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Profitability and Efficiency in the U.S. Life

Insurance Industry

WILLIAM H. GREENE wgreene@stern.nyu.edu

Department of Economics, Stern School of Business, New York University, NY, USA

DAN SEGAL dsegal@rotman.utoronto.ca

Department of Accounting, Rotman School of Management, University of Toronto, Toronto, Canada

Abstract

This study explores the relationship between cost inefficiency and profitability in the U.S. life insurance industry. Earnings have particular importance to life insurance companies because earnings and capital determine the viability of the insurer. Since the life insurance industry is mature and highly competitive, cost efficiency may be the main driver of profitability.

We derive cost efficiency using the stochastic frontier (SF) method allowing the mean inefficiency to vary with organizational form and the outputs. In addition, the estimation of the cost efficiency measure takes into account the underlying accounting concepts that generate the data and, consequently, the product mix (long-duration policies vs. short-duration policies) to avoid distorted estimates.

Our results suggest that cost inefficiency in the life insurance industry is substantial relative to earnings, and that inefficiency is negatively associated with profitability measures such as the return on equity. The analysis of inefficiency and organizational form suggest that stock (shareholder-owned) companies are as efficient and profitable as mutual (policyholder-owned) companies.

JEL Classification: G22, M41

Keywords: stochastic frontier, cost inefficiency, profitability, life insurance, organizational form

1. Introduction

‘‘The alleged linkage between operating performance and financial success is actually quite tenuous and uncertain’’ Kaplan and Norton (1992)

The main purpose of this study is to show the linkage of cost inefficiency and cross-sectional variation in firm profitability in the U.S. life insurance industry. The economics literature contains numerous studies of efficiency for many industries, including the life insurance industry. However, none of these studies examines the

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effect of inefficiency on profitability in the life insurance industry.1 The second purpose of this paper is to investigate the association between organizational form, inefficiency and profitability.

The analysis of the association between inefficiency and profitability is compelling for the industry because profitability of a life insurance company is of paramount importance to its operations. To determine the viability of the insurer, regulators rely on the financial reports prepared according to statutory accounting principles (SAP) and particularly on net income and the book value of equity. If regulators determine that the insurer’s viability is at risk, they may seize the firm or take any other action necessary to improve the deficiency in capital. Because of the scrutiny of both net income and equity, the profitability of the insurer determines to large extent its ability to invest and grow.

Cost inefficiency affects profits and growth through the negative effect of wasted resources on earnings and cash flows. The potential reasons for inefficiency are suboptimal usage of the firm’s resources through overpaying for inputs and through employing a technologically inferior operating process. Inefficiency causes realizable levels of earnings and cash flows that are lower than those potentially feasible with optimal operations. The adverse effects on earnings and cash flows translate into lower firm value either through lower dividends or through lower investments that slow the firm’s growth.

Although growth is an important value driver for all firms, it is of particular significance for life insurance firms. The efficient operation of these firms requires considerable economies of scale generated by business volume. Without growth, an insurer may not garner the business volume necessary to ensure the collective pooling of insurance risks under the law of large numbers upon which the insurance operation relies. In the domestic market, growth is achieved primarily through expansion of distribution systems and technology improvements. To provide for future growth, an insurance company must generate and maintain sufficient capital to satisfy regulators as well as to finance its expansion. Although capital may be generated through share issuance in the short run, life insurance companies, like any other companies, must be able to generate capital through profitable operations.

The profitability of a life insurance company is critically dependent on its operating and financial activities. Operating activity consists of insurance operations: selling new policies and servicing existing policies. Financial activity consists of investing the policies’ premiums. The profits from operating activities stem from the difference between premium revenue and the total cost of insurance and operations, whereas the profits from financial activities stem from the difference between actual investment returns and the returns credited to the policies.

The life insurance industry has recently faced structural changes that have adversely affected both aspects of operations and consequently overall profitability. First, demand has shifted towards less profitable life policies and towards products that transfer the investment risk, along with its return, to the customer. Second, increased regulation, triggered by a number of bankruptcies in the late 1980s, has prevented insurers from investing in high-risk products and has consequently limited investment returns. To remain competitive with the providers of other financial

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products, insurers have had to guarantee higher returns or shift the investment returns to the insured, forcing investment income down. Third, the emergence of non-traditional competitors such as banks2that operate with much lower product distribution costs have put considerable pressure on the profit margins of many traditional insurers. In addition to having adverse effects on earnings, these changes have highlighted the importance of growth and cost controls—that is, efficiency in marketing and operations—as crucial determinants of future prospects for an insurer.

Furthermore, the 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 innovations are copied shortly after their introduction. Consequently, success in this industry depends on the insurer’s ability to control costs and on various intangibles, such as clientele and business-risk preference, marketing skills, reputation, and perceived quality of service. Hence, we hypothesize that cost inefficiency explains a significant portion of the variation in the profitability of life insurance companies.

