Academic journal article Seoul Journal of Economics

Do Larger Brokerage Firms Enjoy Larger Economies of Scale and Scope?

Academic journal article Seoul Journal of Economics

Do Larger Brokerage Firms Enjoy Larger Economies of Scale and Scope?

Article excerpt

(ProQuest: ... denotes formulae omitted.)

I. Introduction

This paper examines whether firm size determines the economies of scale and scope in the brokerage sector and, if so, how substantial they are. Quantile regression is used to perform more specific analysis. The findings of this work are expected to contribute to predicting sectoral changes and to guiding financial policies about Systemically Important Financial Institutions. This research can also serve as a useful reference for future research on competitiveness in other industries or countries.

Certain prior studies are remotely related to the concern of the present research and have estimated the cost functions of Korean securities firms (e.g., Lee 1992; Park1994; Chung et al. 2000; Kook et al. 2007; Park et al. 2009), which tend to use the translog cost functions and rely on the records about brokerage, prop-trading, and underwriting. These firms, however, do not consider commission fees by service types. The earlier studies agree that brokerage firms in Korea attain the economies of scale.

Nevertheless, previous studies are characterized by several limitations. First, these works did not estimate the cost functions for all brokerage firms. Translog cost function can account for a U-shaped cost function and generalizes the Cobb-Douglas function. This kind of cost function, however, is inapplicable to small-sized brokerage houses with limited brokerage operations. By comparison, Cobb-Douglas specification can be used to estimate the cost functions of all securities firms based on total assets and total costs. Therefore, previous studies generalized the Cobb-Douglas function, while sacrificing the scope of analysis.1 Meanwhile, the quadratic cost function used in the current study is sufficiently general, which allowed small securities firms to be analyzed.

Second, the estimate cost functions of previous studies assumes that securities firms charge the same commission fee for the same service. In fact, brokerage firms in Korea charge considerably different commission fees even for similar services. Thus, estimating the cost functions based on the profits of brokerage services is more reasonable compared with basing it on the amount of brokerage transactions because cost function is based on cost and profit, not on cost and transaction alone.

II. Previous Research and Model

The extent of economies of scale and scope can be measured via different means. The most widely used specifications are the Cobb-Douglas, translog, and quadratic cost functions. The Cobb-Douglas function has been extensively used to estimate cost functions and to examine the economies of scale and scope (Benston 1965; Bell and Murphy 1968). Cobb-Douglas production is derived as the solution for the following minimization problem:

...

Cost function then becomes

...

By taking log, an empirical specification can be acquired as follows:

...

α1 indicates the economy of scale. If α1 is less than 1, the economy of scale exists. w signifies variable cost and r connotes the cost to fixed capital. When y is 0, cost function is not well defined. This problem can be addressed by setting the below expression.

...

By taking log and conducting Taylor series expansion around κ=0, the following formulas are obtained:

...

Subsequently, the same empirical specification is maintained with y as a nonzero value. However, the Cobb-Douglas production function precludes the U-shaped cost function. This limitation is overcome by studies, which have undertaken on the multi-product translog cost function (Benston 1965; Benston, Hanweck, and Humphrey 1982). Translog function includes the quadratic terms of the log of Cobb-Douglas functions. Mester (1992) used a hybrid translog cost function in estimating economies of scale and scope. This kind of cost function is different from the translog function in the sense that the estimate can be realized at the zero production level. …

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