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Mathematical and Computer Modelling 58 (2013) 948–955
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The convergence test of transformation performance of resource cities in China considering undesirable output Feng Dong a,∗ , Ruyin Long a , Hong Chen a , Xiaohui Li b , Xiaoyan Liu a a
School of Management, China University of Mining and Technology, Xuzhou 221116, China
b
Yantai University, Yantai 246005, China
article
info
Article history: Received 20 December 2011 Received in revised form 11 October 2012 Accepted 15 October 2012 Keywords: Resource cities Transformation performance Convergence test
abstract The main challenge for sustainable development of resource cities is to work out a feasible strategy for transformation processes. This paper introduces a new approach for analysis of transformation performance. Using the environmental production technology and a Malmquist resource performance index (MRPI), we conduct σ , absolute β and conditional β convergence tests for the transformation performance of 21 resource cities in China. The results show that MRPI does not follow the same trend as economic strength of three Chinese regions. In addition, the transformation performance results exhibit a convergence trend for the 21 resource cities. Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction The presence of natural resources leads to the emergence of resource cities. A centralization tendency during industrialization is the primary reason for the development of such cities. Therefore, resource cities can be understood as cities characterized by mineral resource exploitation and processing-oriented manufacturing. There is evidence of a ‘‘curse of natural resources’’ whereby regions with great natural resource wealth tend to grow more slowly than resource-poor regions [1]. Since the mid-1980s, resource extraction industries in a large number of resource cities of China have entered mature and declining stages. This leads to the traditional dilemma of ‘‘mine dried up, city bad’’ and the serious problem of how to maintain sustainable development. Fortunately, since the 1990s, the Chinese government and social institutions have focused on the development of resource cities. Some concepts and models concerning transformation in resource cities are relevant here. Sun et al. probed the urban efficiency of 24 typical resource cities in China from 2000 to 2008 using a data envelopment analysis (DEA) model and a Malmquist productivity index [2]. Taking the south Indian city of Bangalore as example, Pani explored three phases of globalization for resource cities, i.e., the colonial phase, the garment phase and the information technology phase [3]. Yu et al. revealed principal factors controlling the degree of sustainable development of mineral resources in mining cities [4]. Halseth discussed three patterns of employment for resource cities and held the opinion that while most households in resource cities engage in educational and skills upgrading, there are potentially serious limitations to the future efficacy of some coping mechanisms [5]. Houghton studied the development of long-distance commuting patterns in Australia, and analyzed the pros and cons of a model and its impact on social and regional development [6]. Keana pointed out a number of conditions for the sustainable development of coal cities from a natural landscape and community evolution perspective [7]. Leadbeater and Goss analyzed the economic development of a single-industry resource region in Elliot Lake in Canada from the perspective of the residents and employment [8].
∗
Corresponding author. Tel.: +86 15862167293; fax: +86 516 83591280. E-mail address: [email protected] (F. Dong).
0895-7177/$ – see front matter Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2012.10.020
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DEA is popularly used to study the relative efficiency of homogeneous decision-making units since the method was first proposed in 1978 [9] and many scholars have extended and applied it [10–13]. In the environmental and energy fields, DEA models are widely applied. Kortelainen analyzed the dynamic environmental performance of EU-20 countries from 1990 to 2003 using a Malmquist index method based on the concept of eco-efficiency [14]. The CO2 emissions performance of OECD countries has been evaluated at a macro level using different DEA models [15–17]. Hu and Wang defined the concept of total factor energy efficiency (TFEE) as the ratio of the target energy input to the actual energy input in accordance with variable DEA [18]. Hu and Kao proposed a way of calculating the energy-saving rate on a TFEE basis, and then estimated the energy savings rate of APEC countries from 1991 to 2000 using the method [19]. Mukherjee estimated the energy efficiency of manufacturing industry and the six highest energy-intensive industries in the USA using DEA [20]. Oh and Heshmati constructed a continuous Malmquist–Luenberger productivity index to measure environmentally sensitive productivity considering variable technology and CO2 emissions [21]. Undesirable output can be addressed through several different DEA models. Tu calculated environment production efficiency to measure the coordination of environmental and industrial growth according to resource input, industrial production and environmental pollution data for 30 provinces in China [22]. Hu calculated the carbon environment technical efficiency of 30 provinces in China using a sustainability model [23]. Zhou et al. measured the carbon emissions efficiency of 18 countries whose carbon emissions are the highest in the world using a Malmquist productivity index approach based on DEA, and then analyzed the factors influencing this efficiency [24]. Wang et al. set up a Malmquist index using a DEA model containing desirable outputs to explore dynamic changes in carbon emission performance in China [25]. Hamid added environmental factors to a production effectiveness function to construct a dynamic model to analyze long-term economic growth for optimal policy design [26]. Ramanathan analyzed the energy and carbon emission efficiency of 17 countries in North Africa using a DEA method [27]. Lu et al. researched sustainable economic development in China under the constraints of energy