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

2

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

7

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

8

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

13

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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