Journal of Environmental Protection, 2010, 1, 330-336
doi:10.4236/jep.2010.13039 Published Online September 2010 (
Copyright © 2010 SciRes. JEP
Green Inefficiency for Regions in China
Tsz-Yi Ke1*, Jin-Li Hu2, Wen-Ju Yang3
1Department of Economics, Aletheia University, Taipei, Taiwan, China; 2Institute of Business and Management, National Chiao
Tung University, Taipei, Taiwan, China; 3Department of Applied Economics, Yu Da University, Miaoli County, Taiwan, China.
Received June 9th, 2010; revised June 29th, 2010; accepted July 9th, 2010.
We used the directional output distance function to derive estimates of green inefficiency, shadow prices, and waste
costs of three wastes (waste water, waste gas, and solid waste) for thirty regions in China during the 1996-2003 periods.
There is an upward trend in green inefficiency in Chinese regions from 1996 to 2003. The green inefficiency score in
west area is the lowest but in central and east areas are higher. The costs of wastes have an upward trend in east and
central areas but downward trend in west area in the last two observation years.
Keywords: Green Inefficiency, Environment Waste, Directional Output Distance Function, Shadow Price, China
1. Introduction
In the end of 1980’s, China recognized Japan’s Industrial
development policy which supported Japanese small-
sized industries after WWII, and Japan had become the
2nd biggest economic position in the world. Therefore,
China introduced this policy to achieve its target of ex-
pediting domestic economy development.
The industries of mechanical, electronic, petrolic and
chemical have been recognized as the most important
industries in order to improve China’s economy. Never-
theless, these industries also cause the problems of re-
sources depletion and environment pollution. In the
meantime, these industries have been developed quickly,
and the conflict has become worst due to the lacking re-
striction against over resources depletion and environ-
ment pollution since 1980’s. Thus, China has suffered
the three biggest environment wastes which are byprod-
ucts accompany with the production of industries: waste
water, waste gas, and solid wastes (here after: three
Water using and management has become a popular
issue. The waste water is an importan t issue in China [1].
Cities in China discharging 10 b illio n tons of waste water
every year. Pesticides in drinking water have also been a
problem to the health of a community [2]. In 2005 the
chemical firm of Jilin exploded and 100 tons of benzene
flowed into Songhua River, then, had the water supply
system of Harbin shutdown [3].
The main source of industrial waste gas emission is
one of the main sources of air pollution. Most of the ex-
isting analyses of air pollution abatement focus on its
benefit evaluation [4,5], it possible impacts on economic
activities [6], strategies to achieve it [7], or discuss the
indices to measure the air quality [8]. Economically effi-
cient abatements of air, solid, and waste pollution still
receive relatively not much attention [9].
The investigation of industrial solid waste manage-
ment in several countries is getting more important re-
cently. For case studies of industrial solid waste and re-
cycling, Casares [10] investigated Asegra in Spain and
Donnelly [11] researched the United States and Germany.
Moreover, Hogland and Stenis [12] described a method
of organization for an industrial solid waste management
system in Sweden.
China confronts the three waste problems under the
policy of energy-saving. There is no literature taking
environment wastes into account to measure national
green inefficiency in previously. In this study we try to
find out how the environmental problem serious is and
provide our suggestion to improve this situation.
2. Methods
We will describe the methods of estimating the shadow
price, waste cost and evaluating the inefficient of each
province in this section.
Suppose that each decision making unit (DMU) uses N
inputs to produce M desirable and J undesirable outputs
and the output set of production technology can be de-
Green Inefficiency for Regions in China
Copyright © 2010 SciRes. JEP
fined as:
 
P, ,can producex
u: x
u (1)
The undesirable ou tput is the byproduct of the produc-
tion of the desirable output, we assume that desirable and
undesirable outputs are null-joint outputs if
P, and 0 then 0y,uxuy (2)
Equation (2) means that if a desirable output is pro-
duced in a positive amount then some undesirable out-
puts also be produced.
Färe and Primont [13] defined the weak disposability
of undesirable outputs as follows:
 
