Open Journal of Statistics, 2012, 2, 224-235
http://dx.doi.org/10.4236/ojs.2012.22028 Published Online April 2012 (http://www.SciRP.org/journal/ojs)
Productivity Growth, Technological Progress, and
Efficiency Change in Vietnamese Manufacturing
Industries: A Stochastic Frontier Approach*
Nguyen Khac Minh1, Pham Van Khanh2, Nguyen Thi Minh3, Nguyen Thi Phuong Anh4
1Faculty of Economics, Water Resources University, Hanoi, Vietnam
2Military Technical Academy, Hanoi, Vietnam
3National Economics University, Hanoi, Vietnam
4Hanoi University of Science and Technology, Hanoi, Vietnam
Email: khacminh@gmail.com, van_khanh1178@yahoo.com
Received February 3, 2012; revised March 8, 2012; accepted March 19, 2012
ABSTRACT
This study applies a stochastic frontier production approach to decompose the sources of total productivity (TFP)
growth into technical progress and changes in technical efficiency of 8057 firms in Vietnamese manufacturing indus-
tries during 2003-2007. Using both total manufacturing industry and sub-manufacturing industrial regressions, the
analysis focuses on the trend of technological progress (TP) and technical efficiency change (TEC), and the role of
productivity change in economic growth. According to the estimated results, the annual technical progress for the
manufacturing industry and sub-manufacturing industries are calculated directly from the estimated parameters of the
translog stochastic frontier production function by taking a partial derivative of output with respect to time t. The aver-
age technical changes in manufacturing industry and sub-man ufacturing industries are positive, with an average techni-
cal change about 5.2%, 5.8%, 5.4%, 11.8%, 4.6%, 4.1%, 7.3%, 4.8%, 4.8% and 4.8% for total sample, food products &
beverages, textile & wearing apparel, footwear, paper & products, industrial chemicals, rubber & plastic products, non-
metallic mineral, basic & fabricated metal and other sub-industries, respectively. Total TFP in the manufacturing sector
has grown at the annual rate of 0.052, although the rate of growth decreased continuously during the sample period. For
the sub-industry estimates during the sample period, TFP grew fastest in the footwear sub-industry, with annual average
growth rate of 11.8%, followed by the rubber & plastic products with a rate of 7.3%, and the food products & beverages
with a rate of 5.8% pe r ann um .
Keywords: Total Factor Productivity; Technical Efficiency Change; Technological Progress; Stochastic Frontier
Approach; Vietnamese Manufacturing Industry
1. Introduction
In the “Solow residual approach”, technical progress is
usually considered to be the unique source of TFP growth.
TFP growth can be defined as the residual of output
growth after the contribution of labor and capital inputs
and subtracted from total output growth . This appro ach is
based on the assumption that the economies are produc-
ing along the production possibility frontier with full
technical efficiency (it does not allow inefficiency).
The concept of the efficiency frontier has been used to
present inefficiencies.
A varies of methods have been used to measure effi-
ciency and decomposition total factor productivity (TFP)
into technical progress, changes in technical efficiency.
These methods differ to the assumptions on the outer
bound of the frontier, which deterministic or stochastic
frontier production function, and to the method of meas-
urement parametric or non-parametric.
For nonparametric method, such as data envelopment
analysis (DEA). This method cannot separate deviation
from the frontier technology into their systematic and
random components. However, this method has the ad-
vantage of imposing no restrictions on the underlying
technology and have an advantage in dealing with disag-
gregated inpu ts and multiple output technologies.
An alternative method is called a stochastic frontier
production function approach. The most important dif-
ference between the stochastic frontier production func-
tion approach and the Solow residual approach to pro-
ductivity growth analysis lies in one assumption that
firms do not fully utilize existing technology since vari-
*The third author was supported by the National Foundation for Science
Technology Development, Vietnam (NAFOSTED), No. II6.2-2010.07.
C
opyright © 2012 SciRes. OJS
N. K. MINH ET AL. 225
ous factors that lead to inevitable technical inefficiencies
in production.
The stochastic frontier production function approach
allows decomposing TFP into efficiency change (TE)
and technical progress (TP). From a policy perspective,
the decomposition of TFP into efficiency changes and
technical changes provides useful information in produc-
tivity analysis.
Since Nishimizu and Page [1] first proposed the de-
composition of TFP into efficiency changes and technical
changes, researchers have applied this approach to vari-
ous datasets in order to investigate productivity growth.
Bauer [2] estimated a translog cost frontier using da ta on
the US airline industry to decompose TFP growth into
efficiency, technical progress, and scale components.
Sangho Kim and Gwangho Han [3] applied a stochastic
frontier production model to Korean manufacturing in-
dustries to decompose the sources of total productivity
(TFP) growth into technical progress, changes in techni-
cal efficiency, and changes in allocative efficiency, and
scale effects. Empirical results based on data from 1980-
1994 showed that produ ctivity growth was driven mainly
by technical progress, that changes in technical effi-
ciency had a significant positive effect, and that alloca-
tive efficiency had a negative effect. They suggested that
specific guidelines are required to promote productivity
in each industry, and provided additional insights into
understanding the recent debate about TFP growth in
Korean manufacturing.
Hailin Liao et al. [4] applied a stochastic frontier ap-
proach to sector-level data within manufacturing and
examined total factor productivity (TFP) growth for eight
East Asian economies during 1963-1998, using both sin-
gle country and cross-country regression. The analysis
focuses on the trend of technological progress (TP) and
technical efficiency change (TEC), and the role of pro-
ductivity change in economic growth. The empirical re-
sults reveal that although input factor accumulation is
still the main source for East Asian economies’ growth,
TFP growth is accounting for an increasing and impor-
tant proportion of output growth, among which the im-
proved TEC plays a crucial role in productivity growth.
Nguyen Khac Minh et al. [5] applied a non-parametric
approach method to decompose the sources of total pro-
ductivity (TFP) growth of three sectors of Vietnamese
economy into technical progress and changes in technical
efficiency.
This study develops the study of Nguyen Khac Minh
et al. [6] “A decomposition of total factor productivity
growth in Vietnamese industries—a stochastic frontier
approach” to decompose TFP growth in Vietnamese
manufacturing industries from 2003-2007. We attempt to
decompose TFP growth in Vietnamese manufacturing
using a stochastic frontier production model, and provide
additional insights into understanding on TFP growth of
Vietnamese sub-manufacturing industries.
This paper is organized as follows. Section 2 presents
a decomposition of TFP and presents the functiona l form
of the estimation model. Section 3 discusses the data and
estimation results. Section 4 contains the conclusions.
2. Decomposition and Functional Form
2.1. Decomposition of TFP
A stochastic frontier production function can be defined
by

