Embed Size (px)
Citation preview
OWNERSHIP FORM AND EFFICIENCY: THE CO-EXISTENCE OF STOCK AND MUTUAL LIFE INSURERS
Leon Chen Assistant Professor, Minnesota State University at Mankato
Office: (507) 389-5336 Fax: (507) 389-5497
Email: [email protected] Address: Department of Finance, College of Business
150 Morris Hall Mankato, MN 56001
David L. Eckles Assistant Professor, University of Georgia
Office: (706) 542-3578 Fax (706) 542-4295
Email: [email protected] Address: Terry College of Business
Department of Insurance, Legal Studies, and Real Estate 206 Brooks Hall
Athens, GA 30602
Steven W. Pottier* Associate Professor, University of Georgia
Office: (706) 542-3786 Fax (706) 542-4295
Email: [email protected] Address: Terry College of Business
Department of Insurance, Legal Studies, and Real Estate 206 Brooks Hall
Athens, GA 30602
March 29, 2013
*corresponding author
1
OWNERSHIP FORM AND EFFICIENCY: THE CO-EXISTENCE OF STOCK AND MUTUAL LIFE INSURERS
Abstract
This paper explores the question of whether stock and mutual life insurers differ with respect to firm-level efficiency. It is the first study to compare directly the efficiency of stock and mutual life insurers, and the first study to compare activity choices and insurer characteristics of stock and mutual life insurers using consolidated, group-level data. It also extends the work of Cummins, Weiss and Zi (1999) on cross-frontier efficiency of property-liability insurers to life insurers, and additionally investigates revenue and allocative efficiency. Because mutual and stock insurers differ in their owners, each ownership form is characterized by differing incentive conflicts; the owner-policyholder conflict is likely to be greater in stock firms while the owner-manager conflict is likely to be greater in mutual firms. These differences have given rise to three main hypotheses: the managerial discretion hypothesis, the maturity hypothesis and the expense preference hypothesis. Consistent with the managerial discretion and maturity hypotheses, our analysis indicates that mutual and stock life insurers are indeed operating on separate efficient frontiers, and therefore appear to utilize distinct technologies. However, we find no evidence in support of the expense preference hypothesis.
Keywords: Organizational form, Efficiency, Life Insurance
2
1. Introduction
The different ownership forms in the insurance industry have been of enduring interest to
academic researchers. The coexistence of these two types of life insurers for over a century
suggests that neither form is dominant, but rather that each ownership form has different costs
and benefits or different comparative advantages in certain business lines or activities. Prior
insurance research provides some insights into mutual versus stock life insurer differences with
mixed results. Erhemjamts and Leverty (2010) investigate life insurer demutualizations and find
that converting firms experience an increase in efficiency.1 Cummins et al. (2010) examine scope
economies and find that mutual life insurers are significantly less revenue efficient than stock life
insurers, but do not find significant differences for cost efficiency. However, these papers do not
answer the question of whether stock and mutual life insurers differ with respect to efficiency
and do not present a comprehensive study of all types of efficiencies.2
In this study, we explore the question of whether stock and mutual life insurers differ
with respect to technical, allocative, cost, and revenue efficiency. Similar questions have been
explored by Cummins, Weiss and Zi (1999) for property-liability insurers. They find that for
property-liability insurers, firms with differing organizational forms were indeed operating on
differing technical and cost frontiers. Though our paper is most comparable to Cummins, Weiss
and Zi (1999) in research design, we conduct our analysis for life insurers which has not been
done in prior research.
1 These authors focus on cost and technical efficiency. They also present an analysis of cross-to-own technical efficiency ratios at the individual insurer level and find that mutual life insurer cross-to-own technical efficiency ratios are significantly below one even after controlling for other firm characteristics, suggesting that mutual insurers are less technically efficient than stock insurers. 2 The potential for lower (higher) cost efficiency being offset by higher (lower) revenue efficiency makes the examination of both types of efficiency important. Similarly, the components of cost efficiency, technical and allocative efficiency, may offset one another leading to the same cost efficiency score.
3
In many respects, the life insurance industry is distinct from the property-casualty
insurance industry. Life insurers rely on actuarial tables for pricing life, annuity and disability
insurance products, and have less exposure to catastrophic risk and legal liability risk exposures.
Life insurance and annuities product often have product life spans of several decades or more.
Life insurers are also subject to less rate regulation than property-casualty insurers. Unlike
automobile or homeowners insurance, or other property-casualty lines of coverage, life, annuity
and health insurance products are not generally legally required. Further, life insurer
investments, like their products, tend to be of longer duration than property-casualty insurer
investments. These differences, individually and collectively, make the issue of life insurer
ownership form efficiency differences worthy of separate analysis. Further, to the extent that
differences in product characteristics, regulations, markets and underlying technologies impact
economic efficiency, empirical findings are likely to differ between property-casualty and life
insurers. Results consistent with Cummins, Weiss and Zi (1999) would indicate that firms with
different organizational forms within the life insurance industry are operating on distinct efficient
frontiers. Results counter to Cummins, Weiss and Zi (1999) would suggest the opposite. Either
way, determining the degree to which life insurer efficient frontiers differ, by organizational
form, is of interest to researchers examining organizational form.
In addition to extending the organizational form and efficiency literatures to include life
insurers, our paper is also the first to test hypotheses related to life insurer organizational form
and revenue efficiency. Similar to Cummins, Weiss and Zi (1999), we test hypotheses regarding
the relative efficiency of the stock and mutual organizational forms using nonparametric frontier
efficiency methods, and also employ cross-frontier analysis to compare stock and mutual life
insurers (that is, we examine stock (mutual) firms relative to mutual (stock) efficient frontiers).
4
Firm ownership is treated differently within stock and mutual firms. The owners of stock
insurance firms, in general, are not the managers or customers of the insurer. The stock form
separates the ownership, management, and customer functions. These separate groups sometimes
have different and conflicting interests and incentives. In the stock form, owners, therefore, have
an incentive to expropriate wealth from policyholders by increasing risk after policies have been
issued. The mutual form merges the customer and ownership function, and in so doing, aligns the
interests of these two groups, eliminating the owner-policyholder conflict. The mechanisms to
monitor managers are more plentiful for stock firms. For instance, capital markets and financial
analysts play a more active role than policyholders. Stock firms are also able to design incentive
compensation connected to stock market value. In sum, the owner-policyholder incentive
conflict is likely to be greater in stock firms, and the owner-manager conflict is likely to be
greater in mutual firms. These differences have given rise to three main hypotheses. First, since
the stock form of ownership allows for managers to be given ownership stakes, the managerial
discretion hypothesis suggests that stock firms are best suited to undertake lines of business that
are subject to more managerial discretion. Second, since longer-term contracts put policyholders
at significant risks (due to reserving, dividends, etc.), the maturity hypothesis suggests that by
combining the owner and policyholder functions, mutual firms are more appropriate for lines of
business involving longer-term contracts. Finally, the expense preference hypothesis suggests
that the dilution of owners within mutual firms gives managers the ability to expropriate wealth
from policyholders/owners by perquisite consumption. These hypotheses and their implications
are further developed in relation to stock and mutual life insurers in the context of economic
efficiency in the hypotheses section below.
5
These predicted differences in stock and mutual insurers may lead to differences with
respect to cost minimization and revenue maximization. Different insurer organizational forms
may differ in their relative ability to transform economic inputs into economic outputs.
Alternatively, it is possible that the different organizational forms are operating on different
efficient frontiers. That is, the organizational forms implement different technologies in
transforming inputs (e.g. agent labor) into outputs (e.g. insurance products). If firms with
different organizational forms are indeed operating on differing frontiers, it becomes
inappropriate to compare one with the other, from an efficiency standpoint.3
With regards to technical and cost efficiency, Cummins, Weiss and Zi (1999) have
previously shown that different organizational forms are operating on different efficient frontiers
within the property-liability industry. However, no research has examined whether or not stock
and mutual life insurers are also operating on separate frontiers. Further, no research has
examined whether or not insurers of any type are operating on different revenue frontiers.
