A study on consistency in aggregation in index decomposition analysis

A STUDY ON CONSISTENCY IN AGGREGATION IN INDEX DECOMPOSITION ANALYSIS ALEXIA VAN DER CRUISSE DE WAZIERS NATIONAL UNIVERSITY OF SINGAPORE 2005 A STUDY ON CONSISTENCY IN AGGREGATION IN INDEX DECOMPOSITION ANALYSIS ALEXIA VAN DER CRUISSE DE WAZIERS A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2005 Acknowledgements ACKNOWLEDGEMENTS I would like to thank my supervisors Professor Ang Beng Wah and Associate Professor Tan Kay Chuan for their guidance and support throughout this research. I would also like to thank all the members of the ISE Department, especially my laboratory mates, who have made my experience in Singapore unforgettable. Finally, I am grateful to the National University of Singapore, whose financial support has been essential to the completion of this study. -I- Table of Contents TABLE OF CONTENTS ACKNOWLEDGEMENTS I TABLE OF CONTENTS II SUMMARY VI NOMENCLATURE VIII LIST OF TABLES IX LIST OF FIGURES XI CHAPTER INTRODUCTION 1.1 Index Decomposition Analysis 1.2 Research objectives 1.3 Thesis structure CHAPTER INDEX DECOMPOSITION ANALYSIS METHODS 2.1 The decomposition approach 2.1.1 The aggregate indicator 2.1.2 Additive approach to IDA 2.1.3 Multiplicative approach 10 2.2 Methods linked to the Laspeyres index 2.2.1 Laspeyres and Paasche indexes 2.2.2 Marshall-Edgeworth index 2.2.3 Fisher Ideal index 11 11 13 13 2.3 The Divisia index methods 15 2.3.1 The principles 2.3.2 AMDI (Törnqvist index) 2.3.3 LMDI I (Vartia I) 2.3.4 LMDI II (Sato-Vartia) 15 18 18 19 2.4 20 Other methods -II- Table of Contents 2.4.1 2.4.2 Stuvel index Mean Rate of Change Index 20 21 2.5 Summary of all the methods presented 21 2.6 The methodological issues: the test approach 24 2.7 Conclusion 27 CHAPTER THEORY OF CONSISTENCY IN AGGREGATION 29 3.1 Disaggregation 30 3.1.1 Definition 3.1.2 Importance of disaggregation in decomposition studies 3.1.3 Limits of disaggregation in decomposition studies 30 30 32 3.2 33 The price and quantity index 3.3 Consistency in aggregation 3.3.1 Definition: The aggregation 3.3.2 Definition: Consistency in aggregation 34 34 35 3.4 Approximate consistency in aggregation 3.4.1 The functional form of the aggregator 3.4.2 Numerical approximation 3.4.3 The residual term 36 37 39 40 3.5 Three types of consistency in aggregation 41 3.6 Advantages of the consistency in aggregation 44 3.7 Conclusion 46 CHAPTER CONSISTENCY IN AGGREGATION AND INDEX DECOMPOSITION ANALYSIS 47 4.1 Consistency in aggregation for IDA 4.1.1 The disaggregation for IDA 4.1.2 Advantages of consistency in aggregation in IDA 4.1.3 Additive and multiplicative approaches 48 48 49 51 4.2 52 Methodology for the study of consistency in aggregation 4.3 The Additive methods 4.3.1 Proof of consistency in aggregation for the methods linked to the Laspeyres index 4.3.2 Consistency in aggregation for AMDI, LMDI I and LMDI II 4.3.3 Consistency in aggregation for the Mean Rate of Change Index 53 53 56 57 4.4 The multiplicative methods 4.4.1 Methods linked to the Laspeyres index 4.4.2 The methods linked to the Divisia Index method 58 59 62 4.5 65 Conclusion CHAPTER CASE STUDY, THE CANADIAN INDUSTRIAL SECTOR 5.1 The Data 68 69 -III- Table of Contents 5.2 Methodology 5.2.1 Decomposition formula 5.2.2 Contributing factors studied 5.2.3 Study of the consistency in aggregation 70 70 71 73 5.3 Additive approach 5.3.1 Results of the decomposition 5.3.2 Consistency in aggregation of the additive methods 75 75 76 5.4 Multiplicative approach 5.4.1 Results of the decomposition study 5.4.2 Consistency in aggregation of the multiplicative methods 77 77 78 5.5 79 Conclusion CHAPTER CONSISTENCY IN AGGREGATION, THE CASE OF PARTIAL FULFILLMENT 82 6.1 Multi-level indexes 6.1.1 The multi-level indexes 6.1.2 The problem found in the literature 6.1.3 Other decomposition formulae affected 86 83 83 84 6.2 The partial consistency in aggregation for multiplicative methods 6.2.1 LMDI I 6.2.2 Laspeyres index 89 89 93 6.3 The issue of partial fulfillment for consistent additive methods 6.3.1 Divisia index methods 6.3.2 Methods linked to the Laspeyres index 6.3.3 The other methods 94 95 96 97 6.4 Case study 6.4.1 Data and methodology 6.4.2 LMDI I multiplicative 6.4.3 The additive Divisia index methods 6.4.4 The Laspeyres index 6.4.5 MRCI 98 98 100 101 102 103 6.5 104 Conclusion CHAPTER CASE STUDY, ENERGY CONSUMPTION IN CANADA 106 7.1 The measurement of energy efficiency 7.1.1 The physical indicators 7.1.2 The current practice in energy efficiency monitoring 107 107 108 7.2 The use of physical indicators 7.2.1 Aggregating