DECOMPOSITION ANALYSIS APPLIED TO ENERGY: SOME METHODOLOGICAL ISSUES LIU FENGLING （Master of Engineering, XJTU） A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2004 Acknowledgements I would like to express my sincere thanks to Professor Ang Beng Wah, my project supervisor, not only for his invaluable guidance throughout research work and thesis writing, but also for his encouragement and caring in the whole period of my study. Special gratitude also goes to all other faculty members of the Department of Industrial and Systems Engineering, from whom I have learnt a lot through coursework and research seminars that are useful to me to complete my PhD thesis. I am grateful to Professor H. S. Chung from Sung Kyun Kwan University, South Korea, for his unselfish help in providing data for the analysis in Chapter and Chapter 8. Also, I would like to give my sincere thanks to Associate Professor Chew Ek Peng for his proof of the similarities between the Refined Lapeyres Index (RLI) method and the Shapley Decomposition Method in Chapter 6. I would like to extend my heartiest thanks to all other members of the Department of Industrial and Systems Engineering, past and present, who have provided useful suggestions and help. Lastly, I would like to express wholehearted thanks to my husband, parents and parents-in-law for their continuous encouragement and support. LIU FENGLING i Table of Contents Acknowledgements…………… …… ……………… …………… .…… i Table of Contents………………………………………………………… . ii List of Figures………………………….………………………………… vi List of Tables ……………………………………………………………… viii List of Notations …………………………………………………………… xi Summary……………………………………………………………………. xiv 1. Introduction 1.1 Introduction to decomposition analysis……………………….… . 1.2 Energy and environmental indicators……………….………….…. 1.3 Decomposition methodologies……………….…………………… 1.4 Structure of the thesis……………….………….……….………… 13 2. Literature Review of Index Decomposition Analysis (IDA) 2.1 Introduction ………………………………………….…………… 18 2.2 Basic forms of IDA…………………………………….….……… 19 2.3 Review of IDA……………………………….………….……… 27 2.4 Summary…………………….…… ……………………………. 43 ii 3. Index Numbers and IDA 3.1 Introduction……… .…………………………………………… 46 3.2 Index number theory……………………………………………… 47 3.3 Eight index numbers and decomposition methods………………. 51 3.4 Some properties ………………………………… …………… . 55 3.5 An illustrative example…………………….…………………… 60 3.6 A case study………………………………………………… 63 3.7 Some issues on method selection………………………………… 65 3.8 Conclusions………………………………………………………. 68 4. Consistent in Aggregation in IDA 4.1 Introduction………………………………………………………. 70 4.2 The log-mean Divisia index method I (LMDI Method I)……… . 71 4.3 Consistency in aggregation………………………………………. 75 4.4 Case studies……………………………………………………… 78 4.5 Special case for consistency in aggregation…………………… 83 4.6 Consistent in aggregation for other IDA methods……………… 87 4.7 Conclusions……………………………………………………… 93 5. Modified Fisher Ideal Index (MFII) Method 5.1 Introduction……………………………………………………… 91 5.2 MFII Method – multiplicative form …………………………… 92 5.3 MFII Method - additive form …………………….…………… . 95 iii 5.4 Properties of MFII method………………………………….…… 98 5.5 An example…………………………………………………… . 104 5.6 Conclusions……………………………………………………… 107 6. Perfect IDA Methods 6.1 Introduction……………………………………………………… 108 6.2 Perfect IDA models……………………………………………… 109 6.3 Generalization of all models…………………… ……………… 117 6.4 Similarities among the methods………… …………………… 118 6.5 A case study ……………………………………………………. 121 6.6 Conclusions…………………………………………………… 123 7. Comparisons Between IDA and SDA 7.1 Introduction………………………………………….…………. 124 7.2 Main features of SDA……………………… …….…… . 124 7.3 Past SDA studies……………… …………………………… 131 7.4 Comparisons between SDA and IDA models.……………… 134 7.5 A case study… …………………………………………….… 141 7.6 Conclusions…………………………………………………… 145 8. Integration of IDA and SDA 8.1 Introduction……………………………….……….…………… 149 8.2 Principle for integration of IDA and SDA…… ………………… 149 iv 8.3 Integrated model for additive decomposition……… .…………. 151 8.4 Integrated model for multiplicative decomposition……… ……. 154 8.5 A case study…… ………………………………………………. 155 8.6 Conclusions………………… …………………………………. 160 9. Conclusions 9.1 Contributions of the research ………………………………… . 163 9.2 Possible future research topics……………………………….… 164 References………………………………………………………………… 166 Appendix A………………….…………………………………………… 185 Appendix B………………….…………………………………………… 188 Appendix C………………….…………………………………………… 189 Appendix D………………….…………………………………………… 193 Appendix E………………….…………………………………………… 194 v List of Figures 1.1 System development process……………………………………………. 1.2 Explanatory or causal relationship ……………………………………. 1.3 Decomposition analysis input-output procedure………………………… 1.4 An overview of decomposition methodology……………… ………… 13 1.5 Structure of the thesis……………… …………………………………. 17 2.1 Number of IDA studies per year and the trend………………………… 38 2.2 Percentage share of IDA studies by application area over time…….…. 39 2.3 Indicators used in IDA studies over time……………………………… 40 2.4 Approaches used in IDA studies over time…………………………… 40 2.5 Methods used for IDA studies over time……………………………… 41 2.6 Perfect or non-perfect methods used in IDA studies over time……… 42 2.7 Main effects of IDA studies…………………………… …………… 43 2.8 Three-dimension developments of IDA studies………………………. 45 4.1 CO2 emissions in manufacturing industry in China…………………… 80 vi 4.2 Global energy-related CO2 emission decomposition………………… 82 7.1 IDA and SDA development direction…………………….…………… 140 8.1 Integration scheme for IDA and SDA………………………………… 151 vii List of Tables 1.1 Effects of structural change in industrial energy use in a country: a simple example……………………………………………………… 1.2 A simple example: energy-related CO2 emissions in a country….…… 2.1 A summary of the formulae of decomposition……………… ……… 21 2.2 Index Number Decomposition Analysis (IDA) studies and their specific features………… …………………………………………… 28 2.3 IDA studies by application area and time period……………………… 39 3.1 Formulae of eight index numbers and integral Divisia indices………… 52 3.2 Formulae for eight decomposition methods………… ……… ……… 56 3.3 Properties of index numbers ………… ……… ……… ……………. 59 3.4 Data for the simple example ………… ……… ……… …………… 60 3.5 Decomposition results based on the data given in Table 3.4 ………… 62 3.6 Decomposition of the aggregate energy in China, 1980-1990………… 64 viii 3.7 Comparisons of methods based on four assessment criteria ………… 68 4.1 Consistency in aggregation in the decomposition based on data in Figure 4.1……… ……… ……… ………………………… . 5.1 84 Decomposing South Korea industrial CO2 emissions between 1990-1995 using MFII………………………………………………… 107 6.1 A summary of perfect decomposition techniques for energy decomposition analysis………… …………… …………………… 109 6.2 Formulae for effect j by different decomposition methods…………… 119 6.3 Decomposition of additive changes in emissions: 4-sector model…… 122 6.4 Decomposition of multiplicative changes in emissions: 7-sector model………………………………………………………… 122 7.1 Input-output table of inter-industry flows of good .…………… …… 127 7.2 Studies of SDA in energy and environmental research.……… ……. 7.3 Decomposition of difference in total CO2 emissions between China, South Korea and Japan by SDA and IDA….… … …………. 135 147 7.4 Summary of comparisons between SDA and IDA… ………… …… 148 8.1 Expected properties of the integrated model… ……………………… 150 ix References Rose, A. and Chen, C.Y. (1991) Source of change in energy use in the US economy 1972-1982. Resource and Energy 13: 1-221. Rose, A. and Miernyk, W. (1989) Input-output analysis: the first fifty years. Economic Systems Research 1: 229-271. Rose, A. and Oladosu, G. (2002) Greenhouse gas reduction policy in the United States: indentifying winners and losers in an expanded permit trading system. The Energy Journal 23(1): 1-18. Rose, A., Chen, C.Y. and Adams, G. (1996) Structural decomposition analysis of changes in material demand. Working paper, The Pennsylvania State Univeristy, United States. Samuel, B.R. (1964) Statistical Analysis. New York, NY, The Ronald Press Company. Sato, K. (1976) The ideal log-change index number. The Review if Economics and Statistics 85(3): 223-228. Schipper, L., Unander, F., Murtishaw, S. and Mike, T. (2001) Indicators of energy use and carbon emissions: explaining the energy economy link. Annual Review of Energy & Environment. 