and environmental security, adopting energy and carbon emission as inputs [28]. Du and Zou estimated carbon emission efficiency in various regions in China from 1995 to 2009, and analyzed regional differences and influencing factors [29]. Chen constructed an input–output database for 38 industries and estimated changes in industrial total factor productivity in China by means of a trans-log production function and green production accounting [30]. In these studies on environmental production efficiency, two approaches are used to deal with undesirable output: one is to set pollutants as undesirable output [22–25] and the other is to set pollutants as inputs [26–30]. Although it is simple to take bad outputs as inputs in a DEA model, this does not reflect the true production process. It is more reasonable to treat bad outputs as undesirable outputs through environmental production technology (EPT), which is just the approach used in this study. The convergence approach has been used to solve practical problems in many social fields. Baumol established a convergence model based on classical economic theory to examine regional economic convergence [31]. Assuming that per capita output has random and linear deterministic trends, Bernard and Durlarf gave a clear definition of convergence and common trends [32,33]. Barro and Islam tested the absolute and conditional convergence of regional economic development gaps [34,35]. Pan and Liu studied the innovation efficiency of industrial enterprises among various regions in China using β convergence [36]. Shi and Li tested the convergence of economic growth in eastern, central and western China using cointegration test methods [37]. Liu and Li investigated the total factor productivity of nationwide industrial enterprises using σ and β convergence [38]. Research on the transformation of resource cities has rarely focused on quantitative analyses and rational evaluation of the transformation process. Moreover, there is no consensus among previous studies on whether differences of the transformation of resource cities will persist. A noteworthy point is that resource cities tend to have more seriously polluted environment. In order to achieve the goals of a harmonious society, regional economic development and the stability of mining and society, resource cities should give priority to the environmental protection during their transformation. In the present study we used DEA and introduced EPT to build an evaluation system for the transformation performance of resource cities. In an empirical analysis of 21 resources cities, we explore differences in their transformation performance by classifying them into three distinct areas, and then apply convergence theory to examine the convergence of this performance. 2. Analysis method 2.1. Transformation performance 2.1.1. EPT (environmental production technology) In general, an economic system generates so-called good output (also called desirable output) such as GDP after certain production elements are invested (capital, labor, energy). To include environmental regulation in the productivity analysis system, a production possibility set containing both good and bad outputs is required. This approach is often referred to as EPT [24,25,39–41]. Assuming an economic system with M types of inputs, N types of good output, and O types of bad output, the production possibility set is defined as P (x) = {(y, c ) : input x} ,
x ∈ QM+ .
(1)
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A relatively common practice is to make full use of DEA to model the ideas of EPT. Suppose that in each period t (t = 1, . . . , T ) the input and output values of region j (j = 1, . . . , J ) are (xtj , ytj , cjt ). A production process under constant returns to scale can be described by the following linear programming model: P (x) = {(y, c )} : J
s.t.
λim xim ≤ xim ,
m = 1, . . . , M ;
i =1 J
λin yi ≥ yin ,
n = 1, . . . , N ;
λio cio = cio ,
o = 1, . . . , O
(2)
i=1 J i=1
where λi ≥ 0 (i = 1, . . . , J ) is the weight for each cross-sectional observation. Since the production technology is under constant returns to scale, the weight variable is non-negative. To express the null-jointness axiom of the output, two constraints are added to the linear programming model: J
cki > 0,
i = 1, . . . , O
(3)
cki > 0,
k = 1, . . . , J .
(4)
k=1 O i=1
Eq. (3) shows that undesirable output in one period is produced in at least one region. In addition, Eq. (4) illustrates that each region is expected to produce at least one type of undesirable output. 2.1.2. Malmquist performance index under environmental regulations The Malmquist productivity index, first proposed by Sten Malmquist in 1953, was used as a productivity index by Cavas et al. to define the Shephard distance function including input and output guidance [42]. The input factors for the transformation performance of resource cities include three indicators: capital stock (K ), human capital (L), and energy input (E; power consumption). Desirable outputs include value added in tertiary industry (T ) and industrial value added in non-resource-based industry (Y ). Undesirable output is the environmental pollution index (I). Following the ideas proposed by Tyteca [43] and Zhou et al. [24], the Malmquist productivity index is combined with EPT to yield a Malmquist resourcecity transformation performance index (MRPI) that considers environmental pollution. MRPI from period t to period t + 1 under environmental regulations is defined as follows:
MRPI0 (t , t + 1) =
Dt0 (K t , Lt , E t , T t , Y t , I t ) · Dt0+1 (K t , Lt , E t , T t , Y t , I t ) Dt0 K t +1 , Lt +1 , E t +1 , T t +1 , Y t +1 , I t +1 · Dt0+1 K t +1 , Lt +1 , E t +1 , T t +1 , Y t +1 , I t +1
,
(5)
where (K t , Lt , E t , T t , Y t , I t ) and (K t +1 , Lt +1 , E t +1 , T t +1 , Y t +1 , I t +1 ) denote the input and output variables and Dt0 and Dt0+1 are the undesirable output-oriented distance function in periods t and t + 1, respectively. MRPI can be obtained by calculating the four distance functions, referring to the technology for different periods. In the EPT framework, the four distance functions for the corresponding period for each region can be solved using the following linear programming problem, in which p and q denote period, p, q ∈ {t , t + 1}. p
D0 K q , Lq , E q , T q , Y q , I q
J
s.t.
