Environmental input output analysis emissions embodied in trade and structural decomposition analysis

ENVIRONMENTAL INPUT-OUTPUT ANALYSIS EMISSIONS EMBODIED IN TRADE AND STRUCTURAL DECOMPOSITION ANALYSIS SU BIN (M.Sc., Academy of Mathematics and Systems Science, Chinese Academy of Sciences) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF INDUSTRIAL & SYSTEMS ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2011 Acknowledgements Acknowledgements First and foremost, I would like to express my sincerest gratitude to my supervisor, Professor Ang Beng Wah, who has supported me with his patience and knowledge throughout my PhD research His amiable personality, systematic way of thinking and passion for research have made him a respected advisor who will always have a strong influence in my life Especially, his open-mind has given me the freedom to the research topics that I am interested in My experience working with him is invaluable to my future research career I would also like to thank Associate Professor Huang Huei Chuen of the National University of Singapore (NUS), Professor Zhou Peng of the Nanjing University of Aeronautics and Astronautics in China, and Professor Choi Ki-Hong of the Korea Polytechnic University, who gave helpful and constructive comments on Chapter and Chapter of this thesis Special thanks are given to Associate Professor Poh Kim Leng and Dr Ng Tsan Sheng, Adam of the NUS, who served as my oral examination committee and provided valuable comments on my research and thesis writing Many thanks are also given to my friends in the Chinese Academy of Sciences, who helped to collect some data for China which was used in the empirical studies in the research I would like to express my gratitude to NUS for offering me a research scholarship, NUS libraries for providing abundant books and e-resources collections, and the Department of Industrial & Systems Engineering for the use of its facilities, without any of which I would not have been able to carry out my research I also wish to thank Ow Lai Chun and Victor Cheo Peng Yim for their excellent administrative support during my PhD studies I also owe my thanks to my friends in laboratory and —i— Acknowledgements classmates within the department Through working together with them, I have thoroughly enjoyed the time participating in coursework, seminars, tutoring, discussions and research work Last but not least, I would like to thank my wife, Ji Yawen, my grandmother, my aunts, my parents and parents-in-law for supporting my decision to pursue a PhD degree and for their continuous encouragement throughout the entire process — ii — Summary Summary With the growing concern about climate change and related energy and environmental issues, the environmental input-output analysis (EIOA) has become an important tool in climate policy analysis Lately, two popular and important areas in EIOA are issues related to emissions embodied in trade (EET) and structural decomposition analysis (SDA) EET studies allow us to understand the embodied emissions flows through international trade and the resulting “carbon leakage” This information is useful for attributing a country’s responsibility to global emissions Through SDA studies, the driving forces of the historical changes of an aggregate indicator, such as carbon dioxide emissions, can be evaluated and quantified This thesis focuses on a number of methodological and application issues in EET and SDA under the EIOA framework First, a literature survey is presented on studies published in the last one to two decades in each of these two areas Following that, the first part of the thesis focuses on EET studies Issues on sector aggregation in EIOA are analyzed and next the possible effects of sector aggregation on estimating a country’s emissions embodied in trade and their practical implications are analytically and empirically