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Measuring the drivers of economic, energy, and environmental changes: an index decomposition analysis
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Measuring the drivers of economic, energy, and environmental changes: an index decomposition analysis
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MEASURING THE DRIVERS OF ECONOMIC, ENERGY, AND ENVIRONMENTAL CHANGES: AN INDEX DECOMPOSITION ANALYSIS by Jie Zhou A Dissertation Presented to the FACULTY OF THE USC SOL PRICE SCHOOL OF PUBLIC POLICY UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF POLICY, PLANNING, AND DEVELOPMENT December, 2014 Copyright 2014 Jie Zhou To my grandparents, who always believe in me and are proud of my every little progress. To my parents, who gave me life and a home full oflove and happiness. To my husband, who gave me generous support and love. 11 Acknowledgments I wish to express my deep respect and gratitude to my advisor, Dr. Adam Rose, for his invaluable guidance and continuous support throughout the course of my Ph.D. research. I truly appreciate and enjoy the opportunity to work with him, so much so that I didn't notice time flew by quickly. He led me to the world of academia and taught me the science, art, and craft of research. He shared his intellectual insights with me in our weekly research meetings and countless email and phone correspondences, from which I was benefited greatly. I'm especially grateful to his generosity and patience during the time I became discouraged and irritated when facing the seemly insurmountable obstacles along the way. It is difficult to have an advisor who can teach you both the intelligence of science and the wisdom of life, not to mention along with the important financial support. I am one of the few luckiest. I also wish to thank my two committee members, Dr. Shui-Y an Tang and Dr. Jeff Nugent, for their insights and advices that helped me to refine my dissertation. I appreciate the opportunities to take their classes and to discuss my dissertation proposal with them, which sharpened my thoughts and broadened my perspectives. I'm grateful to many people who gave me support from time to time and enriched my life in the University of Southern California. I have learned a lot and gained insights from the professors I had class with and/or worked with. I had the pleasure to be in a fabulous research group with many bright people, who all excel in their areas. 111 I want to thank my parents and grandparents for their unconditional love, continuous support and understandings for me to complete my Ph.D. program, to which I am greatly in debt. They have shouldered the responsibility of taking care of the family for too many years. The only consolation for me is that I probably have lived their dreams for them, at a better time, when those opportunities that were beyond their reaches become available. Finally, I want to express my sincere gratitude to my husband. He met me when I was out of funding and discouraged, and not sure when I would be able to graduate. He encouraged me and convinced me that things will be better as he also has experienced the same or worse. He kept the family running and supported me to finish my degree. I would like to express my appreciation to all the people who helped me along the way. I will be responsible for all the mistakes and omissions in this dissertation. IV Table of Contents Acknowledgments .............................................................................................................. iii List of Tables .................................................................................................................... vii List of Figures .................................................................................................................... ix Abbreviations ...................................................................................................................... x Abstract ........................................................................................................................... xii Chapter 1. Chapter 2. 1. 2. 3. 2.1. 2.2. 2.3. 2.4. 2.5. Introduction ................................................................................................... 1 Development ofIDA and the Derivation of Multifactor Multilateral IDA ... 9 Index Decomposition Analysis Questions in General.. ................................. 9 Developments in Index Numbers and IDA ................................................. 13 Early efforts in two-factor, two-case decomposition .................................. 13 Multi-factors two-case decomposition ........................................................ 17 A new framework to connect two-cases index numbers in IDA ................. 26 Multi-cases two-factor decomposition ........................................................ 32 Multifactor multilateral index ..................................................................... 44 Conclusion ................................................................................................... 51 References ..................................................................................................................... 5 8 Chapter 3. 1. 1.1. 1.2. 2. Drivers of C0 2 Emissions from Electricity Generations in the United States: A Multilateral IDA ...................................................................................... 63 Identifying the drivers of emissions by multi-factor multilateral IDA ....... 63 Motivation of the case study ....................................................................... 63 IDA model ................................................................................................... 65 Results ......................................................................................................... 69 3. Interpretation of results ............................................................................... 76 3.1. Interpretation of the additive indices ........................................................... 77 3.2. Interpretation of the multiplicative indices ................................................. 84 3.3. The outliers and differences between index numbers ................................. 91 4. Policy implications ...................................................................................... 94 References ..................................................................................................................... 99 Chapter 4. 1. 1.1. 1.2. Drivers of Green Job Change in the United States: A Temporal Two-Stage IDA ............................................................................................................ 101 Definition of Green Job ............................................................................. 102 Vacancy vs. Employment .......................................................................... 102 Meaning of Green ...................................................................................... 104 v 2. 3. 4. 1.2.1. 1.2.2. 1.3. 1.4. 2.1. 2.2. 2.3. Scope ......................................................................................................... 104 The means of becoming green ................................................................... 107 Compare major definitions and measurements of green jobs ................... 110 The definition and measure of green job used in this study ...................... 114 Decomposition analysis for employment change in the United States ..... 116 The Index Decomposition Analysis model ............................................... 116 Data Sources and Refinements .................................................................. 119 Results and interpretations ........................................................................ 125 Occupation and wage in green job change ................................................ 132 Conclusion ................................................................................................. 136 References ................................................................................................................... 139 Chapter 5. Drivers ofC0 2 Emissions in Electricity Generation in China: A Multi- temporal Multilateral IDA ......................................................................... 141 1. C0 2 emissions from electricity generation in China ................................. 142 2. Index decomposition analysis of the emission drivers .............................. 149 2.1. Index decomposition analysis design ........................................................ 149 2.1.1. Variables and model selection ................................................................... 149 2.1.2. Five-factor FII decomposition ................................................................... 153 2.2. Decomposition results and interpretation .................................................. 155 2.2.1. Drivers ofC0 2 emissions growth rates overtime ..................................... 155 2.2.2. Drivers of space-specific growth rates ofC0 2 emissions ......................... 161 3. Conclusion and policy implications .......................................................... 165 References ................................................................................................................... 173 Chapter 6. Conclusion ................................................................................................. 177 Consolidated Bibliography ............................................................................................. 186 VI List of Tables Table 2-1 Weighting Schemes in Widely-Used Index Numbers ..................................... 31 Table 2-2 Relationship between Multiplicative and Additive Index Numbers ................ 32 Table 2-3 Marginal Contribution Matrix for Three Areas using Price Indices ................ 42 Table 2-4 Multilateral EKS/Shapley Numbers for Commonly Used Indices .................. 43 Table 2-5 Summary and Comparison oflndex Numbers and IDA Approaches ............. 54 Table 3-1 Result of Multiplicative and Additive Multilateral EKS/Shapley Numbers (2009 data) ....................................................................................................... 69 Table 3-2 Additive Decomposition in Percentage Terms ................................................ 81 Table 3-3 Percentage ofCCGR to the Average CCGR by States .................................... 85 Table 3-4 States with Factors being Positive or Negative Drivers .................................. 90 Table 3-5 Policies and Factors ......................................................................................... 96 Table 4-1 Green Job Definitions Comparison ................................................................ 114 Table 4-2 BLS GGS Sectors Scheme Mapped to BEA Sectors ..................................... 122 Table 4-3 Vartia/LMDI Indices for Green-employment, Non-green employment, and Total Employment in the United States, 2010 to 2011 (2010 ~ base) ........... 126 Table 4-4 Drivers of Annual Wage Change between All-green firms and Non-green firms, Non-green firms~ Base ....................................................................... 134 Table 4-5 Drivers of Annual Wage Change between Mixed-green firms and Non-green firms, Non-green firms~ base ....................................................................... 134 Table 4-6 Drivers of Hourly Wage Change between All-green firms and Non-green firms, Non-green firms~ base .................................................................................. 134 Table 4-7 Drivers of Hourly Wage Change between Mixed-green firms and Non-green firms, Non-green firms~ base ....................................................................... 135 Table 5-1 Net Calorific Values, Various Sources (TJ/Gg) ............................................ 144 Table 5-2 Net Calorific Values used in the Study (TJ/Gg or TJ/10 6 *M 3 ) ..................... 146 vu Table 5-3 Carbon Content, Carbon Oxidation Factor, and C0 2 Emission Factors by Fuel Type, Various Sources ................................................................................... 14 7 Table 5-4 Growth Rate of C0 2 Emissions from Electricity Generation over Time, Average and Standard Deviations by Factors, 2006 to 2009 ......................... 155 Table 5-5 Correlations between Total Growth Rate of C0 2 Emissions and the Attributions by Factors, 2006 to 2009 ............................................................ 