The two main organizational forms of life insurance companies are mutual and stock companies. The owners of a mutual company are its policy holders, while the owners of a stock company are its shareholders. By the end of 1998, more than 90%

of U.S. life insurance companies were stock companies, although mutual companies were, on average, larger than stock companies and owned approximately 33%of the total industry assets and 40%of the total amount of insurance. Jensen and Meckling (1976), Fama and Jensen (1985), and Mayers and Clifford (1986, 1988) argue that firms with alternative ownership structures differ in their operations and particularly in their cost of productions. Since the mutual form of ownership gives insurance companies mechanisms for controlling and disciplining managers that are less effective than those available under stock ownership (primarily because the potential risk of takeovers does not exist for mutual companies), stock companies may be more efficient than mutual companies. On the other hand, Cummins and Zi (1998) argue that the mutual form of ownership may be more effective in controlling owner–customer conflicts because the owners of mutual companies are policy holders, and hence mutual companies may be more efficient than stock companies. Although Cummins and Zi (1998) and Gardner and Grace (1993) investigate whether the stock companies are as efficient as mutual companies, both studies address the issue using two-stage analysis; they first estimate the inefficiency of the sample firms and then examine the association of inefficiency with organizational form. Cummins and Zi conduct simple analysis of variance (ANOVA) and other non-parametric tests of the association between inefficiency and organizational form, whereas Gardner and Grace regress inefficiency on several variables including a dummy variable for organizational form. These two-stage estimation procedures provide estimates that are statistically inefficient compared to a single-stage stochastic frontier approach in which the estimated frontier takes into account firm-specific variables (Kumbhakar et al., 1991; Reifschneider and Stevenson, 1991; Huang and Liu, 1994). We control for the difference in organizational form in the estimation of inefficiency directly. In addition, given that most life insurance

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companies engage in more than one line of business, this methodology allows us to explore not only whether different outputs have different cost structure but also whether mean inefficiency is a function of the outputs.

Using panel data on 136 life insurance companies (478 firm-years), we find that the average inefficiency of the industry is 20%. Analysis of the inefficiency estimate reveals that there is no significant association between mean inefficiency and organizational form. The mean inefficiency, however, is positively associated with the investments output, and negatively associated with the annuities output, indicating that the investments (annuities) line of business is the most (least) inefficient.

We provide evidence that inefficiency is paramount to profitability and that the cost of inefficiency is substantial. Specifically, the cost of inefficiency as percentage of earnings before tax and of revenues is 54 and 3%, respectively. Furthermore, inefficiency is negatively associated with the return on equity (ROE) and the return on assets (ROA) ratios, and efficient firms on average have higher cumulative return on equity and on assets. Finally, the effect of inefficiency on ROE, evaluated at the mean inefficiency, is 4 percentage points. Given the mature stage of the industry and that the average ROE in the industry is 12%, our results indicate that inefficiency has substantial economic effect on the profitability of life insurance companies.

The reminder of this article is organized as follows. Section 2 provides a brief review of the stochastic frontier (SF) method. Section 3 describes the outputs, inputs, input prices, and other data used in the estimation of operational inefficiency. Section 4 develops our hypotheses and research design. Section 5 provides the empirical results, and Section 6 concludes the paper.

2. The Stochastic Frontier

The SF method, first suggested by Aigner et al. (1977) and Meeusen and Van Den Broeck (1977), provides means to estimate cost efficiencies. Cost efficiency consists of two components: technical efficiency, which reflects the ability of the firm to obtain maximum output from a given set of inputs, and allocative inefficiency, which reflects the ability of the firm to use the inputs in optimal proportions, given their respective prices. The SF model involves the estimation of a cost frontier, as a function of outputs and input prices, where deviation from the frontier are assumed to be related to cost inefficiency and statistical noise.

To control for random error in the estimation and specification, the cost function is specified with two error components:

lnCi¼lnCðyi;piÞ þuiþvi¼lnCðyi;piÞ þei; ð1Þ where i indexes the firms, ln Ci is natural log of the observed total costs,

lnCðy

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input prices,uiis a one-sided error term that captures cost inefficiencyðui0Þandvi

is a random error term that is assumed to be normally distributed with zero mean and variances2v. In addition,uandvare assumed to be independent. From equation

(1) it follows that expðuiÞ ¼ C=C expðviÞ, so the cost inefficiency—the proportion by which the firm could have reduced its costs and still attain the same level of outputs—is computed as 1expðuiÞ.

With assumed independence of the distributions ofvandu, the computation of the distribution of e and the maximum likelihood estimation are usually straight-forward.3We compute the firm-specific inefficiency,ui, which is not observed directly

as the conditional expectationEðuijeiÞas in Jondrow et al. (1982).

The estimation of the SF along with the inefficiency term involves specifying the cost function as well as the distribution ofu. For the cost function, we use a translog function: lnCit¼a0þ X JaJ lnðPjitÞ þ 1 2 X J X dyJI lnðPjitÞlnðPditÞ þ X mbmYmit þ1 2 X m X ngmnYmitYnitþ X j X mCimPjitYmitþeit; ð2Þ whereYmis the natural-log of outputm,Pjis the price of inputj,iindexes the firms

andtis the time index. To assure the linear homogeneity of the cost function in the factor prices, we divide each of the prices and total costs by one of the prices.

For the one-sided inefficiency disturbance term u, several distributions have been suggested, such as the positive truncation of a normal distribution with zero-mean (half-normal), the positive truncation of a normal distribution with nonzero mean (truncated normal), the exponential distribution, and the gamma distribution.

Huang and Liu (1994) suggest that a statistically efficient test of the relationship between firm-specific variables and inefficiency would be a direct estimation of the frontier where the mean inefficiency is modeled as a function of firm-specific variables, rather than a ‘‘two-stage’’ analysis where the inefficiency term, which is assumed to have zero mean, is regressed on firm-specific variables. We test for the association between mean inefficiency and organizational form and the different outputs by implementing Huang and Liu (1994) approach and assume a truncated normal distribution for the inefficiency term, where the mean of the inefficiency term is formulized as

MEAN INEFFICIENCY¼a0þa1MUTUALþ X

ib

iYiþj

PD; ð3Þ

MUTUAL is a dummy variable valued at 1 for mutual companies and 0 for stock companies.Yi is the natural log of outputi, and PD is a time indicator valued at

1, 2, 3, and 4 for 1995, 1996, 1997, and 1998, the sample years, respectively. This specification of the mean inefficiency also controls for size as mutual companies, in general, are much bigger than stock companies. PD is included to allow for the mean inefficiency to change over time.4

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3. Model Specification and Data 3.1. Outputs

Like all service sectors, the life insurance industry presents difficulties of output definitions and measurement. Most studies identify outputs with lines of business— that is, life policies, annuities, and accident and health (A&H)—whereas some add investment income as an additional output. The major differences among studies of the cost structure of the industry are in output measurement. Geehan (1986) provides a useful discussion of the issues involved, and compares the output measures of major studies.