= min δ
J
λi Kip ≤ Kiq ;
i=1 J
−1
λi Lpi ≤ Lqi ;
i=1
J
λi Eip ≤ Eiq ;
i=1
J i=1
λi Tip ≥ Tiq ;
(6)
J
λi Yip ≥ Yiq ;
i=1
λi Iip = δ Iiq ,
λ i ≥ 0, i = 1, . . . , J .
i =1
2.2. Convergence test According to technological innovation theory, before a new technology permeates into a brand new market, three stages occur: invention, innovation and diffusion. If a developing area is able to absorb and master technology coming from a developed area, the developing area can benefit from the diffusion effect of technical knowledge. Both regions tend to
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converge in terms of economic growth when the developing area achieves a competitive advantage over the developed area because technological innovation costs more than diffusion [44]. According to convergence theory, we tested whether the transformation performance of resource cities shows a convergence trend in various regions in China. There are three types of convergence test: σ , β , and time sequence convergence tests. Time sequence convergence requires more samples and the time span of this study was only from 2001 to 2007, so we adopted σ and β convergence tests. In our σ convergence test, σ is the standard deviation for the efficiency of the transformation performance. If σ gradually decreases over time, we can say that the transformation performance shows a convergence trend. The formula for σ convergence is
σ =
ln MRPIi − ln MRPI
2
/N ,
(7)
where ln MRPIi is the natural logarithm of the transformation performance for city i, ln MRPI denotes the mean, and N is the number of provinces in the test area. Using the approach of Barro and Sala-i-Martin [45], the convergence formula can be expressed as ln MRPIit − ln MRPIi0 T
= C + β ln MRPIi0 + ε,
(8)
where ln MRPIi0 and ln MRPIit are the natural logarithm of the transformation performance city i at the start and at time t. If β < 0, the transformation performance shows a convergence trend. The convergence condition shown in Eq. (8) is also called absolute β convergence. If other control variables are added, the sign and significance of β would change, which is called conditional β convergence. Conditional β convergence reflects the convergence state of the transformation performance for resource cities in various regions that differ in their influential factors. The formula for conditional β convergence is ln MRPIit − ln MRPIi0 T
= C + β ln MRPIi0 + AX + ε,
(9)
where X is a factor that has an impact on the transformation performance. 3. MRPI results 3.1. Samples and indicators 3.1.1. Samples Samples representing 50 resource cities were chosen from 118 cities defined by the State Department as resourcedependent cites by excluding county-level cities and adding the well-known cities of Anshan, Baotou, and Xuzhou. Data on key indicators are available from the sub-industry economic indicators for industrial enterprises derived from the Statistical Yearbook, but difficulties were encountered in the sampling process. Based on information collected through a variety of channels, 21 cities with data available in Statistical Yearbooks from 2000 to 2007 were finally selected. The cities in eastern China included Tangshan, Handan, Xingtai, Anshan, Xuzhou, Zaozhuang, Dongying and Yunfu. The cities in central China included Datong, Daqing, Yichun, Huainan, Ma’anshan, Huaibei, Tongling and Pingdingshan. The cities in western China included Baotou, Chifeng, Ordos, Panzhihua and Tongchuan. 3.1.2. Indicator selection and processing There are no reports on measurement of the transformation performance of resource cities. Our research objective is the transformation performance of resource cities, so the output indicators must reflect the relevant transition conditions. So far, few studies in this field have considered environmental factors. We chose value added in tertiary industry and value added in non-resource-based industry as desirable outputs reflecting transition conditions in resource cities. According to EPT, we define the environmental pollution index as an undesirable output. Besides, as mentioned by Hu and Wang [18], capital stock, human capital and energy inputs (total electricity consumption) are used as indicator inputs when measuring TFEE. Original data for the indicators are available from 2000 to 2007. Data for value added in tertiary industry were derived from the annual China City Statistical Yearbook. Data for value added in non-resource-based industry were measured in accordance with value added in subsectors available from the Statistical Yearbook for prefecture-level cities, determined as value added in above-scale industry minus that in resource-based industry. For capital stock, we developed data for 2000–2007 based on the approach proposed by Zhang et al. [46]. For human capital, we used data from the China City Statistical Yearbook and estimated the number of employees in non-resource-based industries by adding employees engaged in private-owned firms to those in second and tertiary industries. Energy input was represented by the total electricity according to the China City Statistical Yearbook. Three indicators, value added in tertiary industry, value added in non-resource-based industry and capital stock, were adjusted to 2000 prices according to a GDP deflator.
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We used an entropy method to convert six industrial waste streams for each city for 2000–2007 into a unified pollution index. The entropy was calculated as follows: (i) Indicator standardization. Let xij be the value for the ith sample (i = 1, . . . , m) in year j (j = 1, . . . , n) as pollution indicators. The standardization formula is yij = xij
m
xij
(10)
i =1
where yij is the standardized indicator and the summation is for j pollution indicators from year 1 to year m. (ii) Calculation of the jth pollution index:
fj = −
1
m
ln m
yij ln yij .
(11)
i=1
(iii) Calculation of the coefficient of variation for the jth pollution index: g j = 1 − fj .
(12)
(iv) Calculation of the weight for the jth pollution indicator:
wj = g j
n
gj .
(13)
j=1
(v) Calculation of the environment pollution index or year i: Li =
n
yij wj .
(14)
j =1
3.2. MRPI results We calculated the four distance functions in Eq. (6) for the 21 cities, which are 84 solutions in total. From Eq. (5), we obtained the transformation performance index (MRPI). Fig. 1 shows changes in the transformation performance for cities in eastern, central and western China.
Fig. 1. Transformation performance of resource cities by region.
The results reveal differences in transformation performance among the regions. From 2001 to 2002, MRPI was the highest in eastern cities and lowest in central cities. Central cities overtook western cities in 2003 and were ranked second, and overtook eastern cities in 2004 and were ranked first. From 2005 to 2006, the MRPI ranking was consistent with that for the economic strength of the three regions, and as to the economic strength, Eastern China ranked number one, followed by Central China, and Western China in turn in China. In 2007, the MRPI rank was the same as in 2001. Thus, the MRPI ranking among the three regions is not consistent with the economic rank. A reasonable explanation for this is that regional government funding is just one of the elements of successful transformation of resource cities, but is not the decisive factor. In fact, the recent industrial shift from eastern China to central and western China has promoted the successful transformation of resource cities in the latter two regions. Comparison among the three regions also shows that MRPI at the beginning and end of a certain period varies greatly. In the next section, we investigate whether cities with lower MRPI at the start show a higher growth rate than other cities with higher MRPI, namely, whether MRPI shows a convergence trend.
