ANALYSIS OF ENVIRONMENTAL PRODUCTIVIY USING META-FRONTIER. Sang-Mok Kang 1, Moon-Hwee Kim 2

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1 ANALYSIS OF ENVIRONMENTAL PRODUCTIVIY USING META-FRONTIER - MANUFACTURING INDUSTRIES IN KOREA AND CHINA- Sang-Mok Kang 1, Moon-Hwee Kim 2 Professor, Department of Economics, Pusan National University, 30 Jangjeon-dong, Geumjeon-gu Busan , KOREA, smkang@pusan.ac.kr Ph.D candidate, Department of Economics, Pusan National University, 30 Jangjeon-dong, Geumjeon-gu Busan , KOREA, hwee@pusan.ac.kr ABSTRACT The purpose of this study is to analyze the technical efficiency, technology gap and productivity of the manufacturing industries in Korea and China for 2000 through 2004 introducing the meta-frontier model. We compare the general technical efficiency ignoring the pollution with the environmental technical efficiency considering the pollution in order to estimate the influence of environmental factors on the competitiveness for manufacturing industries in the two countries. Whereas the technical efficiency of the manufacturing industries in China is higher on average than that in Korea, both in the case of ignoring and the case of considering the pollution, the productivity of the manufacturing industries in Korea is higher on average than that in China in both cases. This implies that the China has a difficulty in the production activity reducing pollutants and increasing desirable outputs simultaneously. In addition, it implies that Korean manufacturing is closer to sustainable growth than Chinese manufacturing. KEY WORDS: Meta Technical Efficiency, Technical Gap, Meta Productivity Change, Productivity Gap, DEA 1. INTRODUCTION China, whose annual economic growth rate has been recorded at approximately ten percent since its change to reform and openness, is emerging as 'the world's largest manufacturing country. 1 The fact that China has arisen as the world s factory gives a wake-up call to Korea because the manufacturing industry is still important in leading Korean economic growth. That is, not only this rapid growth of China as well as the rapidly 1 The Financial Times reported that China will emerge as the world's largest manufacturing country in 2025 year and will outpace the US. as a result. This is caused by the ratio of production to the world's manufacturing industries increased from 15% in 2008 to 34.7% in 2025 according to the research of Global Insight which is an economic consultant, located in Washington ( changing world situation is an opportunity and a threat to Korea simultaneously. China has upgraded its manufacturing industries such as the heavy and chemical industry, the electrical and electronic industry, and the automobile industry, which are also the main manufacturing industries of Korea. Moreover, the technical gap between Korea and China has decreased gradually since diplomatic relations were established between the two countries. Therefore, Korea is in the situation to consider measures such as productivity improvement based on the sense of this crisis. The competition among manufacturing industries is influenced by various factors such as price and the quality of products. The technical efficiency and productivity are included in one of indices representing the competition in terms of the efficient use of resources. The technical efficiency measures the relative ratio between the case of achieving the maximum output, and that of 1

2 not achieving the maximum output, under the given input; that is, it indicates the ratio of the actual production point over the production point on the production frontier over all the periods. Productivity does not mean just the amount that was produced but the ratio of output produced to the input used. It means that productivity is an important element influencing a firm s sustainable growth and competition. As interest in the environment has increased sharply both at home and abroad recently, considering the environmental element has been widely recognized as being more reasonable than using the method without the environmental element when measuring productivity growth. Hence, this study intends to estimate the environmental productivity including pollution and investigate the environmental productivity gap of the manufacturing industries between the two countries through a comparison of the environmental productivity with the traditional productivity excluding pollution in order to find the meaning of the environmental productivity. The traditional productivity can be derived by deducting the term pollution from the environmental productivity. In this paper, we intend to analyze the technical efficiency, technical gap, and productivity gap between Korea and China empirically using the meta-frontier concept. If the technical efficiencies and productivities of the manufacturing industries in Korea and China are measured, it is difficult to compare them objectively because the frontiers between both countries are different; however, if we include the frontiers of the two countries, it will be advantageous to compare the relative advantage through the meta-technical efficiencies and meta-productivities. The concept of the meta-frontier has been used to compare the technical efficiency of observations which are in different groups such as industries, regions, or countries. Battese and Rao (2002) first introduced the concept of the meta-frontier to estimate the technical efficiency and technology gap effects separately, using stochastic frontier analysis (SFA) and the data envelopment analysis (DEA) simultaneously. Jemaa and Dhif (2005) also estimated the technical efficiency and technology gap effects in European countries. O'Donnell et al. (2008) suggested the basic framework to define the meta-frontier and an empirical example of the meta-frontier model through the parametric method as well as the non-parametric method using cross-country's agricultural sector data. Chen et al. (2008) analyzed the regional productivity in China adopting the metafrontier model and Rngsuriyawilboon and Wang (2008) estimated the agricultural productivity of 28 provinces in China by separating it into technical efficiency, technical progress and scale efficiency using the meta-frontier. 2 Chen et al. (2009) tried to analyze the regional productivity growth in China for They divided inland provinces from coastal provinces and investigated regional disparities based on productivity. In this paper, we will examine the technical efficiency, technology gap, and productivity of the manufacturing industries in Korea and China for , introducing the meta-frontier model of Battese and Rao (2002). Their analysis investigates the two different countries that may not have the same technology and the different industries within each of those countries. Therefore, it may create a bias when adopting the existing frontier model. However, when adopting the meta-frontier model, there is an advantage to conceptualizing the differences among these industries as a technology gap. Furthermore, we should try to examine the influence of environmental factors on the competitiveness of the manufacturing industries between the two countries reflecting the fact that an interest in the environment has recently developed. Through this, we expect to confirm which type of business is closer to sustainable growth. This study differs from the previous ones in terms of suggesting the model which combines the meta-frontier model with the frontier model considering an environmental factor. Therefore, this study has significance for being the first to try considering an environmental element on the manufacturing industries between Korea and China while adopting the meta-frontier model based on the DEA. This paper is organized as follows: Section 2 presents a theoretical model of the meta-frontier based on DEA; Section 3 provides the empirical results, and Section 4 presents the conclusion including political implications. 2 Sang-Mok Kang and Sang-kyu Jo(2009) 2