Grace and Timme (1992), Gardner and Grace (1993), and Fecher et al. (1993) measure outputs as the dollar value of premiums and annuity considerations. Premiums are, however, a questionable measure of life policies. They represent not physical output but rather revenues (price times number of policies). Furthermore, for whole life insurance policies, only a portion of the premium covers the risk-bearing that life insurance companies provide to the insured. The remaining portion covers the savings element of the policy; it therefore actually belongs to the insured and cannot be considered as revenue of the insurer.

Yuengert (1993) measures outputs by additions to reserves. The major problem with this measure is that reserves change when policies age, regardless of whether new policies are sold. In addition, the change in reserves measures the change in liabilities, rather than the output of the selling effort. In a more recent study, Cummins and Zi (1998) distinguish between the two principal services provided by life insurance companies: risk bearing/pooling and intermediation services. As a measure of the former, they use incurred benefits by line of business, whereas for the latter they use additions to reserves. Here, again the output measure is disputable. Benefits represent obligations that were incurred in the past; hence they measure past cumulative output, not current output.

Following Cummins and Zi (1998), we characterize the outputs by the service provided. Life policies give either pure risk protection (through term life policies) or a mix of risk protection and intermediation services (through whole life policies). Annuities can be viewed as saving vehicles and, therefore, the service they provide can be characterized as intermediation. A&H policies, on the other hand, provide risk protection service alone.

The risk bearing/pooling services that companies provide on new life insurance policies can be approximated by the total amount of insurance sold during the year.5 That amount measures the outcome of the selling effort and the additional risk that the company bears and, therefore, can represent the output of the life insurance line of business.6Furthermore, this output measure may be appropriate for all types of life policies, both term life and whole life.

Profits and losses from annuities arise 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 (premiums) the larger is the expected profit. Hence, a plausible proxy for this output is annuity

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considerations, which represent the increase in the earning base of this line of business.

A&H policies primarily provide risk protection. Since one cannot quantify the amount of risk associated with each new policy, we use A&H premiums as a proxy for these policies’ output. In equilibrium, where the risk associated with A&H policies is priced correctly, premiums serve as a good proxy for risk.

In addition, the dollar value of investments is also defined as an output because the investments of insurers’ deposit represent a major activity for most firms, and the cost of the investments activities are included in total general expenses. The inclusion of investment output is consistent with Grace and Timme (1992) and with previous cost studies of financial intermediaries (Gilligan et al., 1984; Mester, 1987).

To sum up, we use four outputs: amount of life insurance, total annuity considerations, total A&H premiums,7and dollar value of investments.

3.2. Inputs and Inputs Prices

We employ three inputs: labor, capital, and materials. Labor is defined as the number of employee and agents days. The price of labor is computed as the total cost of employees and agents divided by their total number. To mitigate the effect of outliers, we truncate the price labor at the ten and ninety percentiles. Capital comprises two components: financial capital, defined as book value of equity plus the asset valuation reserve (AVR);8and physical capital, defined as the sum of capital expenses—rent, rental of equipment, and depreciation.9 We define the price of capital as the opportunity cost of holding the financial capital and measure it as the difference between the ratio of five years’ total net income to total financial capital (ROE) and the ratio of total investment income to total assets (return on investments) over the same period.10,11

Our third input (materials) consists of all operating expenses other than labor and capital expenses. Most of these expenses are related directly to selling and servicing policies. We use the number of policies sold and terminated during the year as a proxy for the number of policies sold and serviced during the year. And we quantify the price of materials as the related expenses divided by the total number of policies sold or terminated.12

3.3. Data

Life insurance companies are required to file two sets of financial statements. One, intended primarily for shareholders, is prepared according to generally accepted accounting principles (GAAP). The other, highly detailed and intended for regulators, is prepared according to SAP.

The primary interest of SAP is measuring the solvency of the firm—that is, the amount of capital needed to cover all obligations under extreme economic conditions, emphasizing financial results under very conservative assumptions. The

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measurement of operational inefficiency requires detailed financial information on the outputs and inputs used in the production process. Given the importance of earnings according to SAP and the level of detail prescribed by those principles, we use the regulatory reports in the analysis.

We obtained the insurance financial data from the regulatory annual statements filed by insurers and reported to the National Association of Insurance Commis-sioners (NAIC) life insurance data tapes for 1995 through 1998. Because the NAIC tapes do not include the number of employees and agents whom insurers employ— information required to adequately estimate labor and its price—we collected these data from two sources: responses to a survey that requested the number of companies’ employees and agents, and the Life Office Management Association’s (LOMA’s) Expense Management Program (EMaP).13

The initial sample consisted of 733 observations (company-years). We excluded from the sample firms that did not sell either term or whole life policies (110 observations), firms for which the data show negative direct premiums, revenues, benefits, commissions, amount of insurance, labor-related expenses, or capital expenses (94 observations), companies that had fewer than 10 employees and agents (44 observations), and firms for which the growth rate in direct premiums could not be computed (four observations). We also excluded an observation with growth rate in premiums of 1,300%. The final sample consists of 136 firms and 478 observations: 118 firms in 1995, 123 firms in 1996, 119 firms in 1997, and 118 firms in 1998. Table 1 presents descriptive statistics for the sample.

