Direct separability in multi-output technologies: An application to the Italian agricultural sector

The hypothesis of direct weak separability of the transformation function places fewer restrictions on production technology than those deriving from alternative multi-stage procedures, based on indirect separability assumptions. We derive an explicit form of the necessary and sufficient conditions for direct weak separability in the multiple output case. These conditions are expressed in elasticity terms, so they can be readily maintained or tested in commonly used flexible functional forms. Parametric restrictions are derived for the multi-output translog profit function. The procedure is applied to the Italian agricultural sector.