investigated The issues of spatial aggregation are then analyzed and a “hybrid emissions embodied in trade” approach for regional emission studies is proposed The impacts of spatial aggregation on EET emission estimates are also evaluated With increasing interest in using multi-regional input-output (MRIO) models by researchers, a new method called the “stepwise distribution of emissions embodied in trade” is proposed to reveal the mechanism of feedback effects in multi-region EET studies The indirect trade — iii — Summary balance of emissions from bilateral trade between any two countries may be derived using the proposed method The second part of the thesis deals with SDA studies applied to energy and emissions The recent methodological developments are first studied, which show a shift towards using SDA methods that are ideal in decomposition Arising from this development, four such methods are compared and guidelines on method selection are provided Following that, a comprehensive comparison between SDA and index decomposition analysis (IDA) based on the latest available information is conducted Since three aggregation issues are involved in SDA studies, the impacts on SDA results of the third aggregation, namely temporal aggregation (on top of sector aggregation and spatial aggregation) is examined The Fisher index and its extensions have been used by researchers in multiplicative SDA but the results derived are only given in the aggregate form An attribution analysis of the generalized Fisher index decomposition in SDA is proposed, where the contributions of the individual components at a finer level can be quantified Finally, a summary of the main findings of our studies is given and suggestions are made for future research — iv — Table of Contents Table of Contents Acknowledgements……………………………………………………………………i Summary…………………………………………………………………………… iii Table of Contents…………………………………………………………………… v List of Tables……………………………………………………………………… vii List of Figures…………………………………………………………………………x List of Abbreviations……………………………………………………………….xiii Chapter Introduction………………………………………………………………1 1.1 Background………………………………………………………………… 1.2 Motivations of environmental input-output analysis……….…………………3 1.3 Research scope and structure of the thesis……………………………………5 Chapter Literature Review………….…………………………………………….9 2.1 Review of EET studies and carbon leakage………………………………… 2.2 Review of SDA studies applied to energy and emissions………………… 20 2.3 Concluding comments……………………………………………………….29 Part I: Emissions Embodied in Trade (EET)………………………………………31 Chapter Sector Aggregation Issues in EET Analysis………………………… 32 3.1 Introduction………………………………………………………………… 32 3.2 The I-O technique and data issues……………………………………… .34 3.3 Issues on sector aggregation……………………………………………… 38 3.4 Effects of sector aggregation on emissions embodied in exports……… .40 3.5 An illustrative example…………………………………………………… 43 3.6 Emissions embodied in China and Singapore’s exports…………………… 45 3.7 Discussion and conclusions……………………………………………… 57 Chapter Spatial Aggregation Issues in EET Analysis………………………….61 4.1 Introduction……………………………………………………………… 61 4.2 Issues on spatial aggregation……………………………………………… 63 4.3 The I-O technique and model selection………………………………… 64 4.4 Effects of spatial aggregation on emissions embodied in exports………… 68 4.5 Emissions embodied in China’s exports…………………………………….70 4.6 Discussion and conclusions………………………………………………….81 Chapter Feedback Effects in Multi-Region EET Analysis…………………….84 5.1 Introduction………………………………………………………………….84 5.2 I-O models and feedback effects…………………………………………….86 5.3 Two general approaches and their relationships…………………………….88 5.4 Stepwise distribution of emissions embodied in trade………………………93 —v— Table of Contents 5.5 Measuring indirect absorption patterns and trade balance of emissions……96 5.6 Empirical study…………………………………………………………… 100 5.7 Discussions