Table 1 shows that the average size (total assets) of the sample firms ranges from $4,546 million in 1995 to $5,568 million in 1998. Mutual companies are on average much larger than stock companies; for most years, the average total assets of mutual companies is more than three times the average total assets of stock companies.14In 1998, the aggregate total assets of the sample firms were about $657 billion, approximately a third of all assets in the industry. Thus, our sample covers a material portion of all firms in the industry. The ROE, ROA and growth rate in direct premiums are fairly stable across the sample period; the average ROE (ROA) is 12% (2%), and the average growth rate is around 7%. These data imply that the industry is mature, with relatively low profitability and growth opportunities, suggesting that cost control is an important driver in determining the profitability of the insurer.

4. Research Design

When measuring inefficiency using data from regulatory reports, one needs to consider the underlying concepts of SAP, which do not distinguish among the durations of different policies and require the immediate expensing of acquisition costs, the major cost associated with the issuance of life insurance policy. The acquisition costs are larger for long-duration policies than for short-duration policies

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Table 1. Descriptive statistics.

Mean Standard Deviation

1995 1996 1997 1998 1995 1996 1997 1998 Outputs (M)

Investments 353 411 420 412 1211 1279 1323 1334

Life Insurance 3,516 4,167 4,518 4,549 9,668 10,922 12,681 11,901

Annuities 361 434 475 546 1,198 1,363 1,518 1,764

Accident and Health 140 138 127 87 659 653 620 312

Input Prices Labor 37,314 44,015 37,692 40,973 26,100 35,322 27,790 29,718 Capital 9.98% 9.83% 9.34% 8.86% 0.08 0.07 0.06 0.06 Materials 207 206 203 245 462 393 397 377 Inputs Labor 5,397 5,619 5,637 6,699 13,563 13,260 13,524 16,759 Capital ($M) 54 63 63 65 158 168 176 178 Materials ($M) 30 32 35 33 121 116 142 108 Assets ($M) SAMPLE 4,546 5,388 5,597 5,568 15,319 16,175 17,431 17,723 STOCK Companies 3,473 3,038 3,530 3,700 10,787 10,248 11,330 12,307 MUTUAL Companies 9,225 12,670 14,226 12,518 27,439 26,362 31,288 29,779 Value Drivers ROE 0.12 0.13 0.12 0.10 0.15 0.17 0.18 0.24 ROA 0.02 0.02 0.02 0.02 0.04 0.05 0.04 0.04 Growth 0.07 0.07 0.09 0.06 0.26 0.23 0.23 0.20 N 118 123 119 118 Notes:

1. Investments is the dollar value of investments. 2. Life Insurance is total amount of insurance. 3. Annuities is annuity premiums.

4. Accident and Health is accident and health premiums.

5. Labor price is computed as total compensation expense divided by the total number of employees and agents.

6. Capital price is computed as the difference between the ratio of five years’ total net income to total financial capital (return on equity) and the ratio of total investment income to total assets (return on investments) over the same period.

7. Materials price is computed as total general expense excluding wages related expenses divided by the total number of policies sold and terminated during the year.

8. Labor input is the total number of employees and agents. 9. Capital input is financial capital.

10. Material input is computed as total general expenses excluding wages related expenses.

11. ROE is return on equity; it is computed as income before taxes in year t divided by the average book value of equity (including the asset valuation reserve) at the end of yeart1 and yeart.

12. ROA is return on assets; it is computed as income before taxes in yeartdivided by the average total assets at the end of yeart1 and yeart.

13. Growth is the growth in direct premiums; it is computed as the one-year growth in direct premiums. 14.Nis the number of observations.

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and generally are recovered several years after the inception of the policy. Hence, SAP effectively ignore the concept of matching expenses with their associated revenues. Since inefficiency is measured with respect to a given level of output, SAP’s failure to account for the type of policy (long-term vs. short-term) would bias the inefficiency scores, and that applies to any choice of outputs. Firms that primarily issue long-term policies would appear to be inefficient while firms that concentrate on short-term policies would appear as efficient because the former incur higher acquisition costs for any given level of output. To control for SAP’s failure to match expenses with their associated revenues, we separate the total amount of insurance output in the cost function into two outputs: total whole life policies’ amount of insurance and total term life policies’ amount of insurance. Whole life policies are considered to be long-term policies, whereas term life policies are considered to be short-term policies.15

We examine the association between profitability and inefficiency by examining the association between annual profitability and inefficiency, and the association between the firm’s cumulative profitability and mean inefficiency over the sample period through a series of regressions. The cumulative regression analysis allows examining whether firms that are efficient on average are also more profitable. Given that the profitability of firms may fluctuate on a yearly basis for reasons not related to economic inefficiency, such as higher than expected mortality rates and unexpected gains or losses on investments, the cumulative regression analysis provides further support to the relationship between inefficiency and profitability.

In the first set of regressions, we use two measures of annual profitability: the ROE, defined as the ratio of income before taxes in year ðtÞ to the average book value of equity in yearstandt1, in one specification, and the ROA, defined as the ratio of income before taxes in yeartto the average of total assets in yearstandt1 in a second specification.

