When cost metafrontiers are nonconvex in the outputs, then the production metafrontier is nonconvex: the price of a convexification strategy

Metafrontier analysis is widely used to account for technological heterogeneity among producers. The approach involves combining a number of group-specific production possibilities sets to form a production possibilities metaset. Even though the union of the group sets normally results in a nonconvex metaset, most authors proceed as if this metaset is convex. Kerstens, O'Donnell and Van de Woestyne (2019) obtain new results on the union operator on sets under various assumptions and empirically illustrate that the popular convexification strategy is highly questionable. In this paper we transpose their results on the union operator from a production to a cost context: this is new. We then explore the extent to which convexity of the cost function is corroborated using a newly developed test. Furthermore, we check to which extent a convexification strategy is tenable when estimating a cost metafrontier. We use an original banking data set from China and the USA to illustrate the main issues. We establish that the cost function is not convex in the outputs for China and that the convexification strategy leads to potentially-biased estimates of the cost metafrontier and associated measures of efficiency.