and conclusions……………………………………………….110 Part II: Structural Decomposition Analysis (SDA)………………………………113 Chapter Methodological Developments in SDA studies…………………… 114 6.1 Introduction……………………………………………………………… 114 6.2 Methodological developments and issues………………………………….116 6.3 General additive decomposition framework……………………………….119 6.4 Empirical study on China’s CO2 emissions……………………………… 126 6.5 Guidelines on SDA method selection…………………………………… 136 6.6 Comparison between SDA and IDA……………………………………….138 6.7 Conclusion………………………………………………………………….145 Chapter Aggregation Issues in SDA studies……………………………………146 7.1 Introduction……………………………………………………………… 146 7.2 SDA and temporal aggregation…………………………………………….149 7.3 Temporal aggregation in additive SDA applied to CO2 decomposition… 151 7.4 Empirical study on China’s CO2 emissions…………………………… 155 7.5 Aggregation issues in environmentally extended I-O analysis…………….167 7.6 Conclusion………………………………………………………………….169 Chapter Attribution Analysis of Generalized Fisher Index………………….171 8.1 Introduction……………………………………………………………… 171 8.2 General Fisher index decomposition……………………………………….173 8.3 Attribution of the generalized Fisher index…………………………… .174 8.4 Multiplicative SDA of emissions embodied in trade……………………….178 8.5 Empirical study in China………………………………………………… 180 8.6 Conclusion………………………………………………………………….186 Chapter Conclusions…………………………………………………………….189 9.1 Summary of the results…………………………………………………… 189 9.2 Future research areas…………………………………………………… 192 References……………………………………………………………………… 195 Appendix A-L………………………………………………………………………209 — vi — List of Tables List of Tables Table 2.1 EET studies and their specific features, 1994-2010……………………15 Table 2.2 SDA studies dealing with energy and emissions and their specific features, 1999-2010…………………………………………………….25 Table 3.1 An example: the data………………………………………………… 44 Table 3.2 An example: the main emission results……………………………… 44 Table 3.3 An example: the effects of sector aggregation (Mt CO2)………………45 Table 3.4 Basic emission and socio-economic indicators for China………………46 Table 3.5 Levels of sector aggregation and the number of sectors at each level…47 Table 3.6 Estimates of emissions for exports by sector at level L1 and the effects of sector disaggregation measured using L1 as base, China (2002)… 51 Table 3.7 Estimates of emissions for exports by sector at level L2 and the effects of sector disaggregation measured using L2 as base, China (2002)… 54 Table 3.8 Basic emission and socio-economic indicators for Singapore…………56 Table 4.1 The eight regions of China used in this study and their constituents and identification (ID) codes……………………………………………… 71 Table 4.2 Basic emission and socio-economic indicators for the eight regions, 1997…………………………………………………………………….72 Table 4.3 The three regional groups and their identification (ID) codes…………72 Table 4.4 Emissions embodied in China’s exports (in aggregate) estimated at three different spatial aggregation levels using the HEET approach (Mt CO2)…………………………………………………………………….74 — vii — List of Tables Table 4.5 Emissions embodied in China’s exports (by region) estimated at three different spatial aggregation levels using the HEET approach (Mt CO2)…………………………………………………………………….75 Table 5.1 Basic emission and socio-economic data by economy/region in the empirical study, 2000…………………………………………………100 Table 5.2 Trade coverage by economy/region in the empirical study, 2000……101 Table 5.3 Comparisons of the results obtained using the EEBT and MRIO approaches to measure the “consumption-based” emissions…………104 Table 6.1 Choices of the constant integral values for ideal decomposition by method……………………………………………………………… 123 Table 6.2 Basic emission and socio-economic data for China (GDP given in 2002 prices)…………………………………………………………………128 Table 6.3 Summary of the results in aggregate for China, 2002-2007 (Mt CO2)………………………………………………………………… 128 Table 6.4 