Analysis technical efficiency, technological gap and total factor productivity of Vietnamese textile and garment industries

ANALYSIS TECHNICAL EFFICIENCY, TECHNOLOGICAL GAP
AND TOTAL FACTOR PRODUCTIVITY OF VIETNAMESE TEXTILE
AND GARMENT INDUSTRIES
Nguyen Van

Faculty of Fundamental Science, Vietnam Maritime University, Hai Phong, Viet Nam

Abstract
The study used meta- frontier framework, data envelopment analysis approach and
the global Malmquist total factor productivity index to analyse technical efficiency and
productivity change as well as its components of Vietnamese textile and garment firms
during 2013-2015. The results show that: (i) The total factor productivity of Vietnamese
textile and garment firms fell in the period 2013-2015, and technical change is the main
reason to constraint productivity growth. (ii) The private garment sector has taken real
effort to improve technology. On the other hand, state-owned and FDI garment sectors
have been significantly improving technical efficiency in the use of production factors.(iii)
FDI textile firms have been improving effectively technology, whereas state-owned textile
firms have showed improvements in technical efficiency. Meanwhile, the private textile
sector has experienced a slowdown in all components of total factor productivity. (iv)
There is a large technological gap among Vietnamese textile and garment sectors, which
has become wide for the garment industry. And this gap is the reason for differences in
total factor productivity between Vietnamese textile and garment sectors.
Keywords: Data envelopment analysis, Global Malmquist total factor productivity,
Meta-frontier, Technical efficiency.
1. Introduction
In recent years, Viet Nam has taken part in international economic integration by
signing many free trade agreements (FTAs) such as: Viet Nam-Europe Union free trade
agreement, Viet Nam- South Korean free trade agreement, Viet Nam-Asean free trade
area, etc ... In negotiation to sign these agreements, Vietnam textile and garment industries
have always been considered to be the industry that have national fundamental interests,
and able to gain great income when these agreements being put into force.

According to the statistics data of the Vietnam Textile and Garment Association,
the average growth rate of export value in the last 5 years is 14.74% per year, export
turnover in 2016 have got 28.5 billion USD, account for 16% of industrial production
value and became the industry whose export turnover was the second position in the
country (after telephone and telephone accessories), contributed significant part to the
national export turnover, and became one of five world's biggest textile and garment
exporters. Having more than 6,000 large and small firms, textile and garment industries

935


have created jobs for 5% of industrial workers, account for more than 2.5 million
employees and one fifth of new jobs every year. Therefore Viet Nam has been considered
the country whose textile and garment export capability ranked 4th position in the world
(after China, India and Bangladesh).
Although the textile and garment industries play an importance role in the
development of economy, the performances of these sectors in recent years has not met
their potential. Foreign direct investment (FDI) textile and garment firms with the advantage
of international integration and many preferential policies of the state just accounted for less
than 20% of firms and about 4% of total labour force. However, the share of export turnover
made up about 70%. State-owned textile and garment firms still have many limits in
management, thus the production cost is high and productivity is low. In addition, private
garment textile and firms are almost small and medium firms. As a result, It is difficult for
them to access capital and land as well as attract high quality labour force in comparison
with FDI textile and garment firms, leading to low production efficiency.
According to the analysis of efficiency and productivity of Vietnamese textile and
garment firms today, It is assumed that state-owned, private and FDI textile and garment
firms have the same production technology at each period, which may lead to biased
estimation of productivity. In order to overcome these drawbacks, the study will analyse
the efficiency and productivity of Vietnamese textile and garment firms by using the metafrontier approach and the global Malmquist total factor productivity ( Malmquist TFP)

index. Each type of textile and garment firms (state, private and FDI textile and garment
firms) is considered to have different technological levels in each period. From that,
technical efficiency, technological gap and total factor productivity of Vietnamese textile
and garment firms are estimated.
2. Method
The concept of meta-frontier was proposed by Hayami (1969), Hayami and Ruttan
(1970). Since then, Battese et al (2002,2004) have developed meta-frontier approach to
estimate technical efficiency, technical change and total factor productivity. The metafrontier approach can be applied in both data envelopment analysis (DEA) and stochastic
frontier analysis (SFA) frameworks.
Up to now, not only Viet Nam but also many countries in the world have studied in
different economic sectors using the DEA approach to estimate meta-frontier. For
example, Rao et al (2003), O'Donnell et al (2008) used DEA approach to analyse
differences in agricultural productivity of 97 countries in Asia, Europe, America and
Africa. Alexandra Kontolaimou and Kostas Tsekouras (2010) studied about the
effectiveness of cooperative banking in Europe. Qunwei Wang et al (2013) analysed
energy efficiency among provinces in China. Nhat.Q.M (2011) used the DEA approach
and meta-technology ratio (MTR) to estimate the technical efficiency of three rice
monocultures and two crop rotation in Tra Vinh province. Bao. H. D (2016) studied
technical efficiency, factor productivity and technological gap between agricultural areas
of Vietnam, etc.

