Post on 12-Sep-2021
1
Distribution Channel Strategy and Efficiency Performance of the Life insurance
Industry in Taiwan
Abstract
Changes in regulations and laws the past few decades have affected Taiwan’s
life insurance industry and caused many insurers to modify their marketing strategies.
This paper analyzes the evolution of the productive patterns in a sample of 24 life
insurers that operated in Taiwan from 1997 to 2006. We estimate Malmquist
productivity indexes and decompose them into four sources of productivity change.
Further, we compare the differences in efficiency scores before and after the change
of distribution channel strategy. The results suggest that a direct distribution channel
strategy performs better than a non-direct distribution channel strategy in terms of
efficiency and productivity change. It means that coexisting direct/indirect
distribution systems cannot improve the efficiency of life insurers.
Keywords: Distribution channel strategy; Data Envelopment Analysis,
Malmquist productivity indexes
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Distribution Channel Strategy and Efficiency Performance of the Life insuranceIndustry in Taiwan
1. Introduction
The Taiwanese life insurance industry has experienced various challenges and
major structural changes since the 1990s. First, after years of restraint, the regulator
permitted the establishment of new domestic insurers in 1992, and six more joined the
market in the subsequent year. The flourish of life insurers presented challenges for
all members of the industry. The newcomers encountered an instant need for agent
recruitment and business exploration, while the others faced competition from those
newly established insurers. Second, the Legislative Yuan amended the Labor
Standards Act (LSA) in 1997 and extended the application of LSA to insurers’
exclusive agents. To cope with the requirements of LSA, life insurers needed to
increase their agents’compensations (minimum wage/pension). This regulatory
change forced insurers to lay off agents with low productivity in order to reduce costs.
Third, the downward trend of market interest rates since 1996 (see Figure1) caused
life insurers to incur huge losses on previously issued policies and led to substantial
increases in new policies’ premiums. (The interest rate used to calculate the policy
premium at that time was down to 2%; the premium was three times higher than a
premium that is calculated using an interest rate of 8%). Furthermore, global stock
markets have risen sharply in recent years, thus, before it crashed, investment-linked
3
products that transfer the investment risk, along with its return, to the policyholders
became the dominant life insurance products in Taiwan.
Intensified competition, rising agent costs, and product transformation have
driven insurers to seek more efficient approaches to operate in the market. Some life
insurers in Taiwan changed their distribution strategies from direct writers to a
coexistence of brokerage and agency distribution systems. (One example is the
Metropolitan Life Insurance Company, which has been in Taiwan for nearly 20 years;
the company laid off all their agents and replaced the traditional agents channel with
bancassurance and telemarketing in 2006) In contrast, some insurers (For example,
Prudential Life Insurance Company in Taiwan ) stuck to a direct distribution channel
strategy.
The literature defined distribution via a company-owned distribution channel
(company sales force and company-owned distribution division) as a direct channel
structure, while contract distribution to an independent organization (outside sale
agents and distributors) was described as an indirect channel structure.1 The pros and
cons of direct/indirect distribution channels have been discussed in many studies
regarding different industries. Generally, the benefits of direct channels are more than
the benefits of indirect channels. 2 When a firm’s marketing strategy demands a high
level of service (before or after sale), it is difficult and costly for the firm to ascertain
4
whether indirect channels are able to provide the service specified in contracts. 3 In
other words, direct channels are more helpful in ensuring that service is performed. 4,
5,6
Indirect channels marketing, on the other hand, were traditionally considered to
have more stages in the distribution process than direct channels marketing7 and to
require fewer investments (in terms of both money and time) by manufacturing firms
than direct marketing. 8, 9 Indirect channels were found to provide many benefits,
particularly for small manufacturing firms. Therefore, the literature does not provide a
conclusive answer as to what the best distribution channel is. At the conceptual level,
it might not seem appropriate to examine the choices of distribution channels
separately—direct versus indirect. However, in practice, these two types of
distribution systems signify two ends of a continuum.
The life insurers’ choices of different distribution channels pose the interesting
question of whether introducing an indirect distribution channel will improve
insurer’s efficiency. Hence, the objective of this paper is to assess the effects of
different distribution channel strategies on productive efficiency in the Taiwanese life
insurance industry. We compare the evolution of productivity under the direct and
coexisting direct/indirect (hereafter, referred to as “non-direct”) distribution channel
strategies.