The primary purpose of this study is to examine efficiency differences and associated
differences in activity choices between stock and mutual life insurer organizational forms. This is
the first study to compare the efficiency of stock and mutual life insurers, and the first study to
compare activity choices and insurer characteristics of stock and mutual life insurers using
consolidated, group-level data. In addition, this is the first study to examine frontier differences
for insurers with respect to revenue efficiency and allocative efficiency.
3 See Cummins, Weiss, and Zi (1999).
6
2. Hypotheses
2.1 Managerial Discretion Hypothesis
Agency theory suggests that certain ownership forms have comparative advantages in
managing conflicts between stakeholders (Mayers and Smith (1981)). For insurers, potential
conflicts exist among policyholders, managers, and owners. The two predominant life insurer
ownership forms, mutual and stock, are used to mitigate some of these conflicts. The mutual
ownership form merges the owner and policyholder function, thereby eliminating the conflict
between the two. Similarly, by providing managers with an ownership stake, the stock form of
ownership can mitigate the conflict between owners and managers. These separate ownership
forms have long co-existed within insurance markets.
According to the managerial discretion hypothesis, the degree of managerial discretion
required to operate in a given line of business is the principal determinant of the ownership form.
Stock insurers are expected to dominate in lines of insurance where managers are given
relatively more discretion in pricing, underwriting or investment decisions, because of the stock
form’s superior ability of allowing owners to control managers. Consequently, stock life insurers
should be more prevalent in group lines and health insurance where the need for managerial
discretion in pricing and underwriting is relatively higher. Mutual insurers are more likely in
activities requiring less managerial discretion, such as personal lines or lines with more reliable
loss or actuarial data.
Previous research has examined the nature of this co-existence. Within the property-
liability industry, several papers (e.g. Mayers and Smith (1988) and Lamm-Tennant and Starks
(1993)) have shown, on a cross-sectional basis, that stock insurers operate in riskier lines of
insurance. This result is generally consistent with the managerial discretion hypothesis, that is,
7
the notion that the stock form has a comparative advantage at aligning the incentives between the
owners and managers. Riskier lines require more managerial discretion, and thus the conflict
between owners and managers is higher. Research in the life insurance industry has found a
similar result. Specifically, Pottier and Sommer (1997) also find, among other results, evidence
consistent with the managerial discretion hypothesis using a sample of life insurers.
The aforementioned studies all examine the managerial discretion hypothesis using cross-
sectional data. Cummins, Weiss and Zi (1999) implement a novel use of frontier efficiency
methodology to examine the managerial discretion hypothesis for property-liability insurers.
Cummins, Weiss and Zi (1999) estimate efficient frontiers for stock and mutual firms and find
that the distinct ownership forms operate with different technologies. Cummins, Weiss and Zi
(1999) also show that the stock (mutual) technology is most efficient for producing stock
(mutual) output, suggesting that each ownership form is efficiently producing its own output.4
Our study extends Cummins, Weiss and Zi (1999) to life insurers. If the managerial
discretion hypothesis holds, we would expect a similar result. Specifically, we expect to find that
the stock (mutual) frontier is the most efficient technology for producing stock (mutual) output.
This result is exactly what the managerial discretion hypothesis would predict.
The managerial discretion hypothesis applied to insurer efficiency states:
Hypothesis 1: Stock insurers should be more efficient than mutual insurers operating in lines
requiring more managerial discretion.
2.2 Maturity and Expense Preference Hypotheses
Cummins, Weiss and Zi (1999) also examine two other hypotheses, the maturity and expense
preference hypotheses. The maturity hypothesis predicts that mutual insurers will be more 4 This would be true for all types of efficiency (cost, technical, allocative, and revenue).
8
prevalent in product lines involving longer-term contracts and services because the longer time
horizon gives owners more opportunity to expropriate wealth from policyholders (e.g. changing
dividend and investment practices), and by merging the owner-policyholder functions, the
mutual form resolves this conflict. Over longer time periods, owners have more opportunities to
change underwriting, investment, dividend and financing policies to the detriment of
policyholders. As with the discussion above, Cummins, Weiss and Zi (1999) argue that stock and
mutual firms separate themselves into lines in which they have a comparative advantage with
regards to this conflict. As such, finding stock and mutual firms to be operating with distinct
technologies (presumably technologies superior for the appropriate line of business) also
suggests support for the maturity hypothesis.5
The maturity hypothesis applied to insurer efficiency states:
Hypothesis 2: Stock insurers should be more efficient than mutual in lines involving relatively
shorter-term products.
Though the mutual form is able to control some conflicts between the owners and
policyholders, resolving these conflicts is not without cost. The expense preference hypothesis
states that mutual firms are less capable of controlling costs because managers will be less
inclined to minimize expenses and more inclined to incur unnecessary expenses due to the
weaker monitoring mechanism.6
5 Again, we test this for four technology frontiers (cost, technical, allocative, and revenue).
Managerial consumption of perquisites in a sense substitutes for
the additional incentive compensation systems available to stock firms. Mutual insurers, unlike
stock insurers, lack the external monitoring of capital markets. Cummins, Weiss and Zi (1999)
hypothesize that mutuals will therefore not minimize costs as well as stocks. They further
hypothesize that the allocation of the costs (i.e. input mix) will be suboptimal. Finding that
6 Managerial perquisite consumption is often given as a prime example of these unnecessary expenses.
9
mutuals are generally less cost efficient than stocks and/or finding that mutuals do not allocate
the costs as well as stocks would be evidence in support of the expense preference hypothesis.
The expense-preference hypothesis applied to insurer efficiency states:
Hypothesis 3: Stock insurers should be more efficient than mutual in controlling expenses.
Finally, we note that these three hypotheses are not mutually exclusive. That is, it is
possible that we observe stock and mutual firms operating in lines of differing risks (managerial
discretion hypothesis), in lines of differing maturities (maturity hypothesis), and with different
cost structures (expense preference hypothesis).
3. Efficiency Estimation
3.1 Efficiency Estimation Method
Efficiency estimation methods involve estimating a firm’s relative efficiency where
efficient firms lie on the “best practices” frontier. Firms on the technical efficiency frontier are
minimizing their input levels for their given output levels. Firms on the cost frontier are
minimizing their costs given their output levels. Firms on the revenue frontier are maximizing
their revenues given their input levels. The present study uses the linear programming approach
to efficiency estimation, data envelopment analysis (DEA) (see Coelli, et al. (2005)) to estimate
technical, allocative, cost, and revenue efficiency scores (see Cummins and Nini (2002);
Cummins, Weiss and Zi (1999); Cooper et al. (2000); Cooper et al. (2006)).
In DEA technical efficiency estimation, a linear combination (i.e., linear sum) of a set of
firms (known as reference set) is identified that produce the same or more outputs with the same
or lower input levels than the firm being evaluated (that is, the firm in question).7
7 It should be noted that the linear programming problem is solved for each firm in the sample, and hence, each firm is assigned a set of weights most favorable to it.
For technical
10
efficiency the linear program finds the maximum reduction in inputs a firm can achieve given
their current output production. For firm i with K inputs and J outputs this linear program is
given as:
Min θi subject to: xi,λi
yi ≤ Yλi (1)
θixi ≥ Xλi
λi≥0
where xi is a k x 1 vector of input quantities, λi is an N x 1 vector representing the combination of
firms that form the cost efficient set for firm i, yi is a j x 1 vector of output quantities, Y is a j x N
matrix of the output quantities for the N firms, where column n contains the output quantities for
firm n, and row j of column n contains firm n’s quantity of output j. X is a k x N matrix of the
input quantities for the N firms, where column n contains the input quantities for firm n, and row
k of column n contains firm n’s quantity of input k. The solution to equation (1), θi*, represents
the degree to which firm i can proportionally reduce all of its inputs and maintain its current
level of outputs. If θi*=1, then the firm is technically efficient and cannot reduce its inputs. We
measure the efficient frontier (for all efficiency scores) assuming constant returns to scale.8
In DEA cost efficiency estimation, the process is similar to that of technical efficiency,
but the reference set is now the set of firms that produce the same or more outputs at the same or
lower cost than the firm being evaluated. The input quantities for this linear combination of firms
are used to calculate the costs of a fully efficient firm using the input prices of the firm being
8 Pottier (2011) estimates the efficiency scores under both variable returns to scale and constant returns to scale for the same dataset, and find that the results are qualitatively the same.