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4. Convergence results for the transformation performance 4.1. σ convergence Fig. 2 shows changes in the standard deviation for ln MRPI for the 21 resource cities over time. The standard deviation for ln MRPI shows an upward trend before 2004 and a downward trend after 2004.
Fig. 2. Results for σ convergence.
4.2. Absolute β convergence The absolute β convergence for the transformation performance of the 21 resource cities is ln MRPIit − ln MRPIi0
= 0.027139 − 0.186415 (0.043710) ln MRPIi0 + ε T Adjusted R2 = 0.662204, F = 18.18880, DW = 2.112671,
(15)
where the number in parentheses is the standard deviation for the coefficient. The regression result indicates that the transformation performance of the 21 cities significantly converges. Thus, the transformation performance of cities with low MRPI approaches that of cities with high MRPI over time, and differences in transformation performance decrease owing to favorable policies promoted by governments in China.
β = − 1 − e−λT /T .
(16)
Using Eq. (16), we can measure the speed of convergence or divergence of the transformation performance. In this case the speed of convergence is 0.00845. 4.3. β conditional convergence The above analysis revealed that the transformation performance of resource cities showed significant β convergence, but the σ convergence trend was not obvious. We carried out a conditional β convergence test to determine whether ln MRPI exhibits significant convergence if some control variables are included. The transformation of resource cities was affected by many factors. According to Wu, the competitiveness of resource cities depends on economic development, social transformation, and environmental transformation [47]. Long and Wang held that the macro-environment, regional economic conditions and other factors influence industrial restructuring of resource cities [48]. Ju suggested that industrial structure and resource consumption are important factors that influence the transformation of resource cities [49]. On the basis of existing research and data availability, we studied four factors that influence the transformation performance of resource cities: economic development, industrial structure, ownership structure, and degree of openness. Economic development (ED) is expressed as GDP per capita; industrial structure (IS) is expressed as the sum of value added in tertiary industry and value added in the non-resource-based industry divided by GDP; ownership structure (OS) is expressed as the ratio of gross industrial output of the state-owned economy to gross industrial output; and degree of openness (OW) is expressed as foreign trade dependence. To include as many samples as possible, the time interval T was set to 1. The formula for conditional β convergence is ln MRPIit +1 − ln MRPIit = C + β ln MRPIit + A1 ED + A2 IS + A3 OS + A4 OW + ε.
(17)
Because conditional β convergence tests are used for panel data regression, we first applied an F test to select between hybrid and fixed effect models. The result showed that a fixed effect model was appropriate. As control variables were
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considered in the modeling process, a fixed effect model should be chosen instead of a random effect model. The regression result obtained was as follows: ln MRPIit +1 − ln MRPIit = Cr + Ct + 0.669339 − 1.240378 (0.098041) ln MRPIit + 2.24 × 10−5
× 1.11 × 10−5 EDit − 0.023564 (0.012454) ISit + 0.003714 (0.006160) OSit + 0.007884 (0.058370) OWit + ε Adjusted R2 = 0.577291,
F = 6.690381,
DW = 2.352654.
(18)
The results indicated that there was significant negative correlation between transformation performance and growth rate for the 21 resource cities when economic development, industrial structure, ownership structure and degree of openness were taken into account. In other words, the α and β test of MRPI for the 21 cities revealed a conditional convergence. The positive correlation between economic development and MRPI implied that industrial structure has a cumulative effect on MRPI. In addition, ownership structure and the degree of openness had significant positive effects on MRPI convergence. Furthermore, there was a significant negative correlation between MRPI and industrial structure for 21 resource cities, which reinforced the fact that the industrial structure played a reverse role in MRPI convergence. 5. Conclusions Transformation of resource cities has become an important regional strategic issue for sustainable growth, social stability, and harmonious development. Environmental protection during the transformation of resource cities cannot be ignored. We introduced EPT to set up a Malmquist performance index for the transformation of resource cities under environmental regulation. We performed σ , absolute β and conditional β convergence tests. The MRPI results reveal great differences in transformation performance in different regions and the MRPI ranking among the three regions is not consistent with the ranking of their economic strength. Furthermore, test results reveal that the σ convergence trend is not obvious, the β convergence trend is significant, and the β conditional convergence is remarkable when some control variables are added. The overall conclusion is that the transformation performance for 21 resource cities shows a convergence trend. In other words, difference in transformation performance among these cities is not apparent. How to achieve economic growth during transformation remains a major issue for resource cities. Development and implementation of transformation strategies should be made after proper evaluation of the conditions for each city. Since resource cities are more environmentally polluted, environmental protection issues should be strongly highlighted during their transformation. However, there is little quantitative research in this field, especially with regard to environmental issues. This paper extends the Malmquist productivity index to a transformation performance index for resource cities using EPT. Using MRPI results for 21 resource cities, we carried out convergence tests. The transformation performance of resource cities can be accurately evaluated using this approach and their individual strengths and weaknesses can be clearly identified from convergence tests. The results provide a theoretical basis for the development of more targeted transition policies that consider environmental protection for resource cities. 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Mathematical and Computer Modelling journal homepage: www.elsevier.com/locate/mcm