3 2. THEORETICAL MODEL produced using given input vector, x, in a certain region, (x, y, b) belongs to the meta-frontier, A *. This means A k including the random production point, (x, y, b), belongs to the technology in a When explaining the theoretical model, we will explain the measurement of the regional technology and the meta-technology after introducing the relationship between the individual technology and the meta-technology 2.1 The relation between individual technology and metatechnology In general, technical efficiency means the capacity to produce output by employing the minimum resource, and the Measurement of its efficiency is based on the Distance Function theory. Let us consider that production can be produced during the periods, p =1,, P in regions K, k = 1,, K and define x R+N as inputs, y R+M as desirable outputs, and undesirable outputs as b R+I. Let us assume that the production function, F(x) is as follows:3 F(x) = {(y, b): (x, y, b): A} (1) certain region, is a subset of A *. It is defined as follows: A A A A (2) Equation (2) satisfies the necessary technology axiom since the sub-set (the individual technology) satisfies a technology axiom. That is, meta-technology forms the meta-frontier including these technologies through a convex combination of the technologies in those certain areas. Thus, meta-technology means the existence of technology (A * ), which takes precedence over all technologies. Each production unit belonging to the region, k, is produced under the individual technology, A (k=1, 2,..., K). In this study, we will use the Directional Distance Function in order to measure sustainable growth more suitably. The Directional Distance Function provides advantages that can give different directions such as increase (+) or decrease (-) to the desirable output and pollution, respectively. This is defined as follows: The production possibility set F(x) is the set of input vector and output vector and it produces the set of outputs and the pollution, (y, b), which can be produced from inputs, x. 4 A means technology, which is a means or the activities transforming given inputs into outputs. We define the entire regional technology as the meta-frontier. For instance, if the random output, y, is 3 The production function ignoring the pollution is defined as F(x) = {(x, y): x can produce y}. 4 According to Fare, Grosskopf, and Pasurka (1986), suppose that the pollution set is weak disposability and the output set is strong disposability. The weak disposability of the pollution can be expressed as (y, b) F(x) and (βy, βb) F(x) if 0 β 1. This represents that the producers should reduce the pollution emission and the production of desirable outputs simultaneously. On the other hand, the strong disposability, producing desirable outputs while reducing the pollution emission freely, can be expressed as (y, b) F(x) and (y', b) F(x) if y' y. D x, y, b: g,g, g maxβ:yβg,bβg F x βg (3) In equation (3), β indicates the concrete level of the Directional Distance Function. When 0 < β, it is inefficient since the observation locates within the frontier. β measures the level of the output which is extendable on the basis of a point on the frontier in order to reach the maximum output from the real output. On the other hand, when β = 0, it represents being efficient as the observation locates on the frontier. The directional vector, g, gives the direction to the desirable output and pollution; here, it gives the direction of increase (+) to the output and the direction of decrease (-) to pollution, respectively. The meta-directional distance function, based on the metatechnology that contains the frontier based on the individual technology, is defined as follows: 3