the physical indicators 7.2.2 The decomposition formula and the physical indicators 111 111 113 7.3 Methodology 7.3.1 Data 7.3.2 Methodology 7.3.3 The decomposition applied to the end-use sectors 115 115 115 116 7.4 Results 7.4.1 Results at the sector level 124 124 -IV- Table of Contents 7.4.2 Results for the entire country 129 7.5 The advantages of the total consistency in aggregation 131 7.6 Conclusion 132 CHAPTER CONCLUSION 134 REFERENCES 138 APPENDIX A SECTOR CLASSIFICATION FOR THE CANADIAN INDUSTRY APPENDIX B DATA FOR THE DECOMPOSITION OF THE INDUSTRIAL ENERGY CONSUMPTION IN CANADA APPENDIX C 146 DATA FOR THE STUDY OF THE CHANGES IN ENERGY CONSUMPTION IN CANADA BETWEEN 1996 AND 2001 APPENDIX E 144 RESULTS FOR THE DECOMPOSITION OF THE INDUSTRIAL ENERGY CONSUMPTION IN CANADA BETWEEN 1990 AND 2000 APPENDIX D 142 151 RESULTS OF THE DECOMPOSITION OF THE CHANGES IN ENERGY CONSUMPTION 159 -V- Summary SUMMARY Decomposition methodology is a statistical technique used to analyze a set of data at the aggregate level. It aims to establish the relative contributions of a set of underlying factors to the changes in an aggregate, such as energy consumption in a country. To conduct decomposition studies, researchers have developed numerous methods based on the index number theory. Researchers are currently seeking a common agreement as to which method is best among those found in the literature. This agreement should be found through the study of the theoretical properties established by a set of predefined tests. Among these tests, the most important are the factor-reversal test, the time reversal test, the proportionality test, and the consistency in aggregation test. This study focuses on only the last test, since it has not yet been thoroughly studied in Index Decomposition Analysis. Hence, the main contribution of this study is to redefine the consistency in aggregation in Index Decomposition Analysis (IDA) and study this attribute for the main IDA methods. Vartia’s definition of the consistency in aggregation (Balk, 1996) is restrictive. Researchers consider three types of approximations: the functional form of the aggregator function, the residual term, and numerical approximations. We define three degrees of consistency in aggregation to include more methods: type A, exact -VI- Summary consistency in aggregation; type B, partial consistency in aggregation; and type C, approximate numerical consistency in aggregation. However, in some situations consistency in aggregation is only partially fulfilled, even with decomposition methods that are consistent with type A. After studying this issue we find that the Log-Mean Divisia Index I (LMDI I) is the best method for considering consistency in aggregation. Finally, through a case study we examine consistency in aggregation with the use of physical indicators in energy-consumption monitoring. -VII- List of Abbreviations NOMENCLATURE AMDI Arithmetic Mean Divisia Index APEC Asia Pacific Economic Cooperation GDP Gross Domestic Product GJ Giga Joules GO Gross Output IDA Index Decomposition Analysis IDM Index Decomposition Methods IEA International Energy Agency LMDI Log-Mean Divisia Index MJ Mega Joules MRCI Mean Rate of Change Index NAICS North American Industry Classification System OECD Organization for Economic Co-operation and Development PJ Peta Joules SIC Standard Industrial Classification TJ Tera Joules -VIII- -18805.1 -58226.1 69475.4 -8228.7 15784.5 0,00 -14566.4 -12929.4 -17799.2 -21431.4 -158.5 -66884.9 -15093.2 -58699.1 -65239.4 -72864.8 -110562.6 -322 459,00 74651.9 124 882,00 236465.3 281 149,00 226292.8 943440.8 -179723.7 374373.2 Coal Petroleum Electricity Gas Other Total Coal Petroleum Electricity Gas Other Total Coal Petroleum Electricity Gas Other Total Residual Total sector -179723.7 374373.2 74651.9 124 882,00 236465.3 281 149,00 226292.8 943440.8 -15093.2 -58699.1 -65239.4 -72864.8 -110562.6 -322 459,00 -14566.4 -12929.4 -17799.2 -21431.4 -158.5 -66884.9 -18805.1 -58226.1 69475.4 -8228.7 15784.5 0,00 results Coal Petroleum Electricity Gas Other Total Direct Calculation Aggregation Laspeyres 0,00 374373.2 65127.5 99927.6 231401.8 259188.1 207106.9 862751.9 -17972.4 -63595.8 -88164.3 -93833.1 -134180.3 -397745.8 -15924.4 -14972.9 -28285.1 -32190.2 739.8 -90632.8 -21980.9 -65323.9 77535.6 -8975.8 18 745,00 0,00 results Aggregation -147- Calculation Fuel mix effect -21980.9 -65323.9 77535.6 -8975.8 18 745,00 0,00 Intensity effect -15924.4 -14972.9 -28285.1 -32190.2 739.8 -90632.8 Structural effect -17972.4 -63595.8 -88164.3 -93833.1 -134180.3 -397745.8 Growth effect 