Academic journal article Journal of Money, Credit & Banking

Banking Costs, Generalized Functional Forms and Estimation of Economies of Scale and Scope

Academic journal article Journal of Money, Credit & Banking

Banking Costs, Generalized Functional Forms and Estimation of Economies of Scale and Scope

Article excerpt

Banking Costs, Generalized Functional Forms, and Estimation of Economies of Scale and Scope

IN THE PAST FEW YEARS, there has been a proliferation of papers concerned with estimation of economies of scale and scope in financial intermediaries. Gilbert (1984) traced the evolution of the research on banking costs through six distinct stages. In the embryonic stages, the pioneering works of Benston (1965) and Bell and Murphy (1968) stand out. These studies estimated banking cost functions using Cobb-Douglas technologies. Much of the debate focused on the definition of "bank output." In the 1980s a new wave of literature replaced the primitive Cobb-Douglas specification with more generalized functional forms. Benston, Hanweck, and Humphrey (1982) estimated a translog function with a composite output index. This average cost curve, in contrast to the Cobb-Douglas, can be non-monotonic. These authors found a significant U-shaped average cost curve, casting much suspicion on the earlier Cobb-Douglas specification.

In the sixth stage of research identified by Gilbert, many authors postulated multiproduct banking units and estimated translog equations. Murray and White (1983), Gilligan, Smirlock and Marshall (1984) and Lawrence and Shay (1986) reported significant economies of scope.(1) However, other studies, such as Benston et al. (1983), Le Compte and Smith (1985), and Berger, Hanweck and Humphrey (1985), found no significant economies of scope.(2) It is thus fair to say that the evidence on cost complimentarity in banking remains inconclusive.

More recently a seventh stage of research has emerged. Clark (1984) and Kilbride, McDonald, and Miller (1986) [henceforth, KMM] specified a special version of a generalized functional form in which all variables were transformed by a Box-Cox transformation.(3) A special case of this specification is the Cobb-Douglas.(4) In both the above articles, the authors claimed that they could not reject the restricted Cobb-Douglas function. Does this imply that we have not progressed beyond the primitive first stage? This would have serious implications for the impact of regulatory policies on the structure of the banking industry.(5)

The problem with the specifications postulated by Clark and KMM is that irrespective of the values of the Box-Cox parameters, the independent variables in the cost function, which are functions of a bank output composite and input prices, are loglinear separable. Thus even if the true underlying cost structure were nonlinear in the logs, such as the translog, one might still fail to reject the restricted Cobb-Douglas specification.(6) This would contradict the findings of Benston, Hanweck, and Humphrey (1982), who, despite their abstraction from cost complimentarity, used a composite output index (as did Clark and KMM) and found a U-shaped average cost function. Furthermore, the specification abstracts from cost complimentarity, and hence is at odds with the studies cited above, which found significant scope economies.

This paper investigates the validity of the methodology prescribed by Clark and KMM and reconciles their findings with those authors in the sixth stage of Gilbert's chronology. We estimate variants of the Box-Cox transformation proposed by Clark and KMM. The model we estimate is a particular generalized functional form which, in contrast to that of the above authors, allows scope economies as well as U-shaped average cost cases. The translog function and the Cobb-Douglas case are all special cases of this specification, thus allowing likelihood ratio tests to determine the validity of nested hypotheses. Our general conclusion is that the nonrejection of the Cobb-Douglas technology by Clark and KMM results from an ad hoc specification that excludes the possibility of multiproduct cost complementarity. However, Box-Cox transformations are rejected in favor of translog specifications.

In section 1 we posit a version of a generalized functional form. …

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