Measuring profit and materials balance-based environmental efficiency with directional distance functions

Incorporating pollution as additional input or output into standard production efficiency models violates the law of mass conservation. Considering the materials balance (MB) outcome similar to the economic outcome deals with this problem and opens perspectives for economic-environmental trade-off analysis. Empirical evidence, however, shows that transparent trade-off analysis gets vanished when multiple inputs or outputs are considered. Possible reasons are leverage effects between changes in cost and mass input minimization and final economic and environmental outcomes, wrongly-defined frontiers and large differences between technical and allocative efficiencies.
The aim of the paper is to derive profit and MB-based environmental efficiency measures with directional distance functions. We estimate a production frontier that complies with the Baumgartner conditions, which set upper bounds for marginal and average products of material resource inputs. We derive a Nerlovian type of MB-adjusted environmental efficiency for 60 typical pig-finishing farms, with marketable pig as output and feed, piglets, pig places, labor and other costs as inputs. We introduce alternative ways of measuring economic-environmental trade-offs.