The flexible reverse approach for decomposing economic inefficiency: With an application to Taiwanese banks

Profit inefficiency is conventionally decomposed into two mutually exclusive components representing profit loss due to technical inefficiency, and, through duality theory, a residual interpreted as allocative inefficiency. Although conventional models solve technical inefficiencies by reducing inputs and increasing outputs, achieving profit efficiency may require larger than observed input quantities and/or smaller than observed output quantities. However, overcoming the restrictions in the direction of the technical adjustments in input and output quantities demands flexibility that existing models do not offer. Thus, to achieve this flexibility, we introduce an endogenous profit inefficiency measure that reverses the subordinate role played by allocative inefficiency. The new measure is based on a monetized version of the weighted additive model seeking maximum feasible profit gains without restricting inputs and output adjustments. This prevents the conflicting prescriptions that the conventional model may offer in the form of non-monotonic input and output changes, thereby reducing adjustment costs. We apply the proposed model to real data from financial institutions. The differences in the managerial and policy recommendations for optimal resource allocation are relevant, with the conventional model wrongly recommending reductions in inputs in terms of the amounts and scale required to maximize profit.