,exp
it itit
y
fxt u
y

1, ,iN
(1)
where it is the output of the ith firm in
the tth time perio d
1, ,tT

;
f
is the production
frontier;
is an input vector, t is a time trend index
that serves as a proxy for technical change; and u (non-
negative) is the outpu t-oriented technical inefficiency.

,
it
f
Taking total differentials xt with respect to
time to get

d
dln,ln,ln,
dd
TP
x
j
jj
jj
j
fxt fxtfxt
tt xt
x




j
(2)
whereas the first and second terms on the right-hand side
are the output elasticit y of fron tier out put with resp ect to
time, defined as TP, the second term measures the input
growth weighted by output elasticities with respect to
input , ln ln
f
x
j
. A dot over a variable in-
dicates its rate change.
The derivative of the logarithm of (1) with respect to
time t and using (3) is gi ven by:
d
TP d
jj
j
u
yx
t
 

(3)
from Equation (3), TFP growth can be defined technical
change (TP) and technical efficiency change.
2.2. Model Specification
In our empirical study, we employ the stochastic frontier
approach. The output of the manufacturing industry (or
sub-industries) is assumed to be a function of two inputs,
namely capital and labor. The components of productiv-
ity change can be estimated within a stochastic frontier
approach, and the time-varying production frontier can
be specified in translog form as:
2
ln ln
11
lnln
22
ln, ,,
itojjit t
j
jl litjittt
jl
tjjt itit
j
yxt
x
xt
txv ujlLK
 

 



(4)
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL.
226
In Equation (4), it is the observed output, t is the
time variable and x variab les are inpu ts, subscrip ts j an d l
index inputs. The efficiency error, u, accounting for pro-
duction loss due to un it-specific technical inefficiency, is
always greater than or equal to zero and assumed to be
independent of the random error, v, which is assumed to
have the usual properties . Equation (4)
can be rewritten as the following form:
y


2
~ 0,
v
iid N
1) Specification model for whole manufacturing in-
dustry

 



0
2
2
1
ln lnln
2
1
lnlnln
21
ln2
jjj
itL it KitLL
jj
KKitLK itit
j
tKittttit it
LnyL K2
ln
j
it
jj
tL it
L
K
LK
Ktttv u
 


 


Lt
where
j
it
y
is the firm’s output. The subscripts i repre-
sent the ith firm for . N is equal to 8057
for the total sample. t represents year for
and so T is equal to 5. The subscripts j represent the jth
industry for,
1,2,,iN
1, 2,,tT
, 1,2,jH
j
it
K
and
j
it
L represent ca-
pital and labor, respectively. The
s
and
s
are un-
known parameters to be estimated.
2) Specification model for each industry

 



0
2
2
1
lnln2
1
lnlnln
21
ln
2
itL it KitLL
KKitLK itit
tKittttit it
LnyL K2
ln
ln
it
tL it
L
K
LK
Kt ttvu
 


 


Lt
u

2
,u
N
(5)
The distribution of technical inefficiency effects, it,
is taken to be the non-negative truncation of the normal
distribution
, following Battese & Coelli [7],
to take the form as

T

tiex
itt ii
uuupt

,
(6)
Here, the unknown parameter
represents the rate
of change in technical inefficiency, and the non-negative
random variable ui, is the technical inefficiency effect for
the ith firm in the last year for the data set. That is, the
technical inefficiency effects in earlier periods are a de-
terministic exponential function of the inefficiency ef-
fects for the corresponding forms in the final period (i.e.)
iTi given that data for the ith firm are available in
period t).
uu
i
is the set of T time periods. A firm with
a positive
is likely to improve its level of efficiency
over time and vice-verse. A value of 0
it
u

TE exp
it it
u
implies no
time-effect.
Since the estimates of technical efficiency are sensitive
to the choice of distribution assumptions, we consider
truncated normal distribution for general specifications
for one-sided error , and half-normal distribution can
be tested by LR test.
Given the estimates of parameters in Equations (5) and
(6), the technical efficiency level of a firm at time t is
defined as
(7)
and TEC is the change in TE, and the rate of technical
progress is defined by,
 
