A Mergers and Acquisitions Index in Data Envelopment Analysis: An Application to Japanese Shinkin Banks in Kyushu

Rolf Färe; Hirofumi Fukuyama; William L. Weber

doi:10.4018/jissc.2010040101

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A Mergers and Acquisitions Index in Data Envelopment Analysis: An Application to Japanese Shinkin Banks in Kyushu

Rolf Färe, Hirofumi Fukuyama, William L. Weber

Source Title: International Journal of Information Systems and Social Change (IJISSC) 1(2)

DOI: 10.4018/jissc.2010040101

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Abstract

In this paper, a dynamic network DEA model is developed to evaluate the potential gains in final output from a merger of two firms. The two firms are allowed to have different production technologies or share a common technology. In a beginning period each firm uses period specific inputs to produce a final output and an intermediate output that becomes an input in the production of final outputs in a subsequent period. Firms that merge can use the intermediate input of one firm to produce final output for the other firm, leading to gains in final output for the two merged firms over what the firms could have produced individually. The method is applied to study Japanese cooperative Shinkin banks during 2003 to 2007. Mergers between banks in Nagasaki, Kagoshima, and Miyazaki prefectures tend to have the highest potential gains, while mergers between banks within Fukuoka prefecture and other prefectures and within Saga prefecture tend to have the smallest potential gains.

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A General Production Technology

We denote A and B as index sets of Regions A and B. Let be a firm in Region A and a firm in Region B. Let represent the number of firms producing in region A and region B. These firms are assumed to maximize final outputs over two periods, t and t+1. Let and denote vectors of N inputs and M outputs for firm at times . We distinguish between final output and intermediate output . Intermediate outputs are produced in one period, t, and used as an input to produce final outputs in the next period, t+1. We would like to examine effects of mergers and acquisitions by a DEA model in which an acquirer (decision maker) can decide the amount of intermediate outputs (inputs) by maximizing the sum of final outputs over time. The production process is based on Shephard's (1953, 1970) production theory and Färe and Grosskopf’s (1996) dynamic production model. The underlying technology for the firm, which locates in Region A, is defined by the firm a-output possibility set for time t: