Multi-Product Marginal Productivity of Efficient Frontiers in Data Envelopment Analysis

Differential characteristics of the production function represent elasticity measures and marginal rates of production technologies. We extend the study by Podinovski and Forsund (2010) and develop multi-product marginal productivity (MP) by showing a consistent estimation of MP generated by data envelopment analysis (DEA), convex nonparametric least squares (CNLS), and directional distance function (DDF). Based on multi-product MP, a meta-DEA approach is developed to address finding the improving direction of the efficient firm on the frontier towards the allocatively efficient benchmarks for marginal profit maximization. This approach, which emphasizes “planning” over “evaluation” and focus on “margin” than “level”, forms the basis for transforming a typical “ex-post” DEA into a novel “ex-ante” DEA study. Two case studies show that the proposed model provides an explicit span of multi-product MP for productivity improvement via a tradeoff between distinct directions.