26: 49-81. Schipper, L. (1994) Energy efficiency: lessons from the past and strategies for the future. Pacific and Asian Journal of Energy 4(2): 155-181. Schipper, L.J., Meyers, S., Howarth, R. and Steiner, R. (1992) Energy Efficiency and Human Activity: Past Trends, Future Prospects. Cambridge, UK: Cambridge University Press, 1992. Schipper, L., Murtishaw, S. and Unander, F. (2001a) Analysing differences in carbon emissions in IEA countries. Energy 22(2): 35–75. Schipper, L., Murtishaw, S. and Unander, F. (2001c) International comparisons of sectoral carbon dioxide emissions using a cross-country decomposition technique. The Energy Journal 22(2): 35-75. Schipper, L., Murtishaw, S., Khrushch, M., Ting, M., Karbuz, S. and Unander, F. (2001b). Carbon emissions from manufacturing energy use in 13 IEA countries: long-term trends through 1995. Energy Policy 29(9): 667-688. Schipper, L., Ting, M., Khrushch, M. and Golove, W. (1997) The evolution of carbon dioxide emissions from energy use in industrialized countries: an end-use analysis. Energy Policy 25(7-9): 651-672. Scholl, L., Schipper, L. and Kiang, N. (1996) CO2 emissions from passenger transport: a comparison of international trends from 1973 to 1992. Energy Policy 24(1): 17-30. 180 References Sheinbaum, C. and Rodríguez, V.L. (1997) Recent trends in Mexican industrial energy use and their impact on carbon dioxide emissions. Energy Policy 25(7-9): 825-831. Shorrock, L.D. (2000) Identifying the individual components of United Kingdom domestic sector carbon emission changes between 1990 and 2000. Energy Policy 28(3): 193-200. Shrestha, R. and Timilsina, G.R. (1996) Factors affecting CO2 intensities of power sectors in Asia: a Divisia decomposition analysis. Energy Economics 18(4): 283293. Shrestha, R. and Timilsina, G.R. (1997) SO2 emission intensities of the power sector in Asia: effects of generation-mix and fuel-intensity changes. Energy Economics 19(3): 355-362. Shrestha, R. and Timilsina, G.R. (1998) A Divisia decomposition analysis of NOx emission intensities for power sector in Thailand and South Korea. Energy 23(6): 433-438. Skolka, J. (1977) Input-output anatomy of import elasticities. Empirical Economics 2: 123-136. Skolka, J. (1989) Input-output decomposition analysis for Austria. Journal of Policy Modeling 11: 45-66. Spyros, M., Steven, C.W. and Victor, E.M. (1978) Forecasting: Methods and Applications. U.S.A., John Wiley & Sons, Inc. Stage, J. (2001) Decomposition of Namibian energy intensity. The South African Journal of Economics 69(4): 698-707. State Statistical Bureau (1986 and 1992), Yearbook of China Energy Statistics, Beijing, China. State Statistical Bureau (1987 and 1993), Yearbook of Statistics, Beijing, China, Sterner, T. (1985) Structural change and technology choice: energy use in Mexican manufacturing industry, 1970-81. Energy Economics 7(2): 77-86. Stevens, B.H. and Moore, C.L. (1980). A critical review of the literature on shift-share as a forecasting technique. Journal of Regional Science 20: 419-437. Stuvel, G. (1957) A new index number formula. Econometrica 25(1): 123-131. Sun, J.W. (1998a) Changes in energy consumption and energy intensity: a complete decomposition model. Energy Economics 20(1): 85-100. Sun, J.W. (1998b) Accounting for energy use in China, 1984-94. Energy 23(10): 835949. 181 References Sun, J.W. (1999) Decomposition of aggregate CO2 emissions in the OECD: 19601995. The Energy Journal 20(3): 147-155. Sun, J.W. (2000a) An analysis of the difference in CO2 emission intensity between Finland and Sweden, Energy 25(11): 1139-1146. Sun, J.W. (2000b) Is CO2 emission intensity comparable? Energy Policy 28: 10811084. Sun, J.W. (2001a) Energy demand in the fifteen European Union countries by 2010 ¯: a forecasting model based on the decomposition approach. Energy 26(6): 549560. Sun, J.W. (2001b) Understanding the nature of the statistics behind energy-related CO2 emissions. Energy Policy 29(9): 665-666. Sun, J.W. (2003) Dematerialization in Finnish energy use, 1972-1996. Energy Economics 25(1): 23-32. Sun, J.W. and Ang, B.W. (2000) Some properties of an exact energy decomposition model. Energy 25(12): 1177-1188. Sun, J.W. and Malaska, P. (1998) CO2 emission intensity in developed countries 1980-1994. Energy 23(2): 105-112. Sun, J.W. and Meristo, T. (1999) Measurement of dematerialization/materialization: a case analysis of energy saving and decarbonization in OECD countries, 1960-95. Technological Forecasting and Social Change 60: 275-294. Theriault, L. and Sahi, R. (1997) Energy intensity in the manufacturing sector: Canadian and international perspective. Energy Policy 25(7-9): 773-779. Tiwari, P. (2000) An analysis of sectoral energy intensity in India. Energy Policy 28(11): 771-778. Törnqvist, L. (1935) A memorandum concerning the calculation of bank of Finland consumption price index. (in Swedish), unpublished memo, Bank of Finland, Helsinki. Törnqvist, L. (1936) The Bank of Finland’s Consumption Price Index. Bank of Finland monthly Bulletin 10: 1-8. Törnqvist, L., Vartia, P. and Vartia, Y. (1985) How should relative changes be measured? The American Statistician 39(1): 43-46. Torvanger, A. (1991) Manufacturing sector carbon dioxide emissions in nine OECD countries: 1973-87. Energy Economics 13(3): 168-186. 182 References Unander, F., Karbuz, S., Schipper, L., Khrushch, M. and Ting, M. (1999) Manufacturing energy use in OECD countries: decomposition of long-term trends. Energy Policy 27(13): 769-778. Vartia, Y. (1974) Relative Changes and Economic Indices. (a Licenciate thesis, in Finnish) University of Helsinki, Department of Statistics. Vartia, Y. (1976) Ideal log-change index numbers. Scandinavian Statistics 3: 121-126. Vehmas, J., Kaivo-oja, J., Luukkanen, J. and Malaska, P. (1999) Environmental taxes on fuels and electricity - some experiences from the Nordic countries. Energy Policy 27(6): 343¯355. Viguier, L. (1999) Emissions of SO2, NOx and CO2 in transition economies: emission inventories and Divisia index analysis. The Energy Journal 20(2): 59-87. Werbos, P. (1984) Industrial electricity demand: prospects and uncertainties. In Proceedings: Forecasting the Impact of Industrial Structural Change on US Electricity Demand. Palo Alto, CA: Electric Power Research Institute. Wier, M. (1998) Sources of changes in emissions from energy: a structural decomposition analysis. Economic Systems Research 10(2): 99-112. Wier, M. and Hasler, B. (1999) Accounting for nitrogen in Denmark - a structural decomposition analysis. Ecological Economics 30: 317-331. Worrell, E., Price, L., Martin, N., Farla, J., Schaeffer, R. (1997) Energy intensity in the iron and steel industry: a comparison of physical and economic indices. Energy Policy 25(7-9): 727-744. Worrell, E., Price, L., Martin, N., Hendriks, C. and Meida, L.O. (2001) Carbon dioxide emissions from the global cement industry. Annual Review of Energy and the Environment 26: 303-329. Wu, Y.J., Chung, W. and David, F.J. (2000) Decomposing multi-regional dynamic energy process models. Applied Energy 66(3): 225-235. Zarnikau, J. (1999a) Defining ‘total energy use’ in economic studies: does the aggregation approach matter? Energy Economics 21(5): 485-492. Zarnikau, J. (1999b) Will tomorrow’s energy efficiency indices prove useful in economic studies? The Energy Journal 20(3): 39-145. Zhang, F.Q. and Ang, B.W. (2001) Methodological issues in cross-country/region decomposition of energy and environment indicators. Energy Economics 23(2): 179-190. Zhang, F.Q. and Ang, B.W. (1998) Detecting real business performance using decomposition methodology. In: Proceedings of the 3rd International Conference on Management R194. Shanghai, China, 25-28 July 1998:1-7. 