65127.5 99927.6 231401.8 259188.1 207106.9 862751.9 Total Value 0,00 374373.2 Direct Fisher Ideal -186 246,00 -374373.2 -55855.1 -76354.8 -223826.1 -236038.1 -187814.8 -779888.8 20803.3 66365.5 113967.7 115706.2 158 364,00 475206.8 16934.3 16240.6 41041.1 43888.3 -1549.4 116554.9 25012.6 70781.3 -83526.3 9104.7 -21372.4 0,00 results Aggregation Direct -186 246,00 -374373.2 -55855.1 -76354.8 -223826.1 -236038.1 -187814.8 -779888.8 20803.3 66365.5 113967.7 115706.2 158 364,00 475206.8 16934.3 16240.6 41041.1 43888.3 -1549.4 116554.9 25012.6 70781.3 -83526.3 9104.7 -21372.4 0,00 Calculation Paasche 191388.4 374373.2 9398.4 24263.6 6319.6 22555.4 19 239,00 81 776,00 2855.1 3833.2 24364.2 21420.7 23900.7 76373.9 184,00 1655.6 11620.9 11228.4 -854,00 24 835,00 3103.8 6277.6 -7025.5 438,00 -2 794,00 0,00 results Aggregation 191388.4 374373.2 9398.4 24263.6 6319.6 22555.4 19 239,00 81 776,00 2855.1 3833.2 24364.2 21420.7 23900.7 76373.9 184,00 1655.6 11620.9 11228.4 -854,00 24 835,00 3103.8 6277.6 -7025.5 438,00 -2 794,00 0,00 Calculation Direct Marshall-Edgeworth Table C. 1: Results for the decomposition of the changes in energy consumption of the Canadian industry: Laspeyres, Fisher Ideal, Paasche, and MarshallEdgeworth Appendix C -23254.5 -63742.8 76602 -10784.4 19152.1 -2027.7 -17106.2 -14997 -23024.1 -72428 1500.5 -126054.9 -18748.6 -63251.1 -89396.9 -58232.2 -131371.9 -361000.8 68359.2 98026 228307 265633.6 203130.7 863456.5 374373.2 Coal Petroleum Electricity Gas Other Total Coal Petroleum Electricity Gas Other Total Coal Petroleum Electricity Gas Other Total Coal Petroleum Electricity Gas Other Total Residual Total sector 374373.2 68359.2 98026 228307 265633.6 203130.7 863456.5 -18748.6 -63251.1 -89396.9 -58232.2 -131371.9 -361000.8 -17106.2 -14997 -23024.1 -72428 1500.5 -126054.9 -23254.5 -63742.8 76602 -10784.4 19152.1 -2027.7 MRCI Aggregation Direct results Calculation -148- AMDI Aggregation Direct results Calculation Fuel mix effect -22581.1 -22581.1 -66450.2 -66450.2 77398.4 77398.4 -8583.7 -8583.7 26764.2 26764.2 6547.5 6547.5 Intensity effect -15662.4 -15662.4 -14691.1 -14691.1 -25851.8 -25851.8 -29778.3 -29778.3 912.8 912.8 -85070.8 -85070.8 Structural effect -17605.2 -17605.2 -62626.7 -62626.7 -87783.6 -87783.6 -93653.4 -93653.4 -132361.2 -132361.2 -394030.1 -394030.1 Growth effect 64284.3 64284.3 97468.5 97468.5 231272.8 231272.8 257241.6 257241.6 205771.6 205771.6 856038.8 856038.8 Total Value -9112.1 -9112.1 374373.2 374373.2 374373.2 63908.4 96463 229014.9 256060.4 204032.4 849479.1 -17443 -62163.3 -87054.9 -93308.6 -131664.2 -391634 -15615.8 -14744.5 -25974.7 -29997.3 921.7 -85410.7 -21599.8 -63520.2 76502.8 -8565.5 19121.5 1938.8 374373.2 63908.4 96463 229014.9 256060.4 204032.4 849479.1 -17443 -62163.3 -87054.9 -93308.6 -131664.2 -391634 -15615.8 -14744.5 -25974.7 -29997.3 921.7 -85410.7 -21599.8 -63520.2 76502.8 -8565.5 19121.5 1938.8 LMDI I Aggregation Direct results Calculation 2532.56 374173 35409.51 71998.33 285205.7 410677.1 51179.4 854470 -26320.9 -41892.8 -108955 -171395 -33890.6 -382455 -1197.5 -15200.4 -31098.7 -49087.2 -3791.13 -100375 -17951.5 -63633.4 111777.9 -58133.5 27940.53 -42.9579 374173 64254.84 97405.57 230005.4 257550.4 205253.8 854470 -17528.1 -62779.9 -87548.4 -93906.5 -132478 -394241 -15658.8 -14884 -26273.2 -30408.1 863.5551 -86360.6 -22120 -64496.9 76821.77 -8591.52 18733.77 347.1633 LMDI II Aggregation Direct results Calculation Table C. 2: Results for the decomposition of the changes in energy consumption of the Canadian industry: MRCI, AMDI , LMDI I, LMDI II Appendix C Appendix C Table C. 3: Results of the multiplicative decomposition: LMDI II, LMDI I and AMDI Coal Petroleum electricity gas other sector value Dfuel coal petroleum electricity gas other sector value Dint coal petroleum electricity gas other sector value Dse coal petroleum electricity gas other sector value Dgrowth residual total value LMDI II aggregation direct results calculation Fuel mix effect -0,68% -0,87% -2,53% -2,56% 4,41% 3,04% -2,32% -0,34% 1,11% 0,74% 0,00% 0,01% 100,00% 100,01% Intensity effect -0,06% -0,62% -0,60% -0,59% -1,21% -1,04% -1,92% -1,20% -0,15% 0,03% -3,95% -3,42% 96,13% 96,64% Structural effect -1,05% -0,70% -1,66% -2,49% -4,32% -3,47% -6,79% -3,72% -1,34% -5,25% -15,17% -15,63% 85,93% 85,53% Growth effect 1,42% 2,55% 2,85% 3,86% 11,30% 9,12% 16,27% 10,21% 2,03% 8,14% 33,88% 33,88% 140,33% 140,33% Total value 100,00% 100,00% 115,92% 116,00% LMDI I aggregation direct results calculation AMDI aggregation direct results calculation -0,86% -2,52% 3,03% -0,34% 0,76% 0,08% 100,08% -0,86% -2,52% 