The explanatory variables consist of the inefficiency estimate, organizational form, size, mix of life insurance policies (MIX) and growth. We predict that the coefficient of inefficiency is negative, indicating negative association between profitability and inefficiency. We include size among the explanatory variables to account for the negative association between size and economies of scale in the life insurance industry. Grace and Timme (1992) and Segal (2003) find that the largest insurers have lower economies of scale than smaller insurers, but still increasing returns to scale. This implies that larger insurers have lower average cost per unit and, therefore, we expect the size coefficient to be positive. The inclusion of organizational form allows us to test whether profitability is associated with organizational form after controlling for size. We include the mix of life insurance policies among the independent variables in order to account for the effect of SAP’s failure to distinguish properly between long-term and short-term policies. Similarly to the effect on inefficiency, the expensing of commissions regardless of the type of policy (short-term vs. long-term) may cause firms that sell primarily long-term policies to appear not only more inefficient but also less profitable. On the other hand, long-term life policies allow insurance companies to make profit on the two components of the policy, risk protection and savings, and therefore firms that sell

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primarily long-term policies are potentially more profitable. Hence, we do not predict the sign of the coefficient of MIX, which is computed as the ratio of total new whole life policies’ amount of insurance to total term and whole new life policies’ amount of insurance. Finally, we include the growth in direct premiums among the explanatory variables for two reasons. First, because of the immediate expensing of the commissions, the major expense associated with issuance of new policies, fast growing companies may appear less profitable. Second, previous studies on the cost structure of the life insurance industry document overall increasing returns to scale (Grace and Timme, 1992; Cummins and Zi, 1998, Segal, 2003), and therefore, high growth companies may appear more profitable. Given these two confounding effects, we do not predict the sign of the coefficient of the growth variable.

Formally, we estimate the following model:

PMit¼aiþb1INEFitþb2MUTUALitþb3LOGASSTit

þb4MIXitþb5GROWTHitþjit; ð4Þ

whereiindexes firms,tis the time index, PM is the profitability measure—ROA and ROE, INEF is the inefficiency estimate, MUTUAL is a dummy variable with 1 if mutual company and zero otherwise, LOGASST is a proxy for size and is computed as the natural log of total assets, MIX is computed as described above, and GROWTH is the one-year growth in direct premiums. We estimate the model using random effect panel data model, where the standard errors are adjusted for group (firm) wise heteroscedasticity.

In the cumulative regressions, the profitability measures are computed as the sum income before taxes over the sample period scaled by the sum of book value of equity over the same period (CUM_ROE), and the sum of income before taxes scaled by the sum of total assets (CUM_ROA). The explanatory variables consist of the firm’s mean inefficiency estimate, and ORG, a dummy variable which takes the values of 0 if stock company over the sample period, 1 if mutual company over the sample period, and 2 if the company converted to stock company during the sample period.16In addition, we include MN_ASST, the average of the natural log of total assets, MN_MIX, the average of MIX, and CUM_GR, the geometric mean of the growth in direct premiums.

Formally, we estimate the following model:

PMi¼aþb1MN INEFiþb2ORGiþb3MN ASSTiþb4MN MIXi

þb5CUM GRiþxi; ð5Þ

where i is the firms index, PM is the profitability measure—CUM_ROA and CUM_ROE. We estimate the model using simple OLS regression.

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5. Results

Table 2 presents the inefficiency estimates and demonstrates the effect of inefficiency on earnings. Panel A of Table 2 shows the estimated coefficients of the cost function. The estimated cost function satisfies the concavity condition, but does not satisfy the monotonicity condition with respect to the annuities output. It appears that the reason is that the share equations are not included in the estimation; when estimating the cost function jointly with the share equations the marginal cost of the annuities is positive. Consistent with Segal (2003) and Grace and Timme (1992), the estimated cost function indicates that the industry exhibits overall economies of the scale at the mean, median, and 25th and 75th percentiles of the outputs, and that the degree of scale economies decreases with size. However, in contrast to Segal (2003) and Grace

Table 2. Inefficiency estimates.

Panel A: Estimation results of the cost frontier (standard errors in parentheses)ðN¼478Þ

Intercept 68.56 (14.607) Y1Y2 0.011 (0.034) Y4Y5 0.013 (0.004) L 0.397 (0.609) Y1Y3 0.039 (0.026) Y5Y5 0.006 (0.001) K 0.517 (0.685) Y1Y4 0.083 (0.016) LY1 0.078 (0.054) LL 0.172 (0.044) Y1Y5 0.023 (0.008) LY2 0.075 (0.031) LK 0.137 (0.037) Y2Y2 0.135 (0.026) LY3 0.139 (0.017) KK 0.149 (0.069) Y2Y3 0.025 (0.013) LY4 0.038 (0.025) Y1 2.78 (1.24) Y2Y4 0.015 (0.028) LY5 0.001 (0.003) Y2 2.543 (0.865) Y2Y5 0 (0.003) KY1 0.049 (0.05) Y3 1.268 (0.685) Y3Y3 0.018 (0.011) KY2 0.088 (0.038) Y4 1.734 (0.653) Y3Y4 0.065 (0.017) KY3 0.184 (0.025) Y5 0.204 (0.254) Y3Y5 0.006 (0.004) KY4 0.03 (0.021) Y1Y1 0.075 (0.071) Y4Y4 0.077 (0.017) KY5 0 (0.005) Notes:

1.Y1 is dollar value of investments.

2.Y2 is whole life amount of insurance output. 3.Y3 is term life amount of insurance output. 4.Y4 is annuity premiums.

5.Y5 is accident and health premiums.

6.Lis the price of labor scaled by the price of materials. 7.Kis the price of capital scaled by the price of materials.

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Panel C: Descriptive statistics of the inefficiency estimate

Year N Mean Median STD Minimum Maximum

95 118 0.18 0.14 0.13 0.06 0.90

96 123 0.22 0.15 0.15 0.07 0.88

97 119 0.19 0.13 0.14 0.06 0.84

98 118 0.19 0.14 0.13 0.08 0.85

Overall 478 0.20 0.14 0.14 0.06 0.90

Panel D: The median cost of inefficiency as a percentage of income before tax and as a percentage of revenues

Year N EFF_IN EFF_REV

95 118 0.52 0.03 96 123 0.58 0.04 97 119 0.51 0.03 98 118 0.56 0.03 Overall 478 0.54 0.03 Notes:

1. EFF_IN is the ratio of cost of inefficiency over the absolute value of income before taxes. The cost of inefficiency is computed as the inefficiency estimates times the sum of total general expenses and total commissions.