The convergence test of transformation performance of resource cities in China considering undesirable output Feng Dong a,∗ , Ruyin Long a , Hong Chen a , Xiaohui Li b , Xiaoyan Liu a a
School of Management, China University of Mining and Technology, Xuzhou 221116, China
b
Yantai University, Yantai 246005, China
article
info
Article history: Received 20 December 2011 Received in revised form 11 October 2012 Accepted 15 October 2012 Keywords: Resource cities Transformation performance Convergence test
abstract The main challenge for sustainable development of resource cities is to work out a feasible strategy for transformation processes. This paper introduces a new approach for analysis of transformation performance. Using the environmental production technology and a Malmquist resource performance index (MRPI), we conduct σ , absolute β and conditional β convergence tests for the transformation performance of 21 resource cities in China. The results show that MRPI does not follow the same trend as economic strength of three Chinese regions. In addition, the transformation performance results exhibit a convergence trend for the 21 resource cities. Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction The presence of natural resources leads to the emergence of resource cities. A centralization tendency during industrialization is the primary reason for the development of such cities. Therefore, resource cities can be understood as cities characterized by mineral resource exploitation and processing-oriented manufacturing. There is evidence of a ‘‘curse of natural resources’’ whereby regions with great natural resource wealth tend to grow more slowly than resource-poor regions [1]. Since the mid-1980s, resource extraction industries in a large number of resource cities of China have entered mature and declining stages. This leads to the traditional dilemma of ‘‘mine dried up, city bad’’ and the serious problem of how to maintain sustainable development. Fortunately, since the 1990s, the Chinese government and social institutions have focused on the development of resource cities. Some concepts and models concerning transformation in resource cities are relevant here. Sun et al. probed the urban efficiency of 24 typical resource cities in China from 2000 to 2008 using a data envelopment analysis (DEA) model and a Malmquist productivity index [2]. Taking the south Indian city of Bangalore as example, Pani explored three phases of globalization for resource cities, i.e., the colonial phase, the garment phase and the information technology phase [3]. Yu et al. revealed principal factors controlling the degree of sustainable development of mineral resources in mining cities [4]. Halseth discussed three patterns of employment for resource cities and held the opinion that while most households in resource cities engage in educational and skills upgrading, there are potentially serious limitations to the future efficacy of some coping mechanisms [5]. Houghton studied the development of long-distance commuting patterns in Australia, and analyzed the pros and cons of a model and its impact on social and regional development [6]. Keana pointed out a number of conditions for the sustainable development of coal cities from a natural landscape and community evolution perspective [7]. Leadbeater and Goss analyzed the economic development of a single-industry resource region in Elliot Lake in Canada from the perspective of the residents and employment [8].
∗
Corresponding author. Tel.: +86 15862167293; fax: +86 516 83591280. E-mail address: [email protected] (F. Dong).
0895-7177/$ – see front matter Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2012.10.020
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DEA is popularly used to study the relative efficiency of homogeneous decision-making units since the method was first proposed in 1978 [9] and many scholars have extended and applied it [10–13]. In the environmental and energy fields, DEA models are widely applied. Kortelainen analyzed the dynamic environmental performance of EU-20 countries from 1990 to 2003 using a Malmquist index method based on the concept of eco-efficiency [14]. The CO2 emissions performance of OECD countries has been evaluated at a macro level using different DEA models [15–17]. Hu and Wang defined the concept of total factor energy efficiency (TFEE) as the ratio of the target energy input to the actual energy input in accordance with variable DEA [18]. Hu and Kao proposed a way of calculating the energy-saving rate on a TFEE basis, and then estimated the energy savings rate of APEC countries from 1991 to 2000 using the method [19]. Mukherjee estimated the energy efficiency of manufacturing industry and the six highest energy-intensive industries in the USA using DEA [20]. Oh and Heshmati constructed a continuous Malmquist–Luenberger productivity index to measure environmentally sensitive productivity considering variable technology and CO2 emissions [21]. Undesirable output can be addressed through several different DEA models. Tu calculated environment production efficiency to measure the coordination of environmental and industrial growth according to resource input, industrial production and environmental pollution data for 30 provinces in China [22]. Hu calculated the carbon environment technical efficiency of 30 provinces in China using a sustainability model [23]. Zhou et al. measured the carbon emissions efficiency of 18 countries whose carbon emissions are the highest in the world using a Malmquist productivity index approach based on DEA, and then analyzed the factors influencing this efficiency [24]. Wang et al. set up a Malmquist index using a DEA model containing desirable outputs to explore dynamic changes in carbon emission performance in China [25]. Hamid added environmental factors to a production effectiveness function to construct a dynamic model to analyze long-term economic growth for optimal policy design [26]. Ramanathan analyzed the energy and carbon emission efficiency of 17 countries in North Africa using a DEA method [27]. Lu et al. researched sustainable economic development