Modelling environmental inefficiency under a quota system

This paper introduces the methodology necessary to evaluate inefficiency of regulated decision making units that operate under quotas through data envelopment analysis, accounting for both quotas restrictions and negative environmental externalities of production. Three technical inefficiency measures are proposed: inefficiency in the production of marketed output, environmental inefficiency, and inefficiency with quotas. It is then shown how to aggregate these measures in order to obtain indicators of overall performance. The new approach is illustrated through a numerical example that uses real data available for the European Union dairy sector. The results show that considerable differences in inefficiencies could be found when quotas restrictions are accounted for in the model than in the model without quota imposition, indicating that not accounting explicitly for quotas when measuring performance in regulated sectors may lead to a not accurate estimation of firms' technical inefficiency.