5
In order to assess the impact of distribution channel adjustments on the
Taiwanese life insurance industry, this paper estimates the evolution of productivity
during the 1997–2006 period with a sample of 24 life insurers and identifies the
sources of productivity changes. The rest of this paper is organized as follows. The
next section presents a literature review and patterns of Taiwanese life insurance
market distribution. Section 3 describes the sources of data and the definitions of
input and output variables. Section 4 provides a nonparametric model that permits the
measurement of productivity changes in the life insurance industry over the years. In
addition, the decomposition productivity changes two indexes related to efficiency
gains and two indexes related to technical change are discussed. Section 5 presents the
empirical estimation and a discussion of the results. Section 6 concludes the paper.
2. Literature review and patterns of the Taiwanese life insurance market
2.1 Literature review
Similar to the situation in the U.S. life insurance market, a variety of distribution
channels are currently applied by Taiwanese life insurers. Based upon the degree of
vertical control of the sales force, comparative studies on insurance distribution
systems typically group the various systems into two main categories. The two broad
categories are “direct writer”and “independent agency”(referred to as indirect writer).
10 The direct writer category encompasses mass marketing and the use of employee
6
sales agents and exclusive agents. (The agents at firms that impose such restrictions
are often known as “exclusive” or “tied sales” agents.)Exclusive dealing
arrangements restrict sales agents to offer the product of only a single firm. 11 The
independent agency category encompasses both the independent agency system of
marketing and the use of insurance brokers. Generally, direct writer is the insurer’s
exclusive distribution system, in which life insurers have strong vertical control of the
sale force. Under the independent agency or brokerage system, the insurer-agent
relationship is that of an independent contractor, and agents can sell policies from
many companies. Therefore, if life insurers contract with independent agencies or
brokerages, they cannot control the sales force nor the amount and the quality of
polices from indirect writers.
One of the focal points of most academic studies is to find the most efficient
distribution channel for insurers. Because the differences across life insurance
distribution systems in the United States are less profound than those in
property-liability insurance, the vast majority of academic studies of distribution
channels have focused on property-liability insurers rather than life insurers. For
example, Joskow conducted the pioneer research of cost and profit comparison. 12 In
his detailed study of the property and liability insurance industry in the United States,
he concluded that the combined influence of state regulation, cartel pricing, and other
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legal considerations has caused several problems in the property and liability
insurance industry. One problem that he mentioned is the use of an inefficient sales
technique. Joskow estimated that the expense ratios of insurers using direct writers
were approximately 11% lower than those of insurers using independent agencies.
More studies that are recent examine cost differences for later periods and incorporate
model specification and data refinements in Joskow’sbasic analysis. Others still find
results that are consistent with Joskow’s.13, 14
Regan extends this analysis to a much larger sample of firms and finds that direct
writers’cost advantages differ significantly across lines. 15 Rather than testing for
differences in expense ratio, Berger, Cummins, and Weiss use a frontier efficiency
analysis to examine differences in both cost and profit efficiency across
property-liability insurance distribution systems.16 Consistent with results from earlier
studies, these authors find that insurers using independent agencies are significantly
less cost efficient than those using direct writers. Regan and Tzeng find a strong
correlation between ownership form and distribution system in the aggregate data. 17
They provide the foundation for an expected association between stock firms and the
broker distribution systems. The results indicate a high level of monitoring under both
the stock firm and broker distribution. Following this study, Baranoff and Sager,
applying life insurer data from 1993 to 1999, model the four key insurer
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decisions—capital structure, asset risk, organizational form, and distribution
system—as an endogenous choice in a single interrelated set of simultaneous
equations. Confirming previous studies, they found a positive relationship between
capital ratios and asset risks, and discovered an association between stock ownership
and brokerage distribution, which was not found in prior studies. 18 In addition, direct
channels were found to be more effective when the products required specialized
knowledge or when difficult tasks were involved in the sales relationship, because
firms could better monitor and motivate their difficult-to-replace distribution agents.
