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

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

Rolf Färe, Hirofumi Fukuyama, William L. Weber
Copyright: © 2012 |Pages: 17
DOI: 10.4018/978-1-4666-0927-3.ch010
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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 978-1-4666-0927-3.ch010.m01 be a firm in Region A and 978-1-4666-0927-3.ch010.m02 a firm in Region B. Let 978-1-4666-0927-3.ch010.m03 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 978-1-4666-0927-3.ch010.m04 and 978-1-4666-0927-3.ch010.m05 denote vectors of N inputs and M outputs for firm 978-1-4666-0927-3.ch010.m06 at times 978-1-4666-0927-3.ch010.m07. We distinguish between final output 978-1-4666-0927-3.ch010.m08 and intermediate output 978-1-4666-0927-3.ch010.m09. 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 firm978-1-4666-0927-3.ch010.m10, which locates in Region A, is defined by the firm a-output possibility set for time t:

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