,
ln
TPln ln
it t
itttttLitKi
fx LK
t
 


(8)
If technical change is non-neutral then this technical
change may vary for different input vectors. Hence, we
use the geometric mean between adjacent periods as a
proxy,


12
,1, 1
ln ln
TP 111
1
it jit t
it
fx fx
tt







 







TEit TPit
(9)
Both and vary over time and across the
firms.
The output elasticities of input K and L are
ln ln ln
ln
ln ln ln
ln
K
KKKKLKt
LL KLLLLt
Y
K
Lt
K
Y

K
Lt
L

 
 
e
The above equations indicate the percentage change in
output due to a 1% change in inputs. They can be used to
obtain an estimate of aggregate return to scale. The elas-
ticity of scale is defined as : e
K
L
.
The elasticity of scale (e) measures how output varies
as a particular input bundle is augmented by a scalar. If
the scale elasticity is unity, then the technology exhibits
constant returns to scale.
3. Data and Empirical Results
3.1. Data Issues
The panel data of Vietnamese manufacturing sectors’
annual time-series during 2003-2007 are used in esti-
mating production functions. The sectors and their SIC
classification numbers are listed in Table 1.
The sample consists of 8057 firms in Vietnamese
manufacturing industries. Data for these firms have been
taken for 5 years from 2003 to 2007. All these firms that
are selected at least 5 workers.
The basic data for the analysis have been drawn the
Database, 2007 version from General Statistics Office
(GSO). It contains information for about characterized
enterprises. The coverage includes public, private, and
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL. 227
Table 1. Manufacturing sectors.
1) Manufacturing sector (Total
sample) 6) Industrial chemicals
2) Food products an d beverages 7) Rubber and plastic products
3) Textile and wearing apparel 8) Non-metallic mineral
4) Footwear 9) Basic & fabricated metal
products
5) Paper & products 10) Other manuf act uring industries
joint sector companies. The coverage of this database is
total manufacturing firms that existed from 2003 to 2007
with number of workers greater than 5.
The available Information includes data from the en-
terprises’ profit, balance sheets. Key variables on which
data were collected for this study include gross fixed
assets, wages, revenue, gr oss out put a n d fo re ign eq uity .
3.2. Variables for the Estimation of the Model
As discussed above, a two-input production function
framework is used to estimate technical efficiency. This
requires, for each firm, data on output, labor input and
capital input.
Deflated revenue has been taken as the measure of
output. For this purpose, the products of each enterprise
were matched with the wholesale price indices classifica-
tion, and the best available price series was chosen for
deflation.
Total number of employees connected to the produc-
tion has been taken as the measure of labor input for each
firm in our sample.
Gross fixed capital stock at constant prices (at year
2000) has been taken as the measure of capital input.
4. Empirical Results
The estimation of parameters in the stochastic frontier
mode given by Equations (8) and (9) are carried out via
maximum-likelihood method, using the program FRON-
TIER 4.1. Two kinds of panel are constructed. Individual
sub-Industry panel is used in the single regression, con-
sisting of total sample and 9 sub-manufacturing sectors
and 5 years’ observations; panel data is used in the re-
gression. Instead of directly estimating 2
v
and 2
u
,
FRONTIER 4.1 seeks estimates of
22
u

, 222
uv


v v
(10)
which are also reported in the result table. These are as-
sociated with the variances of the stochastic term in the
production function, it and the inefficiency term it .
The parameter
must lie between zero and one. If the
hypothesis 0
is accepted, this would indicate that
2
u
is zero and thus the efficiency error term,
should be remove from the model, leaving a specification
with parameters that can be consistently estimated by
OLS. Conversely, if the value of
is one, we have the
full-frontier model, where the stochastic term is not pre-
sent in the model.
4.1. Hypotheses Tests and Preferred Model
Chosen
We performed a number of LR test to identify the ade-
quate functional form and presence of inefficiency. We
examine various hypotheses, such as non-presence of
technical inefficiency effects, which can be tested by
using the generalized likelihood ratio statistics
, given
by:
it
v


01
2ln lnLH LH

where L(H0) is the value of the likelihood function for
the frontier model in which the parameter restrictions
specified by the null hypothesis H0 are imposed and L(H1)
is the value of the likelihood function for the general
frontier model. If the null hypothesis is true, then
has
approximately a mixed Chi-Squared distribution with
degrees of freedom equal to the difference between the
numbers of parameters estimated under H1 and H0, res-
pectively.
4.2. Hypotheses Tests for Aggregated Samples
Table 2 presents the test results of various null hypothe-
ses on the total sample.
1) The first null hypothesis that the technology in
Vietnamese manufacturing is a Cobb-Douglas
:0H
 
oLL KKKL tt
, is rejected for the total
sample and all aggregated-samples. Thus, the Cobb-
Douglas production function is not an adequate specifi-
cation for the Vietnamese manufacturing sector, given
the assumptions of the translog stochastic frontier pro-
duction function model, implying that the translog pro-
duction function better describes the technology for
Vietnamese manufacturing industries.
2) The second null hypothesis, that there is no techni-
cal change
:0H
 
o ttKtLtt
 is strongly
rejected by the data in all cases. It implies that the exis-
tence of technical progress, given the specified produc-
tion model.
3) The third null hypothesis, that technical progress is
neutral
:0H