165 Table 6-1 Example Use ofIDA to Assist Policy Analysis ............................................ 185 V111 List of Figures Figure 1-1 Development oflndex Number Theory, IDA, and Our Contributions ............ 3 Figure 3-1 Additive EKS/Shapley Number for Fuel Mix's Contribution to C0 2 Emissions from Electricity Generation in the United States ............................................. 79 Figure 3-2 Additive EKS/Shapley Numbers for Energy Conversion Coefficient's Contribution to C0 2 Emissions from Electricity Generation in the United States ................................................................................................................ 80 Figure 3-3 Additive EKS/Shapley Numbers for C02 Emission Coefficient's Contribution to C0 2 Emissions from Electricity Generation in the United States ................ 80 Figure 5-1 C02 Emissions from Electricity Generation by Province in China, 2006-2009 ........................................................................................................................ 149 Figure 5- 2 Growth Rates of C02 Emissions from Electricity Generation over Time Attributed to Five Drivers by Province, 2006 to 2009 ................................... 157 Figure 5-3 Space-specific Growth Rate of C0 2 Emissions from Electricity Generation over Time Attributed to Five Drivers by Provinces, 2006 to 2009 ................ 165 lX Abbreviations AMDI Arithmetic-Mean Divisia Index BLS U.S. Bureau of Labor Statistics CCD Caves, Christensen, & Diewert (1982) CCGR Continuously Compounded Growth Rate CHP Combined Heat and Power DOL U.S. Department of Labor EKS Elteto, 6., & Koves, P. (1964, 1973), Szulc, B. (1964) EPA U.S. Environmental Protection Agency Fii Fisher Ideal Index GGS Green Goods and Services GGS-OCC Occupational Employment and Wages in Green Goods and Services GHG Green House Gas IDA Index Decomposition Analysis IPCC International Panel of Climate Change LMDI Log-Mean Divisia Index LMDI Log-Mean Divisia Index LPG Liquefied Petroleum Gas NAICS North American Industry Classification System NCVs Net Calorific Values NDRC National Development and Reform Commission of the People's Republic of x OECD QCEW SARs SDA SSI TTI UNEP VI WMO China Organization for Economic Co-operation and Development Quarterly Census of Employment and Wages Special Administrative Regions Structural Decomposition Analysis Shapley/Sun Index Tiirnqvist-Theil Index United Nations Environment Program V artia Index World Meteorological Organization XI Abstract This dissertation examines the theoretical roots of index decomposition analysis (IDA), fills in some key gaps and extends this method, and applies it to three cases to provide policy and planning insights. IDA is a widely used tool in energy use and pollutant emissions studies to estimate the directions and magnitude of the driving forces of a change in a key economic variable. The usefulness of index decomposition analysis resides in the fact that policy makers and planners sometimes need a way to distinguish how one factor affects a certain change of interest at the macro level when the change is a combined effect of multiple factors on a group of items. IDA can separate the contributions of drivers to the explained variable change and can aggregate the effects at the group level. Therefore, it provides a quantitative way to reveal the significance of drivers to a change and can help policy makers and planners develop remedies where necessary. This dissertation consists of six chapters. The theoretical foundation and nearly a century of studies on index numbers were summarized briefly in Chapter 1 and in detail in Chapter 2. Chapter 1 also describes how this dissertation is organized. By reviewing the history and recent developments in index numbers and IDA, I identified several remaining issues and proposed a new approach to generate multifactor multilateral index numbers. I discussed the issue of consistencies in the ranking of factors between multiplicative IDAs and their additive counterparts. I also united both the widely-used Laspeyres-based and Divisia-based index numbers under the framework of discrete Xll approximation of Divisia index, which has the advantage to identify the source of differences across index numbers and to reveal the link between the multiplicative index numbers and their additive counterparts. Index numbers were first studied in the field of wealth and income to obtain the price level and quantity level changes between multiple time periods and/or areas. Major contributions include the derivation of index number formulas/approaches, the meaning of index numbers, and their connections with economic theory (see, e.g. Fisher, 1922; Samuelson & Swamy, 1974; Diewert, 1976; van Veelen & van de Weide, 2008). IDA can be seen as the extension of index number theory to the field of energy use and pollutant emissions, in which the number of explanatory factors usually exceeds two. Major contributions in IDA include the extension of the index numbers to the new field, the derivation of multi-factor index number formulas, the introduction of additive decomposition, and the derivation of the additive counterparts of multiplicative index number formulas (see, e.g., Ang, 1994; Ang, 2004; Sun, 1997). We identified multi-factor multilateral IDA as a gap in the literature and suggested that the Shapley value can be used to derive transitive multilateral index numbers. The transitivity is ensured by obtaining one value for each area first and obtaining the multilateral index numbers by using the quotient of the values, which is also the approach suggested in van Veelen (2002). The one value for each area is the Shapley value with bilateral index numbers as marginal contributions. We were able to obtain the EKS and xm CCD indices and extended the widely-used LMDI and all additive index numbers to multilateral cases. We also examined the inconsistencies in the ranking of factors between the multiplicative indices and their additive counterparts by using the example of the Fisher Ideal Index (FII) and the Shapley/Sun Index (SSI). Even though the inconsistencies are recognized in the literature (see, e.g. Ang, 1994), it is the first time that they are studied extensively. We showed that the inconsistencies between FII and SSI only exist when the number of factors exceeds two, and provided a proof of the inconsistencies when the number of factors are three, which can be further extended to the n number case. We also carried on an analysis of consistencies in the ranking of factors in our study of multi-factor multi lateral decomposition analysis. The inconsistencies between the multiplicative index and their additive counterparts exist in multi-factor multilateral decompositions as well. As they provide different rankings of factors, the disparity can cause difficulties in the interpretation of results and weaken the influence of IDA in policy guidance. When we have no reason to discriminate one method over another, we may choose to examine the range of the disparity to see how bad it can be. We thus adjusted the three-factor Laspeyres Index and Paasche Index and their additive counterparts, and used them to bound the three-factor multilateral Fisher Ideal Index and its additive counterpart, the Shapley/Sun Index. The range they set can be seen as the sensitivity range in which the Fisher Ideal Index and the Shapley/Sun Index can vary. XIV Our last contribution is to provide a new framework to better reveal the differences across the widely-used index numbers and the links between the multiplicative index numbers and their additive counterparts. We transformed the Laspeyres-based index numbers into the formation of discrete approximation of Divisia index. When all the widely-used index numbers are written in the same form, we can easily spot that the differences lie in the weighting schemes used to aggregate the item level change. It provides a new perspective to look at and compare the index numbers and for further studying the inconsistencies between multiplicative and additive index numbers. Chapter 3 utilized the derived multi-factor multilateral index numbers to study the drivers in C0 2 emissions from electricity generation by states in the United States: fuel mix, electricity conversion coefficient, and C0 2 emission factor. We obtained the data from U.S. Energy Information Administration (EIA). The result identified whether each U.S. state emitted more or less than the average C0 2 emissions from electricity generation driven by one factor only. For example, we identified that California performs better than average in C0 2 emissions from electricity generation, because of its relatively low carbon emitting fuel mix, which is offset somewhat by its higher than average C0 2 coefficient for the subset of fossil fuels. We then provided examples of policies to improve the environment that policy makers may wish to consider. Chapter 3 also can serve as an illustration of the points we made in Chapter 2 regarding the use of multilateral multifactor index numbers, differences between well-behaved index numbers, and consistencies between the multiplicative index numbers and their additive counterparts. xv For example, we showed the variations in weighing schemes of FII and LMDI in the three-factor case and delineated the sensitivity ranges for FII and its additive counterpart. Chapter 4 seeks to extend the use ofIDA to the study of green job changes. We presented a framework to evaluate the existing definitions of green jobs and selected the definition and dataset published by the U.S. Bureau of Labor Statistics to analyze the drivers of green job change in the United States. A temporal two-stage Index Decomposition Analysis (IDA) model is used to identify and measure the direction and magnitude of four drivers of green job change: labor productivity, green revenue share within industry, economic/industrial structure, and total economic output. The green job increase in the period from 2010 to 2011 is largely driven by the increased green revenue share within industries and the increased total economic output of the U.S. economy. Labor productivity and economic structure are minor negative and positive drivers of green employment change, respectively. We also calculated the wage level changes in companies with all, part of, or none of the revenues from green products and services, eliminating the impacts from occupational and industrial variations. We found that, in the examined period, the wage levels in companies with all or part of their revenue from green products and services are lower than the wage levels in companies with no revenue from green products and services. Chapter 5 studies the C0 2 emissions from electricity generation by province in China over time and over space. While Chapter 3 performed the decomposition over space for a single period of time and Chapter 4 covered the decomposition over time for a single area, XVI Chapter 5 seeks to explore the issues in decomposition analysis for balanced panel data. The results of decomposition over time first and then over space and the decomposition over space first and then over time are the same in our case due to data characteristics and the proportionality property of the chosen index numbers. It thus simplified the selection of decomposition sequence between time and space. The continuously compounded growth rate (CCGR) of C0 2 emissions in electricity generation was first decomposed into five indexes, each of which represents the CCGR of C0 2 emissions in electricity generation attributed to one factor change, by using chained (Year n compare to Year n-1) temporal decomposition for each province. The CCGR was then decomposed to two parts: the average CCGR of all Chinese provinces and the residual, which is the space-specific CCGR for each province. The average CCGR can reflect the general trend across all provinces, such as the effects of national policies and economic conditions that affect all of them. The space-specific CCGRs can reflect the regional disparities in C0 2 emissions attributed to each driver. The five factors in the IDA model are: population, per capita electricity consumption, the location factor (indicating the percentage of import and export across provinces), fuel conversion efficiency, and fuel structure. The result indicated that at the average level, fuel conversion efficiency and fuel structure contributed to a decrease in the growth rate of C0 2 emissions from 2008 to 2009, which was offset by per capita electricity consumption and population