The LMDI approach to decomposition analysis-a practical guide.pdf
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1、Energy Policy 33 (2005) 867871 The LMDI approach to decomposition analysis: a practical guide B.W. Ang* Department of Industrial and Systems Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Abstract In a recent study, Ang (Energy Policy 32 (2004) com
2、pared various index decomposition analysis methods and concluded that the logarithmic mean Divisia index method is the preferred method. Since the literature on the method tends to be either too technical or specifi c for most potential users, this paper provides a practical guide that includes the
3、general formulation process, summary tables for easy reference and examples. r 2003 Elsevier Ltd. All rights reserved. Keywords: Decomposition analysis; Index decomposition analysis; Divisia index; LMDI 1. The LMDI formulation process Let V be an energy-related aggregate. Assume that there are n fac
4、tors contributing to changes in V over time and each is associated with a quantifi able variable whereby there are n variables, x1;x2;y;xn: Let sub- script i be a sub-category of the aggregate for which structural change is to be studied. At the sub-category leveltherelationshipVi x1;ix2;i?xn;iholds
5、.The general index decomposition analysis (IDA) identity is given by V X i Vi X i x1;ix2;i?xn;i:1 The aggregate changes from V0 P ix 0 1;ix 0 2;iyx 0 n;i in period 0 to VT P ix T 1;ix T 2;iyx T n;i in period T: In multiplicative decomposition, we decompose the ratio: Dtot VT=V0 Dx1Dx2yDxn:2 In addit
6、ive decomposition we decompose the difference: DVtot VT? V0 DVx1 DVx2 ? DVxn:3 The subscript tot represents the total or overall change and the terms on the right-hand side give the effects associated with the respective factors in Eq. (1). In the logarithmic mean Divisia index (LMDI) approach,1the
7、general formulae for the effect of the kth factor on the right-hand side of Eqs. (2) and (3) are respectively: Dxk exp X i LVT i ;V0 i LVT;V0 ln xT k;i x0 k;i ! ! exp X i VT i ? V0 i=ln V T i ? ln V0 i VT? V0=ln VT? ln V0 ? ln xT k;i x0 k;i ! ;4 DVxk X i LVT i ;V0 iln xT k;i x0 k;i ! X i VT i ? V0 i
8、 ln VT i ? ln V0 i ln xT k;i x0 k;i ! ;5 where La;b a ? b=ln a ? ln b as defi ned in Ang (2004).2The general formulae in the formulation process are summarized in Table 6 in Appendix A. 2. Two illustrative cases Changes in industrial energy consumption may be studied by quantifying the impacts of ch
9、anges in three different factors: overall industrial activity (activity effect), activity mix (structure effect) and sectoral energy intensity (intensity effect). The sub-category of the ARTICLE IN PRESS *Tel.: +65-687-422-03; fax: +65-677-714-34. E-mail address: iseangbwnus.edu.sg (B.W. Ang). 1The
10、LMDI is used here to refer to the logarithmic mean Divisia method I (LMDI I). A related version, the LMDI II, has a weighting scheme slightly more complex than LMDI I (Ang et al., 2003). 2For more on Eqs. (4) and (5), see Ang and Liu (2001) and Ang et al. (1998), respectively. 0301-4215/$-see front
11、matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.enpol.2003.10.010 aggregate is industrial sector. The IDA identity in Eq. (1) is E X i Ei X i QQi Q Ei E X i QSiIi;6 where E is the total energy consumption in the industry, Q P iQi is the total industrial activity level, and Si Qi=QandI
12、i Ei=Qiare,respectively,the activity share and energy intensity of sector i: From Eqs. (2) and (3), Dtot ET=E0 DactDstrDint;7 DEtot ET? E0 DEtot DEact DEstr DEint:8 The subscripts act, str and int denote the effects associatedwiththeoverallactivitylevel,activity structure and sectoral energy intensi
13、ty, respectively. The LMDIformulae can be readily worked out from Table 6 and they are summarized in Table 7 in Appendix A. Changes in CO2emissions from industry may be studied by quantifying the contributions from changes in fi ve different factors: overall industrial activity (activity effect), in
14、dustry activity mix (structure effect), sectoralenergyintensity(intensityeffect),sectoral energy mix (energy-mix effect), and CO2emission factors (emission-factor effect). The sub-categories of the aggregate are industrial sector and fuel type. The IDA identity in Eq. (1) may be written as C X ij Ci
15、j X ij Q Qi Q Ei Qi Eij Ei Cij Eij X ij QSiIiMijUij;9 where C is the total CO2emissions and Cijis the CO2 emissions arising from fuel j in industrial sector i; Eijis the consumption of fuel jin industrial sectori, whereEi P jEij; thefuel-mixvariableisgiven by Mij Eij=Ej and the CO2emission factor by
16、 Uij Cij=Eij: From Eqs. (2) and (3), we have Dtot CT=C0 DactDstrDintDmixDemf;10 DCtot CT? C0 DCact DCstr DCint DCmix DCemf:11 The subscripts act, str, int, mix and emf, respectively, denote the effects associated with overall activity, activity structure, sectoral energy intensity, sectoral energy m
17、ix and emission factors. The LMDI formulae are summarized in Table 8 in Appendix A. 3. Numerical examples We collected the 1990 (Year 0) and 2000 (Year T) energy and CO2emission data for industry in Canada from Nyboer (2002) and Nyboer and Laurin (2002). The database includes a total of 23 industria
18、l sectors and 14 energy sources. The aggregate CO2emissions in million tonnes of CO2(MTCO2), energy consumption in petajoules (PJ) and gross industrial output in Canadian dollars (C$) are shown in Table 1.3The observed changes in energy consumption and CO2emissions are shown in the fi rst column of
19、Tables 25. The other columnsofthetablesgivethedecomposition results obtained using the decomposition formulae in Appendix A.4 From Tables 2 and 3, it can be seen that Canadian industrial energy consumption increased by 16.2% or 377.8PJ from 1990 to 2000. The LMDI decomposition ARTICLE IN PRESS Table
20、 1 Aggregate data for Canadian industry, 1990 and 2000 YearC (MTCO2)E (PJ)Q (gross output, 1986 C$ billions) 1990114.312336.5295.2 2000135.112714.3442.5 Table 2 Results of industrial energy consumption decomposition for Canada, 19902000: multiplicative decomposition DtotDactDstrDint 1.1621.4980.8060
21、.963 Table 3 Results of industrial energy consumption decomposition for Canada, 19902000: additive decomposition (PJ) DEtotDEactDEstrDEint 377.81018.6?544.7?96.1 Table 4 Results of industry energy-related CO2emission decomposition for Canada, 19902000: multiplicative decomposition DtotDactDstrDintDm
22、ixDemf 1.1821.4930.8140.9510.9801.044 3Nyboer (2002) and Nyboer and Laurin (2002) do not give CO2 emissions arising from electricity consumption. We estimated the equivalent emission factors for electricity from the 1990 and 2000 Canadian energy balances in International Energy Agency (1993, 2002),
23、by dividing the total emissions for fuel consumption in electricity generation by the total fi nal electricity consumption in Canada in the respective years. 4Due to differences in data source, industry coverage, sector classifi cation, industrial activity measurement and decomposition technique, th
24、e additive decomposition results obtained here are different from those in Natural Resources Canada (2002). B.W. Ang / Energy Policy 33 (2005) 867871868 results show that the activity effect led to an increase almost three times that margin, and the much lower growth observed was due to structural c
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