Some Evidence of Scale Economies in Workers' Compensation Insurance
研究了工伤保险中是否存在规模经济，发现获取、现场监督和收款费用存在显著规模经济，而损失、理赔费用和一般费用仅显示微弱证据，所有权形式对多数成本项目无影响。
The issue of possible scale economies in workers' compensation insurance is addressed in this study. Important results include that (1) statistically significant scale economies are present for acquisition, field supervision, and collection expenses, (2) only weak evidence of size efficiency is noted for losses, loss adjustment expenses, and general expenses, and (3) the ownership form does not affect most insurer cost items. Although economies of scale in the property-liability insurance industry have been a concern to regulators, academicians, and consumers, studies have reported conflicting results. Doherty [2], Hammond, Melander, and Shilling [4], and Skogh [10] have noticed moderate or profound size efficiency in the Canadian, U.S., and Swedish property-liability insurance industries. Johnson, Flanigan, and Weisbart [7] report less efficient operations for small and medium insurers, and increasing returns to scale for large insurers. However, Allen [1] notes signs of scale diseconomies for medium and large insurers. A major problem is that most studies have used aggregate cost functions, in which output and cost are aggregated across all property-liability insurance lines of a given insurer. Such aggregate cost functions are inappropriate mainly because different insurers have different product mixes.' For a meaningful investigation of this subject, it is essential to examine an individual line of insurance that produces a relatively homogeneous product. Workers' compensation insurance is ideal for two reasons. First, although the quality and quantity of services provided by different insurers may vary, coverages that they offer are relatively homogeneous in a given state because Dongsae Cho is Assistant Professor in the Carlson School of Management at the University of Minnesota. He earned the Ph.D. in Finance from the University of Illinois and has published several risk and insurance articles in JRI, The Journal of Insurance Issues and Practices, and The Geneva Papers. The author thanks two anonymous referees and the Associate Editor for valuable comments. An earlier version of this article was presented at the 1987 Annual Meeting of the Western Risk and Insurance Association in San Antonio, Texas. 'In order to partially solve this problem, the translog cost function has been suggested for multiproduct financial institutions (e.g., Murray and White [8]). This multiproduct cost function is also subject to the criticism that property-liability insurers offer heterogeneous products even in a given line. This content downloaded from 207.46.13.111 on Sun, 22 May 2016 06:34:18 UTC All use subject to http://about.jstor.org/terms Some Evidence of Scale Economies 325 state laws govern types and levels of workers' compensation benefits.2 Second, each insurer must file with the National Council on Compensation Insurance considerable financial data related to workers' compensation insurance in each state. Such segregated data are unobtainable for other lines of propertyliability insurance. The purpose of this study is to investigate possible size efficiency in workers' compensation insurance by using these data. Cost, Output, and their Relationship Multiple regression models have been widely used to measure scale economies in the insurance industry [1, 2, 3, 4, 5, 7, 10]. This method requires measures of output and insurer cost. Also the functional relationship between them must be specified. Cost of Workers' Compensation Insurance Past studies on scale economies in the property-liability insurance industry have focused on underwriting expenses such as losses, loss adjustment expenses, and commissions [1,2,4,10]. For workers' compensation insurance, underwriting and other expense data are readily available in greater detail as listed in the next section. In this study the presence or lack of scale economies is tested for most of these cost items, and for losses and expenses combined. Output Measures Some popular measures of insurer output are premium income, claims paid, net worth, and index measures. Most of these output measurements have some limitations for the study. Claims paid as an output variable is subject to serious criticisms because the insurance product includes auxiliary services as well as claims paid and claims paid is a kind of insurer cost. Therefore, when it is used as the output proxy, one cannot measure the presence or lack of scale economies in this important cost item. The net worth of an insurer is inappropriate because it is a residual variable subject to manipulation (see Johnson, et al. [7]). Since using a single scale variable as output is improper for a multiproduct insurer, an index measure has been used for the life insurance industry [3,6]. The index is calculated as the volume of various kinds of life insurance products weighted by their respective unit cost. This index is inappropriate for the study because only one line of insurance is being examined. For the present study, premium income is used as the most appropriate output proxy because workers' compensation insurance, since it is governed by state statutes, is a relatively homogeneous product in a given state. Workers' compensation premium income may be measured by written premium, net earned premium, or standard earned premium. Written premium is the premium collected during an accounting period on a cash 2The insurance product consists of the combination of coverage and service. Due to the diversity of insurer services even within a state, workers' compensation insurance is not a perfectly homogeneous product. This content downloaded from 207.46.13.111 on Sun, 22 May 2016 06:34:18 UTC All use subject to http://about.jstor.org/terms 326 The Journal of Risk and Insurance basis; earned premium is the one measured on an accrual basis. Naturally earned premium is superior to written premium. Standard earned premium means the premium after prospective experience rating but before premium discount or retrospective rating; net earned premium is the one that the insurer actually earned during a period, i.e., premium after prospective experience rating and premium discount or retrospective rating. In this study, therefore, the net earned premium is chosen as the output measurement. Functional Relationship between Cost and Output Once the relevant cost items and the output measurement are identified, the appropriate functional relationship between cost and output should be selected. Although some studies support linear cost functions [4, 9], the log-log specification is superior because it conforms to the Cobb-Douglas production function [1, 2, 7, 10]. For this reason the log-log form is postulated and used to evaluate scale economies in workers' compensation insurance in this study. Other Relevant Variables Aside from cost and output, traditionally some other variables have also been examined, e.g., distribution system, ownership form, and insurer capacity. Due to limited data availability, only the ownership variable is included.