An economic analysis of life insurance company expenses

Segal, Dan

ABSTRACT

This study provides an economic analysis of life insurance company expenses and develops a methodology for the construction of benchmark expense factors. These benchmarks can facilitate the pricing of new business, cost control within companies, and expense comparisons among companies. We derive the expense factors by estimating a cost function wherein total general expenses are modeled as a function of input prices and physical outputs, and the physical outputs are proxies for the cost drivers of the different lines of business. This methodology has two important advantages: first, the derived expense factors are independent of the methods that insurers use in allocating total expenses across lines of business. Second, the estimated cost function explicitly accounts for different degrees of economies of scale and consequently in the present value of marginal expenses across insurers. Hence, this study demonstrates that economies of scale and, in turn, size must be considered when constructing an expense table.

1. INTRODUCTION

The life insurance industry can be characterized as mature and highly competitive, with fairly homogeneous products and services and comparable providers of insurance. Few financial inventions can be patented, and most are copied shortly after their introductions. Consequently, success in this industry depends on an insurer’s ability to control costs.

This study provides an economic analysis of life insurance company expenses and develops a methodology for the construction of benchmark expense factors. These benchmarks can facilitate the pricing of new business, expense control within companies, and expense comparisons among companies; they can also be used in dividend illustrations.

We derive the expense factors in two steps. In the first step, we estimate a cost function wherein total general expenses are modeled as a function of input prices and physical outputs, and the physical outputs are proxies for the cost drivers of the different lines of business. In the second step, we compute the expense factors using the estimated parameters of the cost function and assumptions about the ratio of acquisition and maintenance expenses to total costs, the average duration of whole and term life policies, and the discount rate of the insurers.

The Society of Actuaries’ (SOA) Committee on Life Insurance Research undertook the task of developing for the industry a Generally Recognized Expense Table (GRET). The expenses to which it refers are the general insurance expenses life insurance companies report annually to the National Association of Insurance Commissioners (NAIC). GRET’s main purpose is to provide benchmark costs for various products that life insurance companies offer. Actuaries and the insurance industry are allowed to use the larger of marginal expenses or these benchmark costs in compliance with the NAIC Life Insurance Model Regulation on Life Insurance Sales Illustration.

Using statutory data, the SOA developed GRET on the basis of general cost formulas that take into account as cost drivers the number of policies, the amount of insurance, and the amount of premiums. The model also controls for the type of distribution system and for first-year expenses versus renewal expenses. The general cost formulas assume a linear relationship between the general expenses allocated to the life insurance line of business and the cost drivers, so the expected general expenses of the life insurance line of business is the product of the cost drivers and their expense factors. The latter were based on an expense analysis of the 200 largest companies, as measured by life insurance expenses.

The result of the SOA model, however, is not encouraging. The ratio of actual expenses to expected expenses exhibits large variations among companies. There are three potential reasons for the results obtained by the SOA. First, the model relies on the general expenses allocated to the life insurance line of business. The allocation methods, however, are arbitrary, and therefore the data may not be meaningful in a cross-sectional analysis. Life insurance companies must allocate their general expenses across all lines of business, where the main lines of business are life insurance, annuities and other accumulation products, and accident and health (A&H). The method used by an insurer to allocate these expenses across lines of business is crucial because each method may yield different allocations of the same costs. Relying on the allocations made by the companies in determining the expense factors may provide biased estimates.

Second, the cost formulas assume a linear relationship between the cost variable and the costs drivers. This description of the cost structure of the life insurance industry is probably too simplistic. It may also be too restrictive in that it constrains the economies of scale across companies to be constant. Third, the SOA’s model fails to account for the size of the insurer.

In contrast, our approach has two important advantages. First, the derived expense factors are independent of the allocation methods the insurers use. Second, we allow the present value of marginal expenses to vary by insurer and hence are able to show that size is a factor that must be considered when constructing an expense table. In addition, estimating a cost function permits us to examine several properties of the cost structure of life insurance companies, such as economies of scale, marginal costs, and association with size and the distribution system.

