Bounded additive models in data envelopment analysis (DEA) under the assumption of constant returns to scale (CRS) were recently introduced in the literature (Cooper et al. in J Product Anal 35(2):85–94, 2011; Pastor et al. in J Product Anal 40:285–292, 2013; Pastor et al. in Omega 56:16–24, 2015). In this paper, we propose to extend the so far generated knowledge about bounded additive models to the family of directional distance function (DDF) models in DEA, giving rise to a completely new subfamily of bounded or partially-bounded CRS-DDF models. We finally check the new approach on a real agricultural panel data set estimating efficiency and productivity change over time, resorting to the Luenberger indicator in a context where at least one variable is naturally bounded.

.T. Pastor, J. Aparicio, J. Alcaraz and F. Vidal thank the financial support from the Spanish Ministry for Economy and Competitiveness (Ministerio de Economía, Industria y Competitividad), the State Research Agency (Agencia Estatal de Investigacion) and the European Regional Development Fund (Fondo Europeo de DEsarrollo Regional) under Grant MTM2016-79765-P (AEI/FEDER, UE).

We thank the guest editors of the special issue DEA 2017 and two anonymous referees for providing constructive comments and help in improving the contents and presentation of this paper