otK tL.
Not that the translog parameterization of this stochas-
tic frontier model allows for non-neutral TP. TP is neu-
tral if all tj
s are equal to zero. Total sample, food &
beverages, footwear, paper & products, Industrial chemi-
cals, non-metallic mineral, basic & fabricated metal and
ther manufacturing industries cannot reject the hypothe- o
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL.
Copyright © 2012 SciRes. OJS
228
Table 2. Generalized likelihood ratio of hypotheses for parameters of the SFPF for Vietname se manufac turing industries.
Hypothesis Log-likelihood value Test statistics Critical value Decision
1% 5%
Cobb-Douglas production function, H0: all
s are equal to zero (df = 6)
Total sample –48319.83 21475.94 16.81 12.59 reject
Food products & be verages –7559.98 31.65 16.81 12.59 reject
Textile & wearing apparel –4781.91 41.92 16.81 12.59 reject
Footwear –1007.15 29.69 16.81 12.59 reject
Paper & products –2731.46 25.00 16.81 12.59 reject
Industrial chemicals –1604.32 21.13 16.81 12.59 reject
Rubber & plastic products –2238.63 50.15 16.81 12.59 reject
Non-metallic mineral –3394.03 107.98 16.81 12.59 reject
Basic & fabricated me tal –10757.17 94.99 16.81 12.59 reject
Others –9754.55 86.46 16.81 12.59 reject
No technical change, 0
H

:0
ttLtKtt
 

0:0
tL tK
H

(df = 4)
Total samp le –38319.59 1475.40 13.28 9.49 reject
Food products & beverages –7700.38 312.45 13.28 9.49 reject
Textile & wearing apparel –4871.20 220.51 13.28 9.49 reject
Footwear –1038.66 92.71 13.28 9.49 reject
Paper & products –2786.94 135.95 13.28 9.49 reject
Industrial chemicals –1622.30 57.08 13.2 8 9.49 reject
Rubber & plastic products –2339.36 51.61 13.28 9.49 reject
Non-metallic mineral –3408.05 136.03 13.28 9.49 reject
Basic & fabrica ted metal –10900.30 381.25 13.28 9.49 reject
Others –9871.85 32.06 13.28 9.49 reject
Neutral technical progress :
0:0

(df = 2)
Total sample –37582.35 0.99 9.21 5.99 accept
Food products & beverages –7551.48 14.65 9.21 5.99 reject
Textile & wearing apparel –4765.83 9.77 9.21 5.99 reject
Footwear –992.42 0.23 9.21 5.99 accept
Paper & products –2719.95 1.98 9.21 5.99 accept
Industrial chemicals –1595.48 3.44 9.21 5.99 accept
Rubber & plastic products –2216.81 6.49 9.21 5.99 reject at 5%
Non-metallic mineral –3340.88 1.68 9.21 5.99 accept
Basic & fabricated metal –10709.84 0.33 9.21 5.99 accept
Others –9712.29 1.93 9.21 5.99 accept
No technical inefficiency, H
 (df = 3)
Total sample –48321.28 21477.8 4 10.501 7 .045 reject
Food products & beverages –9464.15 3839.99 10.501 7.045 reject
Textile & wearing apparel –5977.24 2432.59 10.501 7.045 reject
Footwear –1277.32 569.79 10.501 7.045 reject
Paper & products –3658.84 1877.77 10.501 7.045 reject
Industrial chemicals –2113.51 1036.06 10.501 7.045 reject
Rubber & plastic products –3076.49 1725.86 10.501 7.045 reject
Non-metallic mineral –4358.00 2035.93 10.501 7.045 reject
N. K. MINH ET AL. 229
Continued
Basic & fabrica ted metal –13321.73 5223.78 10.501 7.045 reject
Others –12002.09 4579.61 10.501 7.045 reject
Half-normal distribution of technical inefficiency, 0:0H
(df = 1)
Total sampl e –37582.35 837.03 6.63 3.84 reject
Food products & beverages –7544.15 96.11 6.63 3.84 reject
Textile & wearing apparel –4760.95 169.35 6.63 3.84 reject
Footwear –992.42 32.43 6.63 3.84 reject
Paper & products –2719.95 91.22 6.63 3.84 reject
Industrial chemicals –1595.48 12.31 6.63 3.84 reject
Rubber & plastic products –2213.56 25.55 6.63 3.84 reject
Non-metallic mineral –3340.88 162.24 6.63 3.84 reject
Basic & fabrica ted metal –10709.84 191.64 6.63 3.84 reject
Others –9712.29 229.34 6.63 3.84 reject
Time invariant technical inefficiency, 0:0H
(df = 1)
Total samp le –37115.2 97.27 6.63 3.84 reject
Food products & beverages –7496.09 12.46 6.63 3.84 reject
Textile & wearing apparel –4676.28 32 6.63 3.84 reject
Footwear –976.21 33.96 6.63 3.84 reject
Paper & products –2674.30 32.97 6.63 3.84 reject
Industrial chemicals –1589.31 0.16 6.63 3.84 accept
Rubber & plastic products –2199.78 43.45 6.63 3.84 reject
Non-metallic mineral –3258.92 4.01 6.63 3.84 reject at 5%
Basic & fabricated metal –10614.02 21.32 6.63 3.84 reject
Others –9597.62 8.81 6.63 3.84 reject
The critical value for this test involving γ = 0 is obtained fr om Table 1 of Kodde and Palm (1986).
sis. Then, the existence of neutral technical progress in
the data set of these industries. In the case of food prod-
ucts & beverages, textile & wearing apparel and rubber
& plastic products, the hypothesis is rejected it implies
that the existence of non-neutral technical progress in the
data set of these industries.
4) Given the specification of stochastic frontier model,
there is a particular interest in testing the hypothesis of
the non-existence of sector-level inefficiency, expressed
by 0:0H