1,19,20 Baranoff also finds that broker-oriented insurer will increase agency expenses
and reduced return of capital due to the necessity of maintaining two distribution
systems, in comparison with agency-oriented companies, which operate with a single
system. 21
2.2 Patterns of Distribution in the Taiwanese life insurance market
Based on the 2006 statistic report from Swiss Re Sigma, the total premium
income of Taiwan’s life insurance industry is US$45,992,000,000—ranked 15th in
the world. Taiwan’s insurance penetration is the highest in the world. Specifically,
Taiwanese people spend an average of US$2,145.50 each year on life insurance
products.
9
Over the course of the past decade, the life insurance industry grew rapidly in the
wake of economic developments. The supervisory authority gradually liberalized the
regulations that enhance competition among firms. Moreover, under the influence of
economic, social, regulatory, and consumer pattern changes, life insurers are now
confronted with greater challenges. As mentioned earlier, due to the effects of the
regulations, insurance laws, and low interest rates, along with the diversification in
the demand for financial products and the introduction of new products, life insurers
are bound to launch new products and develop new channels. In Taiwan, the
exclusive agent channel was the major channel of life insurers in the early days, but
the utilization of multiple-distribution channels (ex. Agency, Brokerage, Direct
Marketing, and Banc assurance etc.) has become increasingly prevalent in recent
years. In order to adapt to environmental changes, life insurers continue to develop
their direct marketing, brokerage, and agency distribution channels in order to secure
market shares, to better control the operations of intermediaries’selling, and to use
excess funds generated in the business. 22
Although multiple channels enable firms to capture customers in different market
segments, they pose many challenges, including channel conflict 23 and pricing policy
for different distribution channels strategies.24 Therefore, in the earlier era in Taiwan,
direct writers were the major distribution channel. Later, insurers developed direct
10
marketing, brokerage systems, and bancassurance channels in response to the
regulations and product changes confronting the environmental changes. Yet, many
challenges resulted from adopting an indirect distribution channel. First, the premium
income from an indirect distribution channel will depend on the content of and
commissions on the products. Second, a new channel will cause channel conflict and
market overlap due to the inappropriate product segment. Third, Pang-Ru Chang et al.
finds that bancassurance channels have a higher complaint rate than traditional
channels.25 Therefore, some life insurers began to question the establishment of
indirect distribution channels because they were unable to control the quality and
quantity of business. For instance, Coelho et al. examined 62 United Kingdom (UK)
financial services organizations and found that multiple channels are associated with
higher sales performance and lower channel profitability.26 Ironically, the utilization
of indirect distribution channels is steadily increasing and direct channel strategies are
becoming less popular in practice. 16, 27- 30
Following the international development trend in the financial service industry,
(Based on a sample of 153 products in the UK financial services industry,
Easingwood and Storey verified that multi-channel strategies were being used in 85%
of cases. 28) the utilization of indirect channels is now more popular in the Taiwanese
life insurance market. In order to make systematic channel decisions, it is important to
11
understand the relationship between distribution channel strategies and their
efficiency and productivity.
3. Data
The primary source of data in this study is the Statistics of the Taiwanese Life
Insurance Business. A total of 24 Taiwanese life insurers with complete data available
for the 10 sample years (1997–2006) are included in our sample. These firms
accounted for 92.77% of industry assets in 2001, the midpoint of the sample period.
Most life insurers changed their distribution system in 2003. All output and input
quantities are deflated to Taiwan’s 1997 Consumer Price Index (CPI).
To compute the indexes of efficiency and productivity, following the insurance
literature, we select premium income as our output variable. 31-33 We further
categorize premium into life and annuity insurance (LAP) and health and accident
insurance (HAP). We combine the individual policy and the group insurance policy
together because many insurers in Taiwan do not sell group policies. The premium
income of insurers is deflated to the base year 1997 using the Taiwanese CPI.
Two inputs are used in this study: equity capital and total expenses. The total
expenses refer to the total compensation to agents, business and administration
expenses, and miscellaneous expenses. Because each insurer has a different
distribution system and different accounting items regarding expense categories, we
12
are not able to separate all expenses into labor expenses or business service expenses.