936


The figure 1 below presents definition of technical efficiencies in meta-frontier and
group frontiers.
Figure 1: Technical efficiency and technology gap ratio in meta-frontier framework
Output(y)
Meta-frontier
G

F
D
B

E

Group frontier 2

Group frontier 3

C
A

Group frontier 1

O

Input(x)

Let‘s consider firm A in the group 1, there are two measures of technical efficiency
that can be derived. Firstly, technical efficiency with respect to meta-frontier. It is defined
by using concept of output oriented distance function and using meta-frontier:
TE(x,q)=Do(x,q)=OB/OF

(1)

Secondly, using the group frontier to define technical efficiency.
TEk(x,q) = Dko(x,q) = OB/OD

(2)

Where TE(x,q) is always less than or equal TEk(x,q)
The Figure 1 shows that, there is a gap between meta-frontier and group frontiers,
which reflects the backwardness between group technology and meta- technology. This
gap is measured by the concept of technology gap ratio (TGR) (Battese et al. 2004).
The output orientated technology gap ratio (TGR) for group kth is defined as:
D ( x, q) TE ( x, q)
TGR k ( x, q)  ok

Do ( x, q) TE k ( x, q)
(3)
The formula (3) can re-write as:

TE( x, q)  TE k ( x, q).TGRk ( x, q)

(4)

The formula (4) shows that technical efficiency with respect to meta-frontier
consists of two components: Firstly, the current knowledge of production, natural
environment, socio-economic of each group (TEk). Secondly, the technology gap of each
group over the whole industry (O'Donnell et al. 2008). Oh and Lee (2010) proposed the
concept of technology gap change to measure the trend of technology gap ratio as:
TGC 

TGRt 1
TGRt

(5)

937

TGC> 1 means the production technology gap of groups is getting closer.
Unlike traditional DEA studies that focus only on efficiency and technological gap
at a specific time. The global Malmquist TFP index was proposed by Pastor and Lovell
(2005) and developed by Oh and Lee (2010) to measure technical efficiency change,
technical change and productivity growth. The Figure 2 describes concept of the global
Malquist TFP as:
Figure 2: The concepts of the meta-frontier Malmquist indexes

E2
C32
C31

I3

E1

D2

C12
A2

B2

D1

C22

B1

A1

C11

I1

C21
I2

Where Cij are contemporaneous frontiers of groups at a specific time, Ii are intertemporal frontiers for groups and there is only one global frontier G.
The contemporaneous Malmquist TFP index of an observation within group kth is
defined at technology of period t as:

 D ( xt 1 , qt 1 ) D ( xt 1 , qt 1 ) 
M ( x , q , x , q )   t 1 t t  t

Dt ( xt , q t ) 
 Dt 1 ( x , q )
t
C

t

t

t 1

0.5

t 1

(6)

Where M is Malmquist TFP index, Dt(.) is output orientated distance function with
respect to frontier of period t.
The inter-temporal Malmquist TFP index of an observation for each group is
defined as:
M I ( xt , qt , xt 1 , qt 1 ) 

D I ( xt 1 , qt 1 )
D I ( xt , q t )

(7)

Where MI is inter-temporal Malmquist TFP index, DI (.) is output orientated
distance function with respect to inter-temporal frontier of group I.
Following Pastor and Lovell (2005), this index can be decomposed as:

M I ( xt , qt , xt 1 , qt 1 ) 

938

Dt 1 ( xt 1 , qt 1 )  D I ( xt 1 , qt 1 ) Dt ( xt , qt ) 

 I t t 
t 1
t 1
Dt ( xt , qt )
 Dt 1 ( x , q ) D ( x , q ) 

(8)


t 1
t 1
t 1
t
t
t
t 1
t
Due to D ( x , q ) / D ( x , q )  TE / TE  TEC , the first component in the