183 References Zhang, F.Q. and Ang, B.W. (2000) Cross country/region decomposition of energy and environment indicators. Energy Economics 23(2): 179-190. Zhang, Z.X. and Folmer, H. (1996) The Chinese energy system: implications for future carbon dioxide emissions in China. The Journal of Energy and Development 21(1): 1-44. Zhang, Z.X. and Folmer, H. (1998) Economic modelling approaches to cost estimates for the control of carbon dioxide emissions. Energy Economics 20(1): 101-120. Zhang, Z.X. (2003) Why did the energy intensity fall in China’s industrial sector in the 1990s? The relative importance of structural change and intensity change. Energy Economics 25(6): 625-638. 184 Metallurgical Chemical Mechanical Building materials Textiles Paper making Food Others Total Coal 1985 1990 2455.03 3275.77 1373.86 1906.72 651.62 723.03 1835.79 2144.21 463.31 596.78 262.97 345.11 517.72 704.82 710.81 875.41 8271.11 10571.85 Energy Consumption Natural gas Oil 1985 1990 1985 1990 180.23 249.4 20.33 38.32 678.56 901.75 163.45 190.82 121.77 123.09 23.07 14.47 157.2 199.37 7.04 10.17 167 235.09 8.6 14.47 20.22 17.9 1.17 0.78 33.61 42.15 1.17 1.1701 110.99 133.14 25.81 6.65 1469.58 1901.89 250.64 276.8501 Data source: State Statistical Bureau (1986, 1989 and 1992) and State Statistical Bureau (1987-1993), China. Note: Energy consumption in PJ and industrial production in 100 Million RMB at 1982 constant price. Sector Electricity 1985 1990 194 298.21 193.86 280.8 115.69 132.2 80.04 119.49 79.14 110.89 29.22 43.27 39.23 65.85 116.31 196.89 847.49 1247.6 1990 1232.9 2145 4881.1 726.2 2364.5 219.6 1773.4 2043.6 15386.3 Industrial Production 1985 727.7 1018.8 2465.1 382 1400.8 118.3 1046.1 1000.6 8159.4 Appendix A.1 Sector classification, energy consumption and production in China industry (1985-1990) Appendix A Data for Case Studies in Chapters and 185 Metallurgical Chemical Building material Paper making Total 1985 2455.03 1373.86 1835.79 262.97 5927.65 Coal Mechanical Textiles Food Others Total 1985 651.62 463.31 517.72 710.81 2343.46 1990 723.03 596.78 704.82 875.41 2900.04 Coal Oil Energy Consumption Natural gas 1990 1985 1990 249.4 20.33 38.32 901.75 163.45 190.82 199.37 7.04 10.17 17.9 1.17 0.78 1368.42 191.99 240.09 Energy consumption Natural gas 1990 1985 1990 123.09 23.07 14.47 235.09 8.6 14.47 42.15 1.17 1.1701 133.14 25.81 6.65 533.47 58.65 36.7601 1985 180.23 678.56 157.2 20.22 1036.21 Oil Data source: Table A.1. Note: Energy consumption in PJ and industrial production in 100 Million RMB at 1982 constant price. Sector 1985 121.77 167 33.61 110.99 433.37 1990 3275.77 1906.72 2144.21 345.11 7671.81 Group B: Less energy intensive sectors Sector Group A: Energy intensive sectors Appendix A.2 Group A and B for China industry (1985-1990) Electricity 1985 1990 115.69 132.2 79.14 110.89 39.23 65.85 116.31 196.89 350.37 505.83 Electricity 1985 1990 194 298.21 193.86 280.8 80.04 119.49 29.22 43.27 497.12 741.77 1990 1232.9 2145 726.2 219.6 4323.7 1985 2465.1 1400.8 1046.1 1000.6 5912.6 1990 4881.1 2364.5 1773.4 2043.6 11062.6 Industrial Production 1985 727.7 1018.8 382 118.3 2246.8 Industrial Production Appendix A Data for Case Studies in Chapters and 186 LDCs OECD LDCs OECD 32 4030 Latin America 544 317 99 South Asia Africa Latin America 7353 330 East Asia 423 Pacific 2572 1955 China 1113 Europe North America Coal 400 5554 143 Africa 7598 824 286 292 731 443 833 2399 1790 Oil CO2 Emission 102 76 134 150 East Asia South Asia 170 618 2215 128 294 Pacific 1845 Oil CO2 Emission 739 1147 North America China 1391 Europe Coal 2839 212 90 77 173 36 211 1345 695 Gas 1589 64 22 1281 199 Gas 2042 25 82 140 84 664 134 582 331 Coal 1098 37 39 34 190 82 338 370 Coal 2737 281 97 99 264 164 309 873 650 Oil 1969 137 34 27 58 43 229 789 652 Oil 27 12 13 Nuclear 1209 93 39 34 76 17 73 576 301 Gas 553 27 76 212 225 Nuclear Energy Consumption 677 28 548 86 Gas Energy Consumption 190 43 10 16 11 56 42 Hydro 92 37 28 Hydro Data source: International Energy Agency (1998). Note: CO2 emission in MTCO2, energy consumption in MTOE, GDP in 100 Million USD at 1982 constant price, population in Million. Total World 1995 Total World 1971 36 13 Renew Renew 27651 2634 1080 1548 2462 3404 2848 6710 6965 GDP 12033 1186 578 528 499 484 1249 3580 3929 GDP Appendix A.3 Global energy-related CO2 emissions, energy consumption, GDP and Population, 1971 and 1995. 5097 478 705 1219 583 1206 147 293 466 Population 3337 289 366 716 360 845 121 230 410 Population Appendix A Data for Case Studies in Chapters and 187 Appendix B Data for Korea Industry CO2 Emissions: 7-sector Model Appendix B Data for Korea Industry CO2 Emissions: 7-Sector Model Data for the Korea industrial CO2 emissions decomposition in 7-sectors are from Chung H.S. and Rhee, H.C. (2001a). Details as follows: f0 = [0.000080 0.000101 0.000000 0.000055 0.000189 0.000148 0.000108] ft = [0.000073 0.000133 0.000000 0.000043 0.000147 0.000193 0.000071] D0 = [1.143 0.035 0.000 0.362 0.030 0.008 0.034 0.010 1.014 0.000 0.017 0.056 0.135 0.018 0.019 0.024 1.000 0.022 0.042 0.594 0.027 0.183 0.057 0.000 1.519 0.089 0.021 0.115 0.248 0.370 0.000 0.497 2.179 0.161 0.408 0.034 0.044 0.000 0.041 0.076 1.082 0.049 0.163 0.237 0.000 0.329 0.360 0.132 1.361] Dt = [1.086 0.011 0.000 0.274 0.019 0.003 0.025 0.006 1.008 0.000 0.011 0.038 0.049 0.011 0.015 0.023 1.000 0.017 0.033 0.499 0.019 0.189 0.037 0.000 1.492 0.071 0.013 0.098 0.255 0.295 0.000 0.432 2.116 0.122 0.371 0.033 0.048 0.000 0.037 0.070 1.061 0.041 0.210 0.280 0.000 0.351 0.365 0.111 1.404] u0 = [0.023 -0.012 -0.029 0.192 0.182 -0.001 0.645] ut = [0.027 -0.009 -0.026 0.127 0.224 0.008 0.649] y0 = 178317431 yt = 375802932 188 Appendix C Proof of the Similarity among Shapley, RLI and MFII Methods Appendix C Proof of the Similarity among Shapley, RLI and MFII Methods We follow the notations in Section 6.2. Assume that there are n factors such that V = x1x2 .xn and let N = {1, 2, …, n}. In the allocation scheme of the refined Laspeyres index method proposed in Sun (1998), the contribution of the change of factor i effect to the aggregate V is ∏x ∆xi o j j∈N \{i} ∆xi + ∆xi ⎞ ⎛ ⎜ ∆x j ∏ xro ⎟ + ∆xi ⎟ ⎜ j∈N \{i} ⎝ r∈N \{i . j } ⎠ ∑ ⎛ ⎞ ⎜ ∆x j ∆x k ∆xl ∏ x ro ⎟ + … + ⎜ ⎟ n j , k ,l∈N \{i} ⎝ r∈N \{i , j , k ,l } ⎠ ∑ ⎞ ⎛ ⎜ ∆x j ∆x k ∏ x ro ⎟ + ⎟ ⎜ j , k∈N \{i} ⎝ r∈N \{i , j , k } ⎠ ∑ n ∏ ∆x j j =1 where ∆xm = xmT - xmo . Substituting ∆xm = xmT - xmo , m ≠ i, in the above equation, we have ∆xi ∏x o j j∈N \{i} + ∆xi ⎛ T ⎞ ⎜ ( x j − x oj ) ∏ xro ⎟ + ⎜ ⎟ j∈N \{i } ⎝ r∈N \{i . j } ⎠ ∑ ∆xi ⎛ T ⎞ ⎜ ( x j − x oj )( x kT − x ko ) ∏ x ro ⎟ + ⎜ ⎟ j , k∈N \{i} ⎝ r∈N \{i , j , k } ⎠ ∆xi ⎛ T ⎞ ⎜ ( x j − x oj )( x kT − x ko )( xlT − xlo ) ∏ x ro ⎟ + … + ∆xi ∑ ⎜ ⎟ n j , k ,l∈N \{i } ⎝ r∈N \{i , j , k ,l } ⎠ ∑ n ∏ (x T j − x oj ) j =1 j ≠i Consider all coefficients consisting of the combination of the following terms ∆xi , x aT , xbT and remaining terms with x ro , for r ∈ N \ {I, a, b}. It can easily be shown that the coefficients for the these combination of terms are 189 Appendix C Proof of the Similarity among Shapley, RLI and MFII Methods o r r∈N \{i , a ,b} ∆xi xaT xbT ⎛ o o ⎞ o ⎜ xl x v ⎟ - … +(-1)n-3 ∆xi xaT xbT x ∏ r ⎜ ⎟ n l ,v∈N \{i , a ,b} ⎝ r∈N \{i , a ,b ,l ,v} ⎠ ∏x - ∆xi xaT xbT ⎞ ⎛ o ⎜ xl ∏ xro ⎟ + ⎟ ⎜ l∈N \{i , a ,b} ⎝ r∈N \{i , a ,b ,l } ⎠ ∆xi xaT xbT ∑ ∑ ∏x o r r∈N \{i , a ,b} ⎡ ⎛ n − 3⎞ ⎛ n − 3⎞ ⎛ n − 3⎞ ⎛ n − ⎞⎤ ⎟⎟⎥ ∆xi xaT xbT ⎟⎟ + . + (−1) n −3 ⎜⎜ ⎟⎟ + ⎜⎜ ⎟⎟ − ⎜⎜ = ⎢ ⎜⎜ − n 3 4 ⎠⎦ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎝ ∏x o r r∈N \{i , a ,b} In general, we can show for any Y ⊆ N\{i} and Q = N – (Y ∪ {i}), we have n ∑ (−1) s − y −1 s = y +1 ⎛ n − y − 1⎞ ⎜ ⎟ ∆xi s ⎜⎝ s − y − 1⎟⎠ ∏x ∏x T j j∈Y o k k∈Q / and Q = N\{i}, we have where y=card|Y|. When Y = O n ∑ (−1) s =1 s −1 ⎛ n − 1⎞ ⎜ ⎟ ∆xi s ⎜⎝ s − 1⎟⎠ ∏x o k k∈N \{i} Hence, another way of representing the refined Laspeyres index model is given below n ∑ (−1) s −1 s =1 ⎛ n − 1⎞ ⎜ ⎟ ∆xi s ⎜⎝ s − 1⎟⎠ ⎛ n ⎞ ⎛ n − y − 1⎞ ⎟⎟∆xi ∏ x Tj ∏ x ko ⎟⎟ x + ∑ ⎜⎜ ∑ (−1) s − y −1 ⎜⎜ ∏ s ⎝ s − y − 1⎠ Y ⊆ N \{i } ⎝ s = y +1 j∈Y k∈Q k∈N \{i} ⎠ o k n ⎛ n − 1⎞ T ⎟⎟ ( xi − xio ) = ∑ (−1) s −1 ⎜⎜ s ⎝ s − 1⎠ s =1 ⎛ n ∑ ⎜⎜ ∑ (−1) Y ⊆ N \{i} s − y −1 ⎝ s = y +1 n ⎛ n − 1⎞ ⎟ = ∑ (−1) s −1 ⎜⎜ s ⎝ s − 1⎟⎠ s =1 ∏x o k + k∈N \{i} ⎞ ⎛ n − y − 1⎞ T ⎟⎟( xi − xio )∏ x Tj ∏ x ko ⎟⎟ ⎜⎜ s ⎝ s − y − 1⎠ j∈Y k∈Q ⎠ ⎞ ⎛ T ⎜ xi ∏ x ko − ∏ x ko ⎟ + ⎟ ⎜ k ∈N ⎠ ⎝ k∈N \{i} ⎛⎛ n ⎞⎞ n − y − 1⎞ ⎞⎛ T o T o ⎟ ⎜ ⎜ ∑ (−1) s − y −1 ⎛⎜ ⎜ ⎟ ⎟ ⎟ x x x x − ∏ ∏ ∏ ∏ j k j k ⎜ s − y − 1⎟ ⎟⎜ ⎜ ⎟⎟ ⎜ s Y ⊆ N \{i} ⎝ ⎝ s = y +1 j∈Y k∈Q ∪( i ) ⎠ ⎠ ⎝ ⎠ ⎠⎝ j∈Y ∪{i} k∈Q ∑ If we define the function U(Z) = ∏x ∏x T j j∈Y ∪{i} k∈Q o k and U(Z-{i}) = ∏x ∏x T j j∈Y o k , where k∈Q ∪{i } Z = Y ∪ {i} then the above equation becomes 190 Appendix C Proof of the Similarity among Shapley, RLI and MFII Methods ⎛⎛ n ⎞ n − z ⎞⎞ ⎜ ⎜ ∑ (−1) s − z ⎛⎜ ⎟(U ( Z ) − U ( Z − {i})) ⎟ ⎟ ∑ ⎟ ⎜ ⎜⎜ ⎟ s ⎝ s − z ⎠ ⎟⎠ Z ⊆ N⎝ ⎝ s= z ⎠ Z ∋i n ∑ (−1) where z = card |Z| . Denote θ n (z ) as s=z s−z (A1) 1⎛n − z⎞ ⎜ ⎟ . Interestingly, we can show s ⎜⎝ s − z ⎟⎠ that the function θ n (z ) can be expressed recursively as θ n (z ) = θ n −1 ( z − 1) - θ n ( z − 1) for z ≥ (A2) Proof: 1⎛ n− z ⎞ ⎟(−1) s − z +1 ⎜⎜ ∑ s ⎝ s − z + 1⎟⎠ s = z −1 n −1 = = n −1 ⎡ s = z −1 ⎣ ∑ ⎢(−1) n −1 ⎡ s=z ⎣ ∑ ⎢(−1) n = ∑ (−1) s=z s − z +1 s− z s−z n ∑ (−1) s − z +1 s = z −1 ⎛ n − z + 1⎞ ⎜ ⎟ s ⎜⎝ s − z + 1⎟⎠ 1⎛ n− z ⎞ ⎛ n − z + 1⎞⎤ ⎛ n − z + 1⎞ ⎟⎟⎥ − (−1) n − z +1 ⎜⎜ ⎟ ⎟⎟ − (−1) s − z +1 ⎜⎜ ⎜⎜ s ⎝ s − z + 1⎠ s ⎝ s − z + 1⎠⎦ n ⎝ n − z + 1⎟⎠ ⎛ n − z ⎞⎤ ⎛n − z⎞ ⎟⎟⎥ + (−1) n − z ⎜⎜ ⎜⎜ ⎟ s ⎝ s − z ⎠⎦ n ⎝ n − z ⎟⎠ ⎛n − z⎞ ⎜ ⎟ s ⎜⎝ s − z ⎟⎠ Hence, instead of computing the function directly for different values of z and n, we can use the recursive equation given in (A2) to determine the value of the function. Furthermore, this recursive equation will be used as part of the proof to show that Sun’s function and Shapley’s function are exactly the same. Consider the function γn(z) defined in Shapley (1953), which can be expressed as ( z − 1)! . By comparing Sun’s function given in (A1) n(n − 1)(n − 2) .(n − z + 1) with Shapley’s function given in Shapley (1953), it is sufficient to show that θ n (z ) is equal to γn(z) for any values of n and z to complete the proof that Sun’s function and Shapley’s function are exactly the same. Proof: 191 Appendix C Proof of the Similarity among Shapley, RLI and MFII Methods Let z = 1. It can easily be verified that θ n (1) = n ∑ (−1) s =1 s −1 ⎛ n − 1⎞ ⎜ ⎟ = (same value with Shapley function, γn(1)). s ⎜⎝ s − ⎟⎠ n Let z = 2. From (A2), θ n (2) = θ n −1 (1) - θ n (1) = = n(n − 1) 1 n −1 n (same value with Shapley function, γn(2)). By induction, let it be true for z = m – 1, m ≥ 2. Then for z = m, θ n (m) = θ n −1 (m − 1) - θ n (m − 1) = (m − 2)! (m − 2)! (n − 1)(n − 2) .(n − m + 1) n(n − 1) .(n − m + 2) = (m − 1)! (same value with Shapley function, γn(m)). n(n − 1)(n − 2) .(n − m + 1) 192 Appendix D Source Data for Korea Industry CO2 Emissions: 4-sector Model Appendix D Source Data for Korea Industry CO2 Emissions: 4-sector Model Source data for the Korea industrial CO2 emissions decomposition as 4-sectors are as follows: f0 = [0.000080 0.000055 0.000185 0.000108] ft = [0.000073 0.000043 0.000150 0.000071] D0 = [1.144 0.363 0.030 0.035 0.185 1.522 0.092 0.118 0.337 0.617 2.471 0.543 0.171 0.339 0.378 1.373] Dt = [1.086 0.275 0.020 0.026 0.190 1.493 0.072 0.099 0.331 0.525 2.323 0.471 0.218 0.358 0.373 1.413] u0 = [0.023 0.192 0.140 0.645] ut = [0.027 0.127 0.197 0.649] y0 = 178317431 yt = 375802932 193 Simulation Data Based on CO2 Emissions of Japan and Korea in 1990 Yi e' 2.94 2.81 2.79 2.84 2.75 2.90 2.92 2.81 2.51 3.23 3.89 3.63 3.63 3.82 3.79 4.51 4.20 3.56 1.69 1.56 2.07 2.14 0.00 0.00 S1 0.000 0.000 0.000 0.005 0.002 0.007 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 40 S2 0.000 0.000 0.000 0.001 0.002 0.147 0.046 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 S3 0.020 0.002 1.004 0.020 0.002 0.001 0.025 0.007 0.006 0.010 0.017 0.013 0.099 0.021 0.003 0.001 0.028 0.006 0.018 0.001 0.004 0.062 0.009 0.035 0.050 0.015 0.006 0.005 0.001 0.006 0.017 0.015 0.046 0.019 0.003 0.006 0.002 0.020 0.060 0.042 0.070 0.101 0.090 0.007 0.136 0.000 0.000 0.000 0.000 0.003 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.000 0.000 0.000 -0.002 0.000 0.000 0.000 0.010 0.069 S4 S4 0.005 0.001 0.002 1.015 0.001 0.001 0.011 0.003 0.002 0.003 0.008 0.008 0.060 0.018 0.002 0.000 0.010 0.004 0.007 0.001 0.002 0.021 0.005 0.020 0.040 0.008 0.003 0.003 0.000 0.001 0.011 0.005 0.015 0.016 0.005 0.003 0.001 0.015 0.028 0.017 0.072 0.077 0.057 0.005 0.055 0.000 0.002 0.000 0.000 0.006 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.012 0.012 S5 S5 0.017 0.001 0.003 0.021 1.001 0.001 0.011 0.003 0.002 0.004 0.009 0.007 0.084 0.027 0.003 0.000 0.044 0.004 0.010 0.003 0.003 0.017 0.006 0.009 0.037 0.024 0.008 0.003 0.001 0.011 0.012 0.017 0.104 0.019 0.004 0.005 0.002 0.007 0.041 0.015 0.039 0.080 0.038 0.003 0.048 0.000 0.000 0.000 0.001 0.004 0.003 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.018 0.012 S6 S6 0.008 0.001 0.002 0.025 0.001 1.003 0.017 0.007 0.008 0.006 0.012 0.010 0.031 0.046 0.002 0.001 0.027 0.004 0.015 0.000 0.003 0.027 0.007 0.025 0.033 0.051 0.006 0.004 0.001 0.005 0.014 0.005 0.288 0.019 0.003 0.007 0.003 0.010 0.055 0.028 0.058 0.068 0.080 0.003 0.091 0.000 0.001 0.000 0.001 0.005 0.002 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.000 S7 S7 0.311 0.062 0.002 0.014 0.002 0.002 1.214 0.008 0.004 0.008 0.051 0.020 0.025 0.023 0.002 0.002 0.057 0.005 0.031 0.001 0.012 0.022 0.010 0.034 0.022 0.014 0.003 0.002 0.001 0.002 0.010 0.005 0.047 0.010 0.003 0.007 0.004 0.009 0.124 0.018 0.040 0.081 0.047 0.003 0.057 0.000 0.000 0.000 0.001 0.000 0.005 0.004 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.000 283 S8 S8 0.067 0.002 0.003 0.021 0.001 0.001 0.025 1.509 0.004 0.007 0.041 0.016 0.051 0.032 0.003 0.002 0.190 0.005 0.028 0.000 0.005 0.012 0.008 0.009 0.028 0.011 0.003 0.003 0.001 0.006 0.016 0.008 0.032 0.016 0.004 0.007 0.004 0.010 0.130 0.020 0.050 0.092 0.078 0.004 0.066 0.000 0.000 0.000 0.001 0.000 0.006 0.014 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.005 0.004 33 S9 S9 0.032 0.003 0.002 0.013 0.001 0.002 0.037 0.419 1.049 0.008 0.035 0.026 0.032 0.020 0.002 0.001 0.084 0.005 0.043 0.000 0.004 0.013 0.008 0.013 0.019 0.010 0.003 0.002 0.001 0.026 0.012 0.008 0.029 0.014 0.005 0.004 0.004 0.013 0.172 0.019 0.045 0.091 0.067 0.003 0.061 0.000 0.000 0.000 0.002 0.000 0.003 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.000 72 S10 S10 0.219 0.002 0.003 0.013 0.003 0.003 0.031 0.018 0.005 1.201 0.044 0.013 0.030 0.021 0.005 0.001 0.088 0.004 0.031 0.001 0.019 0.076 0.016 0.045 0.034 0.013 0.004 0.003 0.001 0.007 0.012 0.005 0.047 0.015 0.003 0.014 0.004 0.009 0.125 0.017 0.041 0.073 0.058 0.003 0.056 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.000 23 S11 S11 0.024 0.002 0.005 0.025 0.001 0.004 0.022 0.017 0.004 0.077 1.486 0.027 0.067 0.037 0.003 0.002 0.095 0.005 0.033 0.001 0.007 0.017 0.007 0.011 0.024 0.012 0.003 0.003 0.001 0.002 0.020 0.006 0.047 0.011 0.003 0.010 0.006 0.010 0.145 0.026 0.053 0.097 0.061 0.003 0.086 0.000 0.000 0.000 0.002 0.000 0.003 0.035 0.000 0.002 0.000 0.000 0.000 0.000 0.002 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.006 0.019 S12 S12 0.011 0.001 0.002 0.013 0.002 0.002 0.016 0.015 0.004 0.019 0.182 1.132 0.030 0.019 0.002 0.002 0.110 0.005 0.072 0.000 0.005 0.018 0.012 0.012 0.017 0.011 0.006 0.022 0.001 0.006 0.010 0.007 0.031 0.015 0.008 0.005 0.004 0.010 0.093 0.022 0.044 0.105 0.046 0.003 0.073 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.000 17 S13 S13 0.005 0.001 0.028 0.132 0.001 0.001 0.011 0.003 0.002 0.005 0.009 0.011 1.019 0.064 0.017 0.001 0.012 0.005 0.008 0.000 0.004 0.023 0.007 0.012 0.084 0.007 0.006 0.004 0.001 0.002 0.038 0.004 0.016 0.011 0.002 0.012 0.002 0.009 0.045 0.016 0.054 0.095 0.060 0.003 0.053 0.217 0.000 0.002 0.000 0.001 0.003 0.205 0.000 0.007 0.000 0.000 0.000 0.000 0.027 0.055 0.000 0.004 0.000 0.023 0.001 0.277 0.000 0.000 0.000 35 S14 S14 0.004 0.001 0.002 0.500 0.001 0.002 0.008 0.003 0.002 0.003 0.007 0.006 0.038 1.044 0.001 0.000 0.014 0.003 0.006 0.001 0.003 0.014 0.004 0.014 0.030 0.006 0.003 0.002 0.000 0.001 0.009 0.004 0.012 0.010 0.003 0.013 0.001 0.010 0.043 0.013 0.046 0.055 0.052 0.003 0.042 0.000 0.002 0.000 0.001 0.005 0.002 0.012 