A new inverse DEA cost efficiency model for estimating potential merger gains: a case of Canadian banks

Estimating potential gains from mergers is an important strategic decision-making problem. This paper introduces a new inverse data envelopment analysis (DEA) based on a cost efficiency model for estimating potential gains from mergers. There are restructuring scenarios for firms that want to minimize cost. The existing inverse DEA technical efficiency models are not appropriate for estimating merger gains in these situations. It is also shown that the proposed inverse DEA cost efficiency model can reveal more merger gains than the inverse DEA technical efficiency model. The applicability of the proposed method is shown through an application in Canada's banking sector to determine the required level of inputs and outputs for a merged bank to achieve target levels of cost and technical efficiencies. The results highlight the potential financial gains to improving both technical and cost efficiencies as efficiency-seeking banks increasingly become large and complex institutions through growth, mergers and acquisitions in a financial environment that is being shaped by reforms and technological innovation.