growth. Space-specific analysis also revealed the variations across regions on how the drivers contributed to the emissions. This is important because for a country as large as China, provinces exemplify different development stages and strategies that are influenced by both of the national and XVll provincial level policies, all of which can affect the CCGR of C0 2 emissions. At present, few multilateral IDA are conducted to reveal the disparities. The analysis is done to provide the critical piece of information. Chapter 6 summarized our contributions to the IDA literature and the three case-studies of ID As in policy analysis and pointed out the directions of future research. We suggest that future research can work on enforcing the links between ID A and the economic theory and providing a general framework for policy analysis. The differences across index numbers and the inconsistencies between multiplicative and additive index numbers can also be further studied under the united framework we proposed in Chapter 2. The link between the Shapley number and multilateral index numbers can also be a rewarding future research topic. XV111 Chapter 1. Introduction This dissertation seeks to introduce index decomposition analysis (IDA) to policy makers and planners in a systematic way. It seeks to advance the methodological development and empirical applications of this valuable tool. Index decomposition analysis refers to the re-development and application of index number theory. Originally applied to the study of income and wealth, it has recently been applied primarily to energy use and pollutant 1 emissions. Intuitively, IDA simply exploits the change in the dependent variable of an identity to determine the contribution to the change by several pre-defined independent variables. A single IDA requires at least two cases. The cases can either be two periods of time, two places, or even the stages before and after any decision making. The change of status is always the result of a combination of two or more factors. Indices, in such cases, can be seen as an aggregate level measure that associates the change of status to changes of explanatory factors. The construction and/or selection of an identity usually mark the starting point of an IDA. Pre-defined factors can be introduced into the identity by adding and eliminating their effects one by one but keeping the left and right sides of the identity balanced. In practice, the selection of identity usually is quite open. It can be an identity constructed by the researcher, or a well-known identity used in the field, e.g., the Kaya identity in studying 1 Most of the pollutant emissions studied in the literature were GHGs and C02 emissions, even though most of them are not classified as air pollutants in the published list of hazardous air pollutants by the US. Environmental Protection Agency (EPA) (EPA, 2013). Due to the ambiguities in scientific studies and political dynamics, we adopt a broader definition of pollutant emissions as all emissions that can have negative impacts to the environment simply to summarize the IDA studies. However, the application of IDA is not restricted to GHGs and C02 emissions. 1 anthropogenic greenhouse gas emissions. In studying energy use and pollutant emissions, IDA is comparable to Input-Output Structural Decomposition Analysis (SDA), though the latter can further separate out indirect effects but requires a more extensive database. The root ofIDA can be traced back to the inquiry of the true cost of living under a set of living conditions in which the consumers have the ability to adapt to the changing environment. The living conditions are reduced to two sets of vectors: the prices of the goods and the quantities of the goods that were consumed in the two situations. The trick is to compute the indices of price level and quantity level, respectively, by using the individual data points of prices and quantities that we obtained in the real world. The inquiries represented the development of two-factor IDA by the framework in Figure 1-1. In Figure 1-1, we categorized the development in index number theory and IDA by the number of cases for decomposition and the number of factors, and listed the major achievements and milestones in the four quadrants. The upper right quadrant, which represents the multifactor multilateral IDA, is a gap in the current literature and one of the focuses in this dissertation. We will discuss the contents in each quadrant in detail in Chapter 2. 2 0: 0 :~ ,; ~ 0 ~ 0. ~ e 0 ;! u ::! " A .... <2 ~ ';J " ~ ~ 0 "' "' u a """' ~ ~ 0 ·t. .... ";! " .D a e ~ 0 i 0 ,. i,.. Number of Factors Two More than Two The property of D eri vati on of transitivity; apJ"oaches multifactor multilateral to derive multilateral index numbers,. index numbers,. their property of transitivity; comparisons and application of the index connections with numbers economic theory Index nurn ber Derivation of multi.factor derivation approaches,. index :r.n.un b ers, their connection to application in studying economic theorf, energy use and pollutant. applications in emissions~ use of stucl:ying ?'ice !eve~ additive decompositions J"Ocluctivity; etc. c • c Wealth and Income Energy use and Emissions(IDA) This dissertation Figure 1-1 Development of Index Number Theory, IDA, and Our Contributions The study of index numbers was pioneered by many prominent scholars since the early 1900s (see e.g. Fisher, 1922; Konils & Byushgens, 1926). The questions posed revolved around the derivation of the true cost of living and/or the real income, considering the adaptive behaviors of consumers and the variations in utility functions. The main argument of expenditures not being the "true cost of living'' and of"real income" is that the representative consumer always adapts to the changed environment, represented by the changed prices, by changing the quantities of goods purchased, so to maximize his/her utility. Thus, when the customer's expenditure is doubled due to the price increase, the "true" cost of living may not increase twice because of consumer's adaptive behaviors. In the similar vein, nominal income cannot be used as a measure of real 3 income when considering customer's adaptive behaviors. Deriving an index to measure the "true" cost of living and/or the "real" income became a challenging task for scholars. Scholars presented many index number formulas and approaches to obtain index numbers. Some of the most widely recognized index numbers are the Fisher Ideal Index (FII), Tiirnqvist-Theil Index (TTI), Vartia Index (VI), etc. There were debates on how to evaluate different index number formulas and which one should be the most appropriate for use under various circumstances. Two major approaches were taken to evaluate index numbers, which at the same time represent two major approaches of index number derivations. The first approach starts with the ideal index number we would like to obtain and identifies characteristics that such an ideal index number should possess, which often are called axioms, and creates index numbers through logic. It corresponds to the test or axiomatic approach to generate index numbers. Fisher (1922) used the test approach to derive the Fisher Ideal Index. But this approach is gradually considered more as an index number evaluation approach other than derivation approach. Major criteria that scholars believe an ideal index number should meet include the time reversal, factor reversal, proportionality test, zero robust, and the consistency in aggregation (see e.g. Fisher, 1922; Diewert & Nakamura, 1993; ILO/IMF/OECD/UNECE/Eurostat/The World Bank, 2004). The second approach is based on economic theory of production and consumption and obtains indices via utility and/or cost optimization models. Progress was made in the 1970s in strengthening the link between economic theory and index number derivation (see e.g. Samuelson & Swamy, 1974) and the flexibility of using index numbers to approach arbitrary aggregator functions (Diewert & Nakamura, 1993). Other maJor 4 approaches of index number derivations include the Divisia approach, stochastic approach, etc., though the latter approaches are rarely used to compare and evaluate index numbers. The research and application of index numbers in the analysis of energy use and pollutant emissions developed relatively late compared to the index number studies of income and wealth. This advance is led by scholars such as Ang (e.g. Ang & Choi, 1997; Ang, 2004a; Ang, 2004b ), etc. The common approach is to start with an identity and decompose the changes in the explained variable to several indices, each of which presents one pre- defined explanatory variable in the identity. It is often referred to as the Index Decomposition Analysis (IDA) in the field of energy and emission studies. IDA is often used to study the effects of structural change, energy efficiency change, energy use in industries, etc. The transition of index number studies in a new field triggered the inquiry of index number decomposition for more than two factors and the derivation of more index numbers, e.g. additive indexes. For ease of communication, we will use "index number study" or "index number theory" to refer to index number studies in wealth and income, and use "index decomposition analysis" or "IDA" to refer to the decomposition analysis in energy use and pollutant emissions. The IDA studies of energy use and pollutant emissions introduced and applied additive decompositions extensively2. Additive IDA is quite similar to multiplicative IDA. It starts 2 Traditional index number theory literature has a different definition of multiplicative and additive decompositions of index numbers (see, e.g. Balk, 2004; Hallerbach, 2005), which we will explain in detail in Chapter 2. In short, traditional index number theory literature only handles multiplicative index numbers as defined in IDA Taking a price index as an example, it defines additive decomposition as writing the 5 with the same identity but assumes that the change in dependent variable resembles the summation rather than the product of all the indices. Scholars in the field also have identified additive counterparts for all the widely-used multiplicative index numbers, e.g. the Shapley/Sun Index (SSI) for the Fisher Ideal Index (FII), additive Log-Mean Divisia Index (LMDI) for LMDI, etc. The introduction of additive counterparts of the previous multiplicative IDA triggered the question of their consistencies. We will further discuss and tackle the issue in Chapter 2. It is worth mentioning that index decomposition analysis (IDA) developed in parallel with structural decomposition analysis (SDA) - an input-output based approach that not only enables the user to identify structural change, energy efficiency change, etc. such as in IDA, but also to distinguish direct and indirect effects in a given variable (see, e.g. Rose & Casler, 1996). More complicated approaches in SDA also allow for interaction terms (see Rose & Casler, 1996). SDA has also been applied extensively to analyze the drivers of emissions and/or energy use (Rose and Chen, 1991; Casler and Rose, 1998; Hoekstra and den Bergh, 2003). The advantage of IDA compared to SDA is that it requires less data and is not constrained by the input-output framework. However, the advantages also reflect IDA's major weakness: the lack of an economic framework and the lack of principles in defining factor other than the requirement of forming an identity. The often-selected pre-defined factors in IDA are energy intensity, fuel mix, economic structure, economic activities, and so on. In SDA, Rose and Chen (1991) derived 14 price index as weighted arithmetic average of price relatives, and multiplicative decomposition as writing the logarithm of index numbers as a weighted arithmetic average of logarithmic price differences, or, say, as a weighted geometric average of price relatives (Balk, 2004). 