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 29 S15 S15 0.013 0.002 0.504 0.027 0.002 0.001 0.018 0.005 0.004 0.008 0.014 0.011 0.080 0.040 1.161 0.001 0.010 0.005 0.013 0.001 0.004 0.042 0.008 0.027 0.053 0.016 0.005 0.004 0.001 0.004 0.021 0.013 0.047 0.015 0.004 0.060 0.006 0.015 0.101 0.030 0.063 0.089 0.082 0.005 0.096 0.000 0.000 0.000 0.001 0.000 0.000 0.001 0.000 0.000 0.002 0.000 0.000 0.099 0.000 0.001 0.002 0.038 0.002 0.219 0.000 0.000 0.000 0.006 0.001 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39 S40 S41 S42 S43 S44 S45 0.006 0.014 0.021 0.019 0.009 0.010 0.008 0.009 0.008 0.007 0.008 0.008 0.009 0.008 0.064 0.019 0.006 0.005 0.005 0.009 0.006 0.018 0.004 0.006 0.110 0.009 0.012 0.006 0.009 0.066 0.001 0.002 0.002 0.001 0.001 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.001 0.042 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.025 0.002 0.002 0.001 0.002 0.014 -0.001 0.010 0.003 0.004 0.080 0.011 0.038 0.006 0.011 0.005 0.005 0.004 0.003 0.002 0.003 0.004 0.002 0.001 0.001 0.001 0.001 0.002 0.001 0.001 0.001 0.001 0.001 0.000 0.001 0.002 0.176 0.054 0.013 0.025 0.047 0.026 0.021 0.020 0.014 0.011 0.013 0.014 0.011 0.009 0.017 0.015 0.012 0.056 0.088 0.056 0.047 0.009 0.005 0.008 0.010 0.005 0.009 0.004 0.009 0.015 0.001 0.007 0.002 0.003 0.002 0.003 0.043 0.185 0.023 0.011 0.009 0.021 0.007 0.007 0.011 0.005 0.001 0.001 0.002 0.001 0.001 0.001 0.000 0.000 0.001 0.001 0.001 0.000 0.001 0.002 0.001 0.005 0.003 0.003 0.127 0.103 0.004 0.002 0.002 0.002 0.003 0.002 0.003 0.003 0.036 0.020 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.001 0.001 0.001 0.001 0.000 0.001 0.002 0.015 0.026 0.032 0.019 0.018 0.018 0.013 0.013 0.015 0.014 0.014 0.015 0.018 0.016 0.025 0.016 0.012 0.010 0.011 0.016 0.013 0.017 0.008 0.012 0.302 0.019 0.025 0.012 0.016 0.175 0.004 0.006 0.008 0.021 0.006 0.008 0.004 0.004 0.005 0.005 0.011 0.008 0.006 0.009 0.050 0.009 0.006 0.004 0.005 0.006 0.011 0.014 0.003 0.006 0.005 0.004 0.005 0.003 0.006 0.029 0.003 0.003 0.004 0.003 0.006 0.005 0.003 0.003 0.004 0.004 0.003 0.004 0.005 0.010 0.007 0.003 0.005 0.003 0.003 0.005 0.004 0.005 0.004 0.004 0.003 0.002 0.003 0.003 0.007 0.014 0.005 0.008 0.008 0.008 0.010 0.015 0.012 0.010 0.009 0.007 0.008 0.010 0.011 0.008 0.046 0.061 0.007 0.004 0.004 0.011 0.006 0.065 0.004 0.007 0.009 0.005 0.008 0.006 0.010 0.019 0.012 0.047 0.050 0.030 0.050 0.040 0.013 0.013 0.017 0.016 0.017 0.029 0.025 0.024 0.055 0.021 0.015 0.010 0.011 0.022 0.013 0.145 0.009 0.022 0.024 0.007 0.028 0.015 0.014 0.096 0.019 0.020 0.018 0.013 0.012 0.012 0.009 0.011 0.013 0.015 0.014 0.017 0.024 0.018 0.017 0.011 0.016 0.010 0.010 0.012 0.010 0.019 0.020 0.017 0.011 0.007 0.036 0.034 0.028 0.037 0.027 0.072 0.030 0.054 0.139 0.050 0.086 0.072 0.047 0.035 0.036 0.037 0.034 0.026 0.033 0.025 0.060 0.020 0.020 0.020 0.012 0.021 0.015 0.017 0.022 0.013 0.024 0.009 0.020 0.029 0.052 0.096 0.021 0.040 0.069 0.043 0.026 0.025 0.019 0.015 0.018 0.020 0.016 0.014 0.029 0.025 0.013 0.114 0.180 0.112 0.095 0.015 0.007 0.012 0.015 0.007 0.014 0.006 0.014 0.025 -0.037 0.016 0.004 0.006 0.004 0.010 0.079 0.008 0.021 0.010 0.008 0.007 0.004 0.003 0.004 0.006 0.002 0.002 0.002 0.001 0.001 0.002 0.000 0.001 0.002 0.001 0.001 0.001 0.001 0.003 1.009 0.003 0.002 0.002 0.001 0.003 0.003 0.003 0.002 0.001 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.003 0.001 0.001 0.005 0.001 0.002 0.001 0.001 0.003 0.022 1.537 0.159 0.463 0.025 0.052 0.069 0.028 0.041 0.044 0.080 0.070 0.065 0.047 0.133 0.038 0.015 0.018 0.023 0.017 0.015 0.033 0.008 0.012 0.026 0.012 0.032 0.012 0.017 0.068 0.007 0.009 1.071 0.006 0.006 0.005 0.004 0.005 0.004 0.006 0.007 0.007 0.011 0.010 0.005 0.005 0.006 0.004 0.004 0.005 0.004 0.007 0.005 0.005 0.005 0.003 0.053 0.006 0.008 0.015 0.008 0.043 0.050 1.243 0.024 0.016 0.011 0.010 0.016 0.046 0.099 0.067 0.062 0.051 0.152 0.030 0.013 0.019 0.024 0.013 0.013 0.029 0.004 0.009 0.012 0.008 0.013 0.008 0.012 0.029 0.000 0.001 0.001 0.001 1.009 0.073 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.002 0.001 0.006 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.001 0.003 0.010 0.017 0.012 0.023 1.057 0.017 0.009 0.012 0.011 0.019 0.016 0.022 0.021 0.013 0.074 0.005 0.004 0.005 0.003 0.003 0.004 0.001 0.003 0.010 0.004 0.004 0.002 0.004 0.012 0.016 0.024 0.018 0.032 0.032 0.056 1.923 0.018 0.473 0.212 0.161 0.133 0.047 0.048 0.049 0.119 0.020 0.023 0.037 0.016 0.014 0.042 0.004 0.008 0.012 0.010 0.008 0.005 0.016 0.026 0.005 0.040 0.011 0.019 0.008 0.016 0.036 1.712 0.119 0.062 0.051 0.166 0.057 0.051 0.089 0.023 0.006 0.007 0.012 0.005 0.005 0.005 0.002 0.003 0.005 0.003 0.004 0.002 0.006 0.014 0.010 0.026 0.021 0.023 0.016 0.017 0.010 0.010 1.060 0.050 0.028 0.044 0.032 0.029 0.041 0.106 0.008 0.008 0.010 0.007 0.009 0.013 0.002 0.007 0.014 0.007 0.006 0.003 0.011 0.019 0.053 0.040 0.024 0.037 0.057 0.043 0.040 0.045 0.047 1.301 0.184 0.055 0.041 0.037 0.023 0.044 0.026 0.029 0.045 0.023 0.020 0.016 0.008 0.009 0.015 0.025 0.019 0.009 0.039 0.030 0.007 0.011 0.009 0.009 0.020 0.020 0.011 0.013 0.011 0.014 1.559 0.009 0.009 0.008 0.020 0.015 0.103 0.168 0.309 0.072 0.066 0.012 0.005 0.012 0.009 0.005 0.007 0.005 0.042 0.014 0.004 0.004 0.003 0.004 0.006 0.005 0.004 0.005 0.007 0.066 0.076 1.204 0.078 0.038 0.005 0.027 0.008 0.009 0.016 0.006 0.005 0.003 0.001 0.002 0.002 0.003 0.003 0.002 0.006 0.014 0.004 0.003 0.003 0.003 0.004 0.004 0.003 0.003 0.008 0.049 0.031 0.043 1.412 0.186 0.003 0.006 0.004 0.005 0.008 0.003 0.003 0.002 0.001 0.002 0.002 0.005 0.003 0.002 0.012 0.016 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.009 0.004 0.004 0.002 1.146 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.001 0.000 0.002 0.001 0.000 0.002 0.000 0.003 0.001 0.002 0.002 0.002 0.002 0.003 0.004 0.003 0.005 0.003 0.003 0.003 0.002 0.003 0.003 1.042 0.007 0.002 0.001 0.002 0.002 0.002 0.002 0.001 0.002 0.003 0.002 0.004 0.001 0.004 0.012 0.025 0.019 0.011 0.016 0.030 0.023 0.022 0.017 0.017 0.012 0.012 0.014 0.015 0.012 0.011 1.013 0.039 0.015 0.009 0.011 0.017 0.011 0.005 0.012 0.009 0.035 0.013 0.008 0.019 0.014 0.005 0.006 0.008 0.007 0.010 0.008 0.006 0.008 0.008 0.006 0.005 0.006 0.008 0.007 0.006 0.005 1.005 0.004 0.004 0.004 0.005 0.005 0.004 0.010 0.005 0.002 0.005 0.010 0.008 0.006 0.013 0.038 0.025 0.030 0.087 0.091 0.037 0.042 0.031 0.025 0.028 0.027 0.023 0.022 0.062 0.047 0.010 1.081 0.087 0.013 0.011 0.025 0.011 0.021 0.028 0.008 0.015 0.007 0.015 0.035 0.013 0.011 0.011 0.010 0.013 0.012 0.012 0.013 0.015 0.012 0.010 0.011 0.012 0.012 0.024 0.022 0.008 0.008 1.008 0.008 0.009 0.010 0.008 0.023 0.009 0.007 0.012 0.009 0.021 0.018 0.002 0.003 0.006 0.003 0.003 0.004 0.003 0.003 0.005 0.003 0.003 0.003 0.005 0.004 0.003 0.003 0.002 0.002 0.002 1.190 0.002 0.003 0.008 0.006 0.003 0.001 0.005 0.003 0.003 0.005 0.007 0.013 0.006 0.008 0.020 0.019 0.024 0.029 0.015 0.008 0.010 0.009 0.005 0.005 0.010 0.009 0.002 0.019 0.016 0.005 1.423 0.005 0.002 0.002 0.004 0.001 0.002 0.001 0.002 0.006 0.001 0.006 0.004 0.006 0.004 0.006 0.008 0.007 0.005 0.004 0.006 0.008 0.005 0.004 0.004 0.003 0.027 0.005 0.010 0.083 0.014 1.003 0.001 0.008 0.003 0.003 0.002 0.001 0.002 0.005 0.015 0.010 0.022 0.010 0.011 0.009 0.008 0.012 0.010 0.011 0.011 0.010 0.011 0.011 0.014 0.011 0.012 0.012 0.010 0.019 0.017 0.024 1.045 0.025 0.012 0.006 0.017 0.023 0.018 0.017 0.044 0.085 0.068 0.097 0.083 0.087 0.111 0.130 0.095 0.114 0.127 0.109 0.105 0.093 0.134 0.102 0.034 0.075 0.111 0.041 0.047 0.070 0.018 1.033 0.126 0.025 0.052 0.024 0.044 0.180 0.023 0.026 0.023 0.025 0.028 0.028 0.020 0.021 0.024 0.021 0.020 0.022 0.026 0.023 0.024 0.023 0.019 0.015 0.018 0.019 0.020 0.023 0.011 0.017 1.020 0.012 0.017 0.019 0.016 0.328 0.051 0.054 0.050 0.053 0.068 0.058 0.049 0.049 0.050 0.057 0.054 0.057 0.068 0.063 0.055 0.056 0.043 0.070 0.076 0.104 0.110 0.062 0.030 0.076 0.060 1.037 0.058 0.058 0.052 0.156 0.143 0.165 0.284 0.113 0.116 0.091 0.081 0.094 0.084 0.119 0.138 0.142 0.227 0.214 0.094 0.107 0.115 0.075 0.071 0.102 0.072 0.150 0.101 0.101 0.085 0.055 1.163 0.133 0.104 0.182 0.047 0.068 0.044 0.053 0.071 0.065 0.054 0.065 0.050 0.047 