Dynamic directional nonparametric profit efficiency analysis for a single decision-making unit: an aggregation approach

We propose a simple and intuitive nonparametric technique to assess the profit performances of a single decision-making unit over time. The particularity of our approach lies in recognizing that technological change may be present in the profit evaluation exercise. We partition the periods of time into several time intervals, in such a way that the technology is fixed within intervals but may differ between intervals. Attractively, our approach defines a new Luenberger-type indicator for dynamic profit performance evaluation when a single decision-making unit is of interest, and provides a coherent and systematic way to compare the profit performance changes between the periods of time and the time intervals. To define the interval-level concepts, we rely on a flexible weighting linear aggregation scheme. We also show how the new indicator can be decomposed into several dimensions. We illustrate the usefulness of our methodology with the case of the Chinese low-end hotel industry in 2005–2015. Our results highlight a performance regression, which is mainly due to the technical components of the indicator decomposition.