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 conside r output and input dimensions simultaneously in measuring producer performa nce. Hyperbolic efficiency measures have been proposed, but empirical imple mentation has not followed, either in efficiency analysis or in productivit y analysis. The objectives of this paper are to der ne hyperbolic performan ce measures on a graph representation of production technology, to motivate their use by stating some of their advantages over their radial counterpar ts, and to introduce a direct formulation to calculate them making use of D ata Envelopment Analysis techniques. The ideas are illustrated by calculati ng hyperbolic efficiency and Malmquist productivity indexes for a US agricu ltural panel data set.