Summary of the results at sub-category level for China, 2002-2007 (Mt CO2)………………………………………………………………… 129 Table 6.5 The outliers from the results at the sub-category level……………….132 Table 6.6 An illustration of the “mean-rate-of-change” idea leading to two types of outliers……………………………………………………………… 134 Table 6.7 Further decomposition of the Leontief structure effect into two subeffects in aggregate for China, 2002-2007 (Mt CO2)…………………135 Table 6.8 Developments of IDA and SDA applied to energy and emissions and the main features of the two techniques………………………………… 140 Table 7.1 Summary of the results in aggregate obtained using non-chaining analysis and chaining analysis at 38-sector level data for China, 19972007 (Mt CO2)……………………………………………………… 158 — viii — Appendix F ( ɶ C j ( s − 1) = f ' I − A d −1 s −1 ) ∑(B) k yi j + C jj ( s ) + ∑ C ji ( s ) k =0 (F.5) i≠ j ɶ , and its relationship with the next step estimate C j ( s ) as ɶ ɶ C j ( s ) = C j ( s − 1) − ∑ C ji ( s ) + ∑ Cij ( s ) i≠ j (F.6) i≠ j −1 where C jj ( s ) = f ' ( I − A d ) B s y jj is the absorption of embodied emissions at step s , −1 and C ji ( s ) = f ' ( I − A d ) B s e ji is the remaining emissions embodied in trade at step s The adjustment strategy in Eq (F.6) can be interpreted as: country j ’s estimate ɶ ɶ C j ( s ) is computed using that in the previous step C j ( s − 1) minus the remaining emissions embodied in its exports term at step s plus those embodied in its imports term at step s — 220 — Appendix G Appendix G Proof of Eq (5.18) We use the same procedure in the SWD-EET analysis in Appendix E to trace how a country’s embodied emissions are absorbed by other countries’ final demands using the MRIO approach Following the same notations in Section 5.3, country i ’s total CO2 emissions from industry in Eq (5.1) can be expressed in the integrated form ( Cip = f ' I − A d −1 ) (y ii + zi i ) (G.1) where yi i and zi i are two extended integrated vectors with their i th item as and ∑ j ≠i ∑ j yij zij respectively, while all other items are zero Similar as Eq (E.1), we can trace the flow of embodied emissions after the first round of allocation as −1 ( ) (y = f '( I − A )  y   ( ii ( + Aim I − A d i −1 d = f ' I − Ad + zi i ) = f ' I − A d ii Cip = f ' I − Ad ) −1 ( −1 ) (y ii ) ( y + z )   −1 + Aim x i ) (G.2)  yi i + Bi i ( y + z )    where Aim and Bi i are two extended integrated matrices with the same i th row subi matrices as those in A m and B , while other rows are all zero sub-matrices Further expanding item z in Eq (G.2), we can trace the embodied emission flow after infinite rounds of allocation as — 221 — Appendix G ( ) = f '( I − A ) Cip = f ' I − A d −1 d −1  yi i + Bi i y + Bi i z     yi i + Bi i y + Bi i B ( y + z )    k   yi i + Bi i ∑ ( B ) y + Bi i ( B ) z   k =0   s −1  k s  = f ' I − A d  yi i + Bi i ∑ ( B ) y + Bi i ( B ) z  k =0   ∞ −1  k  = f ' I − A d  yi i + Bi i ∑ ( B ) y  k =0   −1 −1 = f ' I − A d  yi i + Bi i ( I − B ) y      −1 ( ) ( ) ( ) ( ) ( ) ∑y   = f ' I − Ad = f ' I − Ad −1 n ij j =1 (G.3) n −1 ɶ + Bi i ( I − B ) yi j  = ∑ Cij  j =1  ɶ where yi i = ∑ j yij , y = ∑ j yi j , Cij = f ' I − A d ( ) −1  y + B ( I − B ) −1 y  with i ≠ j ii ij  ij   is any other country j ’s indirect absorption of country i ’s emissions embodied in ɶ ɶ exports, Cii is country i ’s absorption of its own emissions, and Cii − Cii is country i ’s absorption of its own emissions embodied in exports — 222 — Appendix H Appendix H Proof of Eq (5.24) Defining the new notations uij as follows:  y jj uij =   yij + zij , if i = j (H.1) , if i ≠ j Then we have ui j = ( uij ) n×1 = yi j + zi j and uij = eij with i ≠ j With Eq (5.9), the change of any country j ’s “consumption-based” emissions after the first round of allocation in the SWD-EET analysis can be formulated as ( =∑ i =∑ i =∑ i ) −1 ( ) −1  B ( yi j + zi j ) − zi j  = f ' I − A d ( Bui j − zi j )       fi ' Ld  ∑ Bik ukj − zij  = ∑ f i ' Ld  ∑ Bik ukj − Aij x j  i i  k  i  k     fi ' Ld  ∑ Bik ukj − Aij Ldj  y jj + ∑ e jk   i k≠ j  k     (H.2)   fi ' Ld  ∑ Bik ukj − ∑ Bij u jk  i k  k  ɶ ɶ C j (1) − C j (0) = f ' I − A d = ∑∑ f i ' Ld ( Bik ekj − Bij e jk ) i i k≠ j = ∑∑ f i tot ' ( Bik ekj − Bij e jk ) i k≠ j where f i tot = Ld ' f i is the vector of country i ’s total emission intensity or emission i multiplier Following the two-country illustration in Section 5.4, the change in country 1’s estimate of “consumption-based” emissions after the first round adjustment becomes ɶ ɶ C1 (1) − C1 (0) = ∑∑ f i tot ' ( Bik ek1 − Bi1e1k ) i k ≠1 = ∑ f i tot ' ( Bi 2e21 − Bi1e12 ) i = f1tot ' B12 e21 − f 2tot ' B21e12 — 223 — (H.3) Appendix I Appendix I Transforming the S/S (or D&L) index into the standard additive decomposition form in Eq (6.8) According to Shapley (1953), Ang et al (2003) and Ang et al (2009), the effect from factor xi with S/S (or D&L) index can be formulated as ∆Vxi = ( s − 1)!(n − s )! [v(S ) − v(S − {i})] n! i∈S ⊆ N ,|S | = s ∑ (I.1) where N = {1, 2,… , n} and v( S ) is the characteristic function with detailed formula as m v( S ) = S⊆N ∑∏ x ∏ x 0,q j T j, p j =1 p∈S (I.2) q∈N − S In order to achieve the standard form of the S/S (or D&L) index in Eq (6.8), we introduce the notation v j ( R,{i}) as follows v j ( R,{i}) = i∉R ⊆ N ∏x T j, p p∈R ∏ x 0,q j (I.3) q∈N −{i }− R where i ∈ S ⊆ N , R = S − {i} It is easy to check that the following equation holds m v( S ) − v( S − {i}) = ∑ v ( R,{i})∆x i∈S ⊆ N , R = S −{i} j =1 j j ,i Now Eq (I.1) can be transformed into the standard form in Eq (6.8) as — 224 — (I.4) Appendix I ∆Vxi = = ( s − 1)!(n − s )! [v( S ) − v( S − {i})] n! i∈S ⊆ N ,|S | = s ∑  ( s − 1)!(n − s )!  m  ∑ v j ( R,{i})∆x j ,i  ∑S |=s, n! i∈S ⊆ N ,|  j =1  (I.5) R = S −{i }   ( s − 1)!(n − s )!   ∆x =∑ v j ( R,{i})  ∑  j ,i n! j =1  i∈S ⊆ N ,| S | = s ,   R = S −{i}  m The choice of the constant integral value for S/S (or D&L) index in Eq (6.8) is yj x j ,i L L = ( s − 1)!(n − s )! v j ( R,{i}) n! i∈S ⊆ N ,|S | = s , ∑ R = S −{i} — 225 — (I.6) Appendix J Appendix J Further decomposing the Leontief structure effect in Eq (6.22) Following the notations in Section 6.4.2, we illustrate the use of two techniques, i.e the additive and multiplicative identity splitting, given in Rose and Casler (1996) to decompose changes in the domestic Leontief inverse matrix and then derive two sub-effects ∆Cims and ∆Cinp in Eq (6.22) With the formula in Eq (6.21) and using the additive identity splitting, the first technique can be formulated as ( T =  I − Ad   ( −1 T ≡  I − Ad |0   ( ( −1 −1 d ) −(I − A ) ) − ( I − A )  + ( I − A ) − ( I − A )     T ∆Ld = LT − L0 = I − Ad d d −1 0|T d −1 ) −(I − A ) d ) −1 0|T d  +  I − AT d     ( ( −1 d −1 ) −(I − A ) ) T |0 d ( −1    −1    ) (J.1) ( ) T T 0| ˆ ˆ ˆ ˆ where Ad = I − M T AT , Ad = I − M A0 , Ad |0 = I − M T A0 , Ad T = I − M AT By taking the average of two equivalent decomposition forms in Eq (J.1), the results of additive identity splitting become {( I − A ) − ( I − A )  + ( I − A ) − ( I − A ) } {( I − A ) − ( I − A )  + ( I − A ) − ( I − A ) } + ∆Ld = T d 0|T d −1 −1 0|T d −1 −1 d T |0 −1 d T d −1 −1 d (J.2) T |0 −1 d The first item in Eq (J.2) is related to changes in the imported shares of input ˆ technology in M , while the second item is related to changes in the total production technology in A Putting Eq (J.2) into the “Laspeyres-based” estimates in Eq (6.19), we can derive the aggregate effects of ∆Cims and ∆Cinp — 226 — Appendix J With the formula in Eq (6.21) and using the multiplicative identity splitting, the second technique can be formulated as ∆Ld = LT − L0 = LT ( ∆Ad ) L0 ≡ L0 ( ∆Ad ) LT d d d d d d = (J.3) T  Ld ( ∆Ad ) L0 + L0 ( ∆Ad ) LT  d d d 2 T where ∆Ad = Ad − Ad is the changes in the domestic production coefficient matrix Using the same concept as in Eq (J.2), ∆Ad in