Therefore, we add together the compensation to agents, business and administration
expenses, and miscellaneous expenses as our input (total expenses). The entire input
category is deflated by the 1997 CPI wherever appropriate. Table 1 provides the basic
descriptive statistics of these variables.
[Insert Table 1 here]
4. Methodology
Modern frontier efficiency methodologies have become a dominant approach
to the measure of firm performance. There are two principal types of efficiency
methodologies: the econometric (parametric) approach and the mathematical
programming (non-parametric) approach. 34 The econometric approach requires the
specification of a production, cost, revenue, or profit function as well as an
assumption about the error term. The non-parametric programming approach requires
less specification of the optimization problem. We chose the non-parametric
programming approach because it makes the work less vulnerable to the specification
errors that are common in the econometric approach.
This study uses nonparametric frontier efficiency methods of data envelopment
analysis (DEA) to measure corporate performance. The DEA approach developed by
Charnes et al. represents a method by which non-commensurate multiple inputs and
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outputs of an entity can be combined objectively into an overall measure of firm
efficiency. 35
In the old days, one interpreted productivity change as completely due to and thus
identical with technological change. Not so long ago one came to the insight that
efficiency change is at least as important a factor. Now efficiency appears to be a
multi-faceted phenomenon. A firm can be called efficient if, given the technological
state of affairs and given the input quantities used; it produces the optimal quantities
of output. Reversely, a firm can be called efficient if, given the technological state of
affairs and given the output quantities produced; it uses the optimal quantities of input.
The meaning of "optimal" determines the meaning of "efficiency." The distinction
between technological change and efficiency change can be made by conceiving the
firm as operating in an exogenously determined environment, called the technology,
which is the set of all at a given period feasible combinations of input and output
quantities. A firm, which operates on the boundary of this set, is called technically
efficient, whereas a firm, which operates in the interior of this set, is called technically
inefficient. Technological change then means that the set of feasible combinations
expands or contracts, while technical efficiency change means that the firm moves
closer to or further away from the boundary. These two kinds of movement are clearly
14
independent of each other: there can be technological change without efficiency
change, and efficiency change without technological change.
An important step forward was the development of the Malmquist productivity
index. The Malmquist index combines technological change and technical efficiency
change. Finally, since we are operating in a multiple-input multiple-output framework,
it is to be expected that besides levels (however defined) of input and output
quantities also the input and output-mix might play a certain role in the measures of
productivity change.
It will be clear that the three phenomena discussed, respectively technical change,
technical efficiency change, and scale efficiency change, constitute independent
factors of productivity change. Technical progress as well as increased technical
efficiency means that more output can be produced from given input quantities. The
first phenomenon, however, means that the technological frontier has moved, while
the second means that the firm's position relative to the frontier has changed.
Increased scale efficiency means that the firm has moved to a position with a better
input-output quantity ratio at the frontier, conditional on its input- and output-mix. If
there is no technical change and the firm is operating on the frontier, scale efficiency
change corresponds to a movement along the frontier.
15
All this suggests that an encompassing measure of productivity change could be
obtained by combining the three measures defined in the previous sections. Thus, for
a firm going from base period to comparison period, the (output orientated)
productivity index number should be a combination of an index number of technical
change. To reduce the amount of technical information and analysis in this text, we
put it as an appendix.
5. Results
Table 2 summarizes the evolution of technical and scale efficiency scores of the
Taiwanese life insurance industry from 1997 to 2006. This table shows the yearly
average of the technical efficiency scores computed under constant returns to scale
(DC) and variable returns to scale (DV), along with the residual scale efficiency (SE)
score. The DC score increases after 1997 and reaches its maximum in 2002, then
declines. The table reveals that the directions of movement are the same for DC and
SE. Technical efficiency (DC) decreased from a mean value of 0.932 in 2003 to 0.786
in 2006. This clear drop maybe reflects the fact that the adoption of an indirect
distribution system decreases the efficiency score. Therefore, next section we
compare the different channel strategies by using one-way ANOVA analysis.
The decomposition of the DC index provides some insights into how the overall
reduction in technical efficiency occurred. Table 2 shows that the reduction was
16
largely due to an enormous decrease in SE, from a value of 0.928 in 1997 to 0.835 in
2006. The new distribution strategy adopted by life insurers led them farther from the
optimal scale. The effect has been partially offset by the moderate improvement in
pure technical efficiency (DV).
