Nonparametric Measurement of Potential Gains from Mergers: An Additive Decomposition and Application to Indian Bank Mergers

One of the main incentives for voluntary merger between firms in the same industry is the potential gain in the form of lower cost of producing the combined output of the merging firms. Baumol, Panzar, and Willig (1982) showed that subadditivity of the cost function at the combined output level is a precondition for positive cost gains from a merger. In this paper we build on their theoretical model to derive conditions for potential gains from merger in a short run cost framework where not only the outputs but also the fixed inputs of the merging firms are aggregated through merger. We show that subadditivity of the short run ray total cost curve of the merged firm at the combined output bundle is neither necessary nor sufficient for positive gains from merger. We also provide a decomposition of the potential gain from merger into three components related to convexity of the technology, subadditivity of the short run ray total cost, and decrease in the variable cost due to an aggregation of the fixed inputs. Appropriate linear programming models are formulated for measuring the gain from merger and its components using the nonparametric method of Data Envelopment Analysis. We use data for a number of recent mergers of Indian banks in an empirical application of our proposed models.