11
evaluated. The ratio of the costs of a fully efficient firm to the actual costs of the firm being
evaluated is the cost efficiency score of the firm in question. Consider that insurers decide upon
the combination of inputs and outputs where the number of available inputs is K, and the number
of potential outputs is J. The cost minimization problem for insurer i is specified as:
Min wixi subject to: xi,λi
yi ≤ Yλi (2)
xi ≥ Xλi
λi≥0
where xi, yi, Y, X, and λi are as described above and wi is a 1 x k vector of unit input prices.
Letting xi* be the cost minimizing vector of inputs for firm i, cost efficiency is given by wixi
*/
wixi. Finally, cost efficiency is made up of the product between technical and allocative
efficiency (i.e. CE = TE x AE). Therefore, once we calculate technical and cost efficiency, we
can easily derive allocative efficiency. As a component of cost efficiency, allocative efficiency
here refers to the allocation of inputs that may impact the level of a set of outputs.
Technical and cost efficiency are “input-oriented” approaches to efficiency. Revenue
efficiency, on the other hand, is an “output-oriented” approach. In DEA revenue efficiency
estimation, a set of reference firms with the same or higher revenues and the same or lower input
quantities than the firm being evaluated is identified. The revenues of the firm being evaluated
are then divided by the revenues of a fully efficient firm based on the output quantities of the
linear combination of reference set firms (i.e., firms with revenue efficiency scores of one) and
12
the output prices of the firm being evaluated to obtain the revenue efficiency score for the firm in
question. The revenue maximization problem for insurer i is to maximize revenue, by choosing
optimal output levels. The mathematical specification is given as:
Max piyi (3)
yi,λi
subject to identical constraints as in equation (2), where pi is a 1 x j vector of unit output prices,
and λi is an N x 1 vector representing the combination of firms that form the revenue efficient
set for firm i. Letting yi* be the revenue maximizing vector of outputs for firm i, revenue
efficiency is given by piyi/ piyi*.
3.2 Comparison of Stock and Mutual Life Insurer Efficiency
For our hypotheses, we estimate the efficiency scores described above in three different
ways. First, we estimate what we will refer to as the pooled frontiers for each efficiency score.
The pooled frontier is the frontier estimated using all firms, stock and mutual, in the sample.
Based on the pooled frontier, each firm’s efficiency score for the respective frontier (technical,
allocative, cost, and revenue) is calculated in relation to a reference set that includes all fully
efficient stock and mutual insurers.
Second, we estimate what we will refer to as the separate frontiers, simply the frontiers
for stock and mutual firms estimated separately (these could also be called “own” or “group-
specific” frontiers).9
9 For both pooled and separate frontiers, the efficiency scores are bound between zero and one.
Based on separate frontiers, the reference set for stock firms includes only
fully efficient stock firms and the reference set for mutual firms includes only fully efficient
mutual firms.
13
Finally, we estimate cross-frontier scores (Cummins, Weiss and Zi (1999)). The cross-
frontier approach involves estimating the efficiency of mutual (stock) firms using the stock
(mutual) efficient frontier.10
If mutual and stock firms are operating on different frontiers, and if one organizational
form’s frontier does not dominate the other, there is evidence of the managerial discretion
hypothesis and the maturity hypothesis. Specifically, this result would suggest that mutual and
stock firms are each optimizing inputs and outputs, and mutual (stock) outputs cannot be as
efficiently produced with stock (mutual) technologies. Examining cost efficiency of firms will
allow us to test the expense preference hypothesis. Specifically, finding that mutual firms are
generally less cost efficient than stock firms would be consistent with the expense preference
hypothesis.
In other words, the reference set for mutual (stock) firms includes
only fully efficient stock (mutual) firms.
3.3 Outputs and output prices
Life insurer outputs relate to the services, or benefits, life insurers provide. They are
represented by eleven distinct outputs associated with major lines of business and further divided
based on net incurred claims and invested assets. Panel A of Appendix 1 identifies our outputs.
Our approach to identifying outputs is generally similar to existing life insurer efficiency studies
(see Cummins and Zi (1998); Cummins, Tennyson and Weiss (1999); Cummins, Eckles and Zi
(2008)).
Outputs (i.e. benefits) consist of net incurred claims (i.e., death, annuity, disability,
accident and health benefits) plus additions to reserves and invested assets. Outputs one through
five are the net incurred claims grouped into five lines of business, namely individual life, group 10 The cross-frontier efficiency scores are not bound at one on the upper end.
14
life, individual annuities, group annuities and health (i.e., accident and health). Outputs six
through ten are the average invested assets allocated to these five lines of business based on the
ratio of reserves corresponding to each of the five lines of business to the sum of reserves and
deposit-fund liabilities. Output eleven is the average invested assets allocated to deposit-fund
business based on the ratio of reserves of deposit-fund liabilities.11 Revenues related to the
eleven outputs consists of premium and annuity considerations, net investment income,
commissions and expense allowance on reinsurance ceded, separate account net gain from
operations, separate account fees and deposit-type contract fees.12 The revenues are grouped into
the same five lines as the outputs.13
Since we define output quantities above, and because revenue is quantity times price, we
define output prices for outputs one to five as the ratio of total revenues less net investment
income divided by the output level (each by line amounts). Output prices six to ten are defined as
the ratio of net investment income less interest on deposit funds by line to the corresponding
output level. The output price for output eleven, deposit-fund business, is the ratio of interest on
deposit funds (summed across lines) to output eleven.
14
3.4 Inputs and input prices
11 Deposit-type contracts are defined as any contract “in which the reporting entity does not assume any mortality, morbidity, health benefit costs incurred, or casualty risk and which act exclusively as investment vehicles” (Best Reports (2006b)). Amounts received as payments for deposit-type contracts are recorded as a liability. 12 Separate account assets are maintained independently from an insurer’s general account assets and used primarily for retirement plans, variable life insurance, and variable annuities. The investments are not subject to state investment regulations, such as limitations related to equity investments, or credit quality restrictions. Costs and benefits of separate accounts that flow through the general account annual statement are included. 13 While net realized capital gains (losses) represent a financial intermediation component of revenues, this item is not available by line of business. It averages under one-half of one percent of total revenue for sample firms. To the extent that capital gains (losses) are reinvested, they are included in the balance of invested assets. 14 This approach to defining output prices is generally similar to that in Cummins, Tennyson and Weiss (1999) who employ outputs one through five. The current study separates net investment income from premium (and other) income in the numerator because an additional six outputs that are based on invested assets are used in this study.
15
Life insurer costs, or inputs, are grouped into five categories--agent labor, administrative
labor, business services, policyholder supplied capital and equity capital. Panel B of Appendix 1
identifies our inputs. The sum of the first three inputs is equal to general insurance expenses,
taxes (except federal income taxes), licenses and fees, commissions on direct business, and
commissions and expenses on reinsurance assumed. General expenses include investment
expenses related only to general-account investments, salary and wage expenses and other
operating expenses, except for policyholder claims and benefits. In a study of property-liability
insurer distribution system efficiency, Berger, Cummins and Weiss (1997) use the sum of loss
reserves and unearned premium reserves as their measure of debt capital. Life insurer liabilities
consist mostly of policy reserves and deposit funds, and like risky debt, are costly sources of
capital (Cummins and Danzon (1997)). Policyholder supplied capital consists of policy reserves
and deposit-type funds. Policy reserves consist of aggregate reserves for life, annuity and
accident and health insurance, and are reported by the lines of business used in this study. The
average of the beginning and end of year balance of capital and surplus is used for equity capital.