4 Dx, y, b: g,g, g maxη:yηg,bηg F x ηg (4) Equation (4) is the meta-directional distance function and is integrated by the individual frontiers. The relation between the meta-directional distance function and the individual directional distance function can be expressed as follows: Dx, y, b D x, y, b,k 1,2,,K (5) Equation (5) derives from the fact that the output set of a certain region is a subset of the output from meta-technology. That is, the technical efficiency of the meta-directional distance function is the same with the frontier or it can also be relatively farther away from the frontier compared to the technical efficiency of the individual directional distance function. When a sign is inequality (< or >) in equation (5), it means there is a technology gap between the individual technology of k and the meta-technology. The technology gap can be represented as follows by using the technical efficiencies based on the individual distance function and the meta-distance function. x, y, b D TG,, (6) D,, The technical efficiency of equation (6) can be estimated by the relative ratio between the two technical efficiencies. Of course, equation (6) can also be represented as a multiple of the individual distance function and the technical gap. 2.2 Measurement of the technical efficiency In general, the distance function can be measured by using a linear program. If we assume that the observations in the regions, k=1,,k produced, the outputs, y m, m = 1,,M and pollutions, b i, i =1,,I, the linear program of the individual production unit, K Z b 1βb i 1,, I, k 1,, K, K Z x 1βx n 1,, N, k 1,, K, Z 0 (7) The left side in the restricted conditions in equation (7) means the maximum amount of output and the minimum amount of input, the right side in the restricted conditions means the real amount of output and the real amount of input. This restricted conditions satisfied strong disposability and weak disposability for the output and the pollutant, respectively. Z k is a weighted density vector. A non-negative density vector represents that the production technology is constant returns to scale. 5 β indicates the concrete value of the directional distance function as the technical efficiency of the directional distance function and has the value from zero(0) to one(1). In equation(7), the optimal solution can be acquired when the outputs and pollution have the directions of g{x(1- β), y (1+ β), b (1- β)}. The left side in the restricted conditions means each individual observation vector of the input and the output is combined with each weighted vector, and it forms the maximum amount of output and the minimum amount of input. The right side in the restricted conditions means the real amounts of outputs and the real amount of input, respectively. Here, if the left side is equal to the right side, it means that the maximum amount of output is the same as the minimum amounts of inputs On the other hand, the meta-frontier is formed based on the pooling data integrating Korean individual manufacturing industries and Chinese individual manufacturing industries; that is, the linear programming of the meta-frontier is represented as equation (8) since A A A A : k, of an individual technology set, A, is defined as follows: D x,y,b :x,y,b maxβ K s. t Z y 1βy m 1,, M, k 1,, K, 5 The previous studies mainly assume a certain scale, however, we do not consider the difference accompanied by the different economy scales because the focus in this study is not an economy scale but comparing the technical efficiency and productivity of the manufacturing industries in the two countries. 4

5 D x,y,b :x,y,b maxη J s.t Z y J 1 ηy, j1,,j, k 1,, K Z b 1ηb,i 1,,I,k 1,,K J Z x 1ηx,n 1,,N,k 1,,K Z 0 (8) Equation (8) shows the conditions of maximum output and minimum input integrating individual frontiers. Here, is the actual value of meta-frontier distance function. The metatechnical efficiency becomes farther away from the meta-frontier because it is much more extended than the frontier in the case of measuring production units with respect to individual frontiers. 2.3 Measurement of individual productivity and meta-productivity The directional distance function can be defined in the period, p, and the period, p+1, respectively, and it can be used to estimate the technical efficiency in each period. This directional distance function can also be utilized for measuring the productivity change. This study intends to compare and analyze the general productivity (Malmquist productivity: hereafter M) excluding the pollution, and the environmental productivity (Malmquist- Luenberger productivity: hereafter ML) including the pollution separately. First, the productivity growth based on the directional distance function ignoring the pollution can be estimated by using Malmquist productivity index, developed by Fare, Grosskopf, Norris and Zhang (1994). The productivity change index, M, can be derived by using four directional distance functions in two different time periods: the directional distance functions in the time period p and p+1 respectively, from the perspective of time period p technology, and the directional distance functions in the time period p and p+1, respectively from the perspective of period p+1 technology. This is derived as equation (9): M D,,: D,,: D,,:,,: D In equation (9), the direction vector, g=(-g x,g y,0), is the case that does not give the direction of reduction of pollution. It means an increase in productivity between the two periods if the productivity change index, M, is greater than one (1), and it indicates a decline in productivity between two periods if the productivity change index, M, is less than one (1). After the same fashion, the meta-productivity change index can be derived using the directional distance function defined as meta-technology as equation (10): MG M (11) M The meta-productivity change estimated from the perspective of the meta-frontier can be divided into the individual productivity and productivity gap. The value of the technology gap can be either less than, or greater than, one (1). That is, since the productivity change is intended to measure the productivity change in two different periods, the meta-productivity change can be either less than, or greater than, the individual regional productivity change. As we have already seen, the M productivity index represents the case of the productivity change excluding the environmental element. In this study, we try to identify the ML productivity change giving the direction to decrease the amounts of pollution to the alternative M productivity change. First, the productivity change, including the environmental factor based on an individual frontier by employing the directional distance function, is defined as follows: (9) 5