[Insert Table 2 here]
Further, we analyze the efficiency and productivity difference between the direct
and non-direct strategies of life insurers. Table 3 shows the average of all efficiency
scores, including the technical efficiency and scale efficiency scores. We find that the
technical and scale efficiency scores of direct distribution channel strategy insurers
are higher than those of non-direct distribution channel strategy insurers, and the
differences are statistically significant. These results suggest clear that a direct
distribution channel strategy is better than a non-direct distribution channel strategy.
Technical efficiency implies that natural resources are transformed into goods and
services without waste and that producers are doing the best possible job of
combining resources to make goods and services. In essence, production is achieved
at the lowest possible opportunity cost. Most life insurers, by using a direct writer
distribution system, can vertically control their sales, although life insurers do need to
invest heavily in recruiting and training a dedicated sales force. Our results show that
a direct distribution system produces a higher level of productivity than a non-direct
17
distribution system in Taiwan. It will therefore create higher productivity when the
insurers focus on a direct distribution system.
[Insert Table 3 here]
In Table 4, we further compare the differences in efficiency scores before and
after the change of distribution channel strategy. Due to 12 out of 24 life insurers
changing their distribution channel strategy in 2003, we compare the efficiency
differences of the three previous and the three subsequent years for those life insurers
adopting new distribution channel strategy. The results show that a higher technical
and scale efficiency score is achieved through the adoption of a direct distribution
strategy. Only pure technical efficiency (DV) has no signature difference. After the
change in distribution strategy, the insurers increased their operation costs, resulting
in a decrease in technical and scale efficiency. We thereby find that adopting indirect
distribution systems cannot improve the efficiency of life insurers.
[Insert Table 4 here]
These indexes do not separate the effect of strategy moving toward the
benchmark technology (frontier) from the effect of the intertemporal movements of
the frontier. To separate these sources of productivity change, we must use the
decomposition of the Malmquist productivity index, as shown in Table 5. On average,
productivity grew 3.3% from 1997 to 2006, with 44.4% of the insurers in the sample
18
benefiting from this growth. Yet, the 2003–2004 period shows the largest productivity
decrease, at 6.4%, followed by 2004–2005 with 0.9%. This means that the
productivity decreased after a change in channel strategy. The decomposition of the
Malmquist productivity index helps explain the manner in which this 6.3%
productivity decrease was attained.
Focusing on relative efficiency, the decomposition shows a moderate
contribution of efficiency to productivity growth. However, while 66.7% of the
insurers increased their scores of pure technical efficiency over the period in question,
only 55.6% increased their scale efficiency indexes. Pure technical efficiency
increased by an average of 7.9%.
[Insert Table 5 here]
This paper further compared the Malmquist index change, based on the average
of 2001-2003 to 2004-2006 every single year, for those life insurers adopting new
distribution channel strategy. The results of this assessment are found in Table 6, in
which we have compared the Malmquist index and its components across the channel
strategy. Companies with unchanged channel strategies experienced the greatest
productivity growth, with an average Malmquist index of around 1.510 between 2001
and 2006 and significance at the 10% level, suggesting that direct channel strategy
results in the greatest productivity growth. There are no significant differences across
19
groups with regard to the index of pure efficiency change. This result indicates that
the catching-up effect did not depend on the channel strategy, although life insurers
with a direct channel strategy show the highest index of catching-up, at 1.005. The
same pattern is observed with respect to the change in scale efficiency. Technical
change differs markedly across different strategies, reflecting a direct channel strategy
shift in the production technology that has a significant difference. In particular, some
life insurers could not improve their technical progress after changing their channel
strategy.
[Insert Table 6 here]
6. Conclusion
Changes in regulations and laws the past few decades haveaffected Taiwan’s life
insurance industry and caused many insurers to modify their marketing strategies.
Many life insurers expanded more distribution channels in order to obtain more
business and save costs. Since they began making more contracts with agencies and
brokerages, channel strategies have changed from direct to indirect or non-direct
channels. To assess the impact of these changes on the Taiwanese life insurance
market, this paper estimates efficiency and the sources of productivity change during
the 1997–2006 period in a sample of 24 life insurers.