2. EFF_REV is the ratio of cost of inefficiency over total revenues. The cost of inefficiency is computed as the inefficiency estimates times the sum of total general expenses and total commissions.

Table 2. Continued.

Panel B: Estimated parameters of the mean inefficiency term

Variable Coefficient Standard Error Z

Intercept 2.757 2.337 1.180

MUTUAL 0.656 0.759 0.865

Investments 1.279** 0.226 5.658

Life Insurance 0.220 0.162 1.354

Annuities 0.898** 0.147 6.107

Accident & Health 0.004 0.043 0.092

Pd 0.002 0.164 0.013

Notes:

1. MUTUAL is a dummy variable with 1 if mutual company and zero otherwise. 2. Investments is dollar value investments.

3. Life Insurance is total amount of insurance. 4. Annuities is annuity premiums.

5. Accident & Health is accident and health premiums.

6. PD is a year indicator; PD takes the values of 1, 2, 3, 4 for 1995, 1996, 1997 and 1998, respectively. 7.Zis the ratio of the coefficient estimate divided by its standard error. Z is distributed asymptotically

normal.

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and Timme (1992), the estimated function does not support economies of scope between any of the lines of business.

Panel B of Table 2 presents the estimated parameters of the mean inefficiency term (equation (3)). The coefficient of MUTUAL is positive but not significantly different from zero, indicating that there is no association between inefficiency and organizational form. The coefficients of amount of insurance and accident and health premiums are also not significantly different from zero. The coefficient of investments is positive and significant indicating that the location (mean) of the inefficiency distribution is positively associated with the level of dollar of investments. Conversely, the coefficient of annuities is positive and significant suggesting negative correlation between the level of annuities premiums and mean inefficiency. The coefficient of the time indicator is not significant implying that the distribution of inefficiency has not shifted over the sample period. The likelihood ratio for testing whether the overall mean inefficiency is different from zero is 50, whereas the critical value of a chi-square distribution with seven degrees of freedom at the 5%level is 14. Hence, we reject the null hypothesis that the mean inefficiency is zero.

Panel C of Table 2 provides descriptive statistics of the inefficiency estimates. The overall mean and median inefficiency are 0.20 and 0.14, respectively; in addition, the mean and median inefficiency are stable over the sample years. The mean and median of the inefficiency estimate are lower than those reported in Cummins and Zi (1998) and in Yuengert (1993), which ranges from 30 to 40%. One possible explanation for the discrepancy is that both studies use the zero mean half-normal distribution assumption to estimate inefficiency whereas we use the truncated normal distribution, where the mean inefficiency is estimated as a function of firm-specific variables. In addition, our sample period is later than the sample periods of these studies.

Panel D of Table 2 shows the median cost of inefficiency as a percentage of earnings before income tax and as a percentage of revenues, denoted EFF_IN and EFF_REV, respectively. We compute the cost of inefficiency as the inefficiency estimate times the inputs. We calculate the cost of inefficiency in operating expenses, which comprise labor-related expenses, physical capital, and all other expenses (Thus, our cost of inefficiency does not include any inefficiency in the amount of financial capital held.17) The median of EFF_IN ranges from 51 to 58% and EFF_REV ranges from 3 to 4%. Hence, inefficiency is substantial relative to earnings and revenues.

Table 3 shows the regression results. The simple Pearson correlation coefficients (not tabulated) between the inefficiency estimate and ROE and ROA are0.13 and significant at less than 1%. We estimate the model using random effect panel data to maintain heterogeneity across firms. Hausman test suggests we cannot reject the assumptions of the random effects estimator; in the ROE and ROA regressions the Hausman statistics are 1.66 and 4.94, respectively, whereas the chi-squared statistic with five degrees of freedom is 11.07.

The coefficient of the inefficiency estimate is negative and significant at less than 5%for both ROE and ROA regressions. The coefficient of the inefficiency term in the ROE regression is0.197. The magnitude of the coefficient indicates that the

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effect of inefficiency on ROE evaluated at the mean of the inefficiency estimate is 4%. Given the relatively low ROE in the industry (12%), this result suggests that inefficiency is not only statistically significant but also economically significant. Similarly, we find that the effect of inefficiency on ROA evaluated at the mean inefficiency estimates is1%, which is also substantial given that the average ROA in the industry is 2%.

The coefficient of MUTUAL, a dummy variable with 1 if mutual company and zero otherwise, in the ROE regression is negative and marginally significant, whereas the coefficient of MUTUAL in the ROA regression is not significantly different from zero. These results suggest that there is weak evidence that mutual companies are less profitable than stock companies. As predicted, the coefficient of the size variable is positive and significant in the ROE regression, indicating that larger firms are able to produce at a lower cost per unit. The coefficients of MIX and GROWTH are not significantly different from zero in both regressions.

Table 4 shows the regression results of the cumulative profitability variables. The simple Pearson correlation coefficients (not tabulated) between the firms’ mean Table 3. Random effect panel data estimation results (standard errors, adjusted for firm wise heteroscedasticity, in parentheses)ðN¼478Þ. Profitability Measure ROE ROA INTERCEPT 0.02 (0.045) 0.022* (0.012) INEFFICIENCY () 0.197** (0.078) 0.052** (0.018) MUTUAL (?) 0.043* (0.023) 0.008 (0.005) LOGASST (þ) 0.022** (0.006) 0.002 (0.002) MIX (?) 0.02 (0.034) 0.005 (0.008) GROWTH (?) 0.014 (0.035) 0.009 (0.008) Notes:

1.Nis the number of observations.