3,03% -0,34% 0,76% 0,08% 100,08% -0,959% -2,725% 3,037% -0,342% 0,971% -0,018% 99,982% -0,958% -2,730% 3,076% -0,351% 0,994% 0,030% 100,030% -0,62% -0,58% -1,03% -1,19% 0,04% -3,39% 96,67% -0,62% -0,58% -1,03% -1,19% 0,04% -3,39% 96,67% -0,623% -0,588% -1,033% -1,195% 0,029% -3,410% 96,648% -0,619% -0,661% -1,389% -1,552% 0,027% -4,194% 95,893% -0,69% -2,47% -3,45% -3,70% -5,22% -15,53% 85,62% -0,69% -2,47% -3,45% -3,70% -5,22% -15,53% 85,62% -0,704% -2,513% -3,469% -3,709% -5,237% -15,632% 85,529% -0,698% -2,500% -3,432% -3,672% -5,242% -15,544% 85,604% 2,53% 3,83% 9,08% 10,15% 8,09% 33,69% 140,05% 2,53% 3,83% 9,08% 10,15% 8,09% 33,69% 140,05% 2,560% 3,912% 9,101% 10,176% 8,135% 33,884% 140,332% 2,551% 3,834% 8,789% 9,857% 8,143% 33,174% 139,339% 100,00% 116,00% 100,00% 116,00% 100,015% 116,00% 101,382% 116,00% -149- Appendix C Table C. 4: Results of the multiplicative decomposition: Laspeyres, Paasche, and MarshallEdgeworth Laspeyres aggregation direct results calculation Coal Petroleum electricity gas other sector value 89.84% 81.20% 111.85% 98.82% 102.81% 100.00% 89.84% 81.20% 111.85% 98.82% 102.81% 100.00% coal petroleum electricity gas other sector value 92.13% 95.82% 96.96% 96.93% 99.97% 97.14% 92.13% 95.82% 96.96% 96.93% 99.97% 97.14% coal petroleum electricity gas other sector value 91.85% 81.04% 88.87% 89.55% 80.29% 86.21% 91.85% 81.04% 88.87% 89.55% 80.29% 86.21% coal petroleum electricity gas other sector value 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% residual total value 98.704% 116.00% 98.704% 116.00% Paasche aggregation direct results calculation Fuel mix effect 112.87% 112.87% 126.64% 126.64% 89.27% 89.27% 101.11% 101.11% 96.73% 96.73% 100.00% 100.00% Intensity effect 108.71% 108.71% 106.11% 106.11% 105.27% 105.27% 105.34% 105.34% 99.76% 99.76% 104.30% 104.30% Structural effect 110.70% 110.70% 124.98% 124.98% 114.63% 114.63% 114.09% 114.09% 124.23% 124.23% 117.51% 117.51% Growth effect 71.26% 71.26% 71.26% 71.26% 71.26% 71.26% 71.26% 71.26% 71.26% 71.26% 71.26% 71.26% Total value 100.00% 98.71% 86.20% 86.20% -150- Marshall-Edgeworth aggregation direct results calculation 94.91% 84.38% 112.53% 99.26% 119.83% 105.77% 89.17% 80.03% 111.94% 98.87% 103.11% 100.55% 92.21% 95.64% 97.72% 97.67% 100.42% 97.70% 92.05% 95.07% 95.82% 95.82% 100.11% 96.48% 91.77% 81.06% 89.50% 89.74% 80.48% 86.61% 91.03% 80.51% 87.88% 88.46% 80.41% 85.66% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 140.33% 73.988% 116.00% 68.690% 116.00% Appendix D APPENDIX D DATA FOR THE STUDY OF THE CHANGES IN ENERGY CONSUMPTION IN CANADA BETWEEN 1996 AND 2001 -151- Appendix D Table D. 1: Data for the residential sector Sub-sector Floor space services End-Use services Space heating Equipment Energy use (PJ) 1996 2001 1996 2001 Oil furnace (N-M) 117.00 81.30 1377.00 1500.00 Gas furnace (N-M) 490.70 386.00 34.10 41.60 119.20 112.40 8.30 11.10 12.60 9.30 428.00 542.00 1377.00 1500.00 11069.00 11897.00 11069.00 11897.00 Gas furnace (H) Electric base board heat pump propane space cooling lighting other 2.10 1.30 wood 28.50 24.10 dual wood 85.60 93.40 dual electric 14.40 14.80 Total Space Heating 912.50 775.30 Room 1.80 2.90 Central 7.90 13.70 Total Space Cooling 9.70 16.60 56.10 62.40 Total Lighting Total Floor Space Services household services Appliances 978.30 854.30 Refrigerators 44.5 39.5 Freezers 18.2 15.1 1.5 1.500001 Dishwashers Clothes washers 2.3 2.4 Clothes dryers 28.2 30.3 Ranges 26.8 29.4 Other Total Appliances Water heating Activity (floorspace in million m2) Electricity 57 67.8 178.50 186.00 102 103.2 175.1 176.1 Heating oil 14 13.9 Wood 0.3 0.7 Natural gas Propane 1.6 Coal and other 0.2 0.1 293.20 296.00 Total Water Heating TOTAL Household Services Total residential -152- 471.70 482.00 1450.00 1336.30 Appendix D ● Transport sector Table D. 2: Data for the passenger transport sector Sub-sector End-Use service Road Small Cars Large Cars Light Trucks Motorcycles Total Road School Bus Urban Transit Inter-City Bus Total Bus Bus Air Rail Total Passenger Transport Energy use (PJ) 1996 323.4 319.0 317.1 1.8 961.3 15.2 41.3 7.8 64.3 209.4 2.4 1,237.4 Activity in millions Tones-kilometers 2001 315.7 295.3 417.6 2.0 1,030.6 15.2 42.9 6.1 64.2 218.7 3.0 1,316.5 1996 170,867 129,784 92,725 1,216 2001 156,926 116,473 122,108 1,367 15,013 21,643 7,373 14,776 20,936 6,869 82,120 1,513 522,254 96,989 1,601 538,045 Table D. 3: Data for the freight transport sector Sub-sectors Trucks End-Use service Light Trucks Medium Trucks Heavy Trucks Total Trucks Rail Marine Total Freight Transport Total Transport Energy use (PJ) Activity in millions