P, and 01 imply ,P
 y,uxyux (3)
Equation (3) describes that reduction of undesirable
outputs can reduce desirable outputs simultaneously while
maintaining the same level of inputs.
Färe and Grosskopf [14] defined the directional output
distance function as follow:
sup:, -P
 
x,y,u;g ,g
ygug x
Equation (5) searches for the largest feasible expan-
sion of desirable output vector y in the y
direction and
the largest feasible reduction of undesirable output vector
u in the gu direction. Färe and Grosskopf (2005) pro-
vide a relationship between the revenue function and
directional distance function. The revenue function is
defined as:
 
Rmax- Px,p,r p
ru :
,ux (5)
ppp is the desirable output price vec-
tor and
rrr is the undesirable output price
vector. Equation (5) is the largest feasible revenue that
can be obtained from input x and output price vectors p,
r. If the output set is a closed, nonempty convex set then
the directional output distance function can be obtained
from the revenue function as:
 
inf R--
x,y,u;g ,g
x,p,r p
ru p
We can compute the price of the j’th undesirable out-
put as:
 
mojo m
  
 (7)
After measuring the shadow price from the above
equations, we need alternative method, the directional
output distance function, to get the inefficiency value.
The linear programming problem for each observation k
as follow:
, ,...,
,,; max
1) 1
, 1,...,
kkm mym
 