:0H
The first null hypothesis is str-
ongly rejected at the 1% significance level for all sam-
ples, suggesting that the average production function is
an inadequate representation of the aggregated models
for all cases and will underestimate the actual frontier
because of the manufacturing sector for all cases and will
underestimate the actual frontier because of the existence
of technical inefficiency effects.
5) The fifth null hypothesis, specifying that technical
inefficiency effects have half-normal distribution
0 against truncated normal distribution, is
rejected at the 1% significance level for the total sample
and all sub-samples.
6) The last null hypothesis, that technical inefficiency
is time-invariant
:0H
0
is rejected for total sam-
ple, food products and beverages, textile and wearing
apparel, footwear, paper & products, rubber and plastic
products, non-metallic mineral, basic & Fabricated metal
products and Other manufacturing industries at least the
5% significance level. The industrial chemicals are only
the case that cannot reject the hypothesis.
4.3. Estimation of Stochastic Production
Functions
Given the specifications of translog frontier with time-
varying inefficiency effects the results of statistical tests
of the estimated parameters, the preferred frontier models
are chosen and the estimates of their parameters are
given in Tables 3 and 4.
To estimate production frontier for the total sample
and aggregated samples, the maximum—likelihood es-
timates of the parameters in the translog stochastic fron-
tier production function, defined by Equations (4) and (5),
are employed in this study.
Moreover, since there may exist some uncontrollable
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL.
230
Table 3. Panel estimation of stochastic frontier production and technical inefficiency model.
Total sample Food Textiles Footwear Paper
Variable Coefficient Coefficient Coefficient Coefficient Coefficient
Const t
2.928***
(0.076) 2.2214***
(0.171) 3.6363***
(0.250) 3.272***
(0.477) 4.1904***
(0.256)
lnK
K
0.497***
(0.019) 0.659***
(0.042) 0.5172***
(0.059) 0.403***
(0.124) 0.3306***
(0.070)
lnL
L
0.555***
(0.022) 0.4891***
(0.056) 0.3559***
(0.059) 0.526***
(0.117) 0.4411***
(0.091)
T t
0.13***
(0.01) 0.0968***
(0.029) –0.017***
(0.038) 0.047
(0.062) 0.0816
(0.025)***
tlnK
L
K
0.0092**
(0.004) 0.0088**
(0.004)
tlnL tL
–0.017***
(0.005) 0.0055
(0.004)
lnKlnL
K
L
–0.01***
(0.004) 0.0099
(0.011) –0.0219**
(0.009) –0.086***
(0.024) 0.0011
(0.021)
lnK2
K
K
0.005***
(0.002) –0.0214**
(0.005) 0.0008
(0.005) 0.033**
(0.013) 0.0055
(0.008)
lnL2
L
L
0.005
(0.003) 0.0154
(0.009) 0.0364***
(0.007) 0.066***
(0.016) 0.0226
(0.017)
t2 tt
–0.017***
(0.001) –0.0198***
(0.004) –0.0133***
(0.004) –0.015*
(0.008) –0.0144***
(0.004)
2 0.71***
(0.014) 0.7608***
(0.034) 0.6756***
(0.037) 0.465***
(0.045) 0.4413***
(0.028)
0.676***
(0.006) 0.6524
(0.018)*** 0.6782
(0.012)*** 0.578
(0.042)*** 0.6434
(0.021)***
1.254
(0.032) *** 1.155***
(0.086) 1.3537***
(0.061) 1.003***
(0.14) 1.0657***
(0.067)
0.027***
(0.003) 0.0254***
(0.007) 0.0426***
(0.008) 0.103***
(0.018) 0.0493***
(0.008)
log-likelihood function –37111.57 –7489.87 –4660.92 –959.229 –2657.86
Source: Authors’ estimates from the data source; Note: 1) standard errors are given in the parenthesis; 2) */**/***Denotes statically significant at the 10, 5 and 1
per cent levels, respectively.
stochastic shocks, such as changes of government poli-
cies or other conditions affecting firms’ production effi-
ciency, a stochastic frontier production approach is ap-
plied. Concerning productivity, there are two indices to
indicate whether firms in Vietnamese manufacturing
industry have a high or low production efficiency: 2
represents total variance of output, containing a random
error term v