in China under the constraints of energy and environmental security, adopting energy and carbon emission as inputs [28]. Du and Zou estimated carbon emission efficiency in various regions in China from 1995 to 2009, and analyzed regional differences and influencing factors [29]. Chen constructed an input–output database for 38 industries and estimated changes in industrial total factor productivity in China by means of a trans-log production function and green production accounting [30]. In these studies on environmental production efficiency, two approaches are used to deal with undesirable output: one is to set pollutants as undesirable output [22–25] and the other is to set pollutants as inputs [26–30]. Although it is simple to take bad outputs as inputs in a DEA model, this does not reflect the true production process. It is more reasonable to treat bad outputs as undesirable outputs through environmental production technology (EPT), which is just the approach used in this study. The convergence approach has been used to solve practical problems in many social fields. Baumol established a convergence model based on classical economic theory to examine regional economic convergence [31]. Assuming that per capita output has random and linear deterministic trends, Bernard and Durlarf gave a clear definition of convergence and common trends [32,33]. Barro and Islam tested the absolute and conditional convergence of regional economic development gaps [34,35]. Pan and Liu studied the innovation efficiency of industrial enterprises among various regions in China using β convergence [36]. Shi and Li tested the convergence of economic growth in eastern, central and western China using cointegration test methods [37]. Liu and Li investigated the total factor productivity of nationwide industrial enterprises using σ and β convergence [38]. Research on the transformation of resource cities has rarely focused on quantitative analyses and rational evaluation of the transformation process. Moreover, there is no consensus among previous studies on whether differences of the transformation of resource cities will persist. A noteworthy point is that resource cities tend to have more seriously polluted environment. In order to achieve the goals of a harmonious society, regional economic development and the stability of mining and society, resource cities should give priority to the environmental protection during their transformation. In the present study we used DEA and introduced EPT to build an evaluation system for the transformation performance of resource cities. In an empirical analysis of 21 resources cities, we explore differences in their transformation performance by classifying them into three distinct areas, and then apply convergence theory to examine the convergence of this performance. 2. Analysis method 2.1. Transformation performance 2.1.1. EPT (environmental production technology) In general, an economic system generates so-called good output (also called desirable output) such as GDP after certain production elements are invested (capital, labor, energy). To include environmental regulation in the productivity analysis system, a production possibility set containing both good and bad outputs is required. This approach is often referred to as EPT [24,25,39–41]. Assuming an economic system with M types of inputs, N types of good output, and O types of bad output, the production possibility set is defined as P (x) = {(y, c ) : input x} ,
x ∈ QM+ .
(1)
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A relatively common practice is to make full use of DEA to model the ideas of EPT. Suppose that in each period t (t = 1, . . . , T ) the input and output values of region j (j = 1, . . . , J ) are (xtj , ytj , cjt ). A production process under constant returns to scale can be described by the following linear programming model: P (x) = {(y, c )} : J
s.t.
λim xim ≤ xim ,
m = 1, . . . , M ;
i =1 J
λin yi ≥ yin ,
n = 1, . . . , N ;
λio cio = cio ,
o = 1, . . . , O
(2)
i=1 J i=1
where λi ≥ 0 (i = 1, . . . , J ) is the weight for each cross-sectional observation. Since the production technology is under constant returns to scale, the weight variable is non-negative. To express the null-jointness axiom of the output, two constraints are added to the linear programming model: J
cki > 0,
i = 1, . . . , O
(3)
cki > 0,
k = 1, . . . , J .
(4)
k=1 O i=1
Eq. (3) shows that undesirable output in one period is produced in at least one region. In addition, Eq. (4) illustrates that each region is expected to produce at least one type of undesirable output. 2.1.2. Malmquist performance index under environmental regulations The Malmquist productivity index, first proposed by Sten Malmquist in 1953, was used as a productivity index by Cavas et al. to define the Shephard distance function including input and output guidance [42]. The input factors for the transformation performance of resource cities include three indicators: capital stock (K ), human capital (L), and energy input (E; power consumption). Desirable outputs include value added in tertiary industry (T ) and industrial value added in non-resource-based industry (Y ). Undesirable output is the environmental pollution index (I). Following the ideas proposed by Tyteca [43] and Zhou et al. [24], the Malmquist productivity index is combined with EPT to yield a Malmquist resourcecity transformation performance index (MRPI) that considers environmental pollution. MRPI from period t to period t + 1 under environmental regulations is defined as follows:
MRPI0 (t , t + 1) =
Dt0 (K t , Lt , E t , T t , Y t , I t ) · Dt0+1 (K t , Lt , E t , T t , Y t , I t ) Dt0 K t +1 , Lt +1 , E t +1 , T t +1 , Y t +1 , I t +1 · Dt0+1 K t +1 , Lt +1 , E t +1 , T t +1 , Y t +1 , I t +1
,
(5)
where (K t , Lt , E t , T t , Y t , I t ) and (K t +1 , Lt +1 , E t +1 , T t +1 , Y t +1 , I t +1 ) denote the input and output variables and Dt0 and Dt0+1 are the undesirable output-oriented distance function in periods t and t + 1, respectively. MRPI can be obtained by calculating the four distance functions, referring to the technology for different periods. In the EPT framework, the four distance functions for the corresponding period for each region can be solved using the following linear programming problem, in which p and q denote period, p, q ∈ {t , t + 1}. p
D0 K q , Lq , E q , T q , Y q , I q
J
s.t.