The remainder of this study is organized as follows. The next section provides a literature review. Section III develops the methodology, and Section IV describes the outputs and the input prices used in estimating the cost function. Section V depicts the cost function and the estimation method, and Section VI presents the estimation results. Section VII describes and illustrates a suggested methodology to construct the expense table using the marginal costs of the cost function, and Section VIII concludes the article.

2. LiTERATURE REVIEW

Several studies attempt to allocate and measure the cost drivers of the life insurance industry. Pedoe (1952, 1961) uses an index-based approach to develop two expense-factor formulas based on data from 20 Canadian companies. The formulas are coefficients that are to be multiplied by corresponding cost drivers (activity levels) to produce expected expenses. Pedoe uses the formulas to measure the relative expense positions of life insurance companies in Canada and to examine trends in their expenses between 1939 and 1959.

The stability of the insurers’ product mix is crucial to Pedoe’s model. The past two decades, however, have brought dramatic changes to that mix. The reasons include the introduction of new products, such as variable and universal life policies, and a shift in demand toward less-profitable life policies and products that transfer investment risk, along with its return, to the customer. These changes have strained the reliability of the indexbased approach. In addition, although Pedoe’s formulas contain intuitively reasonable expense factors, he does not explain their derivation in detail.

Brezinski (1976) uses regression analysis to apply Pedoe’s method to U.S. life insurance companies. He incorporates more than 70 cost drivers and uses data from the 1974 annual statements of 292 companies. The results indicate that size and lines of business are important factors in explaining differences in cost structures across companies.

Fortney and Miller (1984) apply the Bayesian approach to estimate the association between total costs and 52 cost drivers using Berzinski’s data and then use the estimated parameters to predict the total costs of the sample firms in 1975. In addition, they compare the Bayesian approach to the least-square approach and find that the former is superior in terms of prediction error. Cherkas and Dicke (1990) use a combination of regression methods and pricing factors to derive expense factors for the ordinary life insurance line of business. Their results indicate that life insurance companies exhibit strong economies of scale and large variations in their expense performance (measured as the ratio of actual to expected costs). The study also reports that about two-thirds of ordinary life expenses are related to acquiring new business.

3. METHODOLOGY

As already noted, insurers may use different methods to allocate total costs across lines of business, so the costs that firms allocate to the life insurance line of business may be a biased estimator of the actual cost of life polices, and expense factors derived from those allocated costs may be arbitrary as well.

To avoid relying on allocated costs to derive expense factors, economic theory mandates the estimation of a cost function that models total costs as a function of input prices and physical outputs. (The physical outputs stand as proxies for the cost drivers of all lines of business.)

We define total costs as total insurance general expenses, as summarized in Exhibit 5 of the regulatory annual statements. Total insurance general expenses include both the costs associated with selling and issuing new policies (acquisition costs) and those of servicing existing policies (maintenance costs). In most industries, the marginal costs of the cost function represent the increase in total costs attributed to the production of an additional unit of output. In the life insurance industry, in contrast, the estimated marginal cost of each output is the incremental cost of selling and maintaining the policy as long as it is in force. In other words, the estimated marginal costs represent the present value of marginal expenses.’

The construction of the illustrative expense table consists of two steps. In the first step, we separate the estimated present value of marginal expenses into acquisition costs and maintenance costs on the basis of an assumption regarding the portion of total costs attributable to each category. In the second step, we compute the yearly charges, so the present values of the first year’s charge and of subsequent years’ charges equal the acquisition and the maintenance costs obtained from the estimated marginal costs, respectively. Operationalizing this second step requires assumptions about (1) the average duration of a typical life policy and (2) the discount rate.

