Revisiting Decomposition Analysis for Carbon Dioxide Emissions from Car Travel: Introduction of Modified Laspeyres Index Method

6 7 Decomposition analyses are helpful to policymakers and analysts who aim to reduce carbon 8 dioxide (CO2) emissions from car travel. A large number of decomposition methods have been 9 proposed till date. However, there is still no consensus regarding the best decomposition 10 method because each method has certain advantages and disadvantages. Which method is 11 valid for the decomposition of the changes in CO2 emissions from car travel? In this paper, we 12 revisit the Refined Laspeyres Index (RLI) method, Logarithmic Mean Divisia Index I (LMDI) 13 method, and Modified Laspeyres Index (MLI) method. After a discussion of theoretical issues, 14 we focus on period-wise, time-series, and cross-region decompositions of the changes in CO2 15 emissions from passenger cars in Japan, using the three methods. While the RLI and LMDI 16 methods are the most widely used by researchers and analysts, these methods contain 17 theoretical problems with the attribution and distribution of interaction terms, particularly 18 when some factors change positively and others change negatively. The recently proposed 19 MLI method helps in resolving these issues by attributing and distributing the interaction 20 terms to related factors according to the changes in each factor. Our case studies in Japan also 21 indicate that differences in the attribution of the interaction term to the related factors between 22 the three methods influence the decomposition results significantly. We conclude that the MLI 23 method generates more valid decomposition results than do the RLI and LMDI methods 24 because of the reasonable attribution and distribution of the interaction terms. 25 TRB 2012 Annual Meeting Paper revised from original submittal. Mishina and Muromachi 3 INTRODUCTION 1 2 Since the oil crisis of 1973, index decomposition analyses have been widely accepted as 3 effective analytical tools for the energy and environmental sectors. Decompositions help in 4 identifying relevant factors that influence changes in an objective variable such as CO2 5 emissions and in quantifying the relative contributions of the changes from the relevant factors. 6 Moreover, the chronological and cross-country/region decomposition of the factors that 7 contribute to a decrease in the CO2 emissions would be helpful to policymakers and analysts 8 who aim to reduce CO2 emissions from various sources such as cars. The world transport 9 sector accounted for as much as 23% of the global CO2 emissions in 2008 (1). Transport, 10 particularly car travel, is one of the key sectors targeted for the reduction of CO2 emissions. 11 Thus, decomposition analysis of the changes in CO2 emissions from car travel, using a valid 12 method, is important for policymaking with regard to the institution of CO2 reduction 13 measures. Moreover, in Japan, CO2 emissions from passenger cars peaked in 2001 and 14 decrease continually thereafter, thus quantitative identification of contributing factors for the 15 rise and decline of CO2 emissions using decomposition methods and discussion on the policy 16 implications of the changes are very helpful to policymaking to reduce CO2 emissions. 17 18 A large number of decomposition methods have been proposed. By far, the most often used 19 decomposition methods in industrial energy and energy-induced gas emission studies are the 20 so-called Laspeyres and Divisia index approaches, respectively based on the Laspeyres and the 21 Divisia indices in economics and statistics (2). However, conventional Laspeyres and Divisia 22 index methods have some drawbacks. Very often, the conventional Laspeyres index method 23 leaves large residual interaction terms after the decomposition, which might make the 24 decomposition analysis less meaningful (3). To overcome this issue, Sun (4) proposed the RLI 25 method, in which the interaction terms are distributed equally among all factors according to 26 the ―jointly created and equally distributed‖ principle. On the other hand, the conventional 27 Divisia index method always leads to a residual term because of the approximation of 28 theoretical and continuous logarithmic Divisia indices, and to a computational problem when 29 the values of the variables are zero (2). To overcome these issues, Ang et al. (5) proposed the 30 additive LMDI method, and Ang and Liu (6) proposed the multiplicative LMDI by applying a 31 logarithmic mean weight function. 