Clustering and meta-envelopment in data envelopment analysis

We propose techniques of classification of a potentially heterogeneous data set into groups in a way that is consistent with the intended purpose of the clustering, which is Data Envelopment Analysis (DEA). Using standard clustering techniques and then applying DEA is shown to be sub-optimal in many instances of empirical relevance. Our methods are based on a novel interpretation and implementation of convex nonparametric least squares (CNLS) which allows not only classification into different clusters but also finding the number of clusters from the data. Moreover, we provide techniques for model validation in CNLS regarding the allocation into groups using efficiency criteria. We provide a prior designed to minimize variation within groups and maximize variation across groups. The new techniques are examined using Monte Carlo experiments and they are applied to a data set of large U.S. banks. Additionally, we propose new techniques for meta-envelopment or meta-frontier formulations in efficiency analysis.