Generalised weak disposability and efficiency measurement in environmental technologies

Weak disposability based models of environmental technologies typically assume equiproportionate trade-offs between desired and undesired outputs. We postulate a generalised version of weak disposability allowing for different types of trade-offs between good and bad outputs and derive a new technology called piecewise Cobb–Douglas environmental technology whose envelopments capture all three types of production structures – concavity, linearity, and convexity. To measure environmental performance with reference to this technology, we develop radial and non-radial directional hyperbolic distance functions. We demonstrate that the value of these functions can be simply computed via the directional distance function as linear programs. We use data from 112 US power plants to illustrate our approach.