Generalized estimation of productivity with multiple bad outputs: The importance of materials balance constraints

Previous research has frequently estimated the directional technology distance function (DTDF) to more flexibly model multiple-input and multiple-output production, firm inefficiency, and productivity growth. For example, with firms such as electric utilities, one must model the production of good and bad outputs using good and bad inputs. Typically, all inputs and outputs are potentially endogenous. In previous work, we show how to identify a DTDF system using price equations based on profit maximization and compute optimal directions for measuring productivity change. However, this work has not imposed restrictions that limit substitution possibilities among inputs and outputs to a feasible set that is consistent with materials-balance constraints. Such constraints require that the weight of all inputs equals the weight of all outputs. The major innovation of this paper is that we include two types of functional relationships that impose the parametric analog of materials balance by modeling the generation of bad outputs and the use of bad inputs. The first requires that bad outputs are functionally related to good inputs and bad inputs. The second requires that bad inputs are functionally related to good inputs. We illustrate these methods using a balanced panel of 80 U.S. coal-fired electric generating plants from 1995–2005. Substantial differences are observed between the specification that includes the materials-balance constraints and the conventional approach that omits them, based on Bayes factors as well as measures of productivity and inefficiency. For many plants, improved management practices can reduce substantial inefficiencies in meeting emission constraints without reducing productivity growth.