I
formula (8) measures technical efficiency change. D ( x, q) / D( x, q) is Best Practice Gap
(BPG) defined by Pastor and Lovell (2005) and Oh and Lee (2010). BPG is ratio of output
orientated distance function with respect to inter-temporal frontier over output orientated

distance function with respect to contemporaneous frontier and takes the value in
BPGt 1 

D I ( xt 1 , qt 1 )
D I ( xt , qt )
t
;
BPG

Dt 1 ( xt 1 , qt 1 )
Dt ( xt , q t )

 0;1

(9)

BPGt 1  BPGt describes technological improvements from period t to period t +
1.
We will use this to describe the concept of Best Practice Gap Change (BPC). BPC
that measures technical change is defined in the global Malmquist TFP index framework
in the flowing way:
t
t
D I ( xt 1 , qt 1 ) D I ( xt , qt ) D I ( xt 1 , qt 1 ) Dt ( x , q )
BPC 
/


Dt1 ( xt 1 , qt 1 ) Dt ( xt , qt ) Dt 1 ( xt 1 , qt 1 ) D I ( xt , q t )

(10)

In summary, inter-temporal Malmquist TFP index can be written as:
M I ( xt , qt , xt 1 , qt 1 )  TEC  BPC

(11)

Because output orientated distance function is homogeneous of degree one in
output, each   then  D( x, q)  D( x, q) (Oh and Lee, 2010). Therefore, the formula
(11) can be re-written as:
BPC 

D I ( xt 1 , qt 1 / Dt 1 ( xt 1 , q t 1 ))
D I ( xt , qt / Dt ( xt , q t ))

(12)

Similarly, the global Malmquist TFP index is constructed as:
M G ( xt , qt , xt 1 , q t 1 ) 

DG ( xt 1 , qt 1 )
DG ( xt , q t )

(13)

G
t
t
Where D ( x , q ) is output orientated distance function with respect to metafrontier. Because there is only meta-frontier in period t to t+1, the formula (13) is not in
the geometric mean form. We can decompose MG into the following components:

 D I ( xt , q t )
DG ( xt 1 , qt 1 ) 
M G ( xt , qt , xt 1 , qt 1 )  TEC  BPC   I t 1 t 1 

DG ( xt , q t ) 
 D (x , q )

(14)

According to the concept of technology gap ratio has been introduced above we have:

939


TGRt1 

TGR

t 1
DG ( xt 1 , qt 1 )
DG ( xt , qt ) TGCt ,t 1 
TGR

t
TGRt
D I ( xt 1 , qt 1 ) ;
D I ( xt , qt ) ;

(15)

Therefore, the formula (14) can be re-written as:
M G ( xt , qt , xt 1 , qt 1 )  TEC  BPC  TGC

(16)

This formula implies that the following steps can be implemented to increase total
factor productivity: Effective exploitation of existing production resources; Technological
improvements within groups; Improvement the technology of industry.
Because output orientated distance function is homogeneous, (14) can be re-written as:
t 1

t 1

MG (x , q , x , q ) 
t

t

Dt1 ( xt 1 , q t 1 )
Dt ( xt , q t )



I
t 1
t 1
t 1
t 1
G
t 1
t 1
I
t 1
t 1

 D ( x , q / Dt 1 ( x , q )) 
  D ( x , q / D ( x , q )) 






I
t
t
t
t
G
t
t
I
t
t
 D ( x , q / Dt ( x , q )) 
  D ( x , q / D ( x , q )) 


(17)

This formula allows to compute the global Malmquist TFP index and its
components by solving linear programming problems. Oh and Lee (2010) constructed six
linear programming problems to determine the value of distance functions:

Dt ( xt , qt )

Dt1 ( xt 1 , qt 1 ) D I ( xt , qt / Dt ( xt , qt )) D I ( xt 1 , qt 1 / Dt1 ( xt 1 , qt 1 )), DG ( xt , qt / D I ( xt , qt ))

DG ( xt 1 , qt 1 / D I ( xt 1 , qt 1 )) , and from the traditional DEA approach we used these
distance functions to measure technical efficiency.
3. Results
3.1. Data description.