4. OUTPUTS, INPUT PRICES, AND DATA

Estimating the cost function requires physical outputs and input prices. While most studies on the cost structure of the life insurance industry agree on the definition of inputs, they differ in the definition and measurement of outputs. What follows is a short description and critique of the outputs used in the literature and descriptions of the outputs and input prices used in this study.2 Outputs

Outputs In the Literature

In insurance, as in all service sectors, defining and measuring output are not trivial undertakings. Most studies define the outputs by lines of business, such as life insurance, annuities, and A&H; some studies add investment income as an additional output. The major difference among these studies is in the measurement of output.

Geehan (1986) provides a useful discussion of the issues involved in output measurement and presents a comparison of major studies that use different output measures. Grace and Timme (1992), Gardner and Grace (1993), and Fecher et al. (1993) use the dollar value of premiums and annuity considerations as proxies for the outputs of the life insurance and annuities lines of business, respectively. Premiums, however, are a questionable measure of the output of life policies. They represent not a physical output, but rather revenue (price per unit multiplied by the number of units of insurance). Furthermore, only a portion of the premium received for a whole life insurance policy covers the risk-bearing service that insurers provide; the remainder covers the cash value of the policy plus future expected dividends (in the case of participating policies). Thus, a portion of total premium actually belongs to the insured and should not be considered as revenue or an output for the insurer.

Yungert (1993) measures outputs by additions to reserves. The major problem with this measure is that reserves change as policies age, regardless of whether new policies are sold. Furthermore, the change in reserves stands in for the change in liabilities rather than the outcome of the selling effort.

Cummins and Zi (1998) distinguish between the two principal services that life insurance companies provide: risk-bearing/pooling and intermediation services. They use incurred benefits by line of business as a proxy for the risk-bearing/ pooling service and additions to reserves for the intermediation service. Yet-incurred benefits are a disputable measure of output because they represent obligations incurred in the past. Hence, benefits do not represent current output, but rather past cumulative output.

Following Cummins and Zi (1998), this paper characterizes the outputs of insurance companies by their primary service. Term life policies provide pure risk protection and whole life policies offer a mix of risk protection, and intermediation services. Annuities can be viewed as savings vehicles and therefore, the service can be characterized as intermediation. A&H policies, on the other hand, provide risk-protection services only.

Life Insurance Output

The risk-bearing/pooling service that is attributed to new life insurance policies can be approximated by the total amount of insurance sold during the year. The total amount of insurance sold during the year measures the outcome of the selling effort and the additional risk that the company assumes; it therefore can represent the output of the life insurance line of business. Furthermore, it is an appropriate measure of both term life and whole life polices.

Because the acquisition and maintenance costs associated with whole life policies differ from those associated with term life policies, we separate the total amount of insurance sold into whole life policies and term life policies. The classification between them is based on amounts reported in annual statements submitted to the NAIC.

Some of the costs associated with life policies are fixed; that is, they are expenses that are not related to the size of the policy. Therefore, we also include the number of life policies as another dimension of output. We assume that the fixed cost is the same for term and whole life policies.

In summary, we use three outputs for the life insurance line of business: the number of life policies sold during the year, the amount of insurance sold in whole life policies, and the amount of insurance sold in term life policies.

Annuities Output

For life insurance companies, profits and losses from annuities stem from the difference between the actual return on investments and the return credited to the contracts. Assuming a positive spread, the larger the annuity considerations, the higher is the expected profit. Hence, a plausible proxy for this output is annuity considerations, which represent the increase in the earnings base of this line of business.

A&H Output

A&H policies provide primarily risk protection. Because we cannot quantify the amount of risk associated with each new policy, we use the premiums as a proxy for the A&H output. In equilibrium, in which the risk associated with such policies is priced correctly, premiums are a good proxy for risk.

In summary, this study uses five outputs: the number of new life policies sold, the amount of insurance sold in whole life policies, the amount of insurance sold in term life policies, total annuity considerations, and total A&H premiums.

Inputs and Input Prices

The general expenses of life insurance companies can be classified broadly into labor-related expenses, capital expenses, and materials, a category that consists of all other expenses.