2) 1-, 1,...,
kkj juj
zuug jJ
, 1,...,
kkn n
zxx nN
1, 0, 1,...,
zz kK
The β is the inefficiency value for observation firm. In
this study, we use this directional output distance func-
tion to derive the estimates of shadow price, measure the
inefficient values and take the shadow prices to compu te
the waste costs.
3. Results and Discussion
The major target of an economy is improving living
standard in economic development processing. The GDP
can be presented as living standard level, so we take
GDP as desirable output. In order to increase the GDP
that there have to cause some pollutions such as three
wastes. We want to increase the GDP but not much pol-
lution. These three wastes are unavoidable when the
economy increases the GDP. Therefore, we call three
wastes as undesirable outputs.
Data of the d esirable outpu t: GDP, be deflated to 1 996
values, in each region is collected respectively as stated
previously. Real capital stocks in 1996 prices are con-
structed based on Li’s method [15].1 The data of regional
labor employment are established from the China Statis-
tical Yearbook. The thirty regions are categorized into
three areas. The three areas are the east area (abbreviated
as ‘E’), the central area (abbreviated as ‘C’), and the west
area (abbreviated as ‘W’).2
From China Statistical Yearbook, we establish a data-
set for 30 regions in China (27 provinces and 3 munici-
1The capital stock data are not available in the China Statistical Year-
book. In this study, every regional capital stock in a specific year is
calculated by the authors according to this formula: capital stock in the
revious year + capital formation in the current year capital deprecia-
tion in the current year. All the nominal values are deflated in 1995
rices before summations and deductions. We find the initial capital
stock (capital stock data in 1995) from the research of Li (2003).
2According to the Grand Western Development Program, Inner Mon-
golia and Guangxi are included in west area.
Green Inefficiency for Regions in China
Copyright © 2010 SciRes. JEP
palities) during 1996 to 2003.3 There are one desirable
output, three undesirable outputs and two inputs in our
directional output distance function model. The values of
monetary output and input are in 1996 prices.
Descriptive statistics for the outputs and inputs are
provided in Table 1. From this table we know that de-
sirable and undesirable outputs satisfy the assumption of
null-joint outputs. All of the outputs are greater than zero
and hence the directional output distance function can be
applied to estimate the inefficiency value.
As Figure 1 illustrates, there is an upward trend in in-
efficiency of annu al aver age fro m 1996 to 20 03. The be st
average efficiency occurred in 1996, after which ineffi-
ciency trends upward. During the Ninth-Five Plan, the
inefficiency value went up in 1997 because of Asian Fi-
nancial Crisis. The State Council of the People’s Repub-
lic of China wanted to reduce the damage, they got an
idea for increasing the Interior-Need and issued bond of
100 billion RMB to improve the economic situation in
1998. The policy reforms of China took place in this pe-
riod that changed the inefficiency value across time.
The inefficient value decreased in 2003. We presume
that the people prefer the economic growth of China be-
cause of the BRIC thesis. It expected the developing
countries include Brazil, Russia, India, and China will
become the biggest and fastest growing emerging markets.
There is an upward trend in inefficiency in east and
west areas from 1996 to 2003. The inefficiency in central
area gets down from 2002. Half of the most seriously
pollution cities of the world are in the center area.4 In
average, the green efficiency in center area is the lowest.
Relative to center area, there is the most efficient in east
We normalized the data, because of convergence
problems, by dividing each output and each input by its
mean value before estimating Equation (14).
The parameter estimates for the quadratic form of the
directional distance function are provided in Table 2.
Using these parameters and Equation (11) can measure
the shadow prices of three wastes. The opportunity cost
can be estimated by shadow price.
Table 3 provides the estimates for the shadow prices
and the costs of wastes. The cost is product of shadow
price and waste quantity. The average shadow price of
waste gas is the highest and the average cost of water
waste has the highest level in sample periods. However,
the aver age shadow pr ice and av erage cos t of solid waste
are the lowest.
China should pay more attention to waste water which
has the highest cost but not the highest shadow price.
Table 1. Describing statistics for the outputs and inputs.
(Base year: 1996).
Variable Mean Standard
deviation Minimum Maximum
Desirable Output
Gross Domestic Product
(million RMB) 235784 183387 6476 780181
Undesirable Outputs
Volume of Industrial
Waste Water
(10,000 tons) 64761.54 51425.24 612.00247524.00
Volume of Industrial
Waste Gas
(10,000 tons) 4680.23 3311.35 10.00 16139.00
Volume of Industrial
Solid Wastes
(10,000 tons) 2707.54 2145.65 1.00 9252.00
Capital Stock
(million RMB) 1008847 838253 804543772421
(10,000 persons) 2094.84 1520.93 117.706307.50
Figure 1. Green inefficiency of annual average.
This implies that the waste water causing high environ-
mental damage but is relatively cheaper to deal with.
Some provinces have made several policies to abate the
waste water and these policies must be enforced persis-
tently, in order to achieve the long run effects.
Figure 2 to Figure 4 show the total costs of waste
water, waste gas and solid waste, respectively. The cost
of three kinds of waste in east is the highest but in west is