6 ML D,, : D,, : / D,, :,, : D (12) in equation (12) estimates the productivity improvement based on the direction not only to decrease pollution, but also the direction to simultaneously increase output. If the pollution abatement activities are not reflected as productivity growth as in equation (12), it is possible to underestimate the productivity and give incomplete information about productivity measurement. On the other hand, if the pollution abatement activities are considered as productivity growth, it can give more realistic information about productivity measurement in view of the disposal of output and pollution in the production activity at the same time. If the ML productivity change index is greater than one, it means productivity improvement. However, it means a drop in productivity if the ML productivity change index is less than one. Next, the metaproductivity change can be derived as equation (13) by using the directional distance function which is defined as the metatechnology: ML 1D 1D x,y,b :g x,y,b :g 1D x,y,b :g 1D x,y,b :g / (13) Equation (13) shows the meta-productivity change on the basis of the meta-frontier which integrates the individual industries' frontiers. If the meta-productivity change is greater than one (1), The meta-productivity change in equation (13) can be decomposed into individual productivity change and productivity gap. Since productivity change estimates the change in two different time periods, the meta-productivity change can be either greater or less than general productivity change. When the metaproductivity change is greater than the individual productivity change, the productivity gap is greater than one, while the productivity gap is less than one when the meta-productivity change is less than the individual productivity change. As described above, the relation between the individual technical efficiency and the meta-technical efficiency, and the relation between the individual productivity change and the meta-productivity change are shown in <Figure 1>. <Figure 1> represents the relation between the individual frontier and metafrontier, the individual productivity change, and the metaproductivity. For the convenience of explanation, let us assume that there are only two individual frontiers. We can measure an individual technical efficiency based on the individual frontier for each first time period (p), respectively, and derive the metafrontier enveloping the two frontiers. When measuring the technical efficiency based on the meta-frontier, it might differ from the technical efficiency based on the individual frontier. Likewise, the meta- productivity change can be estimated on the basis of the meta-frontier for the two time periods. Furthermore, general productivity change can be measured on the basis of the individual frontiers between two time periods. The two productivity changes can show which frontier is farther extended between an individual frontier and a meta-frontier during the two time periods. it means productivity improvement, whereas it means a drop in productivity if the meta-productivity change is less than one. The productivity gap can be defined as follows by using productivity change. MLG ML (14) ML 6

7 were acquired from the statistical report of mining and manufacturing industries( ), and SO emissions for each manufacturing industry provided by CAPSS, were used. The capital stock of each manufacturing industries in China was estimated by accumulating new investment data through the perpetual inventory method. 7 The capital stock in China was estimated by the perpetual inventory method, which is based on the investment of fixed assets from Chinese Statistical Yearbook. Since there is no available data of capital stock by industry in China, we estimated it through the perpetual inventory method based on new investment. Here, the initial capital stock is estimated by using new investment for initial certain periods and the average growth rate of initial new investment, as in Young (1995). 8 Previous studies such as Young (1995) used the depreciation rate of 6 percent. In this study, we will compare 22 business types in Korea with 16 business types in China. The classification of manufacturing industries in China is different from the standard industry classification in Korea. <Figure 1> the relation between individual frontiers and meta-frontiers 3. DATA AND EMPIRICAL RESULT We used inputs (labor and capital), outputs (added value), and a pollutant (Sox) of the manufacturing industries in two countries during In China, the statistical data of inputs and output and emission amounts are available from the Chinese Statistical Yearbook. 6 In Korea, we used the emission amounts of SO from CAPSS (CAPSS: Clean Air Policy Support System). Monthly labor input amounts and capital stock 6 SOx can indicate other air pollutants partially but it cannot reflect levels of water and soil pollutants. However, as China includes only the emission amounts of SOx in the statistical data of pollutants, we use only one pollutant, SOx. Pollutants that are particularly difficult to treat may require additional cost for disposal. But as general pollutants are usually processed in the same manner, pollutant treatment cost does not vary, regardless of pollutant amounts. That is, pollution prevention facilities must be operated to treat one pollutant at least with the whole process of pollution treatment regardless of the types of pollutants. Sang-Mok Kang et al (2008). The manufacturing industries classified into 32 business types are reclassified into 16 so that they are comparable with those of Korea. 9 7 Investment in fixed assets from Chinese Statistical Yearbook was used. 8 Industrialization started in China after its reform and movements and the new investment was available from the early 1980s. However, we estimated the amount of new investment by extending the term to the middle of the 1960s and adopting the average growth rate of the new investment in the 1980s in order to bring them roughly into line with Korea. China has invested mainly in the manufacturing industries, especially in the light industry since its reform and openness so the new investment in the most of the light industry is zero or near zero. The estimation formula according to the perpetual inventory method is as follows: K(1)=I(1)/(δ+g) in which K(1) is capital stock in the 1st term, I(1) is new investment in the first term, δ is the depreciation rate, and g is the annual growth rate of new investment in the five initial years. Therefore, constant capital stock is calculated by the following formula: K(1)=(1-δ)K(t-1)+I(t), t+2,, T The same depreciation rate was applied to consistently analyze capital stock of two countries. 9 In order to compare evenly, it is necessary to unify the statistical data of inputs, outputs, and pollution. In China, the statistical data of inputs and outputs are classified into 16 business types and that of pollution is presented with 32 business types. On the contrary, the manufacturing industries are classified into 23 business types in 7