The Price of Labor

Labor is defined as the total number of employees and agents a company employs. We compute the price of labor as the total cost of employees and agents divided by their total number. The total cost of employees is the sum of salaries, contributions for benefit plans, payments under nonfunded benefit plans, and other employee welfare costs. The total cost of agents is the sum of direct commissions, contributions for benefit plans, payments under nonfunded benefit plans, and other agent welfare costs.

The price of labor is a surrogate for the average cost of employees. Therefore, for companies for which the computed price of labor is less than $15,000, we change the price of labor to $15,000, and for companies for which the computed price of labor is greater than $120,000, we change the price of labor to $120,000.4

The Price of Capital

Capital is defined as the sum of capital expenses: rent, equipment rental, and depreciation? Because we cannot obtain the price of each capital expense, we compute the price of capital as the ratio of capital expense to the number of employees and agents, effectively computing capital expense per employee. Assuming that physical capital per employee (the space each employee occupies and the quality of equipment each operates) is equal across companies, this ratio may serve as a proxy for the price of capital.

7. EXPENSE TABLE

To construct an expense table, we rely on the marginal costs of the life insurance outputs, LIFPOL, WAMT and TAMT, which are evaluated at the sample means and appear in Table 3.14 The table is constructed separately for branch and non-branch firms. It also specifies the first year’s and subsequent years’ charges for whole and term life policies.

Before proceeding with the analysis, one should note that the marginal costs represent the present value marginal expenses of life policies. Therefore, the present value of the first-year and renewal charges set out in the expense table must equal the marginal costs obtained from the cost function.

The following analysis provides a step-by-step description of the construction of an expense table. The first step of the analysis requires an assumption about the relative weights of acquisition and total maintenance costs. The second step is the computation of the yearly charges such that the present value of these charges equals the marginal cost of life policies (term and whole). This step requires assumptions about the discount rate and the average duration of a life policy.

Each of the assumptions can be changed. The following is just an illustration of an expense table, given these assumptions.

Step 1-Separation of Total Costs into Issuance and Maintenance Costs

Table 6 shows the marginal costs per policy and the amount of insurance for whole life and term life policies and for branch and non-branch firms (the table replicates the results in Table 3).

To separate total costs into acquisition and maintenance costs, we assume that the acquisition (maintenance) expenses are 69.37% (30.63%) of total costs. By multiplying the marginal costs of LIFPOL, WAMT, and TAMT by these ratios, we determine the present value of acquisition and maintenance expenses for branch and non-branch firms (see Table 7).

Step 2-Computation of First-Year and Maintenance Charges

We make the following assumptions:

1. Acquisition expenses are recovered in the first year (FY) of the policy, and maintenance expenses are recovered in subsequent years.15

2. The average duration of a whole (term) life policy is 14 (11) years. The duration of the whole and term life policies determines the period in which both the acquisition and maintenance expenses must be recovered. It follows that maintenance expenses associated with whole (term) life policies are recovered in 13 (10) years, because the FY charges cover acquisition expenses only. Because the marginal costs in Table 7 equal the present value of acquisition and maintenance expenses, the present value of the FY charge must equal the marginal cost of the acquisition expense. Also, the present value of the maintenance charges for 13 (10) years of whole (term) life policies must equal the marginal cost of maintenance expenses.

3. All charges are paid at the end of the year. This assumption is made to simplify the computation. (Alternatively, one could assume that the charges are made at the beginning or middle of the year or are made on a monthly basis.)

4. The discount rate of the yearly charges is 10%.

First Year’s (FY) Charges

Given assumptions (1) and (3), the FY charge for each policy is computed as acquisition expense per policy times one plus the discount rate or 1.1. Similarly, the FY charge per thousand of amount of insurance is computed as the acquisition expense per thousand times 1.1, as shown in Table 8.

1 From here on, this paper uses the terms marginal costs and present value of marginal expenses interchangeably.

2 The glossary provides exact definitions of each variable and its reference in the annual statement.

3 The NAIC mandates that insurers classify the number of policies sold and in force to lines of business (that is, life insurance, annuities, and health insurance). The newest versions of the policies-universal, variable, and variable universal-are classified in the same manner. Insurers must also separate into term and whole life the number of life policies sold and in force and the amount of other insurance sold and in force.

