Productivity and Undesirable Outputs: A Directional Distance Function Approach

Undesirable outputs are often produced together with desirable outputs. This joint production of good and bad outputs is typically ignored in traditional measures of productivity since “prices” are typically unavailable for bad outputs. Here we introduce a directional distance function and use it as a component in a new productivity index that readily models joint production of goods and bads, credits firms for reductions in bads and increases in goods, and does not require shadow prices of bad outputs. This index, as an empirical example shows, solves the problem caused by the joint production of good and bad outputs, and provides a practical managerial tool.