6 explanatory factors from a two-tiered production function of capital, labor, energy and materials. This dissertation will be organized as follows. We will address most of the technical and methodological issues of IDA in Chapter 2. These issues include the development of multifactor multilateral IDAs, the discussion on the inconsistencies between multilateral index numbers and their additive counterparts, and the discussion on the differences across index numbers, e.g. the difference between the generalized FII and VI/LMDI. We will then use three cases to illustrate the use of IDA from Chapter 3 to Chapter 5. Chapter 3 includes an IDA study of the drivers of C0 2 emissions from electricity generation by states in the United States. It applied the multifactor multilateral index number we developed in Chapter 2 to obtain a quantitative measure of the spatial variations in C0 2 emissions from electricity generation attributed to the change in fuel mix, fuel electricity conversion efficiency, and fuel C0 2 emission coefficient. It can reveal the areas of focus for policy makers and planners in emission control by comparing the state level emissions and their drivers with other states. In Chapter 4, we develop a two-stage temporal IDA model to study the drivers of the change in green jobs, non-green jobs, and the total employment from 2010 to 2011 in the United States. We also shed light on whether green jobs are good jobs in terms of their wage levels compared to similar non-green jobs. The analysis is limited due to data availabilities. But the chapter can well illustrate the application of IDA into a new field and provide an innovative use of index numbers in a two-stage analysis. 7 Chapter 5 includes a case study of C0 2 em1ss1ons from electricity generation by provinces in China. We will use the case to illustrate IDA over time and over space. Combining IDA over time and over space can help to yield information on the spatial variations of growth rates and the growth rates of spatial variations by regions. In this chapter, we obtained the drivers of the growth rates of C0 2 emissions from electricity generation by provinces in China from 2006 to 2009 and then identified the portion that was associated with the general trend and the portion that was space-specific. Chapter 6 summaries our contributions to the IDA literature and the insights we have obtained in three case studies and points out the areas for future research. In terms of the IDA methodologies, future researches can be developed by linking the two separated pieces of information in game theory and multilateral index numbers via the connection of Shapley value and multilateral index numbers as pointed out in Chapter 2. As we have proposed a new united framework for all widely-used index numbers, further studies of the differences across index numbers and the consistencies between multiplicative and additive index numbers under the new framework can be rewarding. We also suggest that future research be developed around the general policy analysis framework for IDA and/or to strengthen the connection ofIDA and economic theories. 8 Chapter 2. Development of IDA and the Derivation of Multifactor Multilateral IDA This chapter exammes the development of index number theory and IDA with our discussions of new issues and our resolutions interweaved throughout. The chapter mainly focuses on the extension of two-factor index numbers to multi-factor index numbers, multilateral index numbers, and multi-factor multilateral index numbers and the consistency of rankings of factors between multiplicative and additive IDA. 1. Index Decomposition Analysis Questions in General In general, index numbers can be seen as a technique to obtain measures of changes or differences for a group of individual items with various movements. Examples include aggregating the individual price change to the price level change of a bundle of goods, or aggregating the individual quantity change to the quantity level change of a bundle of goods. We do so by assuming a simple relationship, either multiplicative or additive, among the indices and the total group level change. We then transfer the complex relationship between the total group level change and the change of factors for individual items into a simple multiplicative or additive relationship between the observable group level change and the indices by the application of IDA. Therefore index number theory and index decomposition analysis is best suited for cases with the following characteristics: 1) The factors in question can be measured at item level but not at the group level, and we want to obtain the group level measure for comparison; 2) The group level explained variable can be directly measured or calculated; 9 3) The factors of the individual items change values over time or over space at different speed and directions, so aggregating them directly is difficult. For example, policy makers may be interested in the drivers of change in the cost of living in two periods of time but not the price change of every single good in detail. This is a classic example where index number theory finds its best use. An index decomposition model can be fully defined by two elements: 1) The identity it starts with; and 2) The assumed relationship among the indices. Following the framework as presented in Fisher (1922), the identity usually contains three dimensions of elements: 1) The commodity dimension, which defines the members of the group; 2) The factor dimension, which defines the pre-defined explanatory variables that we are interested in; and 3) The case dimension, which indicates the time and/or space the values of factors are associated with. The case dimension usually also implies whether the decomposition will be performed over time or over space. At present, all index number questions and index decomposition analysis starts with the following identity: N N M V' = '\' v' = '\' n x'. Li L ),f' j=l, ... ,M;i=l, ... N;t=l, ... ,T (2-1) i=l i=l }=1 In which V'represents the group level explained variable in time period t or area t, v;' represents the item level explained variable for the i 1 h item in the group in time period tor area t. The group level dependent variable V' is the summation of item level dependent variable v;'. Each item level dependent variable is the product of M item level pre-defined factors. Those item level pre-defined factor are represented by xJ,;, indicating the value of factor j for item i in time period t or area t. We will need at least two sets of values to 10 perform the decomposition, meaning that Twill be larger or equal to two. When the T is larger than two, it is referred to a multi-temporal or multi-lateral decomposition. N and M are usually equal or larger than two as well to make the decomposition analysis worthwhile. In order to identify how each of the pre-defined factors contributes to the group level explained variable, we postulate a simple multiplicative or additive relationship between the group level explained variable change and the group level measure for all pre-defined factors, a.k.a. index numbers, in two time periods or two areas: 1 "<:'N nM 1 M ~ = L.i=l }=1 xj,i = nx'.'1,1,0 VD "<:'N nM XO· J ' L.i=l ]=1 ),[ }=1 j = 1, ... ,M;I = 1, ... ,N (2- 2) v 1 -v 0 = (~ 0 x1\)-(~ 0 x1~;) = ~ ~A.i.o, j = 1, ... ,M;I = 1, ... ,N (2-3) In which xr· 1 • 0 represents the multiplicative index for factor j of time period or area 1 using time period or area 0 as the base, x/· 1 • 0 represents the additive index for factor j of time period or area 1 using time period or area 0 as the base. Our job is to assume either equation (2-2) or (2-3) holds, and to obtain xr· 1 • 0 , j = 1, ... , M or x/· 1 • 0 , j = 1, ... , M, with detailed data forxf;, j = 1, ... ,M; i = 1, ... ,N, andxl;, j = 1, ... ,M; i = 1, ... ,N. It should be noted that in index number studies in wealth and income, additive decomposition are rarely used. But in IDA in energy use and pollutant emissions studies, multiplicative decomposition and additive decomposition are considered equivalent approaches to identify the drivers of changes. 11 It is worth mentioning that the traditional index number theory literature, which is mainly used in studies of wealth and income, has a different definition of multiplicative decomposition and additive decomposition than IDA, which is mainly used in the studies of energy use and pollutant emissions. In the traditional index number theory literature, multiplicative decomposition and additive decomposition refer to two different ways of expressing one index number, which is the multiplicative index number as defined and obtained in IDA, as weighted average of how the value of the exact factor that the index number represents changes at the item or disaggregated level (see, e.g. Balk, 2004). Using the notation in equation (2-1) and equation (2-2), additive decomposition in the traditional index number theory literature handles whether it is possible to express any index number as an arithmetic average of ratios of the factor measured at the item level in the two time periods or two areas, as shown in equation (2-4), while multiplicative decomposition handles whether it is possible to express the logarithm of the index number as an arithmetic average of the log differences of the factor measured at the item level, as shown in equation (2-5). To avoid the confusion, we use the concept of multiplicative decomposition and additive decomposition as defined in the IDA literature throughout the dissertation, which are defined in equation (2-2) and (2-3), respectively. However, it is worthwhile to mention the other set of definitions to avoid confusion. I N X1· X M,1,0 = W· ...Jl:. J l * 0 , X·. i=1 ),l N lnXM.l.D = '\' w' } L i X~· 1 J ·' * n-o-, X·. i=l J ·' N w; 2 0 and L w; = 1 i=1 N w; 2 0 and L w;' i=l =1 (2-4) (2- 5) 12 Index number studies started with two-factor two-case decomposition and then extended to two-factor multi-case decomposition, while IDA usually handles multi-factor decomposition. The original two-factor two-case decomposition and two-factor multi- case decomposition are typically used to study price level and quantity level changes, and are often used in, for example, long-term contract adjustment and compensation policy making. IDA is often used to separate the effects of multiple factors in the change of energy efficiency, energy level, emission intensity, or emission level. 2. Developments in Index Numbers and IDA 2.1. Early efforts in two-factor, two-case decomposition The early efforts in two-factor two-case index number studies revolved largely around the inquiry of the "true" cost of living, the "real" income, and the purchasing power of money. For example, people may want to know how much is needed to maintain the same standard of living in two areas when they are making relocation decisions. When we are trying to obtain the price level change for a bundle of goods, simple arithmetic averages and the weighted arithmetic average will not work. For example, ifthe price of bread changes from $2 to $5, and the price of cloth changes from $10 to $7, we will wrongly get the idea that the price level hasn't changed at all by using the simple arithmetic average of the prices. This way of calculating price level will give us very limited insights on the cost of living changes as it doesn't consider the quantities of the two goods people may consume in the two price situations. Incorporating the quantities in the weight, the weighted average approach leads to two price indices, Laspeyres index, 13 which uses the base period value share as the weight, and Paasche index, which uses the value share calculated by base period price and compare period quantity as the weight. However, such calculated indices are proved to either over-estimate or under-estimate the impact. Many approaches have been proposed to derive good indices to estimate the price levels and quantity levels. Fisher (1922) tested many promising index number formulas and proposed his ideal index as being the geometric average of the Laspeyres and Paasche index. It is also independently derived and recommonded by Koniis & Byushgens (1926), Wald (1939), among others, to be a good approximation of the "true" price index. The main principle Fisher used to construct the Fisher Ideal Index is the "fainess" principle. It requires the consistency in changing places along the commodity, factor, and cases dimensions. Fisher's approach of deriving index numbers represents the test I axiomatic approach of index number development. In general, test I axiomatic approach starts with a set of tests or axioms that the ideal index number should possess, and derives the index numbers by pure logic based on the axioms. Not being as straightforward as the other approaches of obtaining index numbers, the test approach is later treated more as an approach for index number evaluation rather than derivation. The "fairness" principle Fisher proposed is embodied in three tests: commodity reversal test, factor reversal test, and time reversal test. Other major criteria and tests include the proportionality test, zero robust test, the consistency in