passenger-kilometer 1996 2001 1996 2001 134.2 130.8 169.7 164.1 12,271 18,320 15,464 24,196 300.1 342.1 120,000 154,257 565.1 76.7 99.9 741.7 1,979.1 675.9 78.7 123.2 877.8 2,194.3 150,591.0 282,482 191,511 624,584 1,146,838.0 193,917.0 325,708 227,413 747,038 1,285,083.0 -153- Iron and Steel Total Non-Manufacturing Petroleum refining Cement Chemical Smelting and Refining Upstream mining Construction Forestry Pulp and Paper Non Metal Mining Metal Mining Sectors ● Industrial sector Petrochemical Industrial gas Synthetic dye and pigment Other basic Chemical fertilizer and pesticides Total Chemical Pulp Mills Paper Mills Newsprint Mills Paperboard Mills Converted Paper Products Total Pulp and Paper Primary Products Alumina and Aluminum Other non ferrous Total Smelting and Refining Gold and Silver Copper, Nickel, Lead and Zinc Iron Other Metals Total Metal Mining Potash Salt Other Total Non Metal Mining Sub-Sectors 74.9 246.1 311.3 63.5 36.6 9.6 3.1 100.9 51.1 201.3 224.5 2,514.4 81.5 233.3 329.5 58.5 38.1 6.6 4.8 142.4 63.4 255.3 252.1 2,536.1 -154- 13.6 23.1 28.6 8.2 73.5 28.5 2.4 9.2 40.1 408.0 47.8 18.3 403.9 103.8 288.1 70.1 14.1 880.0 171.2 2001 15.1 29.1 36.3 5.5 86.0 31.4 2.9 7.5 41.8 345.0 50.5 9.6 392.5 104.0 297.7 69.2 11.1 874.5 151.8 1996 Energy use in PJ 4,661.0 -21.7 1,573.0 581.0 826.0 224.0 161.0 2,073.0 1,093.0 2,510.0 1,894.0 1,356.0 2,730.0 703.0 423.0 -12.5 953.0 228.0 337.0 -1.7 26,217.0 40,714.0 5,294.0 1,816.0 1,820.0 3,714.0 679.0 2,713.0 1996 2001 5,180.0 1,782.0 635.0 791.0 219.0 147.0 1,933.0 1,444.0 3,281.0 2,357.0 29,645.0 50,346.0 5,737.0 2,134.0 1,848.0 3,649.0 762.0 2,625.0 949.0 234.0 906.0 1,397.0 2,779.0 446.0 706.0 GDP in millions $97 Table D. 4: Data for the Non-Manufacturing sector MJ/ton MJ/m3 MJ/ton MJ/ton MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/ton MJ/$97-GDP MJ/ton MJ/$97-GDP MJ/$97-GDP MJ/$97-GDP MJ/ton MJ/ton MJ/ton MJ/ton MJ/ton MJ/ton MJ/ton Energy Efficiency Indicators Unit MJ/ton MJ/ton MJ/ton MJ/ton 18,567.9 3,266.8 5,210.3 5,674.2 15.2 7.4 24.0 10,772.4 32.3 65,882.9 12.2 1.2 1.4 38,952.1 19,946.8 31,540.8 19,316.4 1.4 3,502.8 436.0 674.2 497.2 220.8 388.2 375.5 1996 15,823.5 2,861.6 4,980.6 3,906.4 16.4 4.7 15.3 8,524.1 22.8 65,330.5 13.8 1.0 3.2 42,199.9 15,225.2 34,840.0 17,710.0 1.6 3,462.6 217.2 565.6 339.4 246.0 373.4 589.7 2001 Energy Intensity Appendix D Sub-Sectors Meat products Fruit and Vegetables Bakery Other Food Dairy Products Beverage Breweries Total Food and Beverages Tobacco Products Rubber Products Plastic Products Resin and Synthetic Rubber Leather and Allied Products Textile Mills Textile Products Clothing Industry Wood Products Furniture Printing and Related Products Fabricated Metal Products Machinery Motor Vehicles Motor Vehicle Parts Computer and Electrical Electrical Equipment and Components Other Manufacturing Total Manufacturing Total Industry Food and beverage Industry Sectors -155- 1,290.0 2,442.0 6,035.0 2,632.0 300.0 1,240.0 840.0 2,790.0 9,903.0 4,761.0 4,306.0 11,063.0 9,717.0 7,091.0 9,556.0 11,949.0 3,897.0 22,364.0 256,081.00 1,532.0 2,069.0 4,565.0 2,354.0 392.0 1,409.0 733.0 3,032.0 7,910.0 3,089.0 4,277.0 7,774.0 9,110.0 5,978.0 7,772.0 6,642.0 3,241.0 18,254.0 214,480.10 2001 3,107.0 2,370.0 2,218.0 6,429.0 2,086.0 1,453.0 2309 1996 2,537.0 1,632.0 2,092.0 5,572.0 1,989.0 1,156.0 2,116.0 1996 15.9 11.6 6.9 43.9 12.0 5.7 5.8 101.8 1.0 10.6 18.5 32.5 1.1 14.4 6.8 4.9 62.8 6.6 7.8 37.9 15.8 26.3 18.4 6.5 8.7 139.6 522.0 3,058.1 2001 20.8 12.7 9.3 43.2 9.6 6.8 5.8 108.2 1.1 11.6 26.9 35.5 0.9 9.1 4.5 5.5 69.9 10.7 9.6 34.9 14.6 25.7 21.8 4.5 6.3 147.5 548.8 3,063.2 GDP in millions $97 Energy use in PJ Table D. 5: Data for manufacturing sector and the entire industrial sector MJ/$97-GO MJ/ton MJ/$97-GO MJ/ton MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/$97-GDP MJ/$97-GDP MJ/$97-GO MJ/$97-GO MJ/$97-GDP MJ/ton MJ/$97-GO MJ/$97-GO MJ/$97-GO MJ/kilolitre MJ/$97-GO MJ/hectoliter Energy Efficiency Indicators 0.4 14,013.4 1.6 12,838.4 1.0 4.0 3.5 0.8 2.9 1.1 0.9 2.0 0.7 3.9 2.4 0.3 1.0 7.9 1996 4,515.2 2.5 1.6 2.3 1,507.6 1.5 253.4 0.4 9,313.3 1.7 10,641.2 0.7 1.7 1.4 0.6 2.5 1.0 0.9 1.3 0.6 3.6 2.3 0.1 0.5 6.6 2001 5,155.4 2.5 1.9 1.9 1,263.6 1.4 227.0 Energy Intensity Appendix D Appendix D ● Commercial and Institutional sector Table D. 6: Data for the institutional sector Sectors Sub-sectors Schools Health Institutional Religious Other Institutions Total Institutional End-Use Services Energy use in PJ Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating Total Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating Total Health Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating Total Religious Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating street lighting Total Other Institutions 1996 7.60 1.60 5.50 1.50 65.50 5.30 87.00 11.20 2.40 8.40 4.70 46.40 19.80 92.90 1.90 0.10 1.10 0.00 10.00 2.00 15.10 4.10 2.20 4.80 0.00 31.90 3.90 7.50 54.40 2001 7.40 1.80 5.50 1.50 67.30 5.60 89.10 11.40 3.20 9.20 4.80 51.50 22.70 102.80 1.90 0.20 1.10 0.00 10.10 2.20 15.50 4.30 3.00 5.10 0.00 34.20 4.70 7.70 59.00 Total 249.40 266.40 -156- Activity in millions m 1996 2001 75.86 86.75 35.71 42.76 8.90 9.48 24.27 27.88 Appendix D Table D. 7: Data for the commercial sector Sectors Sub-sectors Offices Retail Commercial Hotels and Restaurants Recreational Warehouses End-Use Services Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating Total Offices Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating Total Retail Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating Total Hotels and Restaurants Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating Total Recreational Lighting Space cooling Auxiliary motor Auxiliary equipment Space heating Water heating Total Warehouses Total total commercial Total commercial and institutional -157- Energy use in PJ 1996 52.90 13.30 23.40 28.90 177.80 7.20 303.50 36.80 13.00 39.90 15.40 94.70 7.80 207.60 9.70 9.30 5.50 22.80 23.80 8.60 2001 56.40 18.30 24.60 31.80 200.70 8.90 340.70 39.10 16.10 42.60 16.90 99.30 8.70 222.70 9.80 11.60 5.60 24.20 23.00 9.90 79.70 84.10 8.50 0.30 14.50 0.00 36.20 5.00 64.50 15.00 0.80 12.30 0.00 46.70 1.90 76.70 9.00 0.40 15.40 0.00 34.00 5.80 64.60 14.70 0.90 12.10 0.00 45.80 2.00 75.50 732.00 787.60 981.40 1054.00 Activity in millions m 1996 2001 141.80 167.11 112.42 127.62 29.14 32.35 32.95 37.46 52.40 54.41 Appendix D Table D. 8: Data for the agriculture sector Sector Energy use in PJ GDP in million $97 Energy intensity in MJ/$97 1996 2001 1996 2001 1996 2001 non-motive 84.6 72.4 13917.0 14114.0 0.006 0.005 motive 138.3 145.7 13917.0 14114.0 0.010 0.010 total agriculture 222.9 218.1 13917.0 14114.0 Table D. 9: Data for the electricity generation sector Type of fuel Energy use in PJ Electricity generated Energy intensity in GJ/GWh 1996 2001 1996 2001 1996 2001 Natural gas 154.8 334.1 17,150.0 33,164.0 9,026.2 10,074.2 Diesel Fuel Oil, Light Fuel Oil and Kerosene Heavy Fuel Oil 11.1 6.7 1,372.0 877.0 8,090.4 7,639.7 64.4 139.0 6,481.0 13,671.0 9,936.7 10,167.5 Coal 929.6 1,167.7 83,981.0 110,197.0 11,069.2 10,596.5 1,267.9 1,012.0 1,187.6 836.3 352,183.0 87,150.0 329,881.0 72,320.0 3,600.1 11,612.2 3,600.1 11,563.9 Wood and Other 58.8 69.2 5,598.0 6,588.0 10,503.8 10,503.9 Petroleum Coke, Still Gas, Coke and Coke Oven Gas 3.7 20.1 1,534.0 1,497.0 2,412.0 13,426.9 Hydro Nuclear Energy use TOTAL Electricity Generation Electricity generated Energy intensity in GJ/GWh 1996 2001 1996 2001 1996 2001 3,502.3 3,760.7 555,449.0 568,195.0 6,305.3 6,618.7 -158- Appendix E APPENDIX E RESULTS OF THE DECOMPOSITION OF THE CHANGES IN ENERGY CONSUMPTION -159- Industry Main Sector Manufacturing NonManufacturing Sub sector Total Industry End Use Services Total Metal Mining Total Non Metal Mining upstream mining Construction forestry Total Pulp and Paper Total Smelting and Refining Petroleum ref Cement Total Chemical Iron and Steel Total Non-Manufacturing Total Food and Beverages tobacco prod rubber prod plastic prod resin and synthetic rubber leather and allied prod textile Mills Textile prod Clothing Indy Wood products Furniture Printing and related products fabricated metal products Machinery motor vehicles motor vehicle parts Computer and electrical electrical equipment and components other manufacturing Total Manufacturing 4.56 26.80 -128.77 -25.80 -102.40 -224.35 -160- 3.51 7.01 -187.49 25.63 95.39 545.70 1.33 1.38 -5.15 0.04 Results Additive in PJ Profitabi Structure Activity -lity -1.29 -24.52 14.18 -6.22 0.87 7.30 -29.45 -20.93 67.09 -4.18 1.66 8.78 -3.53 -1.32 2.41 -91.37 -88.38 156.67 -14.83 13.44 42.77 -15.74 -17.25 57.21 2.33 -5.47 10.89 23.37 -35.19 40.50 -14.66 -17.39 42.52 -155.56 -194.49 450.31 -3.48 -1.34 18.71 0.28 -0.37 0.19 3.69 -0.14 1.98 0.78 2.26 4.01 5.59 -2.28 6.07 0.42 -0.44 0.18 6.06 -3.54 2.06 2.05 -0.24 1.00 2.53 -1.36 0.93 2.04 3.06 11.84 1.24 2.16 1.52 1.74 -1.49 1.55 -0.16 6.34 6.50 0.16 -1.73 2.71 -2.96 -0.20 4.64 0.11 0.56 3.58 0.78 2.22 0.97 Energy Intensity -0.87 -3.65 46.29 -8.96 11.15 28.59 -28.58 -42.42 -2.75 -82.68 -38.07 -121.95 -7.49 0.00 -4.53 1.36 -6.38 -0.36 -9.88 -5.10 -1.49 -9.84 -0.81 0.00 -15.67 -2.34 -2.08 -0.85 -5.98 7.90 26.80 