Eq (J.3) can be further divided into the following two parts ∆Ad = 1 T 0|T T |0 T |0 0|T  1 T   Ad − Ad + Ad − Ad  +  Ad − Ad + Ad − Ad  ( ) ( ) ( ) ( ) (J.4) The first item in Eq (J.4) is related to changes in the imported shares of input ˆ technology in M , while the second item is related to changes in the total production technology in A Putting Eq (J.4) into Eq (J.3) and then into the “Laspeyres-based” estimates in Eq (6.19), we can derive the aggregate effects of ∆Cims and ∆Cinp In the next step, we consider the possibility of investigating the sub-category effects with respect to individual changes in domestic production technology element Ad , kl to identify the important individual input coefficient changes From the discussions above, the decomposition results using the second technology in Eq (J.3) can be easily expressed as the summation of sub-category effects, while it is difficult to the same for those using the first technology in Eq (J.2) because of the inverse matrix From Eq (J.3), we have — 227 — Appendix J m ∆Ld ,ij = m ∑ L ( ∆A ) L T d ,ik d ,lj d , kl ≡ k ,l =1 LT ,ik L0 ,lj + L0 ,ik LT ,lj d d d d k ,l =1 ∑ d ,ik d , kl T d ,lj k ,l =1 m = ∑ L ( ∆A ) L (J.5) ( ∆A ) d , kl With the “Laspeyres-based” estimate in Eq (6.19), we can decompose the Leontief structure effect into the summation of sub-category effects with respect to individual changes in domestic production technology element Ad , kl as ∆Cstr = str ,ij L m Cij i , j =1 Ld ,ij ∑ L = Cij i , j =1 ∑ ∆C i , j =1 = L m m Ld ,ij ∑ L ∆Ld ,ij  m  LT ,ik L0 ,lj + L0 ,ik LT ,lj d d d d ∑    k ,l =1    m  LT L0 + L0 LT d ,ik d ,lj d ,ik d ,lj = ∑ ∑   k ,l =1  i , j =1   m    ( ∆Ad ,kl )      (J.6) L m  Cij   ( ∆Ad ,kl ) = ∑ ∆Cdpr ,kl  L  k ,l =1  Ld ,ij   where ∆Cdpr ,kl is the sub-category effect with respect to individual changes in ∆Ad ,kl It is possible to further decompose the sub-category effect ∆Cdpr ,kl into those from changes in ∆M kk and ∆Akl using Eq (J.3) The same concepts mentioned above can be applied to the “Divisia-based” estimates through the relationship in Eq (6.13) and then derive the sub-category effect ∆Cdpr ,kl However it should be noted that to further decomposition of changes in ∆Ad into sub-effects, we need to adopt the ad hoc method or D&L, as in the case of the two sub-effects in Eq (J.4) — 228 — Appendix K Appendix K Transforming a geometric mean index into an arithmetic mean index As shown in Eq (8.2) and Eq (8.4), the geometric mean index can be expressed in either multiplicative decomposition form or additive decomposition form with logchanges For any geometric mean index such as Eq (8.16), the index Dx j can be formulated as  xi1, j ln Dx j = ∑ wi , j ln   xi , j i =1  m where ∑ m i =1      xi1, j or Dx j = ∏   i =1  xi , j m     wi , j (K.1) wi , j = We further assume the existence of parameters {π i , j } to make the geometric mean index Dx j into an arithmetic mean index as m ∑π Dx j = i, j i, j x i =1 m ∑π i, j i, j x i =1 where si , j = π i , j xi0, j   π x0 i, j i, j = ∑ m i =1   ∑ π k , j xk , j  k =1 ∑ m m k =1 π k , j xk0, j and ɶ Further assume si , j = π i , j xi1, j   x1 m xi1, j i, j  = ∑ si , j xi , j  xi , j i =1   ∑ ∑ m (K.2) s =1 i =1 i , j m k =1 π k , j xk , j with ∑ m ɶ s = , we have the i =1 i , j following two identities: m m  si , j ɶ ɶ − si , j ) = ∑ L( si , j , si , j ) ln  i, j  si , j i =1  ɶ ∑(s i =1  =0   — 229 — (K.3) Appendix K  m  ∑ π k , j xk , j  si , j  π x  ɶ = = ln  − ln  km1 ln  s   π x    π x0  i, j     ∑ k, j k, j  k =1 i, j i, j i, j i, j    x1  = ln  i0, j    xi , j     − ln Dx j   (K.4) Combing Eq (K.3) and Eq (K.4), we obtain    L( s , s )   x1 ɶi , j i , j  ln  i0, j ln Dx j = ∑  m   xi , j i =1   ɶ  ∑ L( sk , j , sk , j )   k =1  m    π i , j L( xi1, j , xi0, j Dx )   x1  j  ln  i0, j  = ∑ m  i =1     xi , j   ∑ π k , j L( xk , j , xk , j Dx j )   k =1  m   (K.5)   Comparing the two additive