20
Empirical evidence shows that insurers who utilize a direct distribution system
are more efficient than insurers who utilize a non-direct distribution system. The
implication of this result is that insurers may prefer to use a direct distribution system
rather than a combination of direct and indirect distribution systems. Although these
results are contrary to the insurers’ motives, this study provides an important
implication for insurers: they should use a direct distribution channel in order to
achieve better efficiency. This result is confirmed by the literature that we mentioned
earlier. 1, 19, 20 This paper suggests that a direct distribution channel strategy performs
better than a non-direct distribution channel strategy in terms of efficiency and
productivity change.
21
Figure1. Market Interest Rate in Taiwan (1980-2006)
02
468
1012
1416
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
Year
% MarketInterestRate
Table1. Descriptive Statistics of the Data (1997–2006)
MeanStd.
DeviationMinimum Maximum
Outputs
Life and Annuity Premium income(USD in thousands)
793,728 1,421,226 3,639 8,051,207
Health and AD&D Premium income(USD in thousands)
171,598 304,635 1,410 1,444,900
Inputs
Equity (USD in thousands) 225,281 452,277 403 2,414,225Total Business & Administrative
Expenses (USD in thousands)130,007 249,065 1,974 1,798,646
NOTE: 24 insurers
22
Table2. Temporal Evolution of Technical and Scale Efficiency (1997–2006)
Years DC DV SE
1997 0.668 0.717 0.9281998 0.772 0.782 0.9831999 0.839 0.868 0.9682000 0.834 0.893 0.9352001 0.875 0.912 0.9582002 0.945 0.98 0.9632003 0.932 0.966 0.9632004 0.867 0.94 0.9242005 0.811 0.923 0.8762006 0.786 0.946 0.835
Average 0.8329 0.8927 0.9333
NOTE: 24 life insurers; DC = technical efficiency from CRS DEA;DV = technical efficiency from VRS DEA SE = scale efficiency = DC/DV
Table3. Decomposition of Technical and Scale Efficiency by DistributionChannel Strategy (1997–2006)
Variables Strategy Mean Std. D T-value Sig.
DC direct 0.878 0.192 2.950 0.004non-direct 0.795 0.217 ***
DV direct 0.918 0.163 1.824 0.070non-direct 0.872 0.204 *
SE direct 0.954 0.108 2.301 0.022non-direct 0.916 0.133 **
Note: 24 life insurers
23
Table4. Decomposition of Technical and Scale EfficiencyFor 12 Life Insurers Changing Distribution Channel Strategy
Variables Strategy Mean Std. D T Sig.
DC direct 0.958 0.099 3.229 0.002non-direct 0.838 0.194 ***
DV direct 0.971 0.084 0.680 0.499non-direct 0.954 0.123
scale direct 0.985 0.032 3.717 0.001non-direct 0.879 0.163 ***
Table5. Decomposition of the Malmquist Index (1997-2006)
Period CCDM 1, ttPE 1, ttSE 1, ttBCCT 1, ttS
1997-1998 1.248 1.031 1.210 0.892 1.1131998-1999 1.114 1.092 1.021 0.981 1.0931999-2000 1.001 1.011 0.990 1.027 1.0282000-2001 1.061 1.010 1.050 1.042 1.1062001-2002 1.081 1.032 1.048 1.065 1.1522002-2003 0.985 0.995 0.989 1.090 1.0732003-2004 0.921 0.982 0.938 1.054 0.9702004-2005 0.912 1.002 0.910 1.016 0.9262005-2006 0.976 1.010 0.967 0.949 0.927
1997-2006 1.033 1.018 1.014 1.013 1.043S.D 0.10 0.03 0.09 0.10 0.09
>1(%) 44.4 66.7 55.6 55.6 66.7
Note: 24 life insurers
24
Table6. Decomposition of the Malmquist Index for 12 Life InsurersChanging Distribution Channel Strategy
Variables Strategy Mean Std. D T Sig.
