Economies of Scale and Scope at Large Commercial Banks: Evidence from the Fourier Flexible Functional Form

Abstract

The article presents a study on the cost efficiency of commercial banks using evidence from the Fourier Flexible Functional form. It presents the measures of scale and scope economies estimated. It then describes the data and discusses estimation issues. 1986 and 1990 Call and Income Report Data for banks having total assets of $0.5 billion to $100 billion are used to estimate cost equations representing the intermediation and production approaches. The article also presents the estimated cost functions as well as estimated cost economy measures based on them. Several conclusions emerge from this study. First, the industry cost function for large banks does not have the Translog form for either the intermediation or production approaches to bank production. This finding is robust: the data reject the Translog form despite the fact that restricting the sample to relatively homogenous large banks gives the Translog the best chance of performing well. Robust evidence that the bank cost function does not have the Translog form casts doubt on the results of previous studies that use this form, and challenges bank policymakers who have been guided by this research to rethink their decision rules. The efficiency of commercial banks has reemerged as a critical issue to both the public, whose confidence in financial institutions has been shaken by problems in the thrift and insurance industries, and to policymakers, who face increasing pressure to rewrite bank legislation. Cost efficiency represents one facet of efficiency. Most previous studies of cost efficiency compute scale and scope economy measures from Translog cost equations estimated on either the Functional Cost Analysis (FCA) data (Benston, Hanweck, and Humphrey 1982; Berger, Hanweck, and Humphrey 1987; Cebenoyan 1988; Gilligan, Smirlock, and Marshall 1984; Kolari and Zardkoohi 1991) or the Call and Income Report data (Berger and Humphrey 1991; Gilligan and Smirlock 1984, Gropper 1991; Hunter, Timme, and Yang 1990; Noulas, Ray, and Miller 1990). However, the findings of these studies have been called into question by papers that cast doubt on the suitability of the Translog functional form. The Translog represents a second-order Taylor series approximation of an arbitrary function at a point. But White (1980) demonstrates that least squares estimates of a second-order polynomial such as the Translog do not generally correspond to the Taylor series expansion of the underlying function at an expansion point and, hence, are biased estimates of the series expansion. McAllister and McManus (1993) find that estimated Translog cost equations for all banks, large banks, and very large banks are incompatible, a finding indicative of the bias White describes. The inadequacy of the Translog not only casts doubt on the conclusions of previous studies that use this form, it challenges policymakers who have been guided by these studies in making antitrust and bank merger decisions to revise their policy rules. This study contributes new evidence on bank cost efficiency, by using large bank data to estimate cost equations having a functional form that avoids the problems of the Translog. and then using the estimated equations to compute measures of scale and scope economies. The efficiency of large banks is of particular interest due to the increasing size of banks through mergers and the potential for more large banks as a result of interstate banking.