Conjugate Paretian inefficiency measures
本文研究了一种基于S维实数偏序的效率测度方法，通过双重归一化策略定义帕累托无效率测度，并证明其与受限奈洛夫效率测度构成共轭对，为效率分析提供了新的理论工具。
We study efficiency measurement using a partial ordering for the S-dimensional reals that generalizes the canonical less than or equal to partial ordering. We seek measures that judge outcomes as favorably as possible using a dual normalization strategy that generalizes those used in the minimum-norm and efficiency-measurement literatures. We characterize the efficient frontier using dual methods and use that representation to identify a dual Nerlovian inefficiency measure. The Paretian inefficiency measure is defined as the minimal Nerlovian measure while constraining dual variates to fall in a predetermined closed convex set. We show that the Paretian inefficiency measure forms a dual conjugate pair with a restricted Nerlovian efficiency measure. We use those results to develop conditions that ensure that the Paretian inefficiency measure is an exhaustive function (cardinal) representation of the feasible set. We present a series of composition rules for different restrictions on the feasible set and dual-variate normalization that include generalizations of existing inefficiency measures. An empirical illustration of the concepts developed that is based on Catalan farming data closes the substantive part of the paper.