In this study, Vietnamese textile and garment firms are divided into three groups
based on ownership including: State-owned textile and garment firms, private textile and
garment firms and FDI textile and garment firms. Data used in the study are secondary data
collected from the firms survey data of Viet Nam General Statistics Office (GSO) from 2013
to 2015. The author processed and separated the needed data for textile and garment
industries then obtained data of 1455 textile firms, including 287 FDI textile firms, 58 state
textile firms and 1110 private textile firms, as well as data of 3035 garment firms, including
50 state-owned garment firms, 594 FDI garment firms and 1110 private garment firms.
To estimate the productivity growth of textile garment firms as well as their
components by meta-frontier approach, the study uses one aggregated output as added
value, which is calculated according to the guidelines of GSO in the following: Value
Added (VA) = Fixed Assets Depreciation + Total Employee Income + Profit + Indirect
Taxes. Two inputs are labour (L) and capital (K). L is the average number of employees in
the year, which is calculated as the average of the number of employees at the beginning of
the year and the end of the year for each firm. K is the average assets at the beginning of
the year and at the end of the year for each firm. Table 1 summarizes descriptive statistics

940


for three groups of the textile and garment industries in the period of three years from 2013
to 2015.
Table 1: Data summary for value added and inputs of Vietnamese textile and
garment firms in the period 2013-2015
Variable

State-owned
firms group

Private firms

group

FDI firms
group

Mean

34365.28

8342.76

86771.34

Std.Dev

98187.08

30741.81

407948.80

Mean

207296.60

37914.80

354949.30

Std.Dev

954948.90

120602.60

1594758.00

Mean

244.08

67.17

294.56

Std.Dev

663.28

197.44

606.65

Mean

32635.79

15100.21

91798.70

Std.Dev

52742.67

62182.35

141394.90

Mean

57765.41

25635.98

103452.00

Std.Dev

127072.00

109930.00

193588.90

Mean

370.52

173.18

1019.96

Std.Dev

539.48

Value Added (VA)

Capital (K)
Textile
industry

Labor (L)

Value Added (VA)
Garment
industry

Capital (K)

Labor (L)
567.73
1354.71
Source: The author‟s calculation

3.2. Results of the global TFP Malmquist Index.
Based on the theoretical model given above and firms survey data of GSO in the
period 2013-2015, the author used DEAP 2.1 software (Coelli, 1996) to solve linear
programming problems. Then the author calculated the global Malmquist TFP index and

its components TEC, BPC and TGC. The table 2 presents summary of the estimated results
for the global meta-frontier Malmquist TFP index and its components by groups of
garment industry in the period 2013-2015.
Table 2: Meta-frontier Malmquist total factor productivity and its
decompositions of garment industry
Type of firms

TEC

BPC

TGC

TFP

State-owned garment firms

1.009

0.981

0.999

0.989

Private garment firms

0.935

1.069

1.002

1.002

FDI garment firms

1.154

0.873

1.000

1.007

941


Mean

1.033

0.974

1.000

0.999

Source: The author‟s estimation from DEAP 2.1 outputs.
The results show that the meta-frontier total factor productivity of the garment

industry has decreased on average by -0.1% per year. In which, mean technical efficiency
has increased by 3.3% per year, technical change has decreased by -2.6% and there was no
change of technological gap.
As mentioned above, due to differences in production technology between different
types of garment firms, the tendency to change total factor productivity as well as its
components for each type garment firms are also different. FDI garment firms have the highest
total factor productivity growth rate of 0.7% per year. This was followed by the figure for
private garment firms, at 0.2% per year. Meanwhile, state garment firms showed a decrease of
-0.11% per year in total factor productivity. State-owned and FDI garment firms have better
results in improving their technical efficiency, while private garment firms have better results
in technical change. However, the contribution of the average technical change of the garment
industry decreased by -2.6% per year. This suggests that technical change is the main reason
for being constrained to productivity growth of Vietnamese garment firms.
The technological gap ratio change (TGC) estimations show that state-owned
garment firms are shifting farther away from production technology. This means that they
relatively more backward in garment production technology. Otherwise, private garment
sector shows its fastest growth in applying new production technology with 0.2% increase
in technological gap ratio (TGR) and there is no change in TGR for FDI garment sector.
The estimations of technical change show that state-owned garment firms are
backward in technology compared to private and FDI garment firms. Meanwhile, private
garment firms take the lead in technical change. Although the results of technological gap
ratio change are significant, it is only the relative rate of change in the lead in technology
among the types of garment firms. The position of the production technology of each type
of garment firms is more clearly indicated in the calculation of the technology gap ratio.
Table 3: Technological gap ratio (TGR) summary in the meta-frontier DEA of
garment industry
Type of firms