The year-end balances are used for reserves and deposit-funds.
Input prices are determined as follows. For administrative labor, agent labor and business
services, the 2005 national “average weekly earnings of production workers” from the U.S.
Department of Labor Bureau of Labor Statistics for direct life and health insurers, insurance
agencies and brokerages, and professional and business services, respectively, are used, as in
several other studies (Cummins and Zi (1998); Cummins, Tennyson and Weiss (1999);
Cummins, Eckles and Zi (2008)). The cost of equity capital is the 2005 average one-year
Treasury constant maturity rate from the Federal Reserve Bank of St. Louis plus the long-
16
horizon equity risk premium from Ibbotson and Associates (2006).15
The cost of policyholder
supplied capital is assumed to equal 4 percent, which seems reasonable as it is close to
guaranteed minimum interest crediting rates on life insurance policies.
4. Sample Selection
We use life insurer data at the consolidated group and single unaffiliated firm levels, for the 2005
annual financial statement year. Individual insurer and consolidated (i.e., group) financial
statement data are obtained from Best’s Annual Statement File, Life-Health Edition (Best
(2006a)).16 The data from Best (2006a) is supplemented with financial statement and other firm-
specific data reported to the NAIC on the Life-Accident-Health annual statement blank
(subsequently referred to as “NAIC statement”). Ownership form is obtained from Best’s
Insurance Reports, Life-Health Edition (Best (2006b)) and is based on the 2005 annual statement
year. The NAIC database does not include consolidated financial data for life insurers, and in
general, consolidated values are not equal to the sum of individual group member data.17
15 The Treasury rate and equity risk premium are 3.62 and 7.1 percent, respectively, making the assumed cost of equity 10.72 percent.
The use
of group-level financial data and characteristics in this analysis is important because the
centralized management of some activities of affiliated insurance firms and transactions among
group members imply that the group is the relevant decision making unit (Cummins and Zi
16 The consolidated data includes life affiliated insurers only. A single unaffiliated life insurer is defined as an individual life insurance company that does not have any life insurance affiliates filing with A.M. Best Company. Prior-year data (i.e., 2004), where applicable, is obtained from the prior-year's Best’s Annual Statement File. 17 Life insurers do not report consolidated statements to the NAIC. Consequently, we purchased the consolidated data from Best for our study. The results by year and across years are very consistent in Cummins, Weiss and Zi (1999) suggesting that additional years would not change any key conclusions. In general, life insurers do not change their inputs and outputs enough from year to year to change relative efficiency comparisons between stock and mutual firms. Life insurer products either have contract (i.e., policy) periods of multiple years or very high renewal rates on annual contracts that limit changes over all but long time periods.
17
(1998), and thus it is plausible for decision makers to maximize the value of the group, instead of
individual members within the group.
The sample is limited to active life insurers that are not insolvent (i.e., liabilities do not
exceed assets). Specifically, sample insurers must have positive values for admitted assets, gross
premiums written, net premiums written and equity capital. In addition, sample firms must have
reasonable levels of inputs and outputs. Thus, firms with negative total net incurred claims (sum
of outputs one to five) or negative individual inputs are also eliminated. After applying these
sample screens, all remaining firms had values for outputs 6 to 11 greater than or equal to zero.
Sample firms are also required to be in the NAIC and Best databases so that we may create all of
our measures. In addition, all life insurers in a group of affiliated life insurers, as defined by
Best, must be in the NAIC database in order for that group to be included in the sample. This
simply assures that the group data used corresponds to the complete life insurer group. Further,
life insurers that obtain more than 50 percent of their gross premiums from reinsurance assumed
are considered to be primarily engaged in the reinsurance business and are excluded from the
sample. Lastly, single unaffiliated life insurers must be domiciled and licensed in the U.S., and
for consolidated groups, one or more groups members must be domiciled and licensed in the
U.S. The final sample consists of 267 life-health insurers.
We examine the relation of organizational structure to technical, cost, and revenue
efficiency. Summary statistics for our 267 firm sample are presented in Table 1. Approximately
26 percent of the whole sample are “true” mutual firms. True mutual firms are defined as those
firms that are mutual firms at the parent level. Also, nearly half of our sample observations are
consolidated groups. On average, a life-health insurer underwrites around 34 percent of total
premium from the line of accident and health insurance, and around 30 percent of total premium
18
come from the group lines that include group life, group annuity and group health business.
Table 2 shows the mean levels for these variables separated by organizational form. While there
are not many significant differences between the average levels, we do observe that mutual and
stock firms have significant differences in the prices of the outputs.
Insert Table 1 about here
Insert Table 2 about here
5. Estimation Results
Univariate analysis
Summary statistics of all efficiency scores are shown in Table 3.18 We first test the
hypothesis that stocks and mutuals are operating on the same frontiers. That is to say, can
pooled frontiers be used to analyze efficiency differences between the two ownership forms, or,
alternatively, are the two ownership forms operating on distinct frontiers? This test involves first
estimating the pooled frontiers. Then, group-specific mutual and stock frontiers are estimated.
Using these frontiers, we can then test the hypothesis that the pooled frontiers and separate
frontiers are identical. We use ANOVA, Wilcoxon, Van der Waeden and Savage nonparametric
tests to test for differences in efficiency frontiers.19
18 Due to outliers, the cross-frontier efficiency scores (for all frontiers) are truncated at the 95th percentiles (the cross-frontier efficiency scores are still bound by zero, but not bound by 1 as in a standard efficiency analysis). Additionally, the Frevenue scores are truncated at both the 5th and 95th percentiles. There were no outstanding outliers among the F scores when using technical, allocative, or cost efficiency.
19 The Wilcoxon, Van der Waerden, and Savage tests are all tests of differences in distributions. The different tests are useful if the underlying distribution is logistic (Wilcoxon), normal (Van der Waerden), or exponential (Savage). Further description and uses of these alternative statistics can be found in non-parametric statistics textbooks (e.g. Conover (1999) and Hollander and Wolfe (1999). Though the test statistic varies across these measures, the results, with respect to significance were identical across all measures. Therefore, the significance indicated in Table 4 can be viewed as the result of any of the three tests.
19
Pooled and separate technical, allocative, cost and revenue efficiency scores are shown in
Table 4. These tests overwhelmingly reject the hypotheses of equality between the pooled
frontiers and separate frontiers for mutual firms for all frontier types (technical, allocative, cost
and revenue). However, for stock firms, only the cost and allocative frontiers are significantly
different. These results imply that all four types of efficiency comparisons should be based on
separate frontiers.20
Additionally, these results are consistent with the managerial discretion and
maturity hypotheses in that it supports the expectation that the two groups of firms, stocks and
mutuals, are using different technologies with respect to inputs and outputs.
Insert Table 3 about here
Insert Table 4 about here
The four types of efficiency scores based on separate mutual and stock frontiers are
shown in Table 5. Mutual firms are significantly more efficient (with respect to the mutual
frontiers), than stock firms (relative to the stock frontiers). If more complex and heterogeneous
lines are associated with lower average efficiency, then stock insurers may be relatively more
involved in such lines of business, as the managerial discretion hypotheses predicts. However,
these results cannot be interpreted as implying that the output of stock firms would be produced
more efficiently by mutual firms because the firms are operating on different frontiers, and using
different technologies. Such differences reflect different production technologies, different input
allocations, and different output allocations.
20 Our results for differences in technical frontiers for mutual and stock firms are consistent with the results reported for property-liability insurers in Cummins, Weis, and Zi (1999). Cummins, Weiss, and Zi (1999) do not report differences in cost frontiers and do not estimate revenue frontiers.