2
and a technical inefficiency term
2
u
. However large value of 2
does not necessary
mean a less efficient way of production since it includes
two types of production variation.
The estimates of
are positive (or at least zero) in
the cases, except for the non-metallic mineral sub-indus-
try.
Almost coefficients of variables in all equations are
statistically significant. A significant
along with a
positive and significant
implies the existence of tech-
nical inefficiency that declines over the years, except for
the Industry Non-metallic Mineral.
Table 5 presents the average technical efficiency (TE)
for Vietnamese manufacturing industries for time period
during 2003-2007. Estimates of TE vary considerably,
both across manufacturing industries, and cross time pe-
riods. The average TE is 0.309 for the total sample. The
industrial chemical and rubber and plastics industries
have the highest and second highest estimates, 0.417 and
3.91, respectively. and the textile & wearing apparel and
non-metal mineral industries have the lowest and second
lowest estimates, 0.267 and 0.290, respectively. The
other industries have estimates the range from 0.300 to
0.342.
The average TE for all industries improves throughout
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL. 231
Table 4. Panel estimation of stochastic frontier production and technical inefficiency model.
Chemical Rubber Non-metal Basic-metal Others
Variable coefficient Coefficient Coefficient Coefficient Coefficient
Const t
1.6381***
(0.396) 3.3089***
(0.338) 2.079***
(0.22) 3.2191***
(0.152) 3.2944***
(0.152)
lnK
K
0.6885***
(0.107) 0.5934***
(0.089) 0.352***
(0.058) 0.3717***
(0.039) 0.4251***
(0.040)
lnL
L
0.7403***
(0.123) 0.2795
(0.104)** 0.982***
(0.077) 0.6142***
(0.047) 0.4482***
(0.045)
t t
0.1212***
(0.037) 0.0796
(0.047)* 0.138***
(0.028) 0.1571***
(0.019) 0.1733***
(0.020)
tlnK
L
K
0.0111*
(0.006)
tlnL tL
0.0037
(0.008)
lnKlnL
K
L
–0.0783***
(0.024) 0.0174
(0.020) –0.114
(0.012) 0.0026***
(0.010) 0.0252**
(0.008)
lnK2
K
K
0.0087
(0.01) –0.0104
(0.009) 0.041***
(0.005) 0.0084*
(0.004) –0.0003
(0.004)
lnL2
L
L
0.0648***
(0.020) 0.0073
(0.015) 0.063***
(0.012) –0.0103
(0.008) –0.0125*
(0.007)
t2 tt
–0.0114*
(0.006) –0.0283
(0.005)*** –0.012**
(0.004) –0.0218***
(0.003) –0.0224***
(0.003)
2 0.8327***
(0.108) 0.6324***
(0.057) 0.654***
(0.049) 0.6342***
(0.023) 0.6758***
(0.026)
0.7665***
(0.031) 0.7142
(0.026) 0.72***
(0.012) 0.617***
(0.014) 0.6288***
(0.014)
0.8437***
(0.145) 0.8421***
(0.087) 1.372***
(0.06) 1.1383***
(0.063) 1.3038***
(0.053)
0 0.0682
(0.010) –0.004
(0.008) 0.028***
(0.006) 0.016**
(0.006)
log-likelihood function –1589.33 –2178.06 –3256.91 –10603.4 –959 3 .2
Source: Authors’ estimates from the data source; Note: 1) standard errors are given in the parenthesis; 2) */**/***Denotes statically significant at the 10, 5 and 1
per cent levels, respectively.
Table 5. The average technical efficiency (TE) for Vietnamese manufacturing industries.
Eff 2003 Eff 2004 Eff 2005 Eff 2006 Eff 2007 Average
Total sample 0.293 0. 3 0 1 0.309 0.318 0.326 0.309
Food products & beverages 0.319 0.327 0.334 0.342 0.35 0.334
Textile & wearing apparel 0.242 0.254 0.267 0.279 0.292 0.267
Footwear 0.27 0.3 0.332 0.365 0.398 0.333
Paper & products 0.311 0.326 0.342 0.358 0.374 0.342
Industrial chemicals 0.417 0.417 0.417 0.417 0.417 0.417
Rubber & plastic products 0.349 0.37 0.391 0.412 0.433 0.391
Non-metallic mineral 0.293 0.292 0.29 0.289 0.288 0.290
Basic & fabricated metal 0.321 0.33 0.339 0.347 0.356 0.339
Others 0.291 0.296 0.301 0.306 0.31 0.301
S
ource: Authors’ estimates from the data source.
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL.
232
the sample period, and this trend of steady improvement
is also observed in the food, textiles, footwear, paper,
rubber and plastics, basic-metal and other industries. The
average TE unchanging through the years in chemical
and non-metal industries.
Table 6 presents return to scale (RTS) for Vietnamese
manufacturing industries for time period during 2003-
2007. For the total sample, food products & beverages,
textile & wearing apparel, footwear, paper & products,
industrial chemicals, rubber & plastic products, non-
metallic mineral, basic & fabricated metal and other sub-
industries, the estimates of RTS are more than unity.
RTSs are remaining more than unity. For textile & wear-
ing apparel and rubber & plastic products, the estimates
of RTS are 0.976 and 0.984 in 2003, respectively but
continuously increases more than one during the sample
period.
Table 7 shows the means of estimated technical effi-
Table 6. The average RTS for Vietnamese manufac turing industries.
TRS 2003 RTS 2004 RTS 2005 RTS 2006 RTS 2007
Total sample 1.052 1.052 1.052 1.052 1.052
Food products & b e v erages 1.148 1.14 1.131 1.122 1.114
Textile & wearing apparel 0.976 0.993 1.008 1.023 1.033
Footwear 1.026 1.027 1.028 1.028 1.026
Paper & products 1.024 1.027 1.029 1.029 1.031
