Eco-Efficiency and Eco-Productivity change over time in a multisectoral economic system

We measure eco-efficiency of an economy by means of an augmented Leontief input-output model extended by constraints for primary inputs. Using a multi-objective optimization model the eco-efficiency frontier of the economy is generated. The results of these multi-objective optimization problems define eco-efficient virtual decision making units (DMUs). The eco-efficiency is obtained as a solution of a data envelopment analysis (DEA) model with virtual DMUs defining the potential and a DMU describing the actual performance of the economy. In this paper the procedure is extended to an intertemporal approach in the spirit of the Luenberger productivity indicator. This indicator permits decomposing eco-productivity change into eco-efficiency change and eco-technical change. The indicator is then further decompounded in a way that enables us to examine the contributions of individual production factors, undesirable as well as desirable outputs to eco-productivity change over time. For illustration purposes the proposed model is applied to investigate eco-productivity growth of the Austrian economy.