profit technical gap existing between the firm and its frontier projection, and a remaining profit allocative gap, we introduce a decomposition that endogenizes the technical component. This is achieved by securing technical inefficiency reductions that, simultaneously, search to maximize the profit of the projected benchmark. The proposal defines a new measure of technical inefficiency that corresponds to a monetized version of the weighted additive model. We also present a normalized version of the reversed decomposition that is units' invariant through the definition of a suitable normalization factor.