Productivity and economies of scale in the production of bank service value added

This paper uses a new measure of bank service output to estimate various specifications of production and cost functions for Bank Holding Companies (BHCs) over the period 1986 to 1999. The new output series is a true flow measure of bank service value added, and it follows from a unified model of bank operation that integrates risk and the measurement of bank services. The model also establishes separability between the production function of bank services and the funds borrowed and lent-a special intermediate input for banks. The preferred specification of the cost function estimates a large dispersion in productivity levels across BHCs. This implies that one potential benefit of bank mergers is the acquisition by more productive banks of less productive banks, thereby improving the targets' productivity. The cost function also yields an estimate of increasing returns to scale in banking, contrasting with the typical finding in the existing literature of constant returns to scale. On the other hand, the production function estimates decreasing returns to scale. But these estimates are shown to be potentially biased downward, whereas the estimates from the cost function are likely to be biased upward because of measurement errors in the imputed output. The paper tentatively concludes that there is likely to be a modest degree of increasing returns to scale in the production of bank services. If confirmed, this tentative conclusion implies that the cost savings from increased scale of banking institutions should be taken into account in the analysis of mergers and antitrust policy.