32 33 A number of previous studies suggest that the RLI and LMDI have several desirable properties 34 and hence would be the preferred decomposition methods. However, they have certain 35 advantages and disadvantages. Thus, there is still no consensus regarding the best 36 decomposition method. Ang (7) recommends the use of additive and multiplicative LMDIs 37 because of their theoretical foundation, adaptability, and ease of use and the ease of result 38 interpretation; in addition, he points out that the RLI formulae are fairly complex when the 39 number of factors exceeds three. He also recommends the use of the RLI when the data set 40 contains negative values, because the logarithms of a negative value cannot yield a real 41 number. Moreover, Ang (7) recommends the RLI to those who favor methods linked to the 42 Laspeyres index approach. International organizations, national agencies, researchers, and 43 analysts mostly use the RLI (8, 9, & 10) or the LMDI (11, 12, & 13) in their empirical studies, 44 including those on car travel. Steenhof (14) prefers the Laspeyres approach over the Divisia 45 approach because the former is easier to interpret and use, and arguably more assessable and 46 usable by practitioners, policy makers, and other stakeholders. On the other hand, 47 TRB 2012 Annual Meeting Paper revised from original submittal. Mishina and Muromachi 4 Papagiannaki and Diakoulaki (11) point out that the LMDI has the most robust theoretical 1 foundation, provides complete and more stable decomposition results without the residual 2 term, and is very easy to implement for the decomposition of CO2 emissions from passenger 3 cars. 4 5 While decomposition analysis would be helpful to researchers and analysts who aim to reduce 6 CO2 emissions from car travel (15 & 16), previous studies mostly focused on regions or 7 countries where CO2 emissions were increasing. Moreover, most studies do not address the 8 issues of attribution and distribution of the interaction terms in the decomposition methods, 9 particularly when they are applied to a case where some factors change positively and others 10 change negatively. 11 12 Recently, Mishina et al. (17) pointed out a concern over the reliability and accuracy of 13 decomposition using the RLI, particularly in a case where some factors change positively and 14 others change negatively. They then proposed the MLI method. The MLI attributes the 15 interaction terms to the related factors according to the changes in each factor and distributes 16 them in a manner proportional to a symmetrical rate of the changes. However, sufficient 17 experiments have not been carried out to confirm the validity of the MLI. 18 19 In this study, we investigate which among the RLI, LMDI, and MLI is valid for the 20 decomposition of CO2 emissions from car travel. First, we highlight the characteristics of the 21 three methods and some issues. We next identify the differences among the three methods by 22 decomposing a simple hypothetical dataset. Then, using the three methods, we conduct period23 wise and time-series decompositions of the changes in CO2 emissions from passenger cars in 24 Japan over the period 1990–2008 and a cross-region decomposition between metropolitan 25 regions and the remaining regions in Japan in 2008 and then compare the decomposition 26 results. 27 28 THE REFINED LASPEYRES INDEX (RLI) METHOD 29 30 Methodology 31 32 The Laspeyres index measures the percentage change in some aspect of a group of items over 33 time, using weights derived from values in some base year (7). This method isolates a factor’s 34 impact by letting variables related to the other factor at their base-year values (18). The most 35 serious issue in the conventional Laspeyres index method is the existence of a large residual 36 interactive term, which leads to difficulties in the interpretation of the results obtained. Sun (4) 37 proposes the RLI to overcome this issue. 38 39 In a two-change-factor model (F, D), CO2 emissions (CO2: metric tons) from car travel can be 40 determined by the factors F and D. 41 42 CO2 = CF D (1) 43 44 where F and D represent the actual road fuel efficiency (  /km) and the travel distance (km), 45 respectively. For simplification, C representing the CO2 emission factor (metric ton-CO2/  ) is 46 assumed to be constant and equal to 1.0. 47 TRB 2012 Annual Meeting Paper revised from original submittal. Mishina and Muromachi 5 1 Over a period [0, t], the change in the CO2 emissions ( CO2) is given by 2 3  CO2 = CO2 t CO2 0 = F t D t – F 0 D 0 = (F t -F 0 )D 0 +F 0 (D t -D 0 ) + (F t -F 0 )(D t -D 0 ) 4 =  FD + F D + F D (2) 5 6 where  FD 0 and F 0  D represent the changes in the factors F and D as components of 7  CO2 over the given period.  F  D is the residual interaction term resulting from 8 simultaneous changes in the factors. 9 10 Sun (4) proposes equal distribution of the interaction term to the all factors, according to the 11 ―jointly created and equally distributed‖ principle (Figure 1). The contributions of F and D are 12