decomposition forms with the log-change for the index Dx j in Eq (K.1) and Eq (K.5), we can find that π i, j = wi , j (K.6) i, j L( x , xi0, j Dx j ) Together with Eq (K.2), the transformation from a geometric mean index in Eq (K.1) to an arithmetic mean index can be achieved as follows: m Dx j = ∑ si , j i =1 xi1, j xi0, j m  xi1, j  Dx j − = ∑ si , j  − 1  xi , j  i =1   or (K.7) where si , j = wi , j xi0, j L( xi1, j , xi0, j Dx j ) (K.8) m ∑w k, j k, j x k, j k, j L( x , x Dx j ) k =1 The final result is the same as that in Reinsdorf et al (2002) but the derivation presented above is simpler — 230 — Appendix K For the generalized Fisher index Dx1 expressing as the geometric mean index in Eq (8.16), the corresponding arithmetic mean index can be formulated using the general formula in Eq (K.7) and Eq (K.8) as m xi1,1 i =1 xi0,1 Dx1 = ∑ si (K.9) where si = wi xi0,1 L( xi1,1 , xi0,1 Dx1 ) (K.10) m ∑w k ,1 k ,1 x k ,1 k ,1 L( x , x Dx1 ) k =1 — 231 — Appendix L Appendix L Attribution of changes in the generalized Fisher index for three or more factors According to Siegel (1945) and Ang et al (2004), the effect from factor x j with the generalized Fisher index in multiplicative decomposition is given as Dx j =  v( S )    j∈S ⊆ N ,|S | = s  v( S − { j})  ∏ ( s −1)!( n − s )! n! (L.1) where N = {1, 2,… , n} and v( S ) is the characteristic function given by m v( S ) = S⊆N ∑∏ x ∏ i, p i =1 p∈S xi0,q (L.2) q∈N − S Supposing H j = {S | j ∈ S ⊆ N } , then the number of items in set H j is M =| H j |= 2n −1 { We can arbitrary numerate the items in set Hj as } j H j = S1j , S 2j ,⋯ , S M , where S kj is the k th item in set H j and | S kj |= skj As a result, the generalized Fisher index in Eq (L.1) can also be formulated as  v( S )  Dx j = ∏   j k =1  v ( S k − { j})  M j k ( skj −1)!( n − skj )! n! (L.3) For any k th item in Eq (L.3), we have the following identity as  ∏ xi1, p ∏ xi0, q ∏ xi1, p ∏ xi0, q  p∈S j q∈N − S j p∈S j −{ j } q∈N − Skj +{ j } ∑ L  k v(S j ) k , k v( S j − { j}) i =1 k k   m Solving Eq (L.4), we obtain — 232 —     xi1, j   ln    xi , j    v( S kj )   = (L.4)  − ln  v( S kj − { j})    Appendix L ln where ∑ m  xi1, j v( S kj ) = ∑ Wi ,jk ln   xi , j v( S kj − { j}) i =1  m i =1     (L.5) Wi ,jk = and  ∏ xi1, p ∏ xi0,q ∏ xi1, p ∏ xi0,q   p∈S j  q∈N − S kj p∈S j −{ j } q∈N − S kj +{ j } L k , k  j j v( Sk ) v( S k − { j})     j Wi ,k = 1  ∏ xi ', p ∏ xi ',q ∏ xi ', p ∏ xi ',q m  p∈S j q∈N − S kj p∈S j −{ j } q∈N − Skj +{ j } L k , k ∑ v( S kj ) v( S kj − { j}) i '=1        (L.6) Considering all the items in Eq (L.3) such as in Eqs (8.16-8.17), we can express the generalized Fisher index Dx j in Eq (L.3) in the geometric mean index as follows:  M ( skj − 1)!(n − skj )! j   xi , j ln Dx j = ∑  ∑ Wi ,k  ln  n! i =1  k =1   xi , j  m where ∑ m i =1  m  xi1, j  = ∑ wi , j ln   i =1  xi , j       (L.7) wi , j = , and ( skj − 1)!(n − skj )! j Wi , k n! k =1 M wi , j = ∑ (L.8) Using the general formula in Eq (K.7) and Eq (K.8) in Appendix K, we can express the generalized Fisher index in the arithmetic mean index as m xi1, j i =1 xi0, j Dx j = ∑ si , j where ∑ m (L.9) s = , and i =1 i , j — 233 — Appendix L si , j = wi , j xi0, j L( xi1, j , xi0, j Dx j ) m ∑w k, j k, j x k, j (L.10) k, j L( x , x Dx j ) k =1 — 234 — ... Economy-Energy-Environment EET Emissions Embodied in Trade EEBT Emissions Embodied in Bilateral Trade EIOA Environmental Input- Output Analysis ETS Emission Trading Scheme EU ETS European Union Emission Trading Scheme... popular and important areas in EIOA are issues related to emissions embodied in trade (EET) and structural decomposition analysis (SDA) EET studies allow us to understand the embodied emissions. .. Global Trade Analysis Project HEET Hybrid Emissions Embodied in Trade IDA Index Decomposition Analysis IDE-JETRO Institute of Developing Economies, Japan External Trade Organization IEA International