Financial intermediary versus production approach to efficiency of marketing distribution systems and organizational structure of insurance companies

Journal of Risk and Insurance, Sept, 2005 by Patrick L. Brockett, William W. Cooper, Linda L. Golden, John J. Rousseau, Yuying Wang

ABSTRACT

An examination of the efficiency of the marketing distribution channel and organizational structure for insurance companies is presented from a framework that views the insurer as a financial intermediary rather than as a "production entity" which produces "value added" through loss payments. Within this financial intermediary approach, solvency can be a primary concern for regulators of insurance companies, claims-paying ability can be a primary concern for policyholders, and return on investment can be a primary concern for investors. These three variables (solvency, financial return, and claims-paying ability) are considered as outputs of the insurance firm. The financial intermediary approach acknowledges that interests potentially conflict, and the strategic decision makers for the firm must balance one concern versus another when managing the insurance company. Accordingly, we investigate the efficiency of insurance companies using data envelopment analysis (DEA) having as insurer output an appropriately selected (for the firm under investigation) combination of solvency, claims-paying ability, and return on investment as outputs. These efficiency evaluations are further examined to study stock versus mutual form of organizational structure and agency versus direct marketing arrangements, which are examined separately and in combination. Comparisons with the "value-added" or "production" approach to insurer efficiency are presented. A new DEA approach and interpretation is also presented.

INTRODUCTION

This article uses the nonparametric properties of data envelopment analysis (DEA) coupled with distribution-free rank-order statistics to study the relative efficiency of the different organizational structures used by U.S. property and liability insurance companies (cross classified by their marketing distribution systems). Additionally, this article extends the interpretation of DEA toward a goal-directing technique with the goals as outputs rather than simply having a "product" as an output. This provides another focus and interpretation for DEA analysis in the insurance literature. We also use a form of DEA (the Range-Adjusted Measure, or RAM, model), new to the insurance literature, which is able to provide ordinal level efficiency scoring that allows for subsequent nonparametric statistical analysis such as regression, rank statistical analysis, etc. to be performed incorporating efficiency score as an explanatory variable in subsequent analysis. (1)

We dichotomize our results by organizational form into mutual versus stock companies to examine whether these two organizational structures might have differential managerial strategic focus in terms of goals, and have different efficiency and slack variables when using solvency propensity, return on investment, and claims-paying ability as output goals. One might expect potential differences in efficiency between stock and mutual insurers due to the different incentive structures inherent in the two types of organizational forms; in stock companies return on shareholder investment dominates incentives, whereas solvency and claims-paying ability considerations can dominate considerations of mutual insurance company decision makers. Possible efficiency differences between mutual and stock types of organization are intrinsically intertwined with the use of the agency versus direct sales type of marketing distribution systems (2) and these dichotomies are also correlated to emphasis in commercial versus personal lines of insurance. Finally, the differences that can occur by using different DEA formulations (production approach considering losses as the output versus the financial intermediary approach of this article) are explored and discussed.

THE RAM DEA MODEL (3)

There is a theoretical problem in using DEA efficiency numbers from the standard CCR or BCC models for subsequent statistical analysis because, while DEA evaluates the efficiency of each firm, the comparison set for each firm may be different producing potentially nonmetric level data. Accordingly, to address this problem, we introduce here to the insurance literature a new form of the DEA model that was selected for its suitability to the problems that are of interest here. This new model possesses some very desirable properties vis-a-vis other DEA models that have been used in the insurance literature (cf., Brockett and Xia, 1996). This model is a variant of the "additive DEA model" first presented in Charnes et al. (1985), and is discussed in detail in Cooper, Park, and Pastor (1999). To make the current article self-contained we briefly present this model that is formulated as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

In the DEA literature the entities responsible for converting input resources into outputs are referred to as decision-making units (DMU) and j = 1, ..., n indexes the entities being compared and contrasted for relative efficiency determination,

[x.sub.ij] = amount of input i = 1, ..., m used by [DMU.sub.j] [y.sub.ij] = amount of output r = 1, ..., s yielded by [DMU.sub.j], (1a)