Two-stage network DEA with bad outputs

Abstract

Conventional black-box DEA models allow producer performance to be measured for technologies where undesirable outputs are jointly produced by-products of desirable output production. These models allow for non-radial scaling of desirable outputs, undesirable outputs, and inputs and can account for slacks in the constraints that define the technology. We review some of these black-box performance measures and show how to measure performance in two-stage network models. In these kinds of network models inputs are used to produce intermediate outputs in a first stage and then, those intermediate outputs become inputs to a second stage where final desirable outputs and undesirable outputs are produced. The bias from using a black-box model when a network technology exists is examined as well as the bias from ignoring slacks in the constraints defining the network technology.