Measuring efficiency with quasiconcave production frontiers

Comparing with the frontiers derived from the data envelopment analysis (DEA) and Banker-Charnes-Cooper (BCC) methods, the frontier derived from the free disposal hull (FDH) method is the closest to observed decision making units (DMUs), and hence, it can give each DMU the highest efficiency score. However, the frontier from the FDH method may not be a quasiconcave production frontier. The production frontiers derived by Petersen, on the other hand, may overstate inefficiency for some quasiconcave production frontiers. This paper has used the minimum convex input requirement set and maximum convex output possible set to construct the closest quasiconcave production frontier for DMUs. By ordering DMUs by input/output level, the DEA method can be employed to estimate input-based and output-based efficiency scores.