Introducing cross-productivity: A new approach for ranking productive units over time in Data Envelopment Analysis

Abstract

Cross-efficiency has been developed for the evaluation of cross-sectional data in Data Envelopment Analysis. This paper extends cross-efficiency evaluation introducing the concept of cross-productivity. The extension proposed here is aimed at providing a dynamic peer-evaluation of decision making units, based on the standard Luenberger indicator, when the same set of units is observed over time. In particular, we show how to decompose the change in the ranking score of the different units into a component linked to catch-up and a term associated with technical change and innovation. As a result, we determine why the ranking provided by this novel cross-efficiency approach can vary period by period for the assessed set of units. Finally, the introduced cross-productivity approach is illustrated in the context of 28 national innovation systems in Europe, through the panel data included in the European Innovation Scoreboard for the years 2014 and 2015.