CCDM direct 1.510 0.644 5.250 0.000non-direct 1.040 0.587 ***
1, ttPE direct 1.005 0.082 0.199 0.843non-direct 1.003 0.077
1, ttSE direct 1.213 0.209 3.558 0.051non-direct 0.888 0.229 *
1, ttBCCT direct 1.572 0.411 6.391 0.000
non-direct 1.160 0.468 ***1, ttS direct 0.950 0.253 1.284 0.201
non-direct 0.900 0.280
Note: 12 life insurers
25
Appendix
This section explains the foundation of the computation of Malmquist
productivity indexes and their decomposition with non-parametric techniques. In
order to estimate efficiency and productivity growth in the life insurers, we follow a
non-parametric approach to the computation and decomposition of the Malmquist
productivity index. The most commonly used approaches are those proposed by Färe
et al. 36, which assumes a constant returns to scale (CRS) technology, and Ray and
Desli, which does not require that assumption. 37 A third decomposition has been
suggested by Simar and Wilson (1998) and Zofıo and Lovell (1998), which extends
the Ray and Desli (1997) composition. 37-39 More concretely, the technical change
component in Ray and Desli (1997) is further decomposed into a “pure” technical
change of the frontier plus a residual measure of the scale change of the technology. 37
This residual measure evaluates the separation between the CRS and the variable
returns to scale (VRS) technologies. In this paper, we will follow this extended
decomposition because it adds more information about the sources of productivity
change.
The Malmquist productivity index was introduced by Caves et al. as the ratio of
two distance functions pertaining to distinct time periods. 40 The productivity level of
a firm may be measured by the relationship between the inputs employed and the
26
outputs attained. In the case of a technology with just one input and one output, a
productivity index can be computed, using only quantity data, as the ratio yti/xt
i, where
yti is the quantity of output produced by firm i at period t and xt
i is the quantity of input
employed by that firm during the same period. In these cases, it is necessary to use
some criterion to aggregate inputs and outputs. The resulting productivity index can
be defined as mt(yti)/nt(xt
i), where mt(yti) = utyt’ is an output aggregating function with
weight vector ut, and nt(xti) = vtxt an input aggregating function with weight vector vt.
The Malmquist approach allows the above index to be computed using only data on
quantities. It is defined as a ratio between distance functions, and the computation of
these distance functions implicitly generates appropriate weights for inputs and
outputs.
Given that distance functions are computed by comparing a given firm with
another firm that acts as referent or benchmark, the relative productivity (RP) index
has to be defined as the ratio between the absolute productivity indexes of the
benchmark firm. This relative productivity index can be defined as:
tt
tt
ti
t
ti
t
ti
xnym
xnym
RP
*
*
where the symbol (*) represents the benchmark firm, the firm that attains the highest
ratio of absolute productivity. (Note that the relative productivity index of the
benchmark firms must take on a value of one, while the remaining firms will have
27
relative productivities of less than one) It is possible to compute the RP index using
distance functions, but certain assumptions must first be made regarding the
production technology, namely constant returns to scale and separability of inputs and
outputs. The output distance function is defined with respect to that technology as:
tCCR
ti
ti
ti
ti
ti TyxyxDC 1,:min,
Where tCCRT represents the CCR technology, which satisfies the assumptions in
Charnes et al. of constant returns to scale and free disposability of inputs and outputs.
35 The distance function indicates the maximum proportion by which the output vector
can be expanded, holding the input vector constant, in order to obtain the productivity
level of the benchmark firm. Thus, it is a measure of relative productivity. The value
of the distance function for a firm can be computed by solving the following linear
program:
'
'
max,ti
t
ti
tti
ti
ti
xv
yuyxDC s.t.
'
'
ti
t
ti
t
xv
yu ≤1, Jj , tt vu , ≥0
where J represents the set of firms used to construct the empirical reference
technology, which are generically denoted by the sub index j to distinguish them from
the firm that is being evaluated, i. The program finds the weights that maximize the
relative productivity of firm i. The objective function measures the distance that
separates this firm from the benchmark firm in terms of productivity. Thus,
ti
ti
ti
ti yxDCRP ,
28
The Malmquist index introduced by Caves et al. 40 measures the variation in the
relative productivity of a firm between two time periods with respect to the reference
production technology, that is, the benchmark firm, which we hold fixed:
t
iti
ti
ti
ti
tit
CCDyxDC
yxDCM
,
, 11
The benchmark technology is constructed in both periods from the data of period t.
