A general direct approach for decomposing profit inefficiency
本文提出一种基于等式的新分解方法，将利润无效率分解为技术差距价值和前沿基准的利润无效率，避免高估配置效率，适用于多种技术无效率度量。
Considering any graph technical inefficiency measure, we show that the so-called standard or traditional approach for decomposing profit inefficiency relying on Fenchel-Mahler inequalities obtained from duality theory, establishes that profit inefficiency is greater than or equal to the product of technical inefficiency times a positive factor expressed in monetary units. This product is identified as the technical profit inefficiency and its difference with respect to the profit inefficiency as the allocative profit inefficiency. Dividing profit inefficiency by the mentioned positive factor one obtains the normalized (units’ invariant) profit inefficiency of the firm, which is a pure number, and can be decomposed into the sum of technical inefficiency and the normalized allocative profit inefficiency, usually called allocative inefficiency. We propose a new decomposition based on equalities that starts from the input and output slacks connecting the firm with the frontier benchmark, obtained through the pre-specified technical inefficiency measure. Profit inefficiency is then decomposed into the value of the technological gap and the profit inefficiency of the frontier benchmark. Expressing the value of the technological gap as the product of the technical inefficiency times a certain normalizing factor, we deduce a new normalized profit inefficiency decomposition. Our decomposition ensures that the allocative efficiency of a firm corresponds to that of its benchmark on the frontier and therefore avoids the possibility of overestimating it. We compare the traditional and the general direct approach and show that the new decomposition is conceptually sound and more accurate, with the only exception of the family of directional distance functions, for which both decompositions are equivalent.