Metafrontier productivity indices: Questioning the common convexification strategy

While the construction of metafrontiers based on the union of underlying group frontiers normally yields a non-convex metaset, a large majority in the literature seems to assume that a convexification strategy leads to a reasonable convex approximation of this non-convex metafrontier. However, Kerstens, O’Donnell, and Van de Woestyne (2019) recently deliver new results on the union operator on technologies under a variety of assumptions and empirically illustrate that such a convexification strategy is doubtful. The purpose of this contribution is to verify to which extent such a convexification strategy is tenable when computing the Malmquist and Hicks–Moorsteen productivity indices with respect to a metafrontier. Furthermore, the differences between the Malmquist and Hicks–Moorsteen productivity indices are investigated at the metafrontier level. This existing methodology is empirically applied on a secondary data under a wide variety of assumptions: we explore balanced and unbalanced data as well as constant and variable returns to scale. Anticipating our key results, we provide statistical evidence on the potential bias arising from applying the convexification strategy for the metafrontier productivity indices.