Title: When the Production Metafrontier is Nonconvex, then Cost Metafrontiers are Nonconvex in the Outputs: The Price of a Convexification Strategy
Kristiaan Kerstens, Christopher O’Donnell, Ignace Van de Woestyne

 

Abstract: 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 the metaset is convex. Kerstens, O'Donnell and Van de Woestyne (2019) obtain new results on the union operator on sets under various assumptions. They then use a production context to empirically illustrate that the popular convexification strategy is highly questionable. In this paper we transpose their results on the union operator from a production  context to a cost context: this is new. We then explore the extent to which a convexification strategy is tenable when estimating a cost metafrontier. We use a secondary data set to illustrate the main issues. We establish that the convexification strategy leads to potentially-biased estimates of the cost metafrontier and associated measures of efficiency.

Univ. Lille, CNRS, IESEG School of Management, UMR 9221 - LEM - Lille Economie Management, F-59000 Lille, France.