aggregation, and so on (see e.g. Fisher, 1922; Diewert & Nakamura, 1993; ILO/IMF/OECD/UNECE/Eurostat/The World Bank, 2004), although none of the known index number formulas can satisfy all of them. 14 Another major approach to index number derivation uses calculus and is called the Divisia approach (see e.g. Solow, 1957; Hulten, 1973). It starts with the identity as presented in equation 1-1 and uses the partial derivative to obtain the index numbers for the pre-defined factors. The Divisia approach can be seen as the weighted log average of the changes in individual data elements. The challenge in deriving Divisia indices is to get the proper weighting scheme for discrete data, and make sure that the developed indices satisfy the desired characteristics. The famous Tiirnqvist-Theil index number and the Vartia index number are examples of the Divisia-based index numbers, which use the arithmetic average of the value shares and the log-distance function as the weights, respectively. Another major approach of obtaining index numbers is the economic approach proposed firstly in Samuelson & Swamy (1974). The economic approach responds to the criticism regarding the seemingly mechanical approach of obtaining index numbers and its lacking root in economic theory. Progress was made in the 1970s in strengthening the link between economic theory (on agents optimizing behavior according to the production and/or utility functions, referred to as aggregator function thereafter) and index number derivation (see, e.g. Samuelson & Swamy, 1974), and the flexibility of using index numbers to approximate cases with arbitrary aggregator functions (e.g. Diewert & Nakamura, 1993). Samuelson & Swamy (1974) firstly proposed their definition of price index and quantity index based on neoclassical economic theory, and derived the necessary and sufficient conditions under which an invariant index number exists. Diewert (1976) provided the definition of "exact" and "superlative", and proved that both 15 of the Fisher ideal index number and the Tiirnqvist-Theil Index number can be seen as the "true" index number when consumers follow specific type of preference. He defines a quantity index to be "exact" for an aggregator function if the index can be written as the ratio of the compare case and base case aggregator functions (Diewert, 1976). The beauty of using exact index numbers is that we do not have to go through econometric process to obtain the paremeters for the aggregator function (Diewert, 1976). Diewert then defines an index to be "superlative" if it is exact for an aggregator function that can provide a second-order approximation to any linear homogeneous functions (Diewert, 1976). He proved that both of the Fisher Ideal Index number (FII) and Tiirnqvist-Theil Index number (TTI) are superlative index numbers (Diewert, 1976). The index numbers are now widely used in economic statistics. Even though the Laspeyres and Paasche indices are not considered good approximations, they are still widely used in government statistics and reports due to their simplicity in calculation. Below are the major index number formulas that are widely used in literatures and reports. a. Laspeyres Index i = 1, ... ,N b. Paasche Index i = 1, ... ,N c. Fisher Ideal Index 16 i = 1, ... N d. Tiirnqvist-Theil index (Discrete approximation ofDivisia Index) i = 1, ... ,N where, e. Vartia Index (Discrete approximation ofDivisia Index) where, N 1 'I\ p In Vlp =Ls;* In-\;, i=1 P; i = 1, ... ,N y-x L(x,y) = for x =!= y; and L(x,y) = x for x = y logy- logx 2.2. Multi-factors two-case decomposition 2.2.1. The extension of multiplicative two-factor indices Multi-factor index numbers are mainly used in the field of energy use and pollutant emissions rather than in wealth and income. The extensions of two-factor index number formulas to multi-factors are almost straightforward for many index numbers, especially for Divisia-based index numbers. The studies of multi-factor ID As are intensively done in the field of energy use and pollutant emissions and are led by scholars such as Ang (1994, 2004), Boyd et al. (1987, 1988), among others. It is also in the field of energy use 17 and pollutant em1ss10ns that the additive IDA is widely used. However, interest in extending the two-factor index numbers to multi-factors started far before the index numbers were used in the study of energy and emissions. The extension was firstly led by Gini (1937) in his Methods of Eliminating the Influence of Several Groups of Factors, for extending the two-factor Fisher Ideal Index to three factors, and Siegel (1945), for formally deriving the generalized Fisher Ideal Index for multiple factors. Siegel (1945) suggested the use of the geometric mean of all the possible index numbers that can achieve perfect decomposition to form the unique generalized ideal index number. In particular, for n factors and two cases, choosing one case as the base, there are nl possible sets of index numbers that satisfy [1; X; = V, i = 1, ... , n, in which X; is the index number for factor i, respresenting the contribution of factor i in the explained variable changes (V = ~: = ~~: ~~:: :~). And the ideal multi-factor index number for factor i is defined as the geometric average of all the possible X;s. When n is equal to two, the formula reduces to the Fisher Ideal Index. For example, in the two-factor case, Laspeyres price index and Paasche quantity index, and Paasche price index and Laspeyres quantity index, represent the only two sets of index numbers whose product of the elements are identical with the total explained variable (expenditure) change. Thus the ideal index numbers for price and quantity are derived as the geometric mean of the Laspeyres and Paasche price indexes, and the Laspeyres and Paasche quantity indexes, respectively. Siegel (1945) also pointed out that the increasing computational complexity with the increasing number of factors hampered the usage of multi-factor decomposion. In addition, Siegel (1945) mentioned 18 that the cases suitable for and requiring multi-factor decomposition might be limited in practice. Index decomposition analysis (IDA) in energy and emission studies, starting in the 1990s, makes extensive use of multi-factor decompositions. For example, Howarth, et al. (1991) decomposed the changes in energy use in manufacturing industries in eight OECD countries between 1973 and 1987 into the effects of changes in aggregate manufacturing activity, industry structure, and energy intensities measured at the industry group level by using the Laspeyres Index. Schipper, et al. (2001) compared the per-capita carbon emissios across fourteen IEA member countries by sectors via a Mine/Yours Approach, which can be seen as an adjustment of IDA, in response of the international climate change negotiation. It provided great insights to the cross-country GHG emission variations. For example, when a factor linked to GHG emissions is irreducible, such as climate or natural endowment, a certain portion of the GHG emissions may be removed from the negotiation table (Casler & Rose, 1998; Schipper, et al. 2001). The methods adopted in the above two studies are straightfoward, though both of them leave residuals. Recent approaches to obtain perfect decomposition in energy and emission studies includes additive Shapley/Sun decomposition (Sun, 1998), the generalized Fisher Index approach (see. e.g. Ang 2004a; De Boer, 2009), and Log-Mean Divisia Index Method (Ang & Choi, 1997; Ang & Liu, 2001), and their additive counterparts. LMDI corresponds to the Vartia indices I proposed by Vartia (1976) and verified by Sato (1976) to be the exact index number when the preference ordering is 19 addilog, a functional form introduced by Houthakker (1960). Ang (1994, 2004) also have proposed the additive form of LMDI and Tiirnqvist-Theil indices. The evaluation of various multi-factor index number formulas follows the tradition of two-factor index numbers and uses the test/axiomatric approach to evaluate and compare different index numbers, meaning that several ideal characteristics or axioms are proposed and used to check the index number formulas. The ideal characteristics or axioms are almost identical to those proposed for two-factor index numbers. The major axioms used in multi-factor index number evaluations are the time reversal test, factor reversal test, zero robust test, propotinality test, and the test of consistency in aggregation. No new axioms are proposed for multi-factor index numbers compare to two-factor index numbers. 2.2.2. The development of additive index numbers in IDA Other than the extention to multi-factors, it is worth mentioning the development of additive decomposition in IDA. Additive decomposition starts with the same identity as multiplicative decomposition. But rather than assuming the change of value, in terms of ratio between the two periods, being the product of the indices, the additive decomposition assumes the change of value, in terms of difference, being the summation of the indices. The additive relationship between the group value change and the indices can be seen in equation (2-3). Ang (1994; 2004a) proposed additive Divisia-based decomposition formulas for a set of Divisia-based index numbers, including the Tiirnqvist-Theil Index number and the Vartia 20 Index number. In the end of the section, we list the additive version of the index numbers we presented in section 1.2. Ang (2004a) pointed out the following simple relationship between the Vartia I I LMDI I index numbers and its additive counterpart: vi -v 0 x: --- = L(Vi V 0 ) = - v1 , xM' lnvo k k = l, ... ,M (2- 6) In which X fi represents the additive index number for the k-th factor, and X f1 represents the multiplicative index number for the k-th factor. l(V1, V 0 ) is defined as 1 v:-~ 0 0 nv - nv when vi=!= v 0 , and vi when vi= v 0 . The simple relationship between multiplicative and additive decomposition indicated by equation (2-6) is important as it connnects the two decomposition approaches together, indicating that one is the monotonic transformation of the other. Note that for any two cases, L(V1, v 0 )is a constant. That way the assumptions of the multiplicative or additive relationship among the indices will be trivial in terms of the rankings of factors as the rank of factors identified by the two approaches will be identical. The additive version of the Fisher ideal index number is firstly derived by Sun (1998) by using the Shapley value, which was developed to represent the value of game in coorperative game theory. The derived formula in ID A setting is considered the additive counterpart of the Fisher Ideal Index in the IDA literature (see e.g. Ang, 2004b ). Below we listed the additive couterparts of the multiplicative index number we presented in the end of section 2.1. 