Industrial chemicals 1.131 1.127 1.125 1.123 1.116
Rubber & plastic products 0.984 1.001 1.016 1.031 1.045
Non-metallic mineral 1.15 1.148 1.148 1.146 1.146
Basic & fabricate d metal 1.065 1.066 1.067 1.067 1.069
Others 1.115 1.12 1.121 1.122 1.125
Source: Authors’ estimates from the data source.
Table 7. Mean technical efficiency in Vietnamese manufacturing firms, 2003-2007, by ownership category.
2003 2004 2005 2006 2007 Obs
Foreign 0.332 0.341 0.349 0.357 0.366 1325
Total sample Domestic 0.285 0.293 0.302 0.310 0.318 6732
Foreign 0.406 0.414 0.421 0.428 0.436 135
Food products & beverages Domestic 0.311 0.318 0.326 0.334 0.342 1401
Foreign 0.277 0.290 0.303 0.316 0.329 288
Textile & wearing apparel Domestic 0.228 0.240 0.252 0.265 0.278 726
Foreign 0.329 0.360 0.391 0.423 0.455 71
Footwear Domestic 0.243 0.274 0.306 0.339 0.372 158
Foreign 0.350 0.365 0.380 0.395 0.410 50
Paper & products Domestic 0.308 0.323 0.339 0.355 0.371 671
Foreign 0.535 0.535 0.535 0.535 0.535 82
Industrial chemicals Domestic 0.384 0.384 0.384 0.384 0.384 297
Foreign 0.359 0.379 0.400 0.420 0.441 111
Rubber & plastic products Domestic 0.347 0.367 0.388 0.409 0.430 425
Foreign 0.462 0.460 0.459 0.458 0.457 51
Non-metallic mineral Domestic 0.281 0.280 0.279 0.278 0.276 732
Foreign 0.354 0.362 0.371 0.380 0.389 481
Basic & fabricated metal Domestic 0.313 0.321 0.330 0.339 0.348 1810
Foreign 0.331 0.336 0.341 0.346 0.351
431
Others Domestic 0.280 0.285 0.290 0.295 0.300 1591
S
ource: Authors’ estimates from the data source.
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL. 233
ciency for the foreign owned firms, domestically owned
(including private sector firms and public sector firms for
different years during the period, 2003 to 2007).
It is evident from the comparison presented in Table 5
that the mean technical efficiency of foreign firms was
higher than that of domestically owned firms each year
of the period under study. For the five-year period, 2003
to 2007, on an average, technical efficiency of foreign
firms in total sample and sub-samples were higher tech-
nical efficiency than domestically owned firms. The av-
erage technical efficiency levels of foreign firms for in-
dustrial chemicals, non-metallic mineral, footwear over
period 2003-2007 are 0.535, 0.457, 0.455 about, 39, 66
and 22.3 percent higher than that for domestic firms, re-
spectively.
The estimates of the average annual rate of change in
efficiency for the manufacturing industries and some
sub-manufactu ring ind ustries are prese nted in Table 8.
We calculated these efficiency changes using Equation
(2) (Titst ). The rate of growth
in efficiency is an indicator of an industries’ perform-
ance.
echnical change
The estimate of the average rate of growth in effi-
ciency in Vietnamese manufacturing industries suggests
that the level efficiency has increased over the whole
period (except Non-metallic mineral industry). For ex-
ample the sub-industry, with average rate of growth in
efficiency about 8.2% (highest rate) is footwear, follow-
ing by rubber & plastic products (about 6.3%) and textile
& wearing apparel (about 5.4%).
The annual technical progress change estimates for the
manufacturing industry and submanufacturing industries
are presented in Table 9. The technical progress change
index between any two adjacent periods s and t were
calculated directly from the estimated parameters of the
translog stochastic frontier production function by taking
a partial derivative of output with respect to time t. Then,
we calculated technical change for each sub-industry,
and given period by using Equation (3).
Table 10 shows that average technical changes in
manufacturing industry and sub-manufacturing industries
are positive, with an average technical change about 5.2%,
TE TE
Table 8. Technical efficiency change in Vietnamese manufacturing firms, 2003-2007.
TEC 2003-2004 2004-2005 2005-2006 2006-2007 2003-2007
Total sample 0.039 0.04 0.037 0.036 0.030
Food products & b e v erages 0.034 0.03 0.032 0.031 0.025
Textile & wearing apparel 0.071 0.07 0.065 0.062 0.054
Footwear 0.111 0.11 0.099 0.09 0.082
Paper & products 0.065 0.06 0.059 0.056 0.048
Industrial chemicals 0 0 0 0 0.000
Rubber & plastic products 0.087 0.08 0.076 0.07 0.063
Non-metallic mineral –0.006 –0.01 –0.006 –0.006 –0.006
Basic & fabricate d metal 0.036 0.04 0.034 0.033 0.029
Others 0.022 0.02 0.022 0.021 0.017
Source: Authors’ estimates from the data source.
Table 9. Technical progress change in Vietnamese manufacturing firms, 2003-2007.
TPC 2003-2004 2004-2005 2005-2006 2006-2007 2003-2007
Total sample 0.079 0.05 0.011 –0.023 0.023
Food products & b e v erages 0.071 0.05 0.032 0.012 0.033
Textile & wearing apparel 0.041 0.02 –0.011 –0.038 0.002
Footwear 0.047 0.05 0.047 0.047 0.038
Paper & products 0.04 0.01 –0.016 –0.044 –0.002
Industrial chemicals 0.087 0. 0 6 0.041 0.019 0.041
Rubber & plastic products 0.097 0.04 –0.015 –0.071 0.010