20
Insert Table 5 about here
Next, we calculate the technical, allocative, cost and revenue efficiencies of the mutual
firms relative to the stock frontiers, and the corresponding efficiencies of stock firms relative to
the mutual frontiers. These cross-efficiency scores are in Tables 5 and 6. These comparisons
provide evidence of the hypothesis that each group of firms is dominant on average in producing
the output mixes chosen by firms in the group. The stock firms’ cross frontier technical
efficiency scores are greater than one, implying that it is not feasible to replicate stock input-
output combinations using the mutual technology (frontiers). In other words, the stock
technology dominates the mutual technology for producing stock firms’ output mixes. The
mutual firms’ cross frontier technical efficiency scores also average more than one (1.28),
although much lower than the stock cross frontier technical efficiency average scores (2.47). In
addition, since the separate frontier efficiency scores (for technical, cost, and revenue efficiency)
are lower than the cross frontier efficiency scores for stock firms, we can infer that the stock
technology is dominant in relation to stock outputs. However, the evidence for mutual
technology dominance in relation to mutual outputs is much weaker. Only the technical
efficiency score is significantly lower for the separate frontier compared to the cross frontier.
Separate and cross efficiency scores below one imply that firms operate within both frontiers, as
is the case for both stock and mutual firms in regards to cost, allocative, and revenue efficiency.
As both stock and mutual firms have significantly lower cross-frontier efficiency scores relative
to separate frontier allocative efficiency scores, we do not find evidence for the expense
preference hypothesis. However, in the case of stock firms, their significant dominance over
mutuals for stock outputs as reflected in the cross technical efficiency score more than offsets
21
allocative inefficiencies, as the significantly higher cross (versus separate) cost efficiency score
shows. In summary, cross-frontier cost and revenue efficiency scores are lower than separate
frontier scores for mutual firms suggesting that the mutual ownership form is inferior to the stock
ownership form in terms of both cost minimization and revenue maximization.
Insert Table 6 about here
Multivariate analysis
The univariate results make the continued existence of mutual life insurers somewhat
perplexing. Our multivariate analysis presented next provides some insights into specific lines in
which mutual life insurers do in fact dominate stock life insurers. The managerial discretion
hypothesis predicts that mutual life insurers are likely to have a comparative advantage in
individual lines, such as individual life and annuities, and lines with more reliable actuarial
tables, such as life and annuities rather than medical insurance. In addition, the maturity
hypothesis predicts that mutual life insurers will have a comparative advantage in longer-term
product lines, such as individual life, which is more likely to be whole life insurance, than group
life, which is almost completely term life insurance, and similarly individual annuities.
For this analysis, to measure the dominance of stock or mutual insurers, we use the
following variable from Cummins, Weiss and Zi (1999):
(4)
( )ierScoreStockFronttierScoreMutualFronxyF iif −=1,
22
This calculated F value for firm i measures the level of mutual frontier dominance, given the
input-output bundle (yi, xi). A positive F value suggests the mutual frontier dominance. For
example, when calculated for the input-output mix of a stock firm, the numerator of the second
term is a cross-frontier efficiency score, and the denominator is a group-specific (separate)
frontier efficiency score. For that stock firm, if the cross-frontier score is lower than the separate
frontier score, the F value is positive, suggesting that the mutual frontier dominates. If a stock
firm has a higher efficiency with respect to its own frontier than with respect to the mutual
(cross) frontier, then it would have to improve more to become fully efficient relative to the
mutual frontier. Note that when F is calculated for a mutual firm, the numerator is its own
frontier efficiency score, and the denominator is a cross-frontier efficiency score. In that case, a
higher cross-frontier score than the own frontier score yields a positive F value, also suggesting
the mutual frontier dominance.
Similar to Cummins, Weiss and Zi (1999), we regress the Ff scores generated from
equation (5) against size quartile indicator variables (SizeQuartile2, SizeQuartile3 and
SizeQuartile4), an indicator variable equal to one if the firm is a stock firm (Stock), the percent
of insurance output from group life (GrpLife%), individual annuities (IndAnn%), group annuities
(GrpAnn%), accident and health (AH%), and interaction terms between these variables. Table 7
reports the results from these models using technical efficiency, allocative efficiency, cost
efficiency, and revenue efficiency, respectively.
Insert Table 7 about here
23
The omitted categories in the regressions are the first size quartile and individual life
output. Therefore, a negative and significant coefficient on a line of business variables suggests
that stock firms have the dominant technology for that line, relative to individual life. Results for
cost efficiency regressions in Table 7 shows a fairly consistent result of stock technology
dominating group life, group annuity, individual annuity, and accident and health lines of
insurance. Stocks also dominate for the accident and health line in the revenue efficiency
regression. Also, Model (2) results (Table 7) further explain the sources of the stock dominance
for each efficiency using the interaction terms between the line mix and stock dummy. For
example, stock technology dominance in technical efficiency mainly comes from stock firms’
decisions on the line mix, while stock technology dominance in cost efficiency comes from both
stock and mutual firms’ decisions on the line mix. These results are consistent with the
managerial discretion hypothesis that suggests stocks will have a comparative advantage in lines
(i.e. group and accident and health) where managerial discretion is the highest. The evidence is
also consistent with the maturity hypothesis that suggests mutuals will have a comparative
advantage in long term lines (i.e. individual life) where the policyholder-owner conflict is
highest.
6. Conclusion
We use modern efficiency analysis to compare stock and mutual life insurer technical,
allocative, cost and revenue efficiency frontiers. Similar to Cummins, Weiss and Zi (1999), we
find that stock and mutual life insurers operate on different frontiers and use distinct technologies
consistent with the managerial discretion and maturity hypotheses by comparing pooled and
group-specific frontiers. We explore efficiency differences further by performing cross-frontier
24
efficiency analysis where each stock (mutual) firm’s efficiency is computed relative to a
reference set consisting of all mutual (stock) insurers. In this way, we can determine which
technology is dominant in a production, cost or revenue sense for each output or input mix
observed in our sample. If a stock (mutual) firm’s efficiency score is greater relative to its
group-specific frontier than to the mutual (stock) frontier (i.e. cross-frontier), then its group’s
technology is dominated by that of the other group. In essence, the firm would have to improve
more to become fully efficient on the other group’s frontier.
Stock insurer technologies generally dominate mutual technologies for stock outputs.
Additionally, mutual insurer production technology (i.e., technical efficiency) dominates stock
production technology for mutual outputs. Multivariate analysis suggests that stock life insurers
are dominant in group lines, annuities, and accident and health insurance for cost efficiency, but
only in accident and health insurance for revenue efficiency. Mutual life insurers are dominant
in individual life insurance. Our findings generally support the managerial discretion and
maturity hypotheses. However, we do not find evidence in support of the expense preference
hypotheses. Ultimately, our results provide further insight into the co-existence of distinct
organizational forms of life insurers and add to the scholarly literature on insurer ownership
structures.
25
7. References
Best, A.M. 2006a, Best’s Annual Statement File, Life-Health 2006 Edition (Oldwick, NJ: A.M. Best Co., Inc.).
Best, A.M. 2006b, Best’s Insurance Reports, Life-Health 2006 Edition, (Oldwick, NJ: A.M. Best
Co., Inc.). Berger, Allen N., J. David Cummins, and Mary A. Weiss, 1997, “The Coexistence of Multiple
Distribution Systems for Financial Services: The Case of Property-Liability Insurance,” Journal of Business, 70:515-546.
Coelli, Timothy J., D.S. Prasada Rao, Christopher J. O’Donnell and George E. Battese, 2005, An
Introduction to Efficiency and Productivity Analysis, 2nd Edition (New York: Springer). Conover, W.J., 1999, Practical Nonparametric Statistics, 3rd Edition (New York: John Wiley &
Sons). Cooper, W.W., L.M. Seiford and K. Tone, 2000, “Data Envelopment Analysis: A
Comprehensive Text with Models, Applications, References and DEA-Solver Software,” (Boston: Kluwer).
Cooper, W.W., L.M. Seiford, and K. Tone, 2006, “Introduction to Data Envelopment Analysis
and Its Uses,” (New York: Springer). Cummins, J. David and Patricia M. Danzon, 1997, “Price, Financial Quality, and Capital Flows
in Insurance Markets,” Journal of Financial Intermediation, 6:3-38. Cummins, J. David, David L. Eckles, and Hongmin Zi, 2008, “Exporting Best Practices: Are
Foreign-Owned Insurers More Efficient in the U.S. Life Insurance Market?” Working paper.