8 <Table 1> shows the individual technical efficiency, the metatechnical efficiency, and the technology gap, which ignore the impact of pollution. The individual technical efficiency excluding the pollution in China (0.879) is higher than that in Korea (0.722). Sang-Mok Kang et al. (2008) explained that the Chinese manufacturing industries are more efficient than the Korean manufacturing industries because the costs of location and production in Korea are much higher than those in China. In Korea, both the tobacco industry, and the coke, refined, petroleum products and nuclear fuel manufacturing industry, show the maximum efficiency, 1.000, respectively; wearing apparel and fur products(0.863), leather, luggage and harness (0.816), Motor vehicles (0.754), and audio-visual equipment(0.739) are more efficient than the average(0.722). In China, leather and fur manufacturing shows the maximum efficiency and coke, refined, petroleum products and nuclear fuel (0.998), machinery and equipment, electric machinery (0.997), food products and beverages, tobacco (0.968), metal products (0.963), manufacture of plastics (0.940) are more efficient than the average. When it comes to the meta-technical efficiency of Korea, tobacco and comparing the technical efficiency of the manufacturing industries in both countries still show the maximum efficiency. Wearing apparel and fur products (0.795), leather, luggage and harness (0.784), and motor vehicles (0.711) are more efficient than the average. Leather and fur manufacturing still shows the maximum efficiency, and machinery and equipment, electric machinery (0.975), metal products (0.940), coke, refined, petroleum products and nuclear fuel (0.927), food products and beverages (0.902), and manufacture of plastics (0.877) are more efficient than the average (844) in China. It is interesting that coke, refined, petroleum products and nuclear fuel, machinery and equipment, electric machinery, food products and beverages in China are very close to the maximum efficiency when it comes to the Korea, with slight difference in each item. Therefore, perfect unification is impossible. Hence, the statistical data of pollution in China is integrated into 16 business types as they are unified into inputs and outputs. individual technical efficiency, however, the technical efficiency decreased relatively when it comes to the meta-technical efficiency. This means that these types of business are outstanding in terms of the relative technical efficiency within the region, but the technical efficiency decreased a lot in terms of the level of the absolute technical efficiency that integrates Korea with China. Comparing the technical efficiency of the manufacturing industries in both two countries, most of those in China have an advantage, while Korea shows an advantage in the industries such as coke, refined, petroleum products and nuclear fuel industry, chemicals and chemical products, and non-metallic mineral products. When it comes to the technical gap ignoring the environmental factor, while Korea shows maximum economic performance in tobacco industry and coke, refined, petroleum products and nuclear fuel industry, China shows maximum economic performance in wearing apparel and fur products industry. The meta-technical efficiency is lower than the individual technical efficiency on average in both the Korean manufacturing industries and the Chinese manufacturing industries in terms of the technical efficiency gap excluding the environmental element. However, the gap between the individual technical efficiency (0.722) and the meta-technical efficiency (0.703) in Korea is lower than the gap between the individual technical efficiency (0.879) and the meta-technical efficiency (0.844) in China. The Korean manufacturing industries are annually higher than the Chinese manufacturing industries in terms of the technical efficiency gap excluding the environmental element, being and 0.960, on average, respectively. This indicates that the frontier of the individual technical efficiency in Korea is closer to the meta-frontier, and that in China is farther from the metafrontier. That is, the technical gap shows how far the individual frontier is from the meta-frontier; if the technical gap is one (1), it means that the two frontiers are the same. Thus, the distortion of the individual production frontier in Korean manufacturing industries is smaller than that in Chinese manufacturing industries since the technical gap of Korean manufacturing industries is relatively closer to the meta-frontier. Especially, while the individual frontier and the meta-frontier of tobacco 8

9 industry and coke, refined, petroleum products and nuclear fuel industry are equal to each other as their the technical gaps are one (1) among Korean manufacturing industries, the technical gap of wearing apparel and fur products is the lowest among Korean ones. <Table 1> the meta-technical efficiency and technology gap excluding pollution ( year) Types of Industries Meta Inv. TG Korea Food Products and Beverages Tobacco Textiles Wearing Apparel and Fur Articles Leather, Luggage and Harness Wood and Wood Products Pulp, Paper and Paper Products Publishing, Printing, and Recorded Media Coke, Refined, Petroleum Products and Nuclear Fuel Chemicals and Chemical Products Manufacture of Rubber and Plastics Non-metallic Mineral Products Basic Metal Fabricated Metal Products Manufacture of Other Machinery and Equipment Other Electric Machinery Audio-visual Equipment Medical and Precision Motor Vehicles Other Transport Equipment Furniture and Other Manufacturing Processing of Recycled Materials Average China Food Products and Beverages, Tobacco Textiles Leather and Fur Products Pulp, Paper and Products Publishing, Printing, and Recorded Media Coke, Refined, Petroleum Products and Nuclear Fuel Chemicals and Chemical Products Medical Products

