Core Deposits and Physical Capital: A Reexamination of Bank Scale Economies and Efficiency with Quasi-Fixed Inputs
Hunter, William C., Timme, Stephen G., Journal of Money, Credit & Banking
Numerous studies have employed multiproduct flexible functional forms to examine the structure of bank cost and production functions. In general, these studies show that estimates of bank cost characteristics are fairly robust to changes in the definition of inputs and outputs.(1,2) In addition, the studies by Hunter, Timme, and Yang (1990) and Lawrence (1989) test the robustness of competing flexible functional specifications (for example, Box-Cox, Cobb-Douglas, minflex Laurent, and translog) and find that the standard translog specification provides an adequate fit of bank cost data.
More recently, researchers have begun to investigate the nature of technical and allocative efficiency in bank production (see Berger, Hunter, and Timme 1993). These studies generally report cost inefficiencies in the range of 20 to 30 percent. In addition, those studies applying multiple methodologies to the same data sets report relatively low correlation between the efficiency rankings of individual banks by the different techniques.(3) Nonetheless, the results from these studies suggest that cost inefficiencies generally dominate the impact of scale and scope diseconomies typically reported in the literature.(4) Therefore, the analysis of bank cost efficiency is important from both a managerial and a policy perspective.
Despite the impressive nature of the results obtained in the bank cost structure literature to date, virtually all studies have used models based on the assumption that all inputs into the intermediary's production function are assumed to be variable. There are, however, reasons to believe that due to such factors as transactions and information costs, a significant proportion of the inputs into bank production functions are quasi-fixed in the short run. The presence of these quasi-fixed inputs is consistent with the notions of "core deposits" and the "customer relationship" in banking, as well as the short-run fixity of bank physical capital. To date, the only bank cost efficiency study that explicitly incorporates quasi-fixed inputs is Berger, Hancock, and Humphrey (1993). However, these authors do not test the robustness of their results to changes in the definition of quasi-fixed inputs or examine the results associated with treating all inputs as variable. In the case of scale economies, the paper by Noulas, Ray, and Miller (1990) improves upon previous studies by incorporating retail deposits as a quasi-fixed input into a variable-cost function. Although these authors allow for a quasi-fixed input, their study suffers from several drawbacks. Neither cost efficiencies nor scope economies are examined in the paper, and no comparison is made of the results obtained from their quasi-fixed specification to alternative specifications. Furthermore, since only one quasi-fixed input - a measure of core deposits - is examined, the importance of quasi-fixed physical capital cannot be determined. Finally, the analysis covers cost data for only one year and therefore does not provide insights into the dynamic aspects of quasi-fixed inputs and the process of adjustment to long-run equilibrium.
In this paper, we compare the empirical results obtained from estimating a bank cost function based on the assumption that inputs into the bank production function are completely variable and hence employed at their long-run equilibrium levels with the results obtained from a specification that takes account of the quasi-fixed nature of core deposits and bank physical capital. Data are examined for the period 1985 through 1990. If the short-run fixity of some bank inputs truly affect bank production, then policy recommendations made on the basis of results obtained from models that ignore these fixities can be questioned. Conversely, if there is little or no appreciable difference in the results obtained from the different specifications, or if these differences are not very meaningful to issues of public policy, then results derived from models that assume that banks are in long-run equilibrium with respect to all factor inputs retain their importance in policy debates. …