Mean

S.D

Min

Max

State-owned garment firms

0.685

0.019

0.640

0.712

Private garment firms

0.914

0.035

0.862

1.000

FDI garment firms

0.952

0.023

0.650

1.000

Source: The author‟s estimation from DEAP 2.1 outputs.
FDI garment firms have the best technology with average TGR of 0.952, following
by private garment firms and state garment firms that have the most backward production
technology.
Combining the findings of the technological gap ratio and the results of the
technological gap ratio change, we can see that the FDI garment sector has the leading

942


technology, however this position may be lost because of slow technical change (BPC). The
private garment sector which was leader the in technological gap ratio change has played an
important role in the development of garment industry, with significant technological change
(6.9% per year). Meanwhile, the state owned garment sector was the least one in production
technology and has become more backward compared to private and FDI garment sectors.
Table 4: Meta-frontier Malmquist total factor productivity and its decompositions of
textile industry
Type of firms

TEC

BPC

TGC

TFP

State-owned textile firms

1.046

0.941

0.996

0.980

Private textile firms

0.999

0.992

0.999

0.990

FDI textile firms

0.993

1.018

0.999

1.010

Mean

1.013

0.984

0.998

0.993

Source: The author‟s estimation from DEAP 2.1 outputs.
In the estimates results productivity of textile industry show that, the average total
factor productivity of this industry has decreased by -0.7% per year. In which technical
efficiency has increased by 1.3%, contribution of technical change has decreased by -1.6%
and technological gap has decreased by -0.2%.
FDI textile firms have got the highest productivity growth rate (1% per year),
whereas there has been a decrease of productivity in state-owned and private textile sector.
State-owned textile firms have taken effort to improve their technical efficiency, while FDI
textile firms have made better progress in technology. Moreover, the private textile sector
has decreased in all components of total factor productivity. Following the estimates
results above, the performance of Vietnamese textile industry has been incomprehensive in
the last few years and backward in technology. All of textile sectors are negative in
technical change as well as technological gap ratio change. These are two major reasons
that cause to reduce productivity of Vietnamese textile industry. Presently, weave and
dyeing processes are still the least developed sectors in Vietnamese textile and garment
industries. In fact, nearly 70% of fibre output is exported because domestic weave and
dyeing firms do not meet the demand of fibre consumption. Meanwhile, garment firms

have imported a large amount of fabric from abroad.
Table 5: Technological gap ratio (TGR) summary in the meta-frontier DEA of
garment industry
Type of firms

Mean

S.D

Min

Max

State-owned textile firms

0.953

0.039

0.744

0.981

Private textile firms

0.996

0.016

0.845

1.000

FDI textile firms

0.849

0.030

0.716

1.000

Source: The author‟s estimation from DEAP 2.1 outputs.
However, only estimation TGC could not reflect positions in production technology
of different textile sectors , that is better explained by examining estimated technical gap

943


ratio (TGR) of each sector in the period shown. The table 5 presents estimated
technological gap ratio of each sector, which shows that private sector is leading by
technology in the period 2013-2015. This is followed by state-owned textile firms and FDI
textile firms that have the most backward production technology. However, because FDI
textile firms have made a great effort in technical change (1.8% annual) while private and
state-owned textile sectors decreased, FDI textile sector may develop strongly and become
the best one. This can be explained by the fact that FDI textile firms investing in Vietnam
have backward technology leading to low production efficiency. However, since the free
trade agreements were signed by Vietnam, the wave of foreign investments in Vietnamese
textile industry have become huge in order to gain benefit from export taxes of textile and