0.047 0.043 0.042 0.048 0.061 0.046 0.265 0.067 0.090 0.062 0.111 0.048 0.023 0.064 0.037 0.078 0.038 1.109 0.026 0.054 0.006 0.004 0.006 0.003 0.004 0.004 0.003 0.003 0.004 0.004 0.003 0.003 0.004 0.003 0.004 0.003 0.003 0.003 0.004 0.002 0.004 0.003 0.002 0.002 0.003 0.002 0.004 0.004 1.001 0.014 0.073 0.084 0.075 0.080 0.090 0.089 0.065 0.068 0.077 0.069 0.064 0.071 0.085 0.075 0.079 0.074 0.063 0.047 0.058 0.061 0.066 0.075 0.036 0.056 0.064 0.038 0.056 0.060 0.052 1.061 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39 S40 S41 S42 S43 S44 S45 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.021 0.099 0.001 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.018 0.007 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.000 0.001 0.000 0.005 0.001 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.001 0.001 0.000 0.000 0.000 0.003 0.001 0.003 0.004 0.000 0.002 0.003 0.000 0.000 0.000 0.000 0.002 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.005 0.121 0.050 0.000 0.004 0.004 0.000 0.000 0.001 0.000 0.002 0.000 0.001 0.002 0.000 0.004 0.001 0.003 0.001 0.009 0.003 0.006 0.002 0.001 0.001 0.001 0.001 0.001 0.002 0.001 0.002 0.000 0.000 0.001 0.055 0.000 0.001 0.003 0.001 0.001 0.004 0.000 0.004 0.000 0.000 0.018 0.001 0.004 0.014 0.021 0.003 0.006 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.175 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.282 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.000 0.000 -0.001 0.000 0.001 0.000 0.004 0.001 0.001 0.002 0.001 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.049 0.000 0.000 0.000 0.000 0.000 0.006 0.000 0.001 0.000 0.001 0.000 0.000 0.001 0.000 0.000 0.004 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.011 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.043 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.100 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.207 0.001 0.002 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.111 0.002 0.000 0.000 0.001 0.003 0.114 0.010 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.003 0.002 0.000 0.000 0.000 0.002 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.098 0.002 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.556 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.008 0.001 0.001 0.001 0.000 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.004 0.001 0.001 0.000 0.001 0.000 0.003 0.008 0.002 0.006 0.024 0.006 0.008 0.007 0.004 0.003 0.002 0.003 0.003 0.002 0.002 0.001 0.013 0.002 0.001 0.002 0.000 0.001 0.003 0.003 0.003 0.002 0.004 0.001 0.003 0.001 0.000 0.009 0.001 0.000 0.036 0.001 0.006 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 24 1 14 185 152 68 106 48 19 824 34 37 31 17 29 498 112 530 611 86 267 Note: e: CO2 emission coefficient K: energy coefficient G: Leontief coefficient Y: GDP. G S1 S2 S3 S1 1.204 0.030 S2 0.006 1.066 S3 0.001 0.001 S4 0.012 0.036 S5 0.001 0.001 S6 0.001 0.001 S7 0.113 0.101 S8 0.006 0.033 S9 0.004 0.007 S10 0.005 0.007 S11 0.031 0.016 S12 0.007 0.013 S13 0.014 0.016 S14 0.021 0.071 S15 0.001 0.001 S16 0.001 0.001 S17 0.092 0.031 S18 0.004 0.008 S19 0.017 0.026 S20 0.000 0.000 S21 0.005 0.003 S22 0.009 0.014 S23 0.005 0.005 S24 0.009 0.008 S25 0.020 0.018 S26 0.011 0.055 S27 0.002 0.006 S28 0.002 0.003 S29 0.000 0.000 S30 0.001 0.003 S31 0.008 0.006 S32 0.003 0.004 S33 0.056 0.026 S34 0.006 0.014 S35 0.002 0.002 S36 0.006 0.008 S37 0.002 0.002 S38 0.005 0.009 S39 0.065 0.077 S40 0.008 0.025 S41 0.022 0.029 S42 0.040 0.052 S43 0.062 0.053 S44 0.001 0.003 S45 0.027 0.080 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14 E15 E16 E17 E18 E19 E20 E21 E22 E23 E24 Appendix E.1 Simulation Data Based on CO2 Emissions of Japan Appendix E Appendix E Simulation Data Based on CO2 Emissions of Japan and Korea in 1990 194 Yi e' 4.59 3.63 3.79 2.81 2.84 2.87 3.00 2.51 2.79 2.79 2.14 3.63 4.51 2.94 0.00 S1 0.000 0.000 0.000 0.004 0.001 0.024 0.001 0.000 0.000 0.000 0.000 0.006 0.000 0.000 0.002 S2 0.000 0.000 0.000 0.002 0.006 0.237 0.035 0.008 0.000 0.000 0.000 0.003 0.000 0.000 0.001 S3 0.000 0.006 0.000 0.001 0.003 0.007 0.011 0.003 0.000 0.000 0.000 0.001 0.000 0.000 0.054 S4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 S5 0.000 0.000 0.000 0.000 0.000 0.024 0.024 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.071 S6 0.001 0.000 0.000 0.009 0.001 0.142 0.018 0.001 0.000 0.000 0.000 0.003 0.000 0.000 0.023 S7 0.000 0.000 0.000 0.002 0.000 0.007 0.038 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.005 20 S8 0.000 0.000 0.000 0.002 0.002 0.005 0.091 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.025 S9 0.000 0.000 0.000 0.002 0.000 0.005 0.020 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.004 10 S10 0.006 0.000 0.000 0.005 0.002 0.019 0.019 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.009 S11 0.000 0.000 0.003 0.006 0.002 0.008 0.143 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.018 S12 0.000 0.001 0.000 0.005 0.002 0.008 0.007 0.002 0.000 0.000 0.000 0.000 0.008 0.000 0.005 S13 0.000 0.136 0.662 0.001 0.011 0.060 0.806 0.022 0.000 0.000 0.085 0.000 0.022 0.000 0.064 S14 0.000 0.000 0.000 0.001 0.009 0.007 0.147 0.014 0.006 0.000 0.000 0.000 0.002 0.000 0.004 S15 0.000 0.000 0.000 0.002 0.000 0.004 0.011 0.000 0.000 0.000 0.000 0.008 0.116 0.000 0.012 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39 S40 S41 S42 S43 S44 S45 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.000 0.001 0.000 0.000 0.001 0.000 0.002 0.000 0.000 0.042 0.021 0.001 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.000 0.000 0.001 0.002 0.000 0.000 0.000 0.000 0.024 0.000 0.009 0.000 0.000 1.882 0.002 0.002 0.031 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.003 0.003 0.003 0.009 0.001 0.002 0.003 0.004 0.003 0.002 0.001 0.003 0.003 0.005 0.004 0.012 0.009 0.286 0.009 0.037 0.007 0.017 0.008 0.005 0.011 0.010 0.021 0.000 0.010 0.007 0.000 0.009 0.006 0.031 0.004 0.004 0.003 0.001 0.001 0.002 0.001 0.001 0.002 0.003 0.003 0.001 0.024 0.000 0.021 0.003 0.001 0.010 0.118 0.002 0.005 0.002 0.002 0.000 0.004 0.010 0.005 0.007 0.040 0.112 0.008 0.025 0.011 0.009 0.006 0.009 0.002 0.006 0.010 0.024 0.442 0.761 0.537 0.006 0.185 0.077 0.005 0.035 0.048 0.017 0.018 0.010 0.031 0.002 0.007 0.075 0.017 0.031 0.041 0.154 0.056 0.050 0.010 0.007 0.008 0.008 0.005 0.005 0.005 0.002 0.023 0.005 0.015 0.002 0.275 0.007 0.000 0.017 0.012 0.015 0.015 0.005 0.017 0.000 0.000 0.004 0.002 0.001 0.006 0.030 0.002 0.002 0.003 0.003 0.001 0.006 0.000 0.001 0.040 0.001 0.000 0.003 0.389 0.000 0.029 0.003 0.002 0.012 0.055 0.002 0.007 0.000 0.005 0.001 0.000 0.068 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.217 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.010 0.002 0.001 0.001 0.001 0.000 0.000 0.001 0.000 0.004 0.000 0.000 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.006 0.001 0.003 0.000 0.000 0.000 0.004 0.022 0.043 0.006 0.006 0.000 0.010 0.000 0.000 0.029 0.001 0.000 0.006 0.008 0.235 0.033 0.000 0.000 0.002 0.000 0.000 0.001 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.023 0.003 0.011 0.067 0.011 0.034 0.021 0.009 0.005 0.004 0.005 0.004 0.007 0.007 0.001 0.039 0.004 0.001 0.002 0.000 0.005 0.007 0.008 0.022 0.015 0.008 0.007 0.005 0.000 2 0 13 15 15 1 40 1 16 16 18 15 Note: e: CO2 emission coefficient K: energy coefficient G: Leontief coefficient Y: GDP. G S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39 S40 S41 S42 S43 S44 S45 S1 1.185 0.004 0.002 0.015 0.001 0.003 0.155 0.004 0.001 0.003 0.013 0.002 0.010 0.022 0.002 0.001 0.100 0.006 0.012 0.001 0.004 0.015 0.005 0.008 0.012 0.008 0.003 0.002 0.001 0.001 0.007 0.001 0.007 0.002 0.001 0.001 0.002 0.005 0.042 0.002 0.015 0.014 0.023 0.001 0.020 S2 0.032 1.028 0.003 0.082 0.003 0.004 0.040 0.043 0.002 0.010 0.016 0.004 0.011 0.119 0.003 0.001 0.048 0.004 0.017 0.001 0.006 0.041 0.013 0.008 0.048 0.061 0.016 0.010 0.006 0.001 0.009 0.001 0.009 0.005 0.003 0.013 0.005 0.009 0.064 0.005 0.033 0.029 0.049 0.010 0.045 S3 0.084 0.001 1.007 0.020 0.004 0.003 0.031 0.006 0.001 0.046 0.011 0.003 0.064 0.026 0.004 0.005 0.074 0.003 0.015 0.001 0.007 