4 The computed price of labor depends on the number of employees, data that were provided by the companies included in the sample. Because some companies may have counted part-time employees as full-time or simply estimated the number of employees, the resulting price of labor varies significantly across companies. In addition, some companies in the sample provided unreasonable figures for the average yearly price of labor (less than $1,000 or more than $200,000, for example). Hence, we modified the price of labor to make it more realistic. Alternatively, we could have omitted these observations, but doing so would have reduced the statistical power of the analysis.

5 It is well established in the literature that financial capital, rather than physical capital, is the preferable proxy for the capital of life insurance companies in estimating an overall cost function for the industry. (See for example Grace and Timme 1992). However, the purpose of this study is to allocate total general expenses, as reported in Table 5 of the annual report, across the three lines of business. These operating expenses are likely to be independent of a company’s financial capital, and therefore it should not be accounted for in the regression estimation. Furthermore, if financial capital were to be used as the capital input, then the cost of holding the capital (which is theoretically computed as the cost of capital times financial capital) should be added to the cost variable. Hence, the end result of the process would be allocation not only of operating expenses, but also of the cost of holding financial capital.

6 The data do not contain information as to the number of insureds under A&H group master policies. Therefore, we use the number of master policies instead.

7 EMaP is a detailed expense study of life insurance companies that chose to participate in the program.

8 We also estimated the translog cost function, which is a flexible functional form that can be used to approximate any twice-differentiable function. The translog is considered superior to all other cost functions because it does not place a priori restrictions on the function. Nevertheless, the results that we obtain using the MCD are qualitatively similar. In addition, the number of parameters to be estimated under the translog cost function is much larger (43 versus 23).

9 Alternatively, one could estimate separate cost functions for each distribution system. Greene (1997), however, suggests that using a dummy variable is better, The reason is that by estimating separately two (or more) cost functions, the statistical power of the regression results is reduced substantially because each regression is estimated based on a smaller set of observations.

10 The results of the estimation of the cost function are invariant to the price we use as a scalar.

11 Sheppard’s (1953) lemma states that the first derivative of the cost function with respect to an input price equals to the input. The share of input I (Si) is computed as (Pi*I)IC. Using Sheppard’s lemma and considering that the cost function is estimated in a log form, the share equations can be obtained by taking the first derivative of In(C) with respect to ln(Pi):

partial In(C)/partial In(Pi) = (Pi/C)*partialC/partialPi = (Pi/C)*I = Si.

Therefore, the first derivative of In(C) with respect to ln(Pi) in Equation (12) equals alpha^sub i^.

12 Because total cost is equal to the sum of labor, capital, and materials expenses, the sum of labor share, capital share, and materials share must equal one because each share represents the percentage of total cost devoted to each of the inputs.

13 The implication is not, however, that the largest firms do not exhibit overall increasing returns to scale. In fact, we find that across all deciles the sample firms exhibit significant returns to scale.

14 The procedure below can be applied to any point in the data. For example, one can construct expense tables stratified by size by evaluating the marginal costs at the means of the size deciles.

15 The general practice in the industry is to recover the acquisition cost and maintenance expense in the first year (first year’s expense) and maintenance expense in subsequent years (renewal expense). We use assumption (1) for the sake of simplicity. This procedure can be conformed easily to the industry’s practice.

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Discussions on this paper can be submitted until April 1, 2003. The author reserves the right to reply to any discussion. Please see the Submission Guidelines for Authors on the inside back cover for instructions on the submission of discussions.

Dan Segal*

* Dan Segal is an Assistant Professor of Accounting at the Rotman School of Management, University of Toronto, 105 St. George St., Toronto, Ontario M5S-3E6, Canada, e-mail: dsegal@rotman.utoronto.ca.

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