garment products. Therefore, in the coming years, the FDI textile sector as well as
Vietnamese textile industry might strongly develop.
4. Discussion and Conclusion
This study uses meta-frontier approach and a global total factor productivity index
to analyse total factor productivity change as well as its components in the Vietnamese
textile and garment sectors. The empirical results show that:
The total factor productivity of Vietnamese textile and garment firms fell in the
period 2013-2015, and technical change is the main reason to constraint productivity
growth. The private sector has taken real effort to improve technology. On the other hand,
state-owned and FDI garment sectors have been significantly improving technical
efficiency in the use of production factors. It is opposite to textile industry, FDI textile
firms have been improving effectively technology, whereas state-owned textile firms have
showed improvements in technical efficiency. At the same time, the private textile sector
has experienced a slowdown in all components of total factor productivity.
There is a large technological gap among Vietnamese textile and garment sectors,
which has become wide for the garment industry. This gap is the reason for differences in
total factor productivity between Vietnamese textile and garment sectors.
The study uses the data envelope analysis method to estimate the meta-frontier and
total factor productivity. Therefore it is sensitive to the dominant observations and the effects
of statistical noise are not taken into account. However, from the study results, some
recommendations can be considered for Vietnamese textile and garment industries as:
The State should have direct support policies and facilitate for textile and garment firms
to raise their scientific and technological capacity as well as increase technology in the
production process. Especially, The government should encourage to invest in weave and dyeing
industrial parks in order to meet the conditions of infrastructure, environment, technology, etc.,
that promotes the development textile industry to meet the demands of the garment industry.
In recent years, the government has offered preferential policies for state-owned and
FDI textile and garment sectors. However, the estimated results show that the
technological change as well as the productivity of these sectors are inadequate. By
contrast, the private textile and garment sector is facing many difficulties in such policies

944


to develop production. As a result, the state should have fair policies for textile and
garment sectors.
In the process of developing Vietnamese textile and garment industries, it is
necessary to focus on the private textile and garment sectors. Because they are important
sectors that account for about 80% of the total Vietnamese textile and garment firms and
attract a huge number of the labour force in the textile and garment industries. The
government should have policies to support private textile and garment firms to access
land, credit support, etc that motivate the private textile and garment sectors development.
5. References
1. Bao. H. D. (2016), Analysis of technical efficiency and total factor productivity,
Hanoi National University Publishing, Hanoi.
2. Nhat. Q. M (2011), 'Using metafrontier and metatechnology ratio tools to expand
data envelopment analysis model in productivity and efficient evaluation.' Can Tho
University‟s Journal of Scientific Research , 18 (1), 210-219.
3. Alexandra Kontolaimou & Kostas Tsekouras (2010), ‗Are cooperratives the
weakest link in European banking? A non-parametric metafrontier approach‘, Journal of
Banking & Finance, 34, 1946-1957.
4. Battese, G.E. & Rao, D.S.P. (2002), ‗Technology gap, efficieny, and a stochastic
metafrontier function‘. International Journal of Business and Economics, 1(2), 87-93.
5. Battese, G.E., Rao, D.S.P. & O‘Donnell, C.J. (2004), ‗A metafrontier production
function for estimation of technical efficiencies and technology potentials for firms
operating under different technologies‘, J Product Anal, 21, 91–103.
6. Coelli, T.J. (1996), A guide to DEAP version 2.1: a data envelopment analysis
(computer) program. CEPA working paper 96/8. Armidale, Australia, Department of
economectris, University of New England.
7. Hayami, Y. (1969), ‗Sources of agricultural productivity gap among selected

counties‘, American Journal of Agricutural Economic, 51(3), 564-575.
8. Hayami, Y. & Ruttan, V.W. (1970), ‗Agricultural productivity differences among
counties‘, American Economic Review, 60(5), 895-911.
9. O‘Donnell, C.J. (2008), ‗ An aggreagate quantity-price framework for measuring
decomposing productivity and profitability change‘, Working Papers, Australia.
10. O‘Donnell, C.J., Rao, D.S.P. & Battese, G.E. (2008), ‗Metafrontier frameworks for
the study of firm-level efficiencies and technology ratios‘, Empirical Economics, 34, 231-255.
11. Oh, D.H. & Lee, J.D. (2010), ‗A metafrontier approach for measuring
Malmquist productivity index‘. Empirical Economics, 38, 47-64.
12. Pastor, J.T. & Lovell, C.A.K. (2005), ‗ A global Malmquist productivity index‘
Economics Letters, 88(2), 266-271.
13. Q. Wang, Z. Zhao, P. Zhou, D. Zhou (2013), ‗Enery efficiency and production
technology heterrogeneity in China: a meta-frontier DEA approach‘, Economic Modelling , 35,
283-289.

945


14. Rao, D.S.P., Coelli, T.J. (2003), ‗ Total factor productivity growth in
agriculture: a Malmquist index analysis of 93 countries, 1980-2000, CEPA working paper
02/2003. Armidale, Australia, School of economics, University of New England.

946