0.074 0.014 0.008 0.044 0.030 0.022 0.007 0.003 0.001 0.020 0.011 0.013 0.005 0.001 0.001 0.003 0.006 0.041 0.004 0.018 0.034 0.041 0.001 0.036 S4 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 S5 0.028 0.001 0.010 0.035 1.005 0.006 0.030 0.009 0.002 0.016 0.015 0.003 0.102 0.046 0.006 0.007 0.174 0.002 0.022 0.004 0.009 0.088 0.017 0.016 0.076 0.014 0.022 0.009 0.004 0.001 0.030 0.003 0.009 0.003 0.004 0.001 0.003 0.009 0.049 0.005 0.035 0.028 0.075 0.002 0.044 S6 0.017 0.001 0.004 0.037 0.003 1.003 0.021 0.006 0.001 0.010 0.008 0.002 0.038 0.052 0.003 0.003 0.051 0.001 0.015 0.001 0.006 0.046 0.010 0.010 0.054 0.049 0.010 0.006 0.002 0.001 0.023 0.003 0.011 0.004 0.002 0.002 0.002 0.007 0.030 0.004 0.066 0.020 0.030 0.002 0.033 S7 0.582 0.033 0.003 0.023 0.003 0.005 1.226 0.009 0.001 0.004 0.044 0.003 0.019 0.032 0.003 0.002 0.095 0.014 0.030 0.001 0.010 0.030 0.010 0.022 0.017 0.012 0.005 0.004 0.002 0.005 0.008 0.002 0.014 0.003 0.002 0.001 0.004 0.009 0.086 0.004 0.025 0.037 0.038 0.002 0.034 S8 0.116 0.002 0.008 0.050 0.004 0.010 0.055 1.814 0.003 0.004 0.049 0.006 0.066 0.070 0.006 0.005 0.376 0.003 0.024 0.001 0.008 0.035 0.015 0.012 0.044 0.011 0.010 0.006 0.003 0.007 0.012 0.002 0.015 0.005 0.004 0.002 0.004 0.013 0.083 0.007 0.042 0.043 0.105 0.003 0.062 S9 0.113 0.005 0.005 0.035 0.004 0.007 0.156 0.562 1.246 0.004 0.056 0.008 0.039 0.049 0.004 0.003 0.255 0.004 0.043 0.001 0.007 0.028 0.014 0.013 0.027 0.010 0.007 0.005 0.002 0.014 0.010 0.002 0.014 0.005 0.005 0.002 0.004 0.013 0.116 0.006 0.040 0.042 0.083 0.003 0.054 S10 0.310 0.003 0.007 0.032 0.008 0.007 0.066 0.026 0.005 1.245 0.039 0.005 0.034 0.044 0.007 0.003 0.160 0.004 0.043 0.002 0.018 0.115 0.029 0.034 0.032 0.019 0.007 0.005 0.002 0.002 0.010 0.002 0.039 0.005 0.004 0.001 0.008 0.013 0.103 0.005 0.036 0.043 0.076 0.003 0.048 S11 0.054 0.002 0.007 0.048 0.006 0.014 0.041 0.028 0.003 0.006 1.832 0.007 0.064 0.066 0.005 0.005 0.221 0.003 0.032 0.003 0.018 0.040 0.027 0.011 0.031 0.012 0.008 0.005 0.003 0.001 0.012 0.003 0.017 0.005 0.003 0.002 0.005 0.012 0.081 0.005 0.042 0.041 0.094 0.003 0.048 S12 0.048 0.002 0.008 0.035 0.009 0.011 0.045 0.188 0.049 0.039 0.194 1.025 0.036 0.049 0.007 0.003 0.241 0.003 0.072 0.004 0.029 0.080 0.040 0.024 0.032 0.014 0.015 0.047 0.004 0.003 0.010 0.003 0.015 0.006 0.007 0.002 0.005 0.014 0.097 0.006 0.043 0.042 0.086 0.003 0.057 S13 0.014 0.001 0.059 0.116 0.002 0.004 0.016 0.003 0.001 0.006 0.008 0.002 1.090 0.119 0.006 0.074 0.074 0.001 0.007 0.002 0.009 0.026 0.009 0.007 0.017 0.006 0.018 0.006 0.004 0.001 0.058 0.003 0.008 0.002 0.002 0.002 0.003 0.005 0.029 0.003 0.015 0.028 0.037 0.001 0.025 S14 0.005 0.000 0.001 0.736 0.001 0.008 0.007 0.002 0.000 0.001 0.005 0.001 0.009 1.070 0.001 0.001 0.036 0.001 0.004 0.001 0.002 0.017 0.004 0.010 0.011 0.003 0.002 0.002 0.002 0.000 0.003 0.001 0.003 0.001 0.001 0.002 0.001 0.003 0.013 0.001 0.008 0.014 0.012 0.001 0.011 S15 0.061 0.001 0.666 0.029 0.004 0.004 0.029 0.007 0.002 0.033 0.011 0.003 0.057 0.039 1.025 0.004 0.064 0.002 0.015 0.002 0.010 0.063 0.014 0.009 0.041 0.031 0.019 0.007 0.003 0.001 0.018 0.037 0.054 0.005 0.002 0.005 0.031 0.008 0.042 0.004 0.025 0.034 0.044 0.003 0.038 S16 0.004 0.000 0.001 0.625 0.001 0.001 0.007 0.002 0.000 0.001 0.003 0.002 0.006 0.105 0.001 1.174 0.012 0.001 0.002 0.000 0.001 0.009 0.002 0.002 0.008 0.005 0.001 0.002 0.001 0.000 0.004 0.001 0.003 0.002 0.002 0.001 0.001 0.004 0.021 0.001 0.012 0.017 0.088 0.002 0.012 S17 0.038 0.002 0.018 0.119 0.012 0.038 0.061 0.012 0.002 0.004 0.037 0.006 0.061 0.170 0.021 0.005 1.738 0.004 0.036 0.003 0.018 0.044 0.031 0.026 0.033 0.014 0.009 0.006 0.005 0.002 0.013 0.003 0.017 0.006 0.004 0.003 0.005 0.012 0.091 0.006 0.038 0.056 0.076 0.003 0.059 S18 0.087 0.002 0.004 0.024 0.004 0.008 0.062 0.012 0.002 0.004 0.056 0.007 0.022 0.034 0.003 0.002 0.141 1.185 0.019 0.004 0.034 0.023 0.022 0.014 0.014 0.011 0.005 0.005 0.003 0.002 0.010 0.004 0.009 0.016 0.006 0.001 0.003 0.014 0.070 0.007 0.048 0.168 0.062 0.003 0.068 S19 0.058 0.002 0.011 0.064 0.008 0.018 0.046 0.090 0.002 0.004 0.043 0.008 0.052 0.090 0.011 0.004 0.715 0.003 1.097 0.003 0.019 0.062 0.027 0.018 0.042 0.012 0.010 0.009 0.004 0.002 0.011 0.003 0.015 0.006 0.005 0.003 0.004 0.013 0.089 0.006 0.039 0.046 0.077 0.003 0.053 S20 0.023 0.001 0.124 0.040 0.015 0.108 0.022 0.006 0.001 0.009 0.082 0.003 0.124 0.052 0.005 0.009 0.060 0.002 0.018 1.016 0.026 0.080 0.020 0.008 0.053 0.029 0.019 0.007 0.003 0.001 0.016 0.005 0.024 0.004 0.005 0.003 0.009 0.009 0.040 0.004 0.033 0.040 0.058 0.002 0.034 S21 0.021 0.001 0.022 0.060 0.006 0.152 0.029 0.009 0.002 0.006 0.046 0.004 0.048 0.085 0.005 0.004 0.108 0.002 0.017 0.123 1.058 0.064 0.014 0.010 0.042 0.031 0.010 0.006 0.003 0.001 0.012 0.007 0.028 0.004 0.003 0.005 0.009 0.010 0.058 0.005 0.040 0.030 0.068 0.002 0.046 S22 0.021 0.001 0.061 0.038 0.072 0.018 0.026 0.007 0.002 0.009 0.016 0.003 0.081 0.051 0.085 0.006 0.078 0.002 0.013 0.006 0.043 2.350 0.081 0.013 0.055 0.015 0.018 0.008 0.003 0.001 0.021 0.006 0.025 0.004 0.003 0.004 0.010 0.011 0.085 0.004 0.032 0.036 0.081 0.003 0.042 S23 0.024 0.001 0.017 0.044 0.261 0.006 0.032 0.010 0.002 0.010 0.018 0.004 0.091 0.059 0.013 0.007 0.137 0.002 0.016 0.003 0.014 0.062 1.767 0.014 0.045 0.015 0.016 0.007 0.005 0.001 0.018 0.005 0.021 0.005 0.004 0.003 0.007 0.012 0.071 0.005 0.035 0.036 0.099 0.003 0.051 S24 0.027 0.002 0.023 0.031 0.045 0.010 0.037 0.010 0.002 0.015 0.024 0.005 0.053 0.042 0.030 0.004 0.097 0.002 0.024 0.004 0.026 0.784 0.169 1.049 0.075 0.015 0.021 0.013 0.008 0.002 0.014 0.004 0.018 0.005 0.004 0.003 0.006 0.012 0.085 0.006 0.038 0.038 0.081 0.003 0.060 S25 0.024 0.001 0.014 0.027 0.026 0.009 0.034 0.012 0.003 0.009 0.023 0.004 0.039 0.037 0.018 0.003 0.103 0.002 0.039 0.003 0.025 0.439 0.100 0.037 1.308 0.038 0.068 0.053 0.025 0.002 0.012 0.003 0.015 0.007 0.005 0.002 0.005 0.013 0.096 0.006 0.037 0.043 0.069 0.003 0.055 S26 0.024 0.001 0.013 0.027 0.020 0.008 0.031 0.024 0.002 0.011 0.022 0.004 0.036 0.037 0.016 0.003 0.127 0.002 0.080 0.003 0.025 0.362 0.068 0.034 0.227 1.222 0.059 0.050 0.015 0.002 0.011 0.003 0.014 0.005 0.004 0.002 0.005 0.012 0.100 0.005 0.035 0.043 0.075 0.002 0.048 S27 0.027 0.002 0.011 0.036 0.045 0.011 0.038 0.017 0.002 0.007 0.045 0.006 0.042 0.049 0.011 0.004 0.181 0.003 0.069 0.006 0.043 0.189 0.268 0.026 0.060 0.013 1.212 0.156 0.024 0.002 0.013 0.003 0.017 0.006 0.006 0.002 0.005 0.014 0.108 0.006 0.041 0.051 0.075 0.003 0.059 S28 0.025 0.002 0.008 0.027 0.017 0.015 0.035 0.016 0.002 0.006 0.041 0.006 0.033 0.037 0.007 0.003 0.132 0.003 0.062 0.009 0.075 0.108 0.096 0.017 0.038 0.011 0.067 1.704 0.014 0.002 0.011 0.003 0.016 0.006 0.008 0.002 0.005 0.015 0.111 0.006 0.041 0.062 0.068 0.002 0.056 S29 0.025 0.002 0.009 0.028 0.022 0.014 0.035 0.017 0.005 0.006 0.042 0.007 0.037 0.038 0.008 0.003 0.126 0.003 0.069 0.009 0.068 0.143 0.119 0.030 0.047 0.031 0.087 0.209 1.115 0.002 0.011 0.003 0.014 0.006 0.008 0.002 0.005 0.015 0.100 0.006 0.042 0.058 0.090 0.003 0.056 S30 0.052 0.021 0.007 0.039 0.030 0.019 0.049 0.207 0.007 0.006 0.104 0.008 0.043 0.055 0.006 0.003 0.232 0.003 0.044 0.003 0.022 0.068 0.187 0.022 0.041 0.014 0.020 0.013 0.004 1.013 0.013 0.003 0.015 0.008 0.005 0.003 0.005 0.014 0.084 0.008 0.052 0.046 0.099 0.003 0.072 S31 0.028 0.001 0.011 0.032 0.012 0.029 0.029 0.010 0.002 0.039 0.025 0.004 0.026 0.045 0.009 0.002 0.081 0.003 0.035 0.034 0.106 0.194 0.041 0.049 0.061 0.014 0.047 0.017 0.005 0.001 1.012 0.003 0.021 0.005 0.003 0.002 0.005 0.011 0.067 0.005 0.045 0.066 0.069 0.002 0.045 S32 0.011 0.001 0.006 0.074 0.003 0.007 0.016 0.006 0.001 0.005 0.008 0.002 0.069 0.105 0.003 0.005 0.030 0.001 0.012 0.002 0.011 0.061 0.012 0.010 0.029 0.114 0.015 0.010 0.008 0.001 0.015 1.001 0.007 0.004 0.001 0.002 0.023 0.006 0.031 0.003 0.020 0.019 0.030 0.001 0.027 S33 0.015 0.001 0.003 0.113 0.003 0.003 0.022 0.010 0.002 0.007 0.011 0.004 0.016 0.164 0.002 0.001 0.045 0.001 0.040 0.001 0.005 0.039 0.009 0.011 0.024 0.087 0.010 0.007 0.002 0.001 0.008 0.004 1.028 0.006 0.003 0.002 0.005 0.009 0.045 0.004 0.038 0.024 0.040 0.004 0.036 