5.10 -2.40 Total -12.50 -1.70 63.00 -2.70 8.70 5.50 12.80 -18.20 5.00 -54.00 -27.60 -21.70 6.40 0.10 1.00 8.40 3.00 -0.20 -5.30 -2.30 0.60 7.10 4.10 1.80 -3.00 -1.20 -0.60 3.40 -2.00 Table E. 1: Results for the industrial sector 92.9% 83.5% 82.6% 50.0% Energy Intensity 98.9% 91.5% 113.1% 83.3% 228.6% 103.3% 88.8% 87.6% 95.6% 69.5% 85.2% 95.3% 93.1% 100.0% 66.5% 106.3% 82.9% 70.0% 42.5% 40.0% 75.0% 86.2% 90.9% 100.0% 65.0% 85.7% 92.3% 95.8% 33.3% 95.9% 103.2% 105.1% 120.4% 94.1% 102.5% 101.3% 100.6% 119.5% 119.6% 119.5% 119.6% Results Multiplicative ProfitabiStructure Activity lity 98.4% 73.5% 119.5% 85.9% 102.1% 119.5% 92.5% 94.6% 119.6% 91.9% 103.4% 119.6% 77.0% 90.6% 119.6% 90.1% 90.4% 119.6% 94.0% 105.8% 119.5% 95.2% 94.8% 119.6% 103.9% 91.4% 119.6% 110.8% 85.7% 119.5% 94.0% 93.0% 119.6% 94.0% 92.6% 119.5% 96.7% 98.7% 119.5% 130.6% 70.4% 119.6% 139.5% 98.7% 119.6% 103.5% 110.6% 119.6% 117.9% 93.5% 119.6% 152.7% 64.0% 119.6% 169.0% 73.6% 119.6% 144.4% 95.9% 119.6% 162.6% 77.0% 119.6% 103.1% 104.7% 119.6% 115.7% 128.9% 119.6% 122.2% 84.2% 119.6% 99.6% 119.0% 119.6% 101.1% 89.2% 119.6% 89.2% 99.2% 119.6% 100.5% 102.8% 119.6% 115.4% 150.5% 119.6% 100.2% 105.7% 105.1% 72.4% Total 85.5% 95.9% 118.3% 94.7% 190.6% 100.6% 105.5% 94.5% 108.5% 78.8% 89.1% 99.1% 106.3% 110.0% 109.4% 145.4% 109.2% 81.8% 63.2% 66.2% 112.2% 111.3% 162.1% 123.1% 92.1% 92.4% 97.7% 118.5% 69.2% Appendix E Transport Commercial and Institutional Residential Main Sector End-Use Services Space Heating Space Cooling Lighting Total Appliances Water Heating Total Schools Health Institutions Religious Other Institutions Total Offices Retail Hotels and Restaurants Commercial Recreational Warehouses Total Total commercial and institutional Total Road Total Bus Passenger Air Transport Rail Total Total Trucks Rail Freight Transport Marine Total Total Transport Agriculture TOTAL Electricity Generation Total residential Household Services Floor Space Services Sub-sectors Energy Intensity -208.80 3.87 1.24 -203.70 -5.64 -18.45 -24.09 -227.79 -9.71 -7.71 -0.57 -3.02 -21.00 -15.64 -12.17 -4.15 -8.18 -4.06 -44.20 -65.21 31.97 2.07 6.89 0.09 41.01 -6.53 -0.82 -1.17 -8.52 32.48 -7.90 -5.45 71.89 3.03 5.06 79.99 13.13 21.25 34.38 114.36 11.81 17.61 0.97 7.27 37.66 52.83 27.27 8.55 8.28 2.86 99.79 137.45 29.59 1.91 6.38 0.08 37.96 110.77 13.91 19.90 144.58 182.54 3.10 263.85 -0.29 0.00 0.00 -0.29 0.01 0.00 0.01 -0.28 0.00 0.00 0.00 0.14 0.14 0.01 0.00 0.00 0.00 0.00 0.01 0.25 7.74 -4.08 -3.96 0.43 0.13 6.56 -11.09 4.58 0.05 0.18 -161- Activity Structure Results Additive in PJ Total -137.20 6.90 6.30 -124.00 7.50 2.80 10.30 -113.70 2.10 9.90 0.40 4.60 17.00 37.20 15.10 4.40 0.10 -1.20 55.60 72.60 69.30 -0.10 9.30 0.60 79.10 110.80 2.00 23.30 136.10 215.20 -4.80 258.40 Table E. 2: Results for the other sectors Energy Intensity 78.0% 135.1% 102.1% 80.0% 97.0% 93.9% 95.1% 84.9% 89.6% 92.4% 96.4% 94.4% 92.1% 95.3% 94.5% 95.1% 88.1% 94.8% 94.3% 93.8% 103.3% 103.3% 103.3% 103.3% 103.3% 99.0% 98.9% 98.9% 99.0% 101.6% 96.5% 99.8% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.8% 93.8% 98.2% 117.5% 100.0% 101.1% 86.7% 104.2% 100.0% 100.0% 100.0% 100.0% Structure 108.9% 126.6% 108.9% 109.1% 107.5% 107.5% 107.5% 108.6% 114.4% 119.7% 106.5% 114.9% 116.0% 117.8% 113.5% 111.0% 113.7% 103.8% 114.0% 114.5% 103.0% 103.0% 103.0% 103.0% 103.0% 119.6% 119.6% 119.6% 119.6% 109.2% 101.4% 107.5% Activity Results Multiplicative 85.0% 171.1% 111.2% 87.3% 104.2% 101.0% 102.2% 92.2% 102.4% 110.7% 102.6% 108.5% 106.8% 112.3% 107.3% 105.5% 100.2% 98.4% 107.6% 107.4% 107.2% 99.8% 104.4% 125.0% 106.4% 119.6% 102.6% 123.3% 118.3% 110.9% 97.8% 107.4% Total Appendix E TOTAL CANADA Electricity Generation Agriculture Transport Commercial and institutional Residential Industry Main Sector -498,22 -5,45 -7,90 32,48 -65,21 -227,79 -224,35 Energy Intensity -128,77 -128,77 Profitability -187,33 0,18 0,25 -0,28 -187,49 Structure -162- 1247,01 263,85 3,10 182,54 137,45 114,36 545,70 Activity Results Additive decomposition in PJ 432,80 258,40 -4,80 215,20 72,60 -113,70 5,10 Total Changes 95,73% 99,85% 96,48% 101,57% 93,77% 84,91% 92,93% Energy Intensity 98,88% 100,00% 100,00% 100,00% 100,00% 100,00% 95,88% Profitability 98,37% 100,01% 100,01% 100,01% 100,00% 99,98% 94,06% Structure 111,56% 107,54% 101,41% 109,15% 114,53% 108,56% 119,52% Activity Results multiplicative decomposition Table E. 3: Results for the Canadian energy economy and the main sectors 103,87% 107,38% 97,85% 110,87% 107,40% 92,16% 100,17% Total Changes Appendix E [...]