10 Chemical Fiber Manufacture of Rubber Manufacture of Plastics Non-metallic Mineral products Refining and Rolling of Metal Refining and Rolling of Non-metal Metal products Machinery and Equipment, Electric Machinery Average ) Meta and Inv. in this table mean meta-technical efficiency and individual technical efficiency, respectively while TG means technology gap. 2) The average was measured by giving a weighted value based on the output (added value). 3) The technical efficiency is efficient if it is zero, however, we use its reciprocal in order to avoid confusing it with the value of productivity (the technical efficiency has the value from zero to one, and it shows being efficient if it is one in this table). <Table 2> shows the productivity growth and the productivity gap of the manufacturing industries in the two countries during the same period. While the technical efficiency compares the different production units in a single time period, the productivity growth represents the degree of the productivity change in two different time periods. In this study, the productivity growth is derived from four directional distance functions in the two time periods, p and p+1. Here, we divide the productivities into the individual productivity change based on the individual frontier, and the meta-productivity change based on the meta-frontier, and the productivity gap between the two productivities. By happenstance, the annual metaproductivity changes of both countries on average are the same as the productivity changes within each country s frontier itself by chance. The individual productivity and the meta-productivity of Korea showed on average, respectively. That is, the annual average growth of Korea is 8.6 percent.. On the other hand, the individual productivity and the meta-productivity of China are on average, respectively. That is, China showed an annual productivity decline of 3.4 percent on average growth, meaning that while the manufacturing industries in Korea have contributed to the rapid extension of the frontier annually, those of China have not. Taking a closer look at each individual industry, the types of manufacturing industries of Korea such as basic metal(1.150), processing of recycled materials, (1.143), chemicals and chemical products(1.118), audio-visual equipment(1.108), motor vehicles (1.103), wearing apparel and fur products(1.095) and other transport equipment(1.090) in descending order, showed productivity improvement, all higher than the average. These were the same types of industries when it comes to both individual productivity and meta-productivity. However, the meta-productivity growth is relatively lower than the individual productivity growth in the cases of publishing, printing & recorded media, and assembling metal products, and other electric machinery. On the contrary, the individual productivity growth is relatively higher than the meta-productivity growth in the cases of manufacture of rubber and plastics, manufacture of other machinery and equipment, medical and precision, and furniture and other manufacturing. On the other hand, nearly half of manufacturing in China industries such as chemical fiber, chemicals and chemical products, refining and rolling of metal, publishing, printing & recorded media, and coke, refined, 10

11 petroleum products and nuclear fuel are higher than the average in terms of the individual productivity. Among them, chemical fiber(1.100), chemicals and chemical products(1.068), refining and rolling of metal(1.048), publishing, printing & recorded media(1.015), coke, refined, petroleum products(1.010), nonmetallic mineral products(1.003), and so on, showed improvement in terms of the productivity growth. However, in the case of China, the meta-productivity indexes of just a few types of industries such as food products and beverages, tobacco, and non-metallic mineral products are higher than the individual productivity indexes. That is, the meta-productivity is relatively low compared to the individual productivity growth in most types of industry such as chemical fiber, coke, refined & petroleum products, medical and precision, manufacture of plastics, and metal products, and manufacture of other machinery and equipment. Therefore, the Korean manufacturing industries show productivity improvement at an annual rate of 8.6 percent while the Chinese manufacturing industries show productivity decline at an annual rate of 3.4 percent in terms of the productivity excluding the environmental element. Each individual frontier and each meta-frontier in both countries are almost identical as shown by the productivity gap of in terms of the productivity gap of each country. The individual technical efficiency, the meta-technical efficiency, and the technology gap, when considering the environmental factor, are shown in <Table 3>. The individual technical efficiency of China (0.903) is higher than that of Korea (0.726), even in terms of the technical efficiency including the environmental factor. In the case of Korea, tobacco, and coke, refined, petroleum products & nuclear fuel showed also the maximum efficiency of as when comparing the technical efficiency including the environmental factor. Wearing apparel and fur products (0.859), leather, luggage and harness (0.824), audio-visual equipment (0.775), and motor vehicles (0.766) are more efficient in descending order, than the average. In China, food products and beverages, tobacco, leather and fur manufacturing, coke, refined, petroleum products & nuclear fuel, manufacture of plastics, non-metal products, and machinery, equipment & electric machinery showed the maximum efficiency in descending order. Metal products (0.965) and publishing, printing, & recorded media (0.921) are more efficient than the average. China (0.874) is higher than Korea (0.724), even in terms of the meta-technical efficiencies considering the environmental element. When it comes to metatechnical efficiency, in the case of Korea, tobacco, and coke, refined, petroleum products & nuclear fuel showed also the maximum efficiency, which are the same as the individual technical efficiencies. Wearing apparel and fur products (0.858), leather, luggage and harness (0.815), audio-visual equipment (0.775), and motor vehicles (0.766) are more efficient than the average (0.724). In the case of China, coke, refined, petroleum products & nuclear fuel (0.978), metal products (0.956), food products and beverages & tobacco (0.929), and manufacture of plastics (0.919) are more efficient than the average (0.874), whereas leather and fur manufacturing and non-metal products, and machinery, equipment & electric machinery showed the maximum efficiency. Comparing the technical efficiencies of both countries manufacturing industries based on the meta-frontier, most of the manufacturing industries in China has an advantage when the environmental factor is excluded. However, Korea still has an advantage for tobacco, and coke, refined, petroleum products & nuclear fuel. The technical efficiency of the industries such as wearing apparel and fur articles, and leather, luggage and harness, and motor vehicles, including the environmental factor, showed higher improvement than the technical efficiency excluding the environmental factor. 11