= min δ
J
λi Kip ≤ Kiq ;
i=1 J
−1
λi Lpi ≤ Lqi ;
i=1
J
λi Eip ≤ Eiq ;
i=1
J i=1
λi Tip ≥ Tiq ;
(6)
J
λi Yip ≥ Yiq ;
i=1
λi Iip = δ Iiq ,
λ i ≥ 0, i = 1, . . . , J .
i =1
2.2. Convergence test According to technological innovation theory, before a new technology permeates into a brand new market, three stages occur: invention, innovation and diffusion. If a developing area is able to absorb and master technology coming from a developed area, the developing area can benefit from the diffusion effect of technical knowledge. Both regions tend to
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converge in terms of economic growth when the developing area achieves a competitive advantage over the developed area because technological innovation costs more than diffusion [44]. According to convergence theory, we tested whether the transformation performance of resource cities shows a convergence trend in various regions in China. There are three types of convergence test: σ , β , and time sequence convergence tests. Time sequence convergence requires more samples and the time span of this study was only from 2001 to 2007, so we adopted σ and β convergence tests. In our σ convergence test, σ is the standard deviation for the efficiency of the transformation performance. If σ gradually decreases over time, we can say that the transformation performance shows a convergence trend. The formula for σ convergence is
σ =
ln MRPIi − ln MRPI
2
/N ,
(7)
where ln MRPIi is the natural logarithm of the transformation performance for city i, ln MRPI denotes the mean, and N is the number of provinces in the test area. Using the approach of Barro and Sala-i-Martin [45], the convergence formula can be expressed as ln MRPIit − ln MRPIi0 T
= C + β ln MRPIi0 + ε,
(8)
where ln MRPIi0 and ln MRPIit are the natural logarithm of the transformation performance city i at the start and at time t. If β < 0, the transformation performance shows a convergence trend. The convergence condition shown in Eq. (8) is also called absolute β convergence. If other control variables are added, the sign and significance of β would change, which is called conditional β convergence. Conditional β convergence reflects the convergence state of the transformation performance for resource cities in various regions that differ in their influential factors. The formula for conditional β convergence is ln MRPIit − ln MRPIi0 T
= C + β ln MRPIi0 + AX + ε,
(9)
where X is a factor that has an impact on the transformation performance. 3. MRPI results 3.1. Samples and indicators 3.1.1. Samples Samples representing 50 resource cities were chosen from 118 cities defined by the State Department as resourcedependent cites by excluding county-level cities and adding the well-known cities of Anshan, Baotou, and Xuzhou. Data on key indicators are available from the sub-industry economic indicators for industrial enterprises derived from the Statistical Yearbook, but difficulties were encountered in the sampling process. Based on information collected through a variety of channels, 21 cities with data available in Statistical Yearbooks from 2000 to 2007 were finally selected. The cities in eastern China included Tangshan, Handan, Xingtai, Anshan, Xuzhou, Zaozhuang, Dongying and Yunfu. The cities in central China included Datong, Daqing, Yichun, Huainan, Ma’anshan, Huaibei, Tongling and Pingdingshan. The cities in western China included Baotou, Chifeng, Ordos, Panzhihua and Tongchuan. 3.1.2. Indicator selection and processing There are no reports on measurement of the transformation performance of resource cities. Our research objective is the transformation performance of resource cities, so the output indicators must reflect the relevant transition conditions. So far, few studies in this field have considered environmental factors. We chose value added in tertiary industry and value added in non-resource-based industry as desirable outputs reflecting transition conditions in resource cities. According to EPT, we define the environmental pollution index as an undesirable output. Besides, as mentioned by Hu and Wang [18], capital stock, human capital and energy inputs (total electricity consumption) are used as indicator inputs when measuring TFEE. Original data for the indicators are available from 2000 to 2007. Data for value added in tertiary industry were derived from the annual China City Statistical Yearbook. Data for value added in non-resource-based industry were measured in accordance with value added in subsectors available from the Statistical Yearbook for prefecture-level cities, determined as value added in above-scale industry minus that in resource-based industry. For capital stock, we developed data for 2000–2007 based on the approach proposed by Zhang et al. [46]. For human capital, we used data from the China City Statistical Yearbook and estimated the number of employees in non-resource-based industries by adding employees engaged in private-owned firms to those in second and tertiary industries. Energy input was represented by the total electricity according to the China City Statistical Yearbook. Three indicators, value added in tertiary industry, value added in non-resource-based industry and capital stock, were adjusted to 2000 prices according to a GDP deflator.
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We used an entropy method to convert six industrial waste streams for each city for 2000–2007 into a unified pollution index. The entropy was calculated as follows: (i) Indicator standardization. Let xij be the value for the ith sample (i = 1, . . . , m) in year j (j = 1, . . . , n) as pollution indicators. The standardization formula is yij = xij
m
xij
(10)
i =1
where yij is the standardized indicator and the summation is for j pollution indicators from year 1 to year m. (ii) Calculation of the jth pollution index:
fj = −
1
m
ln m
yij ln yij .
(11)
i=1
(iii) Calculation of the coefficient of variation for the jth pollution index: g j = 1 − fj .
(12)
(iv) Calculation of the weight for the jth pollution indicator:
wj = g j
n
gj .
(13)
j=1
(v) Calculation of the environment pollution index or year i: Li =
n
yij wj .
(14)
j =1
3.2. MRPI results We calculated the four distance functions in Eq. (6) for the 21 cities, which are 84 solutions in total. From Eq. (5), we obtained the transformation performance index (MRPI). Fig. 1 shows changes in the transformation performance for cities in eastern, central and western China.
Fig. 1. Transformation performance of resource cities by region.
The results reveal differences in transformation performance among the regions. From 2001 to 2002, MRPI was the highest in eastern cities and lowest in central cities. Central cities overtook western cities in 2003 and were ranked second, and overtook eastern cities in 2004 and were ranked first. From 2005 to 2006, the MRPI ranking was consistent with that for the economic strength of the three regions, and as to the economic strength, Eastern China ranked number one, followed by Central China, and Western China in turn in China. In 2007, the MRPI rank was the same as in 2001. Thus, the MRPI ranking among the three regions is not consistent with the economic rank. A reasonable explanation for this is that regional government funding is just one of the elements of successful transformation of resource cities, but is not the decisive factor. In fact, the recent industrial shift from eastern China to central and western China has promoted the successful transformation of resource cities in the latter two regions. Comparison among the three regions also shows that MRPI at the beginning and end of a certain period varies greatly. In the next section, we investigate whether cities with lower MRPI at the start show a higher growth rate than other cities with higher MRPI, namely, whether MRPI shows a convergence trend.
