Marginal values and returns to scale for nonparametric production frontiers

We present a unifying linear programming approach to the calculation of various directional derivatives for a very large class of production frontiers of data envelopment analysis (DEA). Special cases of this include different marginal rates, the scale elasticity and a spectrum of partial and mixed elasticity measures. Our development applies to any polyhedral production technology including, to name a few, the conventional variable and constant returns-to-scale DEA technologies, their extensions with weight restrictions, technolo gies with weakly disposable undesirable outputs and network DEA models. Furthermore, our development provides a general method for the characterization of returns to scale (RTS) in any polyhedral technology. The new approach effectively removes the need to develop bespoke models for the RTS characterization and calculation of marginal rates and elasticity measures for each particular technology

Marginal Trade-Offs for Improved Agro-Ecological Efficiency Using Data Envelopment Analysis

Today’s agricultural management decisions impact food security and sustainable ecosystems, even when operating with back-to-basic operations. In such endeavors, policymakers usually need a quantitative tool, such as trade-offs margins, to effectively adjust resource consumption or production. This paper applies the weighted slack-based measurement (SBM-DEA) program to 136 developing countries’ agricultural performance. First, it finds the current agricultural efficiency and then makes marginal trade-offs on desirable-output variables (such as crop yield and forest area) to see the effective changes in undesirable-output (such as methane and nitrous oxide emissions). The results show that choosing effective marginal trade-offs does not deteriorate the relative efficiency of the decision-making units (DMUs) below the efficient frontier line. Thus, such a method enables the decision-makers to determine the best marginal trade-off points to reach the optimal efficiencies and decide which output factor needs special brainstorming to design effective policy