... research -5- Chapter 1: Introduction Finally, Chapter 8 concludes this dissertation by succinctly recalling the key findings in the research and considering the main areas for future research Chapter 1 Introduction Chapter 2 Chapter 3 Index Decomposition Analysis methods Theory of consistency in aggregation Chapter 4 Consistency in aggregation and IDA Chapter 6 Chapter 5 Consistency in aggregation, ... attributes that have already been studied for each method Chapter 3 reviews the different definitions of consistency in aggregation in the index number theory and approximations to the definition We then use these -4- Chapter 1: Introduction definitions and approximations as a basis for defining three degrees of consistency in aggregation Chapter 4 focuses on consistency in aggregation for the IDA methods... basic multiplicative approach 2.1.1 The aggregate indicator An aggregate indicator is defined as an indicator at an aggregate level This aggregate level incorporates many indivisible processes and disaggregated data at the lower levels of disaggregation (see Chapter 3) Mathematically, we assume that X is an aggregate index and decomposed in r causal factors x: X = ∑ X i =∑ x1,i x 2,i x r ,i and X i = x1,i... the advantage of being intuitive The Laspeyres and Paasche indexes, as superlative indexes (see Diewert, 1976), can be considered discrete approximations of the continuous Divisia index These methods follow the Laspeyres price and quantity index in economics by isolating one of the variables and considering it as a perturbation, while leaving other variables at their base-year value 2.2.1 Laspeyres and... Material flow and dematerialization -1- Chapter 1: Introduction These studies aim at analyzing the development of material use in an economic structure Of interest is a wide range of metallic and non-metallic minerals, coal, oil, and natural gas, which are treated as material rather than energy sources ● Cross-country comparison These studies aim at quantifying the factors contributing to an aggregate... the case of partial fulfillment Case study, The Canadian industrial sector Chapter 7 Case study, the energy consumption in Canada Chapter 8 Conclusion Figure 1-1: Structure of the thesis -6- Chapter 2 Index Decomposition Analysis Methods CHAPTER 2 INDEX DECOMPOSITION ANALYSIS METHODS A wide range of methodologies is available to perform an IDA Determining the most suitable method to conduct the study. .. approach has the advantage of giving concise results, whereas the additive approach provides easily understood -7- Chapter 2 Index Decomposition Analysis Methods information Ang and Choi also stress that the choice depends on the aggregate indicator studied Therefore, we study both approaches for each method We first define an aggregate indicator; then we present the basic additive approach and the basic... (2.24) and we finally obtain the following formula by integrating the formula on the interval [0, T]: T r X − X = ∑∑∑ ∫ wij (t )d ln( x k ,ij ) T 0 k =1 j i (2.25) 0 Discretization The formula is in the form of a linear integral; but given that the data available are given in discrete time intervals, researchers have approximated this integral in the most accurate manner The way the discretization is conducted... Chapter 3 We study numerically the extent of inconsistency in aggregation of the methods previously proven to be theoretically inconsistent and determine whether these methods can be considered approximately consistent in aggregation from a numerical point of view Chapter 6 presents an aggregation issue, which we call partial fulfillment of consistency in aggregation, found in the literature We seek... the Canadian industry based on NAICS B 1 Data for the decomposition of the industrial energy consumption in Canada between 1990 and 2000 C 1 Results for the decomposition of the changes in energy consumption of the Canadian industry: Laspeyres, Fisher Ideal, Paasche and Marshall-Edgeworth C 2 Results for the decomposition of the changes in energy consumption of the Canadian industry: MRCI, AMDI , LMDI . aggregation 41 3.6 Advantages of the consistency in aggregation 44 3.7 Conclusion 46 CHAPTER 4 CONSISTENCY IN AGGREGATION AND INDEX DECOMPOSITION ANALYSIS 47 4.1 Consistency in aggregation. aggregation; type B, partial consistency in aggregation; and type C, approximate numerical consistency in aggregation. However, in some situations consistency in aggregation is only partially fulfilled,. studied in Index Decomposition Analysis. Hence, the main contribution of this study is to redefine the consistency in aggregation in Index Decomposition Analysis (IDA) and study this attribute