Cummins, J. David, and Gregory P. Nini, 2002, “Optimal Capital Utilization by Financial Firms:
Evidence from the Property-Liability Insurance Industry,” Journal of Financial Services Research, 21:15-53.
Cummins, J. David, Sharon Tennyson, and Mary A. Weiss, 1999, “Consolidation and Efficiency
in the U.S. Life Insurance Industry,” Journal of Banking and Finance, 23:325-357.
26
Cummins, J. David, Mary A. Weiss, Xiaoying Xie, and Hongmin Zi, 2010, “Economies of Scope
in Financial Services: A DEA Efficiency Analysis of the US Insurance Industry,” Journal of Banking and Finance, 34:1525-1539.
Cummins, J. David, Mary A. Weiss, and Hongmin Zi, 1999, “Organizational Form and
Efficiency: An Analysis of Stock and Mutual Property-Liability Insurers,” Management Science, 45:1254-1269.
Cummins, J. David and Hongmin Zi, 1998, “Comparison of Frontier Efficiency Methods: An
Application to the U.S. Life Insurance Industry,” Journal of Productivity Analysis 10:131-152.
Erhemjamts, Otg, and J. Tyler Leverty, 2010, “The Demise of the Mutual Organizational Form:
An Investigation of the U.S. Life Insurance Industry,” Journal of Money, Credit and Banking, 42:1011-1036.
Hollander, M. and D.A. Wolfe, 1999, Nonparametric Statistical Methods, 2nd Edition (New
York: John Wiley & Sons). Ibbotson Associates, 2006, Stocks, Bonds, Bills, and Inflation, Valuation Edition, 2006 Yearbook
(Chicago: Ibbotson Associates). Lamm-Tennant, Joan and Laura T. Starks, 1993, “Stock Versus Mutual Ownership Structures:
The Risk Implications,” Journal of Business, 66:29-46. Mayers, David and Clifford W. Smith, 1981, “Contractual Provisions, Organizational Structure,
and Conflict Control in Insurance Markets,” Journal of Business, 54:407-434. Mayers, David and Clifford W. Smith, 1988, “Ownership Structure Across Lines of Property-
Casualty Insurance,” Journal of Law and Economics, 31:351-378. Pottier, Steven W., 2011, “Life Insurer Efficiency and State Regulation: Evidence of Optimal
Behavior,” Journal of Regulatory Economics, 39(2): 169-193 Pottier, Steven W., and David W. Sommer, 1997, “Agency Theory and Life Insurer Ownership
Structure,” Journal of Risk and Insurance, 64:29-543.
27
Table 1: Descriptive Statistics
Variable Mean Median Std. Dev. Min Max
Mutual 0.2586 0.0000 0.4386 0.0000 1.0000
Assets (000,000) 13,189.87 348.2125 47,377.37 2.436585 407,779.8000
Individual Life Premium (%) 0.3703 0.2710 0.3430 0.0000 1.0000
Group Life Premium (%) 0.0724 0.0054 0.1618 0.0000 1.0000
Individual Annuity Premium (%) 0.1739 0.0179 0.2637 0.0000 1.0000
Group Annuity Premium (%) 0.0469 0.0000 0.1351 0.0000 0.8564
Accident/Health Premium (%) 0.3365 0.1369 0.3834 0.0000 1.0000
Individual Life Output (000,000) 216.5575 6.3848 789.4355 0.0000 7,717.2860
Group Life Output (000,000) 64.8953 0.2440 404.9353 0.0000 5,863.7320
Individual Annuity Output (000,000) 249.5022 0.2655 1,219.8630 0.0000 14,251.4500
Group Annuity Output (000,000) 102.3642 0.0000 662.9376 0.0000 8,204.1800
Accident/Health Output (000,000) 261.3159 3.4453 1,289.9070 0.0000 17,718.6700
Ind. Life Inv. Assets (000,000) 2,787.7670 86.1421 11,033.5700 0.0000 98,688.3800
Group Life Inv. Assets (000,000) 202.7584 0.5740 926.8421 0.0000 9,879.4410
Ind. Ann. Inv. Assets (000,000) 2,719.8990 18.0621 12,502.3800 0.0000 141,692.2000
Group Ann. Inv. Assets (000,000) 1,101.4900 0.0000 4,980.8600 0.0000 54,315.4600
Acc./Health Inv. Assets (000,000) 562.0185 5.6210 3,075.5220 0.0000 41,107.2700
Avg. Inv. Assets Deposit (000,000) 1,243.1070 3.1901 6,078.1160 0.0000 54,342.3800
Individual Life Output Price 9.7517 1.5672 82.1261 0.0000 1,243.3680
Group Life Output Price 1.4532 1.0863 2.5507 0.0000 26.8716
Individual Annuity Output Price 1.3617 0.4679 3.0997 0.0000 30.7019
Group Annuity Output Price 2.3503 0.0000 16.0371 0.0000 231.9488
Accident/Health Output Price 3.4868 1.4996 12.4037 0.0000 155.6665
Ind. Life Inv. Assets Output Price 0.3118 0.0503 3.8419 0.0000 62.6394
Group Life Inv. Assets Output Price 0.3950 0.0293 3.5983 0.0000 48.0911
Ind. Ann. Inv. Assets Output Price 0.0485 0.0430 0.1571 0.0000 2.1723
Group Ann. Inv. Assets Output Price 0.0306 0.0000 0.0923 0.0000 1.0757
Acc./Health Inv. Assets Output Price 1.1878 0.0500 12.0861 0.0000 187.2998
Avg. Inv. Assets Deposit Output Price 0.0645 0.0253 0.4152 0.0000 6.5671
Agent Labor Input 114,468.7000 8,525.9000 340,067.5000 0.0000 3,778,487.0000
Administrative Labor Input 228,701.6000 15,481.7800 697,233.5000 0.0000 6,530,204.0000
Business Services Input 148,164.3000 12,496.1400 469,197.0000 85.4057 4,238,581.0000
Equity Capital (000,000) 717.5448 49.7116 2,208.3220 0.2783 19,570.1400
Policyholder-supplied Capital (000,000) 7,352.3280 198.5789 25,692.8500 0.0420 213,613.7000
Agent Labor Price 791.0800 791.0800 0.0000 791.0800 791.0800
Administrative Labor Price 645.0700 645.0700 0.0000 645.0700 645.0700
Business Services Price 618.4600 618.4600 0.0000 618.4600 618.4600
Equity Capital Price 0.1072 0.1072 0.0000 0.1072 0.1072
Policy Reserve Capital Price 0.0400 0.0400 0.0000 0.0400 0.0400
N = 267
28
Table 2: Differences in Means
Variable Mutual (N=69)
Stock (N=198) Pooled
Assets (000,000) 12,079.200 13,576.930 13,189.870 Outputs
Individual Life (000,000) 336.325 174.820 216.558 Group Life (000,000) 54.867 68.390 64.895 Individual Annuity (000,000) 181.632 273.154 249.502 Group Annuity (000,000) 144.010 87.851 102.364 Accident/Health (000,000) 90.599 320.808 261.316 Ind. Life Inv. Assets (000,000) 4,345. 539 2,244.908 2,787.767 Group Life Inv. Assets (000,000) 265.626 180.850 202.758 Ind. Ann. Inv. Assets (000,000) 1,648.704 3,093.195 2,719.899 Group Ann. Inv. Assets (000,000) 778.694 1,213.980 1,101.490 Acc./Health Inv. Assets (000,000) 234.647 676.102 532.019 Avg. Inv. Assets Deposit (000,000) 868.670 1,373.592 1,243.107
Output Prices Individual Life 4.629 * 11.537 9.752 Group Life 1.964 * 1.275 1.453 Individual Annuity 1.973 *** 1.149 1.362 Group Annuity 2.602 2.263 2.350 Accident/Health 1.558 * 4.159 3.487 Ind. Life Inv. Assets 0.082 *** 0.082 0.312 Group Life Inv. Assets 0.888 *** 0.223 0.395 Ind. Ann. Inv. Assets 0.053 *** 0.047 0.049 Group Ann. Inv. Assets 0.035 *** 0.029 0.031 Acc./Health Inv. Assets 0.164 1.544 1.188 Avg. Inv. Assets Deposit 0.038 0.074 0.065
Inputs Agent Labor 109,910.800 116,057.100 114,468.700 Administrative Labor 158,583.100 253,136.800 228,701.600 Business Services 132,126.100 153,753.300 148,164.300 Policy Reserve Capital (000,000) 815.182 683.520 717.545 Equity Capital (000,000) 7,099.707 7,440.362 7,352.328 This table shows mean values for the pooled sample as well as for mutual and stock subsamples. Input prices are not included as they do not vary across firms. ***, **, * indicate significant differences between the mutual and stock samples at the 1%, 5%, and 10% levels, respectively.