21 List of additive index number formulas a. Laspeyres Index i = 1, ... ,N b. Paasche Index Pp = (L p{q{ )- (L pf q{) , v{ = p{q{, i = 1, ... ,N c. Fisher Ideal Index Fllp = (Lp *Pp)*(~) = ((I p{qf +I p{q{) - (L pf qp +I pf q{)) * (~), i = 1, ... N d. Tiirnqvist-Theil index (Discrete approximation ofDivisia Index) where, N 1 '\' P; TT Ip= Ls;* ln 0 , i=1 P; i = 1, ... ,N 1 0 1 S; =: - * (v; + V;) 2 e. Vartia Index (Discrete approximation ofDivisia Index) N 1 '\' P; Vlp = LS;*lno, i=1 P; i = 1, ... ,N where, y-x L(x,y) = 1 1 for x =f:. y; and L(x,y) = x for x = y ny- nx 22 2.2.3. Consistencies in ranking of factors between multiplicative and additive IDA Index decomposition analysis can provide a rank of all the pre-defined factors, in terms of their contributions to the explained variable change. Ang (2004a) pointed out that, unlike the LMDI and its additive counterpart, the link between the Fisher Ideal Index (FII) and the Shapley/Sun Index (SSI) is not straightforward, thus a systematic framework to contain the FII and SSI is lacking. We suggest that to be more specific, when the number of factors is two, FII and the SSI will provide consistent rankings of factors. But the consistencies are not garanteed when the number of factors exceeds two. We can varify this using the two-factor and three-factor Fisher Ideal Index (FII) as an illustration below. Assume that the pre-defined two factors are P and Q in two-factor FII decomposition, and P, Q, and R in three-factor FII decomposition. Without losing the generality, we can assume that we can obtain F/:1>F/f and F/}>F$, in which F/:1 represents FII for P, F/f represents FII for Q, F/} represents Shapley/Sun Index (SSI) for P, and F$ represents SSI for Q. Thus in two-factor FII and SSI decomposition, we have: And Ff} =~*(I plqD - L pDqD + L plql - L pDql) [ [ [ [ <~*(I pDql - L pDqD + L plql - L plqD) = F$ (2- 8) [ [ [ [ Most of the time, we will have p ~ 0 and q ~ 0, so (2-7) can be reduced to 23 And (2-8) can be reduced to The above two inequalities cannot hold at the same time. Therefore, we see that in two- factor cases, the multiplicative FII and additive SSI will always agree with each other. Keep the assumptions unchanged, when the number of factors are increased to three, we will have: And Ft=~* (z *(I p1qoro _ L poqoro + L p1q1r1 _ L poq1r1) + L p1q1ro I f f f f _ L poq1ro + L p1qor1 _ L poqor1) ' ' ' < ~ * (z *(I poq1ro _ L poqoro + L p1q1r1 _ L p1qor1) + L p1q1ro [ [ [ [ [ -L p1qoro + L poq1r1 - L poqor1) = F$ (2- 10) ' ' ' In most empirical work, we will have p ~ 0, q ~ 0, and r ~ 0, so (2-9) can be simplified to 24 And (2-10) can be simplified to It is easy to see that (2-11) and (2-12) can both hold. When L poq1ro > L p1qor1 > L poq1r1 i i i or L poq1ro < L p1qor1 < L poq1r1 i i i There exists Li p 1 q 0 r 0 choosing the value between Li p 0 q 1 r 0 +Li p 0 q 1 r 1 - Li p 1 q 0 r 1 and Li p 0 q 1 r 0 *Li p 0 q 1 r 1 /Li p 1 q 0 r 1 to make both (2-11) and (2-12) hold. Or when L poq1ro > L p1qoro > L poq1r1 i i i or L poq1ro < L p1qoro < L poq1r1 i i i There exist Li p 1 q 0 r 1 choosing the value between Li p 0 q 1 r 0 +Li p 0 q 1 r 1 - Li p 1 q 0 r 0 andLip 0 q 1 r 0 * Lip 0 q 1 r 1 /Lip 1 q 0 r 0 , thus make both (2-11) and (2-12)hold. Looking at the conditions, a simple interpretation is that the disparities appear when the Laspeyres P index falls in the range of Laspeyres Q index and Laspeyres QR index, or the Paasche Q index falls in the range of Paasche P and PR indexes. These are the cases that will never happen in two factor decomposition. The case study in Section 2 of this chapter also confirms the inconsistency between FII and SSL 25 2.3. A new framework to connect two-cases index numbers in IDA Scholars in IDA tend to separate the widely-used multiplicative and additive index numbers into two categories, one based on Laspeyres index, and the other based on Divisia index (see, e.g. Ang, 2004b ). Such category is informative in terms of their historical roots and formalizations, and it has many advantages in extending the analysis (see, e.g. Ang, et al, 2009), but it can only produce little insights on the sources of differences between the index numbers, especially the well-behaved ones, such as the generalized FII and LMDI. As the FII and LMDI are so widely used in all sorts of IDA studies, it is worthwhile to further examine the sources of their variations. In this section, rather than separating the index numbers to Laspeyres based and Divisia based, we united them under the umbrella of discrete approximation of Divisia index and pointed out that their differences lie in the very weighting scheme or aggregation scheme they used to aggregate the item level change to the index numbers. The new framework can also provide insights on the relationship between multiplicative index numbers and their additive counterparts, which provides an explanation on the consistencies and inconsistencies between the two. The ways to obtain the Divisia index is widely-recognized in the literature so we will only briefly describe it here for explanatory purposes. Start with the identity in equation 2-1, Assuming vf and xJ,; are all differentiable on every point along the time dimension, differentiate equation (2-1) with respect to time, we have 26 N M M ~~ = IId:~·i * n xk.i, j = 1, ... , M; i = 1, ... , N; k = 1, ... , M (2-13) i=l }=1 k=l,k':/:.j Divide both sides by yt and simplify the notation, we have , '<:'N '<:'M dxj,i nM . M N ' nM t ~= L.i=1LJ=1 dt * k=1,k-:1:Jxk,i = "\"1"\"1xJ,i * k=lxk,i v '<:'N nM x' LL x . '<:'N nM x' . , L.i=l ]=1 ),[ }=1 i=l ),[ L.i=l k=l k,i j = l,. . .,M;i = l,. . .,N;k = l,. . .,M (2-14) Note that the portion in equation (2-14) other than the value share can be seen as the logarithmic differentiation. Integrate equation (2-14) from time 0 to time 1, with properly defined weighting schemes;, we should be able to obtain vi LM LN x1. ln 0 = si *In-¥, v x. }=1 i=l ),[ Thus we can write index for factor j as L N Xl· lnX 1 = S;*ln-";, X·. i=l ),[ j = 1,. . ., M; i = 1,. . ., N (2-15) j = 1,. . ., M; i = 1,. . ., N (2- 16) The two discrete Divisia indexes we listed in this chapter, the Tiirnqvist-Theil index and the Vartia indexiLMDI, can all be written in the form of equation (2-16). Given equation (2-16), our intention to unite the widely-used Laspeyres-based index numbers with those based on Divisia index can also be framed as whether it is possible to write the logarithm of multiplicative Laspeyres-based index numbers as a weighted average of the log differences of the factor measured at the item level. It is exactly the definition of multiplicative decomposition in the traditional index number theory literature as we mentioned in the early part of the chapter. Many scholars have 27 contributed to the multiplicative and additive decomposition in the traditional index number theory literature. And the framework we proposed here coincides with one of the multiplicative decomposition approaches proposed for Fisher Ideal index. The approach also has the advantage of connecting multiplicative and additive IDAs in a straightforward manner. Other ways proposed in index number theory literature can also be used and their implications for IDAs can be the future research topics. Our next step is to write the previously-categorized Laspeyres indexes in the form as equation (2-16). To do so, we use the logarithmic mean as mentioned in Vartia (1976). It . y-x 1s defined as L(x,y) = for x =/= y; and L(x,y) = x for x = y to transform lny-lnx Laspeyres index, Paasche index, and generalized Fisher Ideal index to the discrete Divisia form. We listed the results of LI, PI, and generalized FII in equation (2-17), (2-18), and (2-19), respectively. I M ln~ 0 = LlnLI 1 +lnRu }=1 M "<:'N I * nM 0 - "<:'N nM 0 L L.t=1 xJ,l k=l,k':!:.J xk,l L.t=1 k=1 xk,l = "<:'N I nM o "<:'N nM o +Jn Ru J=I L(L.l=I XJ.l * k=l.bj xk.l ,L.l=I k=I xk.a M N I nM 0 nM 0 I LL L(x1.1 * k=l.hJ xk.i, k=I xk.;) xJ.i = ('\'N I nM 0 "<:'N nM 0 * ln-0 + In Ru, J=I i=I L\L.l=I xj.l * k=l.bj xk.l ,L.l=I k=I xk.a xj.i j = 1, ... ,M; i = 1, ... ,N; k = 1, ... ,M; l = 1, ... ,N (2-17) where Lli: The Laspeyres index for factor j; Ru: The residual in Laspeyres decomposition. 28 1 M In ~o = L lnPI 1 + lnRp 1 }=1 M '<:'N 0 nM 1 '<:'N nM 1 L L.t=1 xJ,l * k=l,k':!:.J xk,l - L.t=1 k=1 xk,l = N o M 1 N M 1 +In Rp1 1 = 1 LCI1=1 x 1 .1 * nk=l,bJ xk.1,I1=1 nk=1 xk,i) M N 0 nM 1 nM 1 1 LL l(xJ,i * k=l.hJ xk,i, k=l xk,;) xJ,i = N 0 M 1 N M 1 *ln-a-+lnRp,, J=l i=l LCI1=1 x 1 .1 * nk=l,bJ xk.l 'I1=1 nk=1 xk,i) x 1 .1 j = 1, .. ., M; i = 1,. . ., N; k = 1,. . ., M; l = 1,. . ., N (2-18) where P Ii: The Paasche index for factor j; Rp( The residual in Paasche decomposition. Note that the second line of equation (2-17) and (2-18), the numerators are the additive counterpart of multiplicative LI and PI for factor j, respectively. So equation (2-17) and (2-18) also represent the relationship between multiplicative LI and PI and their additive counterpart. We can also easily see that LI and PI will provide consistent rankings of factors between multiplicative form and the additive counterpart due to the above relationship. The discrete Divisia form FII looks more complex than the discrete Divisia form of LI and PL But it is mainly due to the fact that the formula of generalized FII is complicated enough. The idea behind the transformation is the same. 29 1 In Vvo = '\' lnFII1 ='\'In nz i=1 xJ,i * k=l.bJ xi;'. 1 M M ( M-' (LN 1 nM tj,i,k,m)r!(M-r-l)!)M! L L -1 '<:'N 0 nM p,k,m J=l J=l m- L.i=l xJ,i * k=l,k':!:.j xJ,i M zM-i ~N 1 nM tj,i,k,m L L r! (M - r - 1)! Li=l xJ,i * k=l,hJ x 1 ,; = *In~~~~~~~~~~ M' '<:'N 0 nM tj,i,k,m J=l m=l · L.i=l xJ,i * k=l,k':!:.j xJ,i M zM-' '<:'N 1 nM tj,i,k,m '<:'N 0 nM tj,i,k,m = "\"1 "\"1 r! (M - r - 1)! * L.i=1 xJ,i * k=1,k-:1:J xJ,i - L.i=1 xJ,i * k=1,k-:1:J xJ,i L L M' ("'N 1 nM tj,i,k,m '<:'N 0 nM tj,i,k,m) J=1m=1 · L L.i=lxJ,i * k=l,k':!:.JxJ,i 1 L.i=lxJ,i * k=l,k':!:.JxJ,i M zM-i N =LL Lr!(M~~-1)! }=1 m=l i=1 l ( 1 nM t j,i,k,m O nM t j,i,k,m) l xJi * k=lk':J:.Jx. · ,xJi * k=lk':J:.Jx. · (x") * ' ' 1 ,i ' ' 1 ,i * ln .1.:!:.. l ( '<:'N 1 nM tj,i,k,m ~N O nM tj,i,k,m) x9. 1 L.1=1 xJ,l * k=l.hJ xi.l 'Lt=l X1,1 * k=l,hJ x 1 , 1 J,, j = 1, "" M; i = 1,. . ., N; k = 1,. . ., M; l = 1,. . ., N; m = 1,. . ., 2M-l (2- 19) where Fllf The generalized Fisher ideal index for factor j; tj,i,k,m: Either 0 or 1, indicating whether xk; in the mth summation choose the value in base case or compare case; r: r = r(j, m') = I!;1=l,k;<j tj,i,k,m=m'; Note that the third line in equation (2-19) indicates the relationship between the generalized Fisher ideal index and its additive counterpart Unlike the relationship between the multiplicative and additive LI, and between the multiplicative and additive PI, the relationship between the generalized FII and its additive counterpart is not monotonic. It can be spotted in the third line in equation (2-19) as the denominator varies by factors, meaning that the ratio between the generalized FII and its additive counterpart 30 changes by factors. Our analysis in the previous section also confirms the inconsistencies between FII and its additive counterpart. Table 2-1 Weighting Schemes in Widely-Used Index Numbers Name Laspeyres Paasche Fisher Ideal Vartia/LMDI Tiirnqvist Theil/ AMDI Weighting Scheme (s; in equation 1-14) After we transformed the Laspeyres-based index numbers to the form of discrete approximation of Divisia index, we can easily see that the weighting schemes used to aggregate item level changes differ from one index to another. It explains the source of differences across the index numbers. We summarized the weighting schemes, which correspond to s; in equation 2-16, in the index number for factor j in Table 2-1. We also have obtained the relationship between multiplicative index numbers and their additive counterparts. It provides us great insights on the sources of the consistency and 31 inconsistencies of the ranking of factors between the two approaches of decomposition. We showed the link in Table 2-2. Table 2-2 Relationship between Multiplicative and Additive Index Numbers Name Laspeyres Paasche Fisher Ideal Vartia/LMDI Tomqvist Theil/AMDI Relationship between Xf and Xf inxt = A zM-1 r!(M-r-1)! ( N 1 ITM tj,i,k,m N 0 xj = Lm=l M! * Li=l Xj,i * k=l,k*-) xj,i - Li=l Xj,i * IT M tj,i,k,m) k=l,k*-J xJ,i M Xf lnX 1 = ( 1 0 ) L V, V See formulas 2.4. Multi-cases two-factor decomposition 2.4.1. The property of transitivity in multi-temporal and multilateral index numbers We sometimes will encounter index number studies and index decomposition analysis (IDA) that involve more than two cases. Multi-case decomposition analyses are performed in both the fields of wealth and income and of energy use and pollutant emissions. Multi-case decomposition can involve either the decomposition over several 32 time periods or across various geographical areas. Transitivity is a special property with multi-cases index number studies and IDA. In practice, this property is treated differently in multi-temporal and multilateral IDAs as time dimension provides a natural order while the spatial dimension does not provide an order of any kind. As index decomposition can only be performed between two cases at a time, multi-case decompositions are divided into several bi-case decompositions. There are two major approaches to perform multi-cases decomposition. One is choosing an arbitrary case as the base and comparing all the other cases with base. The other is placing the cases in a specific order and choosing the nth case as the compare case and the n-1 th case as the base case. The former is called fixed-base approach and the latter chained approach. The property of transitivity requires that an index number to be consistent no matter how many chained bi-cases decompositions are used between the two cases in multi-cases decompositions. For the multi-temporal decompositions, as time provides a natural ordering of cases, a chained approach usually is adopted and the property of transitivity is ignored, assuming that the order of cases matters but the only legitimate one is the one given by the time dimension. Multi-temporal decompositions are thus reduced to many chained bi-temporal decompositions in a fixed order. For multi-lateral decomposition, the ordering of cases is not that obvious. Therefore, we do not have sufficient reasons to ignore the property of transitivity. Scholars in the field hold different opinions on whether the property of transitivity should be a desirable one for multi-lateral decompositions. The property was firstly rejected by 33 Fisher (1922) on the ground that the irrelevant third party should not be introduced into bilateral decomposition. Dreschler (1973) pointed out that Fisher's discomfort with multilateral index numbers was rooted in his using only the bilateral data to construct index numbers and suggested that when the multilateral data are incorporated into the calculation of bilateral index numbers, transitivity can be preserved (Caves, Christensen, & Diewert, 1982). In the ID A literature, the property of transitivity is not particularly discussed. Most of the decompositions performed for multiple cases are multi-temporal decompositions, in which a chained approach is adopted. Examples of such index decomposition analysis are the analysis of energy intensity drivers in China from 1998 to 2006 done by (Zhao et al., 2010), the analysis of energy-related emissions in UK manufacturing industry from 1990 to 2007 done by (Hammond & Norman, 2012), and the analysis of the change in energy intensity in Lithuania from 1995 to 2009 done by (Balezentis et al., 2011), among others. Most of the analyses use a chained approach for multi-temporal IDA analysis. In this chapter, we will make the first attempt to perform a multi-lateral decomposition in the field of energy use and pollutant emissions. 