Measuring potential gains from specialization under non-convex technologies

In this paper, the Free Coordination Hull (FCH) approach developed by Green and Cook (2004) is combined with the Free Disposal Hull (FDH) model to detect potential gains from specialization. As a non-convex approach that allows both directly observed and summed decision making units (DMUs) to define the production technology, FCH is the relevant model for analyzing optimal reapportionment of activity among smaller and more specialized units. Indeed the convexity assumption in more traditional Data Envelopment Analysis (DEA) models precludes the possibility of detecting potential gains from specialization and can only reveal economies of scope. Therefore non-convex technologies are required to model diseconomies of scope. Based on FDH and FCH technologies, an overall efficiency measure is decomposed into three components, namely technical, size and specialization efficiencies. A database of French farms for the year 2003 is used for illustration. Results indicate that input inefficiency in the agricultural sector is driven mainly by lack of specialization, which represents about 50% of overall inefficiency.