29
Table 2: Differences in Medians
Variable Mutual (N=69)
Stock (N=198) Pooled
Assets (000,000) 975.448 *** 189.678 348.213 Outputs
Individual Life (000,000) 27.797 *** 2.749 6.385 Group Life (000,000) 2.002 *** 0.045 0.244 Individual Annuity (000,000) 7.010 *** 0.012 0.266 Group Annuity (000,000) 0.000 *** 0.000 0.000 Accident/Health (000,000) 6.723 3.099 3.445 Ind. Life Inv. Assets (000,000) 375.284 *** 43.715 86.142 Group Life Inv. Assets (000,000) 2.794 ** 0.039 0.574 Ind. Ann. Inv. Assets (000,000) 184.763 *** 6.034 18.062 Group Ann. Inv. Assets (000,000) 0.568 *** 0.000 0.000 Acc./Health Inv. Assets (000,000) 5.906 5.609 5.621 Avg. Inv. Assets Deposit (000,000) 32.507 *** 1.130 3.190
Output Prices Individual Life 1.580 * 1.556 1.567 Group Life 1.361 *** 0.969 1.086 Individual Annuity 0.867 *** 0.042 0.468 Group Annuity 0.000 *** 0.000 0.000 Accident/Health 1.473 * 1.521 1.500 Ind. Life Inv. Assets 0.056 *** 0.048 0.050 Group Life Inv. Assets 0.053 *** 0.017 0.029 Ind. Ann. Inv. Assets 0.051 *** 0.039 0.043 Group Ann. Inv. Assets 0.016 *** 0.000 0.000 Acc./Health Inv. Assets 0.058 * 0.468 0.050 Avg. Inv. Assets Deposit 0.036 *** 0.017 0.025
Inputs Agent Labor 23,282.340 *** 6,100.480 8,525.900 Administrative Labor 23,226.890 13,513.690 15,481.780 Business Services 21,021.610 *** 9,042.195 12,496.140 Policy Reserve Capital (000,000) 131.800 *** 35.315 49.712 Equity Capital (000,000) 766.209 *** 93.262 198.579 This table shows median values for the pooled sample as well as for mutual and stock subsamples. Input prices are not included as they do not vary across firms. ***, **, * indicate significant differences between the mutual and stock samples at the 1%, 5%, and 10% levels, respectively, using a non-parametric K-sample test.
30
Table 3: Efficiency Summary Statistics Variable Mean Median Std. Dev. Min Max N
Entire Sample Technical Efficiency (Pooled) 0.9196 0.9902 0.1200 0.4211 1.0000 267 Allocative Efficiency (Pooled) 0.6574 0.6878 0.2397 0.0383 1.0000 267 Cost Efficiency (Pooled) 0.6131 0.6309 0.2570 0.0383 1.0000 267 Revenue Efficiency (Pooled) 0.4081 0.3244 0.3216 0.0014 1.0000 267 Technical Efficiency (Separate) 0.9399 1.0000 0.1143 0.4211 1.0000 267 Allocative Efficiency (Separate) 0.7157 0.7533 0.2443 0.0474 1.0000 267 Cost Efficiency (Separate) 0.6826 0.7212 0.2663 0.0474 1.0000 267 Revenue Efficiency (Separate) 0.4716 0.4027 0.3377 0.0015 1.0000 267 Technical Efficiency (Cross frontier) 2.1507 1.3563 1.9653 0.4321 8.8041 255 Allocative Efficiency (Cross frontier) 0.5205 0.5065 0.2398 0.0237 0.9798 255 Cost Efficiency (Cross frontier) 0.8494 0.8090 0.3978 0.0426 1.7783 267 Revenue Efficiency (Cross frontier) 0.7806 0.5091 0.9083 0.0015 3.8568 259 Ftechnical -1.1678 -0.5235 1.9603 -7.8041 0.7252 255 Fallocative 0.1353 0.1826 0.5062 -3.4981 0.9176 255 Fcost -0.3277 -0.2381 0.4520 -1.7594 0.3186 267 Frevenue -0.8994 -0.8001 0.8084 -2.8568 0.3669 259
Stocks Technical Efficiency (Pooled) 0.9147 1.0000 0.1288 0.4211 1.0000 198 Allocative Efficiency (Pooled) 0.6321 0.6365 0.2492 0.0383 1.0000 198 Cost Efficiency (Pooled) 0.5882 0.5803 0.2685 0.0383 1.0000 198 Revenue Efficiency (Pooled) 0.4297 0.3522 0.3383 0.0014 1.0000 198 Technical Efficiency (Separate) 0.9209 1.0000 0.1270 0.4211 1.0000 198 Allocative Efficiency (Separate) 0.6799 0.7170 0.2541 0.0474 1.0000 198 Cost Efficiency (Separate) 0.6367 0.6214 0.2762 0.0474 1.0000 198 Revenue Efficiency (Separate) 0.4445 0.3653 0.3396 0.0015 1.0000 198 Technical Efficiency (Cross frontier) 2.4730 1.5556 2.1726 0.9331 8.8041 186 Allocative Efficiency (Cross frontier) 0.4587 0.4484 0.2190 0.0237 0.8963 186 Cost Efficiency (Cross frontier) 0.8658 0.8207 0.4287 0.0426 1.7783 198 Revenue Efficiency (Cross frontier) 0.9286 0.5961 1.0059 0.0015 3.8568 190 Ftechnical -1.6297 -0.8110 2.1089 -7.8041 0.0181 186 Fallocative 0.3131 0.2630 0.2547 -0.2092 0.9176 186 Fcost -0.4055 -0.3189 0.4584 -1.7594 0.2939 198 Frevenue -1.0013 -0.8829 0.8606 -2.8568 0.3669 190
Mutuals Technical Efficiency (Pooled) 0.9334 0.9490 0.0898 0.4321 1.0000 69 Allocative Efficiency (Pooled) 0.7300 0.7681 0.1939 0.1881 1.0000 69 Cost Efficiency (Pooled) 0.6848 0.7099 0.2061 0.1710 1.0000 69 Revenue Efficiency (Pooled) 0.3461 0.2848 0.2603 0.0062 1.0000 69 Technical Efficiency (Separate) 0.9942 1.0000 0.0173 0.9192 1.0000 69 Allocative Efficiency (Separate) 0.8186 0.8648 0.1787 0.2542 1.0000 69 Cost Efficiency (Separate) 0.8142 0.8648 0.1806 0.2542 1.0000 69 Revenue Efficiency (Separate) 0.5495 0.5100 0.3220 0.0126 1.0000 69 Technical Efficiency (Cross frontier) 1.2821 0.9948 0.7320 0.4321 3.6391 69 Allocative Efficiency (Cross frontier) 0.6869 0.7382 0.2140 0.2223 0.9798 69 Cost Efficiency (Cross frontier) 0.8023 0.8050 0.2893 0.2029 1.4675 69 Revenue Efficiency (Cross frontier) 0.3730 0.2919 0.2967 0.0062 1.2220 69 Ftechnical 0.0774 -0.0027 0.3118 -1.3143 0.7252 69 Fallocative -0.3441 -0.0869 0.6791 -3.4981 0.3495 69 Fcost -0.1044 -0.0290 0.3495 -1.2785 0.3186 69 Frevenue -0.6190 -0.5792 0.5588 -1.7506 0.2073 69
31
Table 4: Separate v. Pooled Frontier
Stock Firms Mutual Firms Separate Frontier Pooled Frontier Separate Frontier Pooled Frontier Technical 0.9209*** 0.9147 0.9942*** 0.9334 Allocative 0.6799*** 0.6321 0.8186*** 0.7300 Cost 0.6367*** 0.5882 0.8142*** 0.6848 Revenue 0.4445*** 0.4297 0.5495*** 0.3461 Note: This table reports the average efficiency scores from the technical, allocative, cost, and revenue frontiers. ANOVA, the Wilcoxon, Van der Waerden, and Savage non-parametric tests are used to test distributional differences for stocks and mutuals with respect to efficiency scores calculated based on separate and pooled frontiers. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. All three tests generated identical significance levels.