2. ROE is the return on equity; it is computed as income before taxes in year t divided by the average book value of equity (including the asset valuation reserve) at the end of yeart1 and yeart.

3. ROA is return on assets; it is computed as income before taxes in yeartdivided by the average total assets at the end of yeart1 and yeart.

4. INEFFICIENCY is the inefficiency estimate.

5. MUTUAL is dummy variable with 1 if mutual company and 0 otherwise. 6. LOGASST is the natural log of total assets scaled by $1 million.

7. MIX is the mix of life policies ratio – amount of insurance of whole life policies sold during the year over the total amount of insurance (wholeþterm).

8. GROWTH is the growth in premiums; it is computed as the one-year growth in direct premiums. 9. * (**) indicates significance level of 10%(5%).

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inefficiency estimate and CUM_ROE and CUM_ROA are 0.27 and 0.24, respectively, and significant at less than 1%. The coefficients of the inefficiency estimate are 0.24 and 0.076 and significant at less than 5% level for the CUM_ROE and CUM_ROA regressions, respectively. The magnitude of the coefficient indicates that the effect on CUM_ROE (CUM_ROA) evaluated at the mean of the inefficiency estimate is around5%(1.5%). These results confirm our findings that the effect of inefficiency on profitability is statistically and economically significant as the mean of CUM_ROE (CUM_ROA) is 8%(1.2%).

The coefficient of the organizational form, ORG, is negative for both regressions but not significantly different from zero, indicating that there is no association between profitability and organizational form. The coefficient of the size variable is positive and significant at less than 5% level in the CUM_ROE regressions, confirming our finding that large firms are more profitable. The coefficient of the mix variable is not statistically different from zero. The coefficient of the growth Table 4. Regression results of cumulative profitability on inefficiency (standard errors in parentheses)

ðN¼136Þ. Profitability Measure CUM_ROE CUM_ROA INTERCEPT 0.157* (0.089) 0.022 (0.025) MEAN_INEF () 0.24** (0.073) 0.076** (0.02) ORG () 0.011 (0.011) 0.002 (0.003) MN_ASS (þ) 0.014** (0.004) 0.001 (0.001) MEAN_MIX (?) 0.003 (0.031) 0.011 (0.009) CUM_GR (?) 0.137** (0.065) 0.039** (0.018) Notes:

1.Nis the number of observations (firms).

2. CUM_ROE is the cumulative return on equity; it is computed as the sum of income before taxes over the years of available data divided by the sum of book value of equity (including the asset valuation reserve) over the same period.

3. CUM_ROA is return on assets; it is computed as the sum of income before taxes over the years of available data divided by the sum of total assets over the same period.

4. MEAN_INEF is the firm’s mean inefficiency estimate.

5. ORG is dummy variable with 0 if stock company over the sample period, 1 if mutual company over the sample period, and 2 if the organizational form has changed during the sample period.

6. MN_ASS is the firm’s mean of natural log of total assets scaled by 1 million over the sample period. 7. MN_MIX is the firm’s mean of mix of life policies ratio—amount of insurance of whole life policies sold

during each year over the total amount of insurance (wholeþterm).

8. CUM_GR is the cumulative growth in premiums; it is computed as geometric average of the growth in direct premiums.

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variables is positive and statistically significant at the 1% level, corroborating the association between economies of scale and profitability.

6. Summary and Conclusion

The main purpose of this study is to explain cross-sectional differences in profit-ability of life insurance companies. Since the life insurance industry is mature and highly competitive, we hypothesize that cost inefficiency may have a strong negative effect on earnings. We estimate inefficiency and compute the profitability measures using the regulatory reports, which are prepared according to the SAP. Since SAP ignores the matching concept, we control for the different types of life policies in the estimation of the inefficiency in order not to bias the inefficiency scores.

We find that the industry is on average 20% inefficient. There is no significant relationship between inefficiency and organizational form. But the mean inefficiency is positively correlated with the investments outputs and negatively correlated with the annuity outputs.

We show that the cost of inefficiency is substantial and that efficiency is paramount to profitability. Specifically, the cost of inefficiency as percentage of earnings before tax and revenues is 54 and 3%, respectively. In addition, inefficiency is negatively associated with the ROE and ROA ratios, and efficient firms on average have higher cumulative return on equity and on assets. Furthermore, the effect of inefficiency on ROE (ROA), evaluated at the mean inefficiency is 4 (1) percentage points. Given the mature stage of the industry and that the average ROE (ROA) of the industry is 12% (2%), our results indicate that inefficiency has substantial economic effect on the profitability of life insurance companies.

Acknowledgments

We appreciate the helpful comments from Joshua Livnat, Ajay Maindiratta, Stephen Ryan, James Ohlson, and workshop participants at the Hebrew University of Jerusalem, New York University, Yale University, London Business School, and the University of Toronto. LOMA kindly provided some of the data.

Notes

1. Cummins and Zi (1998) provides evidence on the simple Pearson Correlation between their inefficiency estimates and two ratios: the ratio of expenses to premiums and the ratio of net income plus benefits to equity. Our study differs from Cummins and Zi on two important grounds. First, we investigate the association of inefficiency with profitability as measured by the return on equity and on assets, and second, we analyze the association controlling for other variables that are related to profitability.

2. Prior to Gramm–Leach–Bliley act of 1999 banks could not underwrite insurance. However, they could sell insurance and have made major inroads into the annuity market.

