Estimation of Economies of Scale in Banking Using a Generalized Functional Form

Abstract

THIS PAPER ADDRESSES four issues that arise in the estimation of economies of scale in the commercial banking industry. First, a common assumption underlying many of the studies of economies of scale in banking is the assumption of a Cobb-Douglas production function with exogenous input prices. The use of a Cobb-Douglas production function facilitates the estimation of the output elasticity of cost. However, there does not appear to be any other reason, a priori, for such an assumption. This paper utilizes a Box-Cox (hereafter B-C) generalized functional form methodology to directly test the assumption of an underlying Cobb-Douglas production function. Second, if the assumption of a Cobb-Douglas production function is inappropriate as a description of the production process of the financial firm, estimates of the output elasticity may be biased. The sensitivity of the estimates of this elasticity to the choice of functional form can also be examined through the use of a generalized functional form methodology. Third, no general consensus has been reached regarding the appropriate definition of bank output. Thus, a diversity of measures of bank output have been employed in previous estimates of economies of scale in banking. The sensitivity of the estimated output elasticity of cost to the selection of several alternative measures of output is examined through the use of the generalized functional form methodology. Finally, the B-C estimates of the cost function for commercial banks can be used