Estimation of Convex and Nonconvex Meta Frontier Production Set With the DEA-Bootstrap Approach: Evidence From Data Banks

The purpose of this chapter is to cover banking efficiency using the concept of the Meta frontier function and to study group and subgroup differences in the production technology. This study estimates the technical efficiency (TE) and technology gap ratios (TGRs) for banks in Islamic countries. Using the assumption of the convex hull of the Meta frontier production set using the virtual Meta frontier within the nonparametric approach as presented by Battese and Rao (2002), Battese et al. (2004), and O'Donnell et al. (2007, 2008) and after relaxing this assumption, the study investigates if there is a significant difference between these two methods. To overcome the deterministic criterion addressed to nonparametric approach, the bootstrapping technique has been applied. The first part of this chapter covers the analytical framework necessary for the definition of a Meta frontier function and its estimation using nonparametric data envelopment analysis (DEA) in the case where we impose the assumption of the convex production set and follows in the case of relaxation of this assumption. Then we estimated the TE and the TGR in concave and nonconcave Meta frontier cases by applying the Bootstrap-DEA approach. The empirical part will be reserved for highlighting these methods on data bank to study the technical and technological performance level and prove if there is a difference between the two methods. Three groups of banks namely commercial, investment, and Islamic banks in 17 Islamic countries over a period of 16 years between 1996 and 2011 are used.