the lowest. From these figures we know that, the most
important environmental problem is waste water which
has the highest total cost. This is maybe the east area has
many downstream rivers flowing into the Pacific Ocean.
The east area has hence to pay more cost to deal with
waste water.
In order to confront this environmental problem, China
built a complete system about water resource manage-
ment and water pollution control and revise Water Law
of the People’s Republic of China in 2002. But it didn’t
3Chongqing became a municipality out of Sichuan in 1997 and in this
study its outputs and inputs are included in Sichuan.
4These cities are Jilin, Shanxi, Henan, and Hubei.
Green Inefficiency for Regions in China
Copyright © 2010 SciRes. JEP
Table 2. Parameter estimates.
Constant –0.039
0.45 0.448
0.273 –0.012 0.036
,input input
–0.451 –0.040 –0.04 –0.573
–0.057 0.154 –0.011 0.154 –0.24 0.035 –0.011 0.035–0.042
,..inputD O
0.101 0.114
,..inputU O
–0.16 0.249 0.012 0.134 –0.022 0.002
0.086 –0.051 -0.018
Note: D.O. is desirable output. U.O. is undesirable output.
Table 3. The estimates for the shadow prices and the costs
of wastes.
Mean Standard
deviation Minimum Maximum
Shadow price
Waste water 0.835 0.618 0.248 3.671
Waste gas 1.212 1.743 0.025 12.648
Solid waste 0.084 0.582 0.000 0.323
Cost of waste (Million RMB)
Waste water 717.38 1097.98 2.35 8064.89
Waste gas 86.01 150.73 0.00 925.58
Solid waste 2.52 3.59 0.00 21.38
Note: Because
, the estimate of shadow
price in solid waste term equals zero.
reduce the cost immediately for waste water in 2003. In
these figures we find that, the total cost of water waste is
the highest. The water problem became a hot issue in
every country in the world in this decade. It is costly to
deal with the water waste no matter in developing or de-
veloped country.
Figure 5 describes the total cost in three wastes in
each regional average. We let the province in east area in
the right, in west area in the left. The top-six waste cost
in regional averages are: Jiangsu (E), Sichuan (W), Guang-
Figure 2. The total cost of waste water.
Figure 3. Areas’ annual total cost of waste gas.
Figure 4. Areas’ annual total costs of solid waste.
dong (E), Shandong (E), Henan (C) and Zhejiang (E).
Most of east areas have higher waste cost. The lower
waste cost in regional averages is: Tibet (W), Qinghai
(W), Hainan (E), Ningxia (W), and Xinjiang (W). Most
of west areas have lower waste cost. The average shadow
price of three kind wastes in Jiangsu and Sichuan with
the highest level especial in waste gas. Therefore, there is
the seriously waste cost in these provinces. There is the
lowest quantity average of three kind wastes especial in
waste gas and solid waste, so the lowest waste cost in
Figure 6 presents the inefficiency in each regional av-
erage. The most efficient regions during the 1996-2003
periods are: Tibet (W), Tianjin (E), Zhejiang (E), Hebei
(E) and Shanghai (E). The most inefficient regions dur-
ing the observation periods as follow: Hubei (C), Henan
(C), Hunan (C), Guangdon (E) and Guangxi (W). We
find that, most of provinces with higher inefficiency
value almost are heavy industry cities.
The inefficiency in the three regions presents a sig-
nificance difference.5 The operating efficiency in east
area is superior to other regions obviously. Even east
5The Kruskal-Wallis test has significance at the 1% level.
Current Distortion Evaluation in Traction 4Q Constant Switching Frequency Converters
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Figure 5. Regional averages of total waste cost.
Figure 6. Regional averages of inefficiency.
area has higher waste quantity and cost. Development
level plays an important role in our analysis process. The
east area has the highest green efficient, because the in-
put and output using is quite well in production proce-
dure rather in other areas.
The inefficiency values of center area are higher then
other areas during this study period obviously. The re-
form policy seems helpful to east area because of the
lowest inefficiency value, but harmful to center area be-
cause it has constrained generation of three wastes to
increase inefficiency value.
4. Conclusions
Environmental protection is an important issues in recent.
We built an observation set for 30 regions in China dur-
ing 1996 to 2003. This set concluded one desirable out-
put, three undesirable outputs, and two inputs.
This study used the directional output distance function
to derive estimates of production inefficiency, shadow
prices, and associated pollution costs of three wastes in
Our results indicate that an upward trend in ineffi-
ciency from 1996 to 2003. The value of inefficiency in
Green Inefficiency for Regions in China
Copyright © 2010 SciRes. JEP
west area is the lowest but in central and east areas are
higher in related. The costs of three wastes have an up-
ward trend in east and central areas but downward trend
in west area in the last two observation years.
We suggest that the China should abate wastes imme-
diately to contract the cost of wastes to get better macro-
economic performance.
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Green Inefficiency for Regions in China
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Abbreviation in provinces.
Province Abbreviation Area
Beijing BJ E
Tianjin TJ E
Hebei HEB E
Shanxi SX C
Inner Mongolia IM W
Liaoning LN E
Jilin JL C
Heilongjiang HLJ C
Shanghai SH E
Jiangsu JS E
Zhejiang ZJ E
Anhui AH C
Fujian FJ E
Jiangxi JX C
Shandong SD E
Henan HEN C
Hubei HUB C
Hunan HUN C
Guangdong GD E
Guangxi GX
Hainan HAN E
Sichuan SC W
Guizhou GZ W
Yunnan YN W
Tibet TB W
Shaanxi SHAX W
Gansu GS W
Qinghai QH W
Ningxia NX W
Xinjiang XJ W