Graph efficiency and productivity measures: an application to US agriculture

Hyperbolic measures of efficiency and productivity change with respect to a graph representation of production technology allow researchers to consider output and input dimensions simultaneously in measuring producer performance. Hyperbolic efficiency measures have been proposed, but empirical implementation has not followed, either in efficiency analysis or in productivity analysis. The objectives of this paper are to define hyperbolic performance measures on a graph representation of production technology, to motivate their use by stating some of their advantages over their radial counterparts, and to introduce a direct formulation to calculate them making use of Data Envelopment Analysis techniques. The ideas are illustrated by calculating hyperbolic efficiency and Malmquist productivity indexes for a US agricultural panel data set.