The same effect could be measured using the period t+1 technology as the benchmark
technology,
t
iti
ti
ti
ti
tit
CCDyxDC
yxDCM
,
,1
1111
To avoid choosing arbitrarily between taking the period t or period t+1 technology as
the reference to compute the Malmquist productivity index, the usual way to proceed
is to take the geometric mean of these indexes,
2
1
1
1111111 ]
,
,
,
,[,,,
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
tit
iti
ti
tiCCD
yxDC
yxDC
yxDC
yxDCyxyxM
If ti
ti
ti
tiCCD yxyxM ,,, 11 >1, the index reflects a productivity growth that may
come from different sources. First, it is possible that the firm improved its level of
efficiency relative to the benchmark firm, i.e., the firm performed relatively better
than the benchmark firm. This effect is commonly referred to as “catching-up.”
Second, the available technology may have also improved. Färe et al. (1994) 41 were
29
the first to propose a decomposition of the Malmquist index that separates both
sources of productivity variation,
2
1
1111
1111111 ]
,
,
,
,[*
,
,,,,
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
tit
iti
ti
tiCCD
yxDC
yxDC
yxDC
yxDC
yxDC
yxDCyxyxM
= efficiency change * [technical change]
= ΔEFit,t+1Δ 1,
,tt
iCCRT
The first ratio reflects the relative efficiency change of the firm evaluated—the
variation in the distance towards its contemporaneous frontier—while the second ratio
(in brackets) shows the productivity change that can be attributed to a movement in
the CCR frontier (benchmark firm) between t and t+1. Notice that, even though this
last component refers to a technical change, it incorporates the sub index of firm i
because it is computed from the activity vectors of firm i. Thus, the technical change
index measures the movement of the frontier at the output level of the firm that is
being evaluated, and is defined as a geometric mean in order to avoid choosing
between periods.
The efficiency change index may in turn be decomposed into two indexes. One
of them measures the change in pure technical efficiency and must be computed with
respect to the variable returns to scale technology, while the other one measures scale
efficiency change. The VRS frontier has the advantage of providing a more
appropriate treatment of firm heterogeneity associated with firm strategy. The VRS
30
frontier provides, for each firm, the best possible production vector. The index is
computed as:
}),(:{min),( 1t,i
tBCC
ti
ti
ti
ti TyyxDV
which is the output distance function defined with respect to the TtBCC technology that
satisfies the assumption in Banker et al. The BCC technology drops the CRS
assumption, and imposes only the assumption of convexity. The BCC production set
is said to satisfy variable returns to scale. We can compute a residual scale efficiency
index that compares the two distance functions defined above:
t
iti
ti
ti
ti
tit
iti
ti
yxDV
yxDCyxSE
,
,,
therefore,
1,1,
1111111111,
),(),(
,,
,
),(
tti
ttit
iti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
ti
titt
i SEPEyxSEyxDV
yxSEyxDV
yxDC
yxDCEF
The Malmquist index is finally decomposed into three indexes that measure pure
efficiency change (relative to the VRS frontier), scale efficiency change (comparing
the VRS benchmark with the CRS benchmark), and an index of technical change that
reflects the movement of the CRS frontier. The Färe et al. 41 decomposition can be
pushed a step further by identifying two components in the index of technical change
using the VRS instead of the CRS production set as the reference technology. The
difference between the Färe et al. 41and the Ray and Desli 37 indexes of technical
31
change can be interpreted as a residual measure of the scale change of the technology.
This latter index indicates whether the projection of the firm on the VRS frontier is
now closer to or farther from the CRS technology than it previously was. The
four-component decomposition of the Malmquist index was developed by Simar and
Wilson (1998) and Zofio and Lovell (1998): 39, 40
1,1,1,1,11 ),,,( tti
ttBCC
tti
tti
ti
ti
ti
tiCCD STSEPEyxyxM ,
where the original index of technical change, in brackets, has been decomposed
into an index measuring the technical change of the BCC frontier,
1,1,,
1,,
tti
ttiBCC
ttiCCR STT . Zofio and Lovell interpret this fourth component as a bias of
technical change with respect to scale, as it reflects a change in the optimal scale of
the technology. 40
32
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