12 <Table 2> the productivity and productivity gap excluding pollution ( year) Types of Industries Meta Inv. MG Korea Food Products and Beverages Tobacco Textiles Wearing Apparel and Fur Articles Leather, Luggage and Harness Wood and Wood Products Pulp, Paper and Paper Products Publishing, Printing, and Recorded Media Coke, refined, Petroleum Products and Nuclear Fuel Chemicals and Chemical Products Manufacture of Rubber and Plastics Non-metallic Mineral Products Basic Metal Fabricated Metal Products Manufacture of Other Machinery and Equipment Other Electric Machinery Audio-visual Equipment Medical and Precision Motor Vehicles Other Transport Equipment Furniture and Other Manufacturing Processing of Recycled Materials Average China Food Products and Beverages, Tobacco Textiles Leather and Fur Products Pulp, Paper and Products Publishing, Printing, and Recorded Media Coke, Refined, Petroleum Products and Nuclear Fuel Chemicals and Chemical Products Medical Products Chemical Fiber Manufacture of Rubber Manufacture of Plastics Non-metallic Mineral Products Refining and Rolling of Metal

13 Refining and Rolling of Non-metal Metal Products Machinery and Equipment, Electric Machinery Average ) Meta and Inv. in this table mean meta-productivity and individual productivity, respectively while MG means productivity gap. 2) The average was estimated by giving a weighted value based on the output (added value). 3) The Productivity change index was estimated by giving a weighted value which was acquired as taking the geometric mean between the period, p and the period, p+1 since the productivity change index represents the productivity change during the two different periods. <Table 3> the meta-technical efficiency and technology gap including pollution ( year) Types of Industries Meta Inv. TG Korea Food Products and Beverages Tobacco Textiles Wearing Apparel and Fur Articles Leather, Luggage and Harness Wood and Wood Products Pulp, Paper and Paper Products Publishing, Printing, and Recorded Media Coke, Refined, Petroleum Products and Nuclear Fuel Chemicals and Chemical Products Manufacture of Rubber and Plastics Non-metallic Mineral Products Basic Metal Fabricated Metal Products Manufacture of Other Machinery and Equipment Other Electric Machinery Audio-visual Equipment Medical and Precision Motor Vehicles Other Transport Equipment Manu Furniture and Other Manufacturing Processing of Recycled Materials Average China Food Products and Beverages, Tobacco

14 Textiles Leather and Fur Products Pulp, Paper and Products Publishing, Printing, and Recorded Media Coke, Refined, Petroleum Products and Nuclear Fuel Chemicals and Chemical Products Medical Products Chemical Fiber Manufacture of Rubber Manufacture of Plastics Non-metallic Mineral Products Refining and Rolling of Metal Refining and Rolling of Non-metal Metal Products Machinery and Equipment, Electric Machinery Average ) Meta and Inv. in this table mean meta-technical efficiency and individual technical efficiency, respectively while TG means technology gap. 2) The average was measured by giving a weighted value based on the output (added value). 3) The technical efficiency is efficient if it is zero, however, we use its reciprocal in order to avoid confusing it with the value of productivity (the technical efficiency has the value from zero to one, and it shows being efficient if it is one in this table). In the case of China, the technical efficiency of the industries such as non-metallic mineral products, and refining and rolling of metal, and refining and rolling of non-metal showed higher improvement than the technical efficiency excluding the environmental factor. When it comes to the technical gap, in the case of Korea, nearly half of the manufacturing industries including tobacco, and coke, refined, petroleum products & nuclear fuel, and chemicals and chemical products recorded high economic performance while, in the case of China, only a few types of industries such as leather and fur products, and refining and rolling of metal, and refining and rolling of non-metal, and machinery, equipment and electric machinery showed high economic performance. This indicates that the Korean manufacturing industries lie in the production condition of sustainable growth by individual industry although they show lower economic performance those in China, on average. When it comes to the meta-frontier, the technical efficiencies including the environmental element in Korea and China show improvement of 2.1 percent and 3.0 percent on average, respectively, compared to the general technical efficiencies. Environmental regulations transform the resources to produce into the resources to decontaminate. That is, the technical efficiencies including the environmental factor become greater than the technical efficiencies excluding the environmental factor, as the production possibility curve shrinks when considering pollution abatement activities. The meta-technical efficiencies including the environmental element of the manufacturing industries in both Korea and China represent a lower level than the individual technical efficiencies in both countries on average. However, the gap between the individual technical efficiency (0.726) and the meta-technical efficiency (0.724) in Korea is comparatively lower than the gap 14