2.4.2. Summary of multilateral index number development The field of wealth and income has a long history of deriving and using multilateral index numbers. The multilateral index number is mainly used in calculating Purchasing Power Parity (PPP) and comparing the real income across countries. Several index number formulas and approaches were proposed. One approach is to derive multilateral index 34 numbers based on bilateral index numbers. As described in Diewert (1988), this approach usually involves two steps: 1) Select a bilateral index number and use it in all pairwise comparisons of the cases in question; 2) Aggregate the bilateral index numbers obtained in step 1 based on a weighting system. For example, in multilateral real output comparison across countries, assuming a star system, a numeraire country will be picked out and the weight will be calculated by using all the bilateral index numbers in reference to the numeraire (Diewert W. E., 1988). The weight can be obtained by using the country's share of real world private product. Suppose that we are constructing multilateral index numbers for M countries, using the real output (quantity index) as example, if we define the real output of country i relative to country j as Q (pi, pi, qi, qi), in the star system, choosing country n as the numeraire, the weight of country i will be i = 1,2, ... ,M Or, we can define country i's contribution to the real world private product as - J i J i - 1 [ M l-1 ai = ~[Q(p ,p ,q ,q )] i = 1,2, ... ,M And country i 's share in the real world private product can be defined as ai = a;/ If1= 1 ak, which forms an own share system as described in Diewert (1988). The own share system can be used to approximate EKS and CCD index when FII and TTI are chosen respectively (Diewert, 1988). 35 Another widely accepted approach to derive multilateral index from bilateral ones is the EKS system. EKS multilateral index number system was proposed by Eltetii & Koves (1964, 1973) and Szulc (1964). EKS index is defined as the geometric mean of all the ratios of all bilateral FII for each area with taking each area in turn as base, as presented in the equation below. 1 EKs Xa ( M FII)M Xij = nxFII , 1=1 jl i = 1, ... ,M;j = 1, ... ,M But the idea was originated in Gini (1924 ). In Gini' s formation of the multilateral index number issue, the multilateral index numbers were chosen to fit the calculated bilateral index numbers by minimization of least squares distances (Deton & Heston, 2010). Not all approaches of obtaining multilateral index numbers are based on bilateral index numbers. One approach that does not build on bilateral index numbers was proposed by Geary and used as the foundation of calculating Penn World Table (Geary, 1958). Geary's approach assumes a true world price of goods and true exchange rate and then solves for the two from independent equations. When the number of countries is reduced to two, the Geary price index number is equal to the weighted sum of prices by using the harmonic means of the quantities (Neary, 2004). It will reduce to the Laspeyres index when all the ratio of quantities in the two cases are all equal and constant (Neary, 2004). Neary (2004) later made the contribution of rationalizing the Geary approach and the Penn World Table. Neary claims that the Geary approach is exact when the preference are non-homothetic Leontief and proposes the Geary-Allen International Accounts 36 (GAIA) system for making multilateral index numbers (Neary, 2004). Suppose there are m countries and n goods, the system can be described as follows: j = 1, ... ,m IT i = 1, ... ,n In which IT; represents the world price of goods i, E 1 represents an exchange rate of the country j's currency to the international currency, q tj represents the virtual quantity a representative customer would choose under the world price ifs/he has country j's level of utility, represented by u 1 in the equations. And the corresponding measure of real income can be expressed as: z] = E 1 * z 1 = '\'n IT .qi 1 = e(IT, uJ), Li=1 i j= 1, ... ,m Thus the GAIA price indices and quantity indices can be written as "\/j, k = 1, ... , m Studies regarding the meanmgs and disparities of various multilateral index numbers continue in the field of wealth and income. A recent paper by van Veelen and van der Weide (2008) reviewed the axiomatic approach and the economic approach, and argued that the differences of the two lie in whether the representative consumers are assumed to 37 optimize the same utility function. Either the axiomatic approach or the economic approach will be preferred to the other depending on whether the homogeneity assumption is suitable to the situations at hand (van Veelen & van de Weide, 2008). 2.4.3. Using the Shapley approach to develop multilateral index numbers The Shapley approach was first introduced to the field of IDA by Sun (1998) to yield a perfect multi-factor decomposition model. The formula derived by Sun using the Shapley approach was later considered the additive counterpart of Fisher Ideal Index (see. e.g. Ang, 2004b ). The Shapley value, introduced by Shapley in 1953 (Shapley, 1953), is a key concept in measuring the expected values of playing a game in cooperative game theory. Since then, the Shapley value has been widely used in measuring power distributions (Shapley & Shubik, 1954), cost distributions (Young, 1988), internet economics (see, e.g. Ma, et al., 2010), etc. The Shapley value can be briefly described as follows. Define an N-person game with characteristic function v: zN --> R, which assign a real value to the possible zN coalitional games, and a marginal contribution matrix m = [··.]zNxN, in which miJ represents the marginal contribution of player j creates by entering the game, following the ith order of entering. The Shapley value of the game is defined as the column average of the marginal contribution matrix. For player j with characteristic function v, it can be written as: '\' (s - 1)! (n - s)! Q\[v] = L n! * [v(S) - v(S\ij})] sr;;;.N 38 where S is any subset of N. Since then, weighted and generalized Shapley values were proposed subsequently by scholars (see, e.g. Kalai & Samet, 1987; Nowak & Radzik, 1995; Radzik, 2012). Even though the weighted Shapley value is beyound the scope of the paper, it can benefit the multilateral index number development and can be the topics of future researches. In this paper, we use the Shapley value with equal weights between players and possible permutations. We suggest that the Shapley approach can be used in deriving multilateral index number as well, with the marginal contribution matrix formed by bilateral index numbers. We found that when the bilateral Fisher Ideal Index is used, we can eventually obtain EKS Index via the process, and the same process can be applied on other bilateral indices as well. Suppose we are considering a closed region consists of N sub-regions. In a multilateral index number system that preserves transitivity, for example, we would expect that if an income E can obtain utility level u 1 for a representative customer in sub region 1 and utility level u; in sub-region i, the ratio of the utility levels of the two regions should not change no matter how we perform the transition. For example, we can transit u 1 to u 2 , u 2 to u;, or u 1 to u 4 , u 4 to u 3 , u 3 to u;, and no matter what we did in between, the ratio of u 1 and u; should be identical. It is simply a longer version of the transitive statement in additive version as Fk; = FkJ + Fj;. But the take away message should be that when we are calculating a bilateral index number in the multilateral system, not only should we consider the current status of the index number, we should also consider where it comes from. For example, in path i --> j --> k, we define bilateral index number as FkJ = Fk; - Fj;. Following the above approach, we transformed the traditional 39 bilateral index number system to the path-dependent bilateral index number systems that satisfy transitivity. We thus can construct the marginal contribution matrix as follows: 1) Calculating all the bilateral index numbers based on the traditional bilateral index number formula; 2) Calculating the vector of path dependent bilateral index number when the path is formed by all the possible permutations of N sub-regions by using m~k = Ffj = Fka(l) - "L{= 1 F;';r(l) where in path a, position one a(l) is always chosen as the common base of all the bilateral index number used in path a. It should be noted that even position one is arbitrarily chosen as the starting point, all the members in the region have equal opportunities to be the base. We put the zN path-dependent bilateral index numbers on the rows of the matrix and the column of the matrix represents the path-dependent bilateral index number for a single region. Following this approach, we will have marginal contribution matrix for each of the factor in question. For example, if we are decomposing the aggregate index into price index and quantity index, we will generate a marginal contribution matrix for price and a marginal contribution matrix for quantity. The last step is to average the column of the marginal contribution matrix to obtain the multilateral index number. Multilateral index MF; for sub-region i is obtained as the average of the path dependent bilateral index numbers as MF; = :! I~~~C:) F;'j. It can also be seen as the expected value of the entire path dependent bilateral index number relates to i when all the sub-regions have the equal opportunities to be the base or any position on the path. 40 Interestingly, we find out that when we add the entire set of path-dependent bilateral index numbers relates to the sub-region together, the path-specific items related to the third parties (other than the base) cancels out when the time reversal condition is met. Therefore, we have MF; =-!; * L.J= 1 FiJ. When the bilateral index number satisfies the time reversal criteria, we actually obtain the same measure for multilateral index numbers with or without forcing the transitivity in the first place. In another words, we can use the bilateral index numbers directly as the elements in the marginal contribution matrix. In this case, the row of the marginal contribution matrix will be the fixed-base bilateral index numbers. And when we get the column average of the matrix, we get the same result as we did above. The traditional EKS multilateral index number can be derived as the direct ratio or differences of the multilateral index number we just defined above. Because the approach is based on the marginal differences rather than ratio, it has the ability to handle zero and negative numbers. Table 2-3 illustrates the elements in the marginal contribution matrix for three areas by using Fisher Ideal Price Index. We can then take the geometric average by column to obtain the Shapley value, which we will refer to as EKS/Shapley number, for each area. 1 For example, the EKS/Shapley number for area A will be ([1~=A pAk)3, k = A, B, C. That is the geometric average of all the bilateral indices by taking each area in turn as base. And the EKS index for any two areas will be equal to the ratio of the EKS/Shapley numbers. If we would like to assume additive relationships, we can define the additive 41 counterpart of the EKS index for any two areas as the difference of the EKS/Shapley numbers, which were obtained by using additive bilateral index numbers. For example, 1 the EKS Price index for area A, taking area B as the base, will be ( IT~=A ;;: ) 3 , k = A, B, C. For the ease of communication and to differentiate the two, we use EKS/Shapley numbers to refer to the number we obtained via the Shapley approach for single area, and use EKS indices to refer to the index we obtained by using EKS/Shapley numbers, which is also the EKS multilateral index mentioned in literatures. In the case study in the next chapter, we will use the EKS multilateral index number decomposition to measure three pre-defined drivers of C0 2 emissions in electricity generation by state in the United States. As the bilateral index numbers that we will choose are superlative index numbers that satisfy time reversal, we will simply use the fixed-based bilateral index numbers directly. Table 2-3 Marginal Contribution Matrix for Three Areas using Price Indices ABC ACB BAC BCA CAB CBA Path pAA pAA pBA pBA;pBC pCA pCA;pCB A Area B Marginal Contribution Matrix pAB pAC;pAB pABjpAC pAC pBB pBC;pBA pBB pBC pCB/pCA pCC pCB" pCC c 42 Table 2-4 Multilateral EKS/Shapley Numbers for Commonly Used Indices Bilateral Index Multilateral Index Name Name Formula Q)z EKS 1 ( m QF)m n!