Non-metallic mineral 0.102 0.08 0.054 0.03 0.053
Basic & fabricate d metal 0.091 0.05 0.004 –0.039 0.021
Others 0.106 0.06 0.016 –0.029 0.031
Source: Authors’ estimates from the data source.
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL.
234
Table 10. TFP change in Vietnamese manufacturing firms, 2003-2007.
TFP 2003-2004 2004-2005 2005-2006 2006-2007 2003-2007
Total sample 0.118 0.08 0.048 0.013 0.052
Food products & b e v erages 0.104 0.08 0.064 0.043 0.058
Textile & wearing apparel 0.112 0.08 0.054 0.025 0.054
Footwear 0.158 0.15 0.146 0.137 0.118
Paper & products 0.105 0.07 0.043 0.012 0.046
Industrial chemicals 0.087 0. 0 6 0.041 0.019 0.041
Rubber & plastic products 0.184 0.12 0.061 0 0.073
Non-metallic mineral 0.096 0.07 0.048 0.024 0.048
Basic & fabricate d metal 0.128 0.08 0.039 –0.006 0.048
Others 0.128 0.08 0.038 –0.007 0.048
Source: Authors’ estimates from the data source.
5.8%, 5.4%, 11.8%, 4.6%, 4.1%, 7.3%, 4.8%, 4.8% and
4.8% for total sample, food products & beverages, textile
& wearing apparel, footwear, paper & products, indus-
trial chemicals, rubber & plastic products, non-metallic
mineral, basic & fabricated metal and other sub-indus-
tries, respectively.
4.4. Total Factor Productivity Change
The total factor productivity (TFP) growth is simply the
sum of efficiency and technical change. These two
changes constitute the TFP change index. The decompo-
sition of TFP change into technical efficient change
(TEC) and technical progress change (TPC) makes it
possible to understand whether the manufacturing indus-
try and sub-industries have improved their productivity
levels simply through a more efficient use of existing
technology or through technical progress. Table 8 shows
the average annual TFP growth for manufacturing indus-
try and for each sub-industry.
As can be seen TFP growth rates of total sample, food
products & beverages, textile & wearing apparel, foot-
wear, industrial chemicals, rubber & plastic products,
basic & fabricated metal and other sub-industries, have
positive due to increase in both TEC and TPC during
2003-2007. While TFP growth rate of paper & products
has positive due to technical change and TFP growth rate
of non-metallic mineral has positive due to TPC.
5. Conclusions
We applied a stochastic frontier production model to
Vietnamese manufacturing industries, to decompose the
sources of total productivity (TFP) growth into technical
progress, changes in technical efficiency during 2003-
2007. In terms of efficiency estimations, the average an-
nual technical change in Vietnamese industries is posi-
tive and less than 1%, except non-metallic mineral
(–0.006). The most important estimate though is that
total factor productivity growth. This study estimates a
rate of productivity growth of 5.2%. The estimated re-
sults show that TFP grew fastest in the footwear sub-
industry, with annual average growth rate of 11.8%, fol-
lowed by the rubber & plastic products with a rate of
7.3%.
The estimated results of our study show that although
productivity growth was driven mainly by technical pro-
gress, changes in technical efficiency had a positive ef-
fect on productivity growth.
REFERENCES
[1] M. Nishimizu and J. M. Page, “Total Factor Productivity
Growth, Technological Progress and Technical Efficiency
Change: Dimensions of Productivity Change in Yugosla-
via, 1965-1978,” Economic Journal, Vol. 92, No. 368,
1982, pp. 920-936. doi:10.2307/2232675
[2] P. W. Bauer, “Decomposing TFP Growth in the Presence
of Cost Inefficiency, Nonconstant Returns to Scale, and
Technological Progress,” Journal of Productivity Analy-
sis, Vol. 1, No. 4, 1990, pp. 287-299.
doi:10.1007/BF00160047
[3] S. Kim and G. Han, “A Decomposition of Total Factor
Productivity Growth in Korean Manufacturing Industries:
A Stochastic Frontier Approach,” Journal of Productivity
Analysis, Vol. 16, No. 3, 2001, pp. 269-281.
doi:10.1023/A:1012566812232
[4] H. Liao, M. Holmes, T. W. Jones and D. Llewellyn,
“Productivity Growth of East Asia Economies’ Manufac-
turing: A Decomposition Analysis,” Journal of Develop-
ment Studies, Vol. 43, No. 4, 2007, pp. 649-674.
doi:10.1080/00220380701259723
[5] N. K. Minh and G. T. Long, “Factor Productivity and
Efficiency of the Vietnamese Economy in Transition,”
Asia-Pacific Development Journal, Vol. 15, No. 1, 2008,
pp. 93-117.
[6] N. K. Minh, N. T. Minh and G. T. Long, “A Decomposi-
Copyright © 2012 SciRes. OJS
N. K. MINH ET AL. 235
tion of Total Factor Productivity Growth in Vietnamese
Manufacturing Industries: A Stochastic Frontier Ap-
proach,” Proceedings of the DEA Symposium, Taiwan,
19-21 January 2010, pp. 164-168.
[7] G. E. Battese and T. J. Coelli, “Frontier Production Func-
tions, Technical Efficiency and Panel Data: With Appli-
cation to Paddy Farmers in India,” Journal of Productiv-
ity Analysis, Vol. 3, No. 1-2, 1992, pp. 153-169.
doi:10.1007/BF00158774
Copyright © 2012 SciRes. OJS