15 between the individual technical efficiency (0.903) and the meta-technical efficiency (0.874) in China. Consequently, the technology gap of Korean manufacturing shows 0.997, on average, and the technology gap of Chinese manufacturing shows 0.968, on average. Thus, it indicates that the frontier of the individual technical efficiency of the Korean manufacturing industries is closer to the meta-frontier that integrates Korea with China rather than the frontier of the individual technical efficiency of the Chinese manufacturing industries. <Table 4> the productivity and productivity gap including pollution ( year) Types of Industries Meta Inv. MLG Korea Food Products and Beverages Tobacco Textiles Wearing Apparel and Fur Articles Leather, Luggage and Harness Wood and Wood Products Pulp, Paper and Paper Products Publishing, Printing, and Recorded Media Coke, Refined, Petroleum Products and Nuclear Fuel Chemicals and Chemical Products Manufacture of Rubber and Plastics Non-metallic Mineral Products Basic Metal Fabricated Metal Products Manufacture of Other Machinery and Equipment Other Electric Machinery Audio-visual Equipment Medical and Precision Motor Vehicles Other Transport Equipment Furniture and Other Manufacturing Processing of Recycled Materials Average China Food Products and Beverages, Tobacco Textiles Leather and Fur Products Pulp, Paper and Products Publishing, Printing, and Recorded Media Coke, Refined, Petroleum Products and Nuclear Fuel Chemicals and Chemical Products

16 Medical Products Chemical Fiber Manufacture of Rubber Manufacture of Plastics Non-metallic Mineral Products Refining and Rolling of Metal Refining and Rolling of Non-metal Metal Products Machinery and Equipment, Electric Machinery Average ) Meta and Inv. in this table mean meta-productivity and individual productivity, respectively while MLG means productivity gap. 2) The average was estimated by giving a weighted value based on the output (added value). 3) The Productivity change index was estimated by giving a weighted value which was acquired as taking the geometric mean between the period, p and the period, p+1 since the productivity change index represents the productivity change during the two different periods. <Table 4> shows the productivity change and the productivity gap of the manufacturing industries considering the environmental factor. Based on the individual productivity change and the meta-productivity change, Korea shows an annual average growth of 2.5 percent (1.025) and 1.5 percent (1.015), respectively. This is a lower level relatively compared to the case of ignoring the environmental element (1.086). While China shows an annual average growth of 0.2 percent (1.002) in terms of the individual productivity, it shows an annual average decline of 0.9 percent in terms of the metaproductivity. However, this value is higher compared to the case of excluding the environmental element. This also suggests that, whereas the manufacturing industries in Korea have contributed to the rapid extension of the frontier annually, those of China have not. Especially, based on the meta-productivity growth index, this means the degree of contribution is larger than one based on the individual productivity growth index. That is, the environmental productivity reflecting the pollution abatement activities of Korean manufacturing industries have increased significantly compared to the Chinese manufacturing industries for the same period. Based on the meta-frontier, the productivity growth of Chinese manufacturing industries including the environmental element, except for chemical fiber, chemicals and chemical products, has increased more than the case excluding the environmental element. This implies that China has made an effort to seek pollution abatement activities as well as economic growth simultaneously since Taking a closer look at this, nearly half of all types of manufacturing industries of Korea showed more productivity improvement than the average (1.015) based on the metaproductivity, including fabricated metal products(1.015), leather, luggage and harness(1.039), other transport equipment (1.036), furniture and other manufacturing (1.035), manufacture of rubber and plastics (1.031), medical and precision (1.031), chemicals and chemical products (1.025), processing of recycled materials (1.020), and so on. These industries make up nearly half of the Korean manufacturing industries. 10 The Chinese government has been interested in international environmental protection since the Earth Summit in The Chinese government started to conduct the maintenance and revision of the environmental laws and regulations after the year 2000, even though the Chinese government promoted the environmental laws and regulations gradually after the middle of 1990s. 16