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4. Convergence results for the transformation performance 4.1. σ convergence Fig. 2 shows changes in the standard deviation for ln MRPI for the 21 resource cities over time. The standard deviation for ln MRPI shows an upward trend before 2004 and a downward trend after 2004.
Fig. 2. Results for σ convergence.
4.2. Absolute β convergence The absolute β convergence for the transformation performance of the 21 resource cities is ln MRPIit − ln MRPIi0
= 0.027139 − 0.186415 (0.043710) ln MRPIi0 + ε T Adjusted R2 = 0.662204, F = 18.18880, DW = 2.112671,
(15)
where the number in parentheses is the standard deviation for the coefficient. The regression result indicates that the transformation performance of the 21 cities significantly converges. Thus, the transformation performance of cities with low MRPI approaches that of cities with high MRPI over time, and differences in transformation performance decrease owing to favorable policies promoted by governments in China.
β = − 1 − e−λT /T .
(16)
Using Eq. (16), we can measure the speed of convergence or divergence of the transformation performance. In this case the speed of convergence is 0.00845. 4.3. β conditional convergence The above analysis revealed that the transformation performance of resource cities showed significant β convergence, but the σ convergence trend was not obvious. We carried out a conditional β convergence test to determine whether ln MRPI exhibits significant convergence if some control variables are included. The transformation of resource cities was affected by many factors. According to Wu, the competitiveness of resource cities depends on economic development, social transformation, and environmental transformation [47]. Long and Wang held that the macro-environment, regional economic conditions and other factors influence industrial restructuring of resource cities [48]. Ju suggested that industrial structure and resource consumption are important factors that influence the transformation of resource cities [49]. On the basis of existing research and data availability, we studied four factors that influence the transformation performance of resource cities: economic development, industrial structure, ownership structure, and degree of openness. Economic development (ED) is expressed as GDP per capita; industrial structure (IS) is expressed as the sum of value added in tertiary industry and value added in the non-resource-based industry divided by GDP; ownership structure (OS) is expressed as the ratio of gross industrial output of the state-owned economy to gross industrial output; and degree of openness (OW) is expressed as foreign trade dependence. To include as many samples as possible, the time interval T was set to 1. The formula for conditional β convergence is ln MRPIit +1 − ln MRPIit = C + β ln MRPIit + A1 ED + A2 IS + A3 OS + A4 OW + ε.
(17)
Because conditional β convergence tests are used for panel data regression, we first applied an F test to select between hybrid and fixed effect models. The result showed that a fixed effect model was appropriate. As control variables were
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considered in the modeling process, a fixed effect model should be chosen instead of a random effect model. The regression result obtained was as follows: ln MRPIit +1 − ln MRPIit = Cr + Ct + 0.669339 − 1.240378 (0.098041) ln MRPIit + 2.24 × 10−5
× 1.11 × 10−5 EDit − 0.023564 (0.012454) ISit + 0.003714 (0.006160) OSit + 0.007884 (0.058370) OWit + ε Adjusted R2 = 0.577291,
F = 6.690381,
DW = 2.352654.
(18)
The results indicated that there was significant negative correlation between transformation performance and growth rate for the 21 resource cities when economic development, industrial structure, ownership structure and degree of openness were taken into account. In other words, the α and β test of MRPI for the 21 cities revealed a conditional convergence. The positive correlation between economic development and MRPI implied that industrial structure has a cumulative effect on MRPI. In addition, ownership structure and the degree of openness had significant positive effects on MRPI convergence. Furthermore, there was a significant negative correlation between MRPI and industrial structure for 21 resource cities, which reinforced the fact that the industrial structure played a reverse role in MRPI convergence. 5. Conclusions Transformation of resource cities has become an important regional strategic issue for sustainable growth, social stability, and harmonious development. Environmental protection during the transformation of resource cities cannot be ignored. We introduced EPT to set up a Malmquist performance index for the transformation of resource cities under environmental regulation. We performed σ , absolute β and conditional β convergence tests. The MRPI results reveal great differences in transformation performance in different regions and the MRPI ranking among the three regions is not consistent with the ranking of their economic strength. Furthermore, test results reveal that the σ convergence trend is not obvious, the β convergence trend is significant, and the β conditional convergence is remarkable when some control variables are added. The overall conclusion is that the transformation performance for 21 resource cities shows a convergence trend. In other words, difference in transformation performance among these cities is not apparent. How to achieve economic growth during transformation remains a major issue for resource cities. Development and implementation of transformation strategies should be made after proper evaluation of the conditions for each city. Since resource cities are more environmentally polluted, environmental protection issues should be strongly highlighted during their transformation. However, there is little quantitative research in this field, especially with regard to environmental issues. This paper extends the Malmquist productivity index to a transformation performance index for resource cities using EPT. Using MRPI results for 21 resource cities, we carried out convergence tests. The transformation performance of resource cities can be accurately evaluated using this approach and their individual strengths and weaknesses can be clearly identified from convergence tests. The results provide a theoretical basis for the development of more targeted transition policies that consider environmental protection for resource cities. 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