=1Qfz Fisher Ideal Index Shapley/Sun Index Qss jl n/a ~ * (I:l CQ]F - QZf)) QTT CCD 1 jl ( m QTT)m nl=1Q!x Tiirnqvist-Theil Index Additive AMDI QAMDI jl n/a ~ * (I:1 (QftMDI - QftDI)) Q}z n/a 1 ( m QV)m n1=1Q£ Vartia/LMDI Additive LMDI QV-A jl n/a ~*(I: CQ}z-A - QJ;z-A)) It is also possible to replace the bilateral Fisher ideal indices by other commonly used index numbers. The characteristic of transitivity in multilateral index numbers can be guaranteed as long as the bilateral index number that we use in forming the marginal contribution matrix satisfies time/space reversal test. For example, if we use the Tiirnqvist-Theil index instead, we will obtain the CCD index, which was proposed by Caves, Christensen, & Diewert (1982). We can also try to use LMDI, Laspeyres, Paasche indices and their additive counterparts to form multilateral index numbers. The results using Fii, TTI, VI/LMDI and their additive counterparts are listed in Table 2-4. Please note that we use the name for the bilateral index numbers to indicate the multilateral numbers in the table. And we use quantity index as an illustration. 43 The above approach derives a vector of N elements that provides a cardinal ranking, and obtain the multilateral index as the quotient as the corresponding two elements of this vector. Transitivity of the so-constructed multilateral index numbers is thus guaranteed. The approach of obtaining a set of cardinal rankings to construct transitive index numbers was first suggested in (Van Veelen, 2002). Even though the Laspeyres and Paasche indices are not considered the superlative or preferred indices by scholars, they are intuitively simple and they provide upper and lower bounds for the FII, which is a preferred index number in theory and in practice. As the Laspeyres and Paasche indices both satisfy the time/space reversal test, their EKS/Shapley numbers will simply be the geometric or arithmetic mean of the bilateral indices, taking all of the cases in turn as the base. We can find out that the EKS/Shapley numbers of Laspeyres and Paasche indices will continue to be the upper and lower bound of the EKS/Shapley number of the Fisher ideal indices. 2.5. Multifactor multilateral index Now we move our discussion to multi-factor and multi-case decomposition. As the chained approach is the common practice in multi-temporal decomposition, we will only discuss the multi-factor multi-lateral decompositions in this section. We will be able to obtain the EKS/Shapley numbers and eventually the EKS multi-factor multilateral index numbers when we use multifactor bilateral index numbers instead of the bi-factor bilateral ones in the EKS/Shapley approach as described in section 2.3. The derived EKS multilateral formulas will not differ much from those listed in Table 2-4, so we will not 44 discuss the formulas specifically in this section. We will simply mention a few concerns when we are using the multi-factor multilateral indices rather than the bi-factor ones. The first thing to keep in mind is that none of the multiplicative multifactor EKS/Shapley numbers will provide consistent ranking of factors with its additive counterpart. As mentioned in section 2.2, in two-case IDA when the number of factors increases from two to many, only the Vartia/LMDI index will provide consistent ranking of factors between multiplicative and additive decompositions. This desirable property of Vartia/LMDI index number no longer exist in multilateral IDAs, if we obtain the corresponding multilateral index numbers via the EKS/Shapley process as mentioned in section 2.3. The Vartia/LMDI and its additive counterpart will still work fine when the chain rule is used in multi-temporal decompositions. Therefore, in multifactor multilateral decomposition, it is possible to see that one factor is indicated to be a positive driver by the multiplicative multilateral EKS/Shapley numbers but to be a negative driver by the additive multilateral EKS/Shapley numbers, though it is only fair to keep in mind that the bilateral multiplicative and additive index numbers, e.g. Fisher Ideal Index and the Shapley value, were developed independently to serve different research purposes. Even though they lead to similar formulas in IDA, other than our aspiration to generate a united and consistent decomposition framework, there is no claim that the two should yield identical orders for factors. It will, however, cause problem in result interpretation in practice. 45 A compromise approach that we use in our case study in the next chapter for three-factor multilateral decomposition is to develop bounds for the index numbers to see how the values vary and in the hope that the upper and lower bounds developed can provide consistent rank of factors between multiplicative and additive ID As. Below we will develop bounds for the three-factor FII and SSI and their multilateral EKS/Shapley numbers. When the number of factors increases, we may use the similar approach to form new bounds for FII and SSI, though the complexities may increase dramatically. We made a simple adjustment on Laspeyres and Paasche indices to form the new bound for multi-factor FII and SSL We can use the ratio between the three-factor FII and the geometric average of Laspeyres and Paasche indices for the multiplicative case and the difference between the three-factor SSI and the arithmetic average of Laspeyres and Paasche indices for the additive case to construct the new bounds. Take the price (p) index as a three-factor Fisher ideal index for example, we can define the adjusted Laspeyres and adjusted Paasche indices as below. Definition 1.1: Assume there are I items, for each we can obtain data of three predefined factors: p, q, and rand an aggregate value v. There is V; = L; p;q;r;, i = 1, ... , /.For the aggregate value v in two cases, 1 and 0, we define the following three-factor multiplicative and additive adjusted Laspeyres and Paasche indices, using the p index as an example, and the bound for the indices of the two other factor, q and r, can be written in a similar way. 46 Multiplicative adjusted Laspeyres p index: Multiplicative adjusted Paasche p index: Additive adjusted Laspeyres p index: adj· LA = 2c * L.i P; q; r; + L.i P; q; r; + L.i P; q; r; + L.i P; q; r; - [cs '\' 1 0 0 '\' 0 1 1 '\' 1 0 1 '\' 1 1 0) l P 6 * (S ..., o o o ..., 1 1 1 ..., o o 1 ..., o 1 o) * L.i P; q; r; + L.i P; q; r; + L.i P; q; r; + L.i P; q; r; Additive adjusted Paasche p index: We show the proof that the above adjusted Laspeyres and Paasche indices can serve as the bounds for multifactor FII and SSI using the p indices. The bound for the indices for factor q and r, and also in additive form can be proved in a similar way. Proof Assume the Fisher ideal p index does not fall into the boundary of the adjusted Laspeyres and Paasche indices as presented above. We will have either Fp > 47 It simplifies to It can be simplifies to Thus we cannot have Fp > LP and Fp > Pp. Similarly we can prove that we cannot have Fp < LP and Fp < Pp either. Therefore, we must have Fp falls into the boundary of LP and Pp, which completes the proof. The adjusted Laspeyres and Paasche indices both provide consistent rankings of the three pre-defined factors between the multiplicative and additive IDAs when p, q, r are all positive real numbers. And one advantage of using the bounds is that it contains the 48 information in allocating the interactive effects. After all, all index numbers use different assumptions or rules to allocate the combined effects, e.g. the fairness principle, the ratio between level scale and log scale, etc. Sometimes it may be better to leave out the interactive effects rather than to allocate it into the indices in some cases. We can verify that, say, in a three factor case, the additive form of the portion that we were using to adjust Laspeyres and Paasche indices is equal to one sixth of tiptiqtir. The residual, if we use the square root of the product of Laspeyres and Paasche indices other than the multi factor Fisher ideal indices, will be half of tiptiqtir. Thus we can see that the multi-factor SSI allocates the residual equally to the three factors. We can also define the following boundary of EKS/Shapley numbers by using the adjusted Laspeyres and Paasche indices. Because the three-factor FII and SSI is bounded by the adjusted Laspeyres and Paasche indices, and the multiplicative and additive EKS/Shapley numbers can be written as the geometric and arithmetic mean of the Fisher ideal indices, we can see that if we define the boundary as the geometric and arithmetic mean of the adjusted Laspeyres and Paasche indices, the multiplicative and additive EKS/Shapley numbers will fall into the boundary. Assume there are m areas and there exist the adjusted Laspeyres and Paasche indices as defined in Definition 1.1. We provide the following definition of adjusted EKS Laspeyres indices and adjusted EKS Paasche indices, which serve as the boundary of EKS numbers. 49 Definition 1.2: For M areas which have definition of adjusted Laspeyres and Paasche indices as in Definition 1.1, we provide the following definition for adjusted EKS Laspeyres indices and adjusted EKS Paasche indices: 1 M M adjEKSL~.m = (nk=l adjL~.m,k) , m = 1, ... , M; k = 1, ... , M m = 1, ... ,M; k = 1, ... ,M 1 IM adjEKSL#.m = M * adjL#.m,k' k=1 m = 1, ... ,M; k = 1, ... ,M 1 IM adjEKSPp~m = M * adjPt,m,k' m=l m=l, ... ,M; k=l, ... ,M In which, adjEKSL~, adjE PPM, adjEKSL# and adjEKSPPA are the multiplicative adjusted EKS Laspeyres p index, additive adjusted EKS Laspeyres p index, multiplicative adjusted EKS Laspeyres p index, and additive adjusted EKS Laspeyres p index, respectively. adjLr;J,m, adjPp~m, adjL#,m, and adjPp~m are the multiplicative adjusted Laspeyres p index for area m The indices for q and r can be defined in a similar way. However, it worth noting that the above bounds only work as the upper and lower bounds for EKS/Shepley numbers, not EKS indices, and not the other multilateral indices we developed by using bilateral indices other than Fisher ideal indices and Shapley/Sun method. 50 3. Conclusion In Chapter one, we sununarized the development of IDAs in the field of energy use and pollutant emissions and its roots in index number theories in a systematic way, and filled in some key gaps in the literature. We discussed the three major issues in this chapter: 1) The development of multifactor multilateral index numbers; 2) Consistencies between multilateral index numbers and their additive counterparts; 3) Source of differences between Laspeyres-based and Divisia-based index numbers. We have shown that the approach to obtain Shapley values in cooperative game theory can be used to obtain multilateral index numbers. It is the first time the Shapley value is used in multilateral index numbers. We also have shown that the Shapley approach can generate transitive multilateral index numbers when the bilateral index numbers that we used in the Shapley approