Input allocation in multi-output settings: Nonparametric robust efficiency measurements

Comparing decision making units to detect their potential efficiency improvement, without relying on parametric unverifiable assumptions about the production process, is the goal of nonparametric efficiency analysis (such as FDH, DEA). While such methods have demonstrated their practical usefulness, practitioners sometimes have doubts about their fairness. In multi-output settings, two main limitations could give credit to their doubts: (1) the production process is modelled as a “black box,” i.e., it is implicitly assumed that all the inputs produce simultaneously all the outputs; (2) only techniques investigating for outliers in all output directions simultaneously exist. In this article, we tackle these two limitations by presenting two new nonparametric robust efficiency measurements for multi-output settings. Our new measurements present several attractive features. First, they increase the realism of the modelling by taking the links between inputs and outputs into account, and thus tackle (1). Second, they provide flexibility in the outlier detection exercise, and thus also tackle (2). Overall, our new measurements better use the data available, and can be seen as natural extensions of well-known nonparametric robust efficiency measurements for multi-output contexts. To demonstrate the usefulness of our method, we propose both a simulation and an empirical application.