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3. Although OLS provides consistent estimates of the parameters with the exception of the constant term, maximum likelihood estimation provides more efficient estimates of the parameters. 4. The model was estimated without forcing the estimated inefficiency term,uðiÞto be the same in every

year, as is often done in panel data analyses using the stochastic frontier model. This assumption leads to implausible estimates of cost inefficiency for nearly every firm. The invariance restriction has produced similarly problematic results in other studies (see Greene (2003)). Whether it is economically reasonable over a long time period (four years) is debatable. Our results were convincing that we should relax this restriction in this study.

5. By using this measure we implicitly ignore the intermediary output associated with whole life policies. In this type of policies, insurance companies make a profit both on the insurance and on the investments of the savings portion of the policy. However, we believe that the main output of the life insurance line of business is the insurance risk assumed by the insurer. Second, given the data limitations, it is impossible to separate the premiums on whole life policies into their insurance and savings components.

6. Another potential proxy is the change in the amount of insurance in force during the year. It would measure the net additional amount of risk that the company assumes during the year. However, this measure could take on negative values in cases of reinsurance or when the amount of insurance paid is greater than the amount of insurance sold in any given year.

7. Cummins and Zi (1998) and Grace and Timme (1992) control also for group and individual policies in the cost function. Given our sample size, we do not control for group and individual policies because of lack of degrees of freedom. Another important aspect that might affect the results is the marketing distribution system of the firm. Insurers use various marketing distribution systems such as branch offices, agencies and direct marketing. The results reported here are possibly associated with the distribution system. Most insurers, however, employ more than one distribution system and hence one cannot determine the unique distribution system of each firm.

8. The AVR does not reflect future obligations (as do other reserves) but is set aside to protect against an extreme decline in the value of the assets that back up liabilities.

9. We are aware that the financial capital is a stock variable while physical capital is a flow variable. We assume that flow is a fixed proportion of the stock.

10. We measure these ratios over five years, rather than averaging the yearly ratios, in order to mitigate the influence of extreme fluctuations in the returns’ ratios on the price of capital. If the price of capital in a particular case is negative—that is, if the five-year investment return was greater than the return on equity—we compute the price of capital as the average price of capital of the sample for that year.

11. We do not account for the price of the physical capital in the aggregate price of capital since the related expenses are rather negligible compared to the magnitude of the financial capital.

12. The data do not contain information as to the number of insured under A&H group master policies. Therefore, we used the number of master policies in the computation.

13. EMaP is a detailed expense study of life insurance companies that chose to participate in the program. LOMA agreed to provide the data as part of a study of the cost structure of the life insurance industry.

14. The increase in the mean total assets of mutual companies in 1996 is attributed to one company for which we have data from 1996 to 1998. The mutual company with the lowest total assets in 1995 converted to stock company in 1996.

15. We separate the amount of insurance to whole life and term life amount of insurance in the cost function and not in the mean inefficiency. When estimating the mean inefficiency we use the total amount of insurance (whole life and term life) as the life insurance input.

16. Twenty companies in the sample have converted from mutual form of ownership to stock form of ownership.

17. We did not include the amount of financial capital in the computation of the cost of inefficiency because we believe that this variable is subject to less discretion by management as compared with other operating expenses.

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References

Aigner, D., K. Lovell and P. Schmidt. (1977). ‘‘Formulation and Estimation of Stochastic Frontier Production Function Models.’’International Economic Review17, 377–396.

Cummins, J. D. and H. Zi. (1998). ‘‘Comparison of Frontier Efficiency Models: An Application to the U.S. Life Insurance Industry.’’Journal of Productivity Analysis10, 131–152.

Fama, F. E. and M. C. Jensen. (1993). ‘‘Separation of Ownership and Control.’’ Journal of Law and Economics26, 301–325.

Fecher, F., D. Kessler, S. Perelman and P. Pestieau. (1993). ‘‘Productive Performance of the French Insurance Industry.’’Journal of Productivity Analysis4, 77–93.

Gardner, L. and M. F. Grace. (1993). ‘‘X-Efficiency in the U.S. Life Insurance Industry.’’ Journal of Banking and Finance17, 497–510.

Geehan, R. (1986). ‘‘Economies of Scale in Insurance: Implications for Regulation.’’ The Insurance Industry in Economic Development, 137–160.

Gilligan, T. and M. Smirlock. (1984). ‘‘Scale and Scope Economies in the Multi-Product Banking Firm.’’ Journal of Monetary Economics1, 203–220.

Grace, F. M. and S. G. Timme. (1992). ‘‘An Examination of Cost Economics in the United States Life Insurance Industry.’’Journal of Risk and Insurance59, 72–103.

Greene, W. (2003). ‘‘The Invariance Assumption in Panel Data Studies of Technical Inefficiency Based on the Stochastic Frontier Model.’’ Manuscript, Stern School of Business, New York University, Department of Economics.

Huang, C. and J. Liu. (1994). ‘‘Estimation of a Non-Neutral Stochastic Frontier Production Function.’’ Journal of Productivity Analysis5, 171–180.

Jensen, M. C. and W. H. Meckling. (1976). ‘‘Theory of the Firm: Managerial Behavior Agency Costs and Ownership Structure.’’Journal of Financial Economics3, 305–360.

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Kumbhakar, S., S. Ghosh and J. McGuckin. (1991). ‘‘A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farm.’’ Journal of Business and Economic Statistics9, 279–286.

Life Office Management Association (LOMA), Inc. (1998). Expense Management Program (Emap) Manual, Expense Year 1997, February 1998.

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Yuengert, A. M. (1993). ‘‘The Measurement of Efficiency in Life Insurance: Estimates of a Mixed Normal-Gamma Error Model.’’Journal of Banking and Finance17, 483–496.

References

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