Table 5: Stock v. Mutual
Separate Frontier Cross Frontier Stocks Mutuals Stocks Mutuals Technical 0.9209*** 0.9942*** 2.4730*** 1.2821 Allocative 0.6799*** 0.8186*** 0.4587*** 0.6869 Cost 0.6367*** 0.8142*** 0.8658 0.8023 Revenue 0.4445*** 0.5495*** 0.9286*** 0.3730 Note: This table reports the average efficiency scores from the technical, allocative, cost, and revenue frontiers. ANOVA is used to test distributional differences between stocks and mutuals. There are 198 stock firms and 69 mutual firms. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. All three tests generated identical significance levels.
Table 6: Separate v. Cross Frontier
Stock Firms Mutual Firms Separate Frontier Cross Frontier Separate Frontier Cross Frontier Technical 0.9209*** 2.4730*** 0.9942*** 1.2821 Allocative 0.6799*** 0.4587*** 0.8186*** 0.6869 Cost 0.6367*** 0.8658 0.8142*** 0.8023 Revenue 0.4445*** 0.9286*** 0.5495*** 0.3730 Note: This table reports the average efficiency scores from the technical, allocative, cost, and revenue frontiers. ANOVA is used to test distributional differences for stocks and mutuals with respect to efficiency scores calculated based on separate and cross frontiers. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. All three tests generated identical significance levels.
32
Table 7: Regression Results
Technical Efficiency Allocative Efficiency Cost Efficiency Revenue Efficiency
Variable Model (1) Model (2) Model (1) Model (2) Model (1) Model (2) Model (1) Model (2)
SizeQuartile2 0.4675*** 0.2616*** -0.5198*** -0.4400*** 0.0069*** -0.0308*** 0.1091*** 0.1588***
(0.7974) ** (0.7907) ** (0.1823)** (0.1685) ** (0.1306) ** (0.1302) ** (0.3406) ** (0.3378) **
SizeQuartile3 0.2692*** 0.1120*** 0.0494*** 0.1543*** 0.1630*** 0.1459*** -0.2589*** -0.2190***
(0.7261) ** (0.7234) ** (0.1660) ** (0.1542) ** (0.1189) ** (0.1191) ** (0.3101) ** (0.3090) **
SizeQuartile4 0.4616*** 0.2007*** -0.1840*** -0.0306*** 0.2484*** 0.1994*** 0.0176*** 0.1554***
(0.7741) ** (0.7875) ** (0.1770) ** (0.1678) ** (0.1265) ** (0.1297) ** (0.3299) ** (0.3364) **
Stock -1.7912*** -0.6434*** 0.6241*** 0.1300*** -0.0459*** 0.0932*** -0.7155*** -0.5633***
(0.6932) ** (0.7784) ** (0.1585) ** (0.1659) ** (0.1127) ** (0.1274) ** (0.2955) ** (0.3317) **
SizeQ2*Stk 0.6984*** 0.9992*** 0.3814*** 0.2612*** 0.0859*** 0.1341*** 0.1315*** 0.1015***
(0.8671) ** (0.8613) ** (0.1983) ** (0.1836) ** (0.1409) ** (0.1406) ** (0.3693) ** (0.3668) **
SizeQ3*Stk 0.5131*** 0.7537*** -0.1906*** -0.3333*** -0.1323*** -0.1045*** 0.7434*** 0.6951***
(0.8134) ** (0.8119) ** (0.1860) ** (0.1730) ** (0.1323) ** (0.1326) ** (0.3469) ** (0.3462) **
SizeQ4*Stk 0.4194*** 0.9042*** 0.1516*** -0.1087** -0.1556*** -0.0762*** 0.6827*** 0.4997***
(0.8374) ** (0.8755) ** (0.1915) ** (0.1866) ** (0.1363) ** (0.1429) ** (0.3571) ** (0.3726) **
GrpLife% -1.5536*** 0.3054*** -0.2750*** -1.3705*** -0.7348*** -0.6707*** -0.4625*** 0.5086***
(0.6642) ** (1.3000) ** (0.1519) ** (0.2771) ** (0.1015) ** (0.2141) ** (0.2822) ** (0.5554) **
IndAnn% -1.7624*** 0.2155*** -0.2490*** -1.2510*** -0.7943*** -0.5130*** -0.0393*** -0.5493***
(0.4825) ** (1.0248) ** (0.1103) ** (0.2184) ** (0.0763) ** (0.1687) ** (0.2048) ** (0.4378) **
GrpAnn% -1.4780*** 0.6088*** -0.2793*** -1.1850*** -0.0905*** 0.2869*** -0.2542*** -0.3500***
(1.0836) ** (1.5902) ** (0.2478) ** (0.3389) ** (0.1631) ** (0.2618) ** (0.4256) ** (0.6793) **
AH% -1.8623*** -0.2601*** -0.2192*** -0.7769*** -1.0182*** -0.7960*** -0.5397*** -0.2138***
(0.3484) ** (0.7093) ** (0.0797) ** (0.1512) ** (0.0552) *** (0.1168) ** (0.1468) *** (0.3030) **
GrpLife%*Stk -2.5446***
1.4799*** -0.0879*** -1.3304***
(1.5053) ** (0.3208) *** (0.2425)*** (0.6419) ***
IndAnn%*Stk -2.6588***
1.3233***
-0.3707*** 0.6145***
(1.1584) ** (0.2469) *** (0.1890)*** (0.4940) ***
GrpAnn%*Stk -3.7407*** 1.6113*** -0.6184*** 0.1827***
(2.1473) ** (0.4577) *** (0.3329)*** (0.8641) ***
AH%*Stk -2.1746*** 0.7731*** -0.2956*** -0.4101***
(0.8117) ** (0.1730) *** (0.1324)*** (0.3453) ***
Constant 0.6749*** -0.1240*** -0.0777*** 0.2689*** 0.1878*** 0.0910*** -0.3667*** -0.4762***
(0.6680) ** (0.7095) ** (0.1527) *** (0.1512) *** (0.1092)*** (0.1168)*** (0.2852) *** (0.3031) ***
Observations 255 255 255 255 267 267 259 259
R2 0.2644 0.2967 0.4233 0.5210 0.6280 0.6404 0.2100 0.2445 Note: The dependent variable is the Ff score generated from the technical, allocative, cost, and revenue frontiers. Standard errors are in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.
33
Appendix 1
Inputs and Outputs
Inputs Agent labor Administrative labor Business services Equity capital Policy reserve capital Deposit-fund capital
Outputs
Individual life insurance, net incurred claims Group life insurance, net incurred claims Individual annuities, net incurred claims Group annuities, net incurred claims Accident and health insurance, net incurred claims Individual life insurance, average invested assets Group life insurance, average invested assets Individual annuities, average invested assets Group annuities, average invested assets Accident and health insurance, average invested assets Deposit-funds, average invested assets