S34 0.012 0.001 0.002 0.125 0.002 0.003 0.018 0.007 0.001 0.002 0.009 0.003 0.009 0.180 0.002 0.001 0.048 0.001 0.045 0.001 0.004 0.034 0.009 0.006 0.022 0.083 0.014 0.007 0.002 0.001 0.006 0.001 0.035 1.003 0.002 0.002 0.008 0.006 0.046 0.003 0.024 0.021 0.041 0.005 0.030 S35 0.017 0.001 0.002 0.169 0.003 0.004 0.027 0.007 0.001 0.003 0.013 0.003 0.014 0.244 0.002 0.001 0.033 0.006 0.012 0.001 0.005 0.036 0.010 0.009 0.028 0.067 0.012 0.011 0.006 0.001 0.015 0.001 0.010 0.007 1.101 0.004 0.127 0.012 0.043 0.005 0.111 0.057 0.039 0.002 0.045 S36 0.025 0.002 0.003 0.132 0.003 0.004 0.040 0.012 0.002 0.004 0.014 0.006 0.015 0.191 0.002 0.002 0.040 0.002 0.012 0.001 0.006 0.042 0.010 0.014 0.028 0.042 0.009 0.013 0.002 0.001 0.025 0.004 0.016 0.008 0.005 1.096 0.151 0.016 0.043 0.007 0.230 0.029 0.083 0.005 0.069 S37 0.026 0.002 0.002 0.031 0.002 0.002 0.043 0.012 0.002 0.004 0.019 0.007 0.017 0.044 0.002 0.002 0.028 0.003 0.012 0.001 0.004 0.028 0.007 0.007 0.036 0.025 0.006 0.007 0.002 0.001 0.014 0.002 0.027 0.016 0.006 0.009 1.004 0.038 0.025 0.008 0.113 0.046 0.065 0.004 0.073 S38 0.010 0.001 0.002 0.008 0.001 0.001 0.016 0.003 0.002 0.002 0.006 0.002 0.015 0.011 0.001 0.001 0.012 0.002 0.004 0.001 0.003 0.010 0.007 0.002 0.008 0.003 0.021 0.019 0.004 0.001 0.009 0.001 0.002 0.002 0.007 0.000 0.002 1.045 0.013 0.003 0.017 0.024 0.019 0.001 0.027 S39 0.022 0.002 0.003 0.023 0.001 0.002 0.036 0.007 0.002 0.002 0.032 0.003 0.020 0.032 0.003 0.002 0.022 0.002 0.008 0.001 0.004 0.015 0.005 0.006 0.011 0.007 0.006 0.005 0.002 0.002 0.020 0.002 0.006 0.008 0.015 0.001 0.003 0.050 1.050 0.006 0.071 0.035 0.042 0.002 0.060 S40 0.018 0.001 0.006 0.048 0.002 0.003 0.020 0.011 0.002 0.017 0.017 0.016 0.041 0.061 0.006 0.011 0.040 0.002 0.020 0.002 0.008 0.019 0.006 0.008 0.011 0.006 0.008 0.005 0.001 0.001 0.026 0.001 0.006 0.004 0.001 0.001 0.001 0.016 0.031 1.003 0.197 0.028 0.046 0.004 0.032 S41 0.011 0.001 0.003 0.014 0.002 0.004 0.016 0.005 0.001 0.005 0.008 0.003 0.028 0.018 0.002 0.004 0.031 0.001 0.007 0.004 0.012 0.027 0.007 0.007 0.012 0.007 0.008 0.006 0.001 0.001 0.099 0.001 0.004 0.003 0.002 0.001 0.001 0.009 0.017 0.003 1.050 0.020 0.064 0.002 0.027 S42 0.027 0.002 0.003 0.019 0.002 0.003 0.037 0.010 0.003 0.005 0.066 0.012 0.022 0.026 0.002 0.003 0.056 0.046 0.014 0.001 0.006 0.017 0.008 0.005 0.014 0.011 0.006 0.012 0.007 0.003 0.015 0.003 0.006 0.007 0.005 0.001 0.002 0.021 0.038 0.006 0.059 1.110 0.031 0.002 0.060 S43 0.021 0.002 0.002 0.013 0.001 0.001 0.035 0.007 0.002 0.002 0.013 0.014 0.017 0.018 0.001 0.002 0.019 0.003 0.006 0.001 0.004 0.011 0.004 0.003 0.009 0.008 0.004 0.009 0.001 0.001 0.014 0.002 0.004 0.012 0.006 0.000 0.002 0.022 0.017 0.006 0.095 0.048 1.110 0.015 0.060 S44 0.039 0.003 0.005 0.030 0.006 0.004 0.060 0.015 0.005 0.007 0.022 0.015 0.022 0.042 0.005 0.003 0.053 0.008 0.019 0.003 0.013 0.084 0.022 0.016 0.131 0.092 0.022 0.031 0.014 0.003 0.042 0.004 0.009 0.011 0.007 0.001 0.003 0.017 0.053 0.011 0.045 0.048 0.046 1.002 0.102 S45 0.344 0.026 0.007 0.032 0.004 0.007 0.604 0.060 0.019 0.010 0.122 0.033 0.029 0.044 0.004 0.003 0.140 0.013 0.039 0.003 0.018 0.042 0.016 0.020 0.025 0.012 0.011 0.011 0.003 0.015 0.020 0.002 0.016 0.005 0.004 0.002 0.005 0.014 0.144 0.111 0.147 0.047 0.092 0.003 1.049 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14 E15 Appendix E.2 Simulation Data Based on CO2 Emissions of Korea Appendix E Simulation Data Based on CO2 Emissions of Japan and Korea in 1990 195 [...]... may not equal to the total effect and there is a residue term DI rsd Decomposition is “perfect” which means leaving no residue in the results if DI rsd =1 1.3.2 Decomposition models From the view of model type, decomposition methodologies can be classified into index decomposition analysis (IDA), structural decomposition analysis (SDA), shift share analysis (SSA), growth accounting analysis (GAA),... Capital, Labor, Energy and Material xiii Summary Decomposition analysis is an important systems analytical tool that has been widely applied in energy and environmental studies during the past two decades A variety of methods have been proposed and empirical studies for a wide spectrum of countries have been reported This thesis focuses on some methodological issues of decomposition analysis Literature... or basic elements” There are many types of decomposition analysis in various fields based on this definition In this thesis, we focus on decomposition methodologies issues that deal with top-down analysis with particular reference to their application to energy and environmental studies By estimating the impact of each variable on the system, decomposition analysis is useful in improving our understanding... lack direct relation to physical laws Hence, decomposing the highly aggregated indicators to understandable effects has become an active area in energy research Decomposition analysis is developed to satisfy this requirement, in order to understand the evolving pattern of energy use By controlling the most significant impacts, energy policy makers may determine ways of saving energy without damaging... coal From year 1 to year 2, the amount of total energy consumption is unchanged (i.e both are 100 TOE) However, the overall CO2 emission increases from 362.2 tones of carbon dioxide (TCO2) to 380.6 TCO2 From analysis on Table 1.1, we know that the change of CO2 emissions may due to changes in the industrial output, production structure, sectoral energy intensity, and fuel mix In order to quantify their... sector i in year t Yt : Total industrial production in year t ( Yt = ∑ Yi ,t ) i S i,t : Production share of sector i in year t ( Si ,t = Yi ,t / Yt ) I i,t : Energy intensity for sector i in year t ( I i ,t = Ei ,t / Yi ,t ) It : Aggregate energy intensity in year t ( I t = Et / Yt ) DI tot : Actual energy intensity change in ratio between year 0 and year T ( DI tot = I T / I 0 ) DEtot : Actual energy. .. environmental studies In this introductory chapter, the concept of decomposition is presented first, which is followed by examples and problems in energy and environmental study areas The structure of the thesis and its contributions are also highlighted 1.1 Introduction to Decomposition Analysis Basically, decomposition analysis is a research topic involving systems analysis and economics Here, we introduce... major impact on the aggregate energy intensity ( I t = Et / Yt ) of industry given by the ratio of total industrial energy consumption to total industrial output This type of change in the production mix, later recognized as structural effect, arises because energy intensity varies among the various sectors of industry Given a certain level of total output, the total energy consumed depends on the... sectoral energy intensity is the same from year 1 and year 2 in each sector in order to eliminate the sectoral intensity effect From the table we can see how a major reduction in the iron and steel industry, with a compensating increase in the “other industry”, leads to a substantial decrease in the aggregate energy intensity for industry as a whole from 1.0 to 0.66 TOE/$1000 even though the sectoral... is 0.34 TOE/$1000 Totally, we have ∆I tot = ∆I str + ∆I int On the other hand, in the ratio change, the unchanged sectoral intensity has no effect, i.e DI int = 1, and, the structural change has an effect of 0.66 In total, we have DI tot = DI str ⋅ DI int Table 1.1 Effects of structural change in industrial energy use in a country: a simple example Year 1 Energy Industrial Year 2 Energy Energy Industrial . DECOMPOSITION ANALYSIS APPLIED TO ENERGY: SOME METHODOLOGICAL ISSUES LIU FENGLING （Master of Engineering, XJTU） A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR. reported. This thesis focuses on some methodological issues of decomposition analysis. Literature review of index decomposition analysis (IDA) concerning energy and environmental studies is. on the methodological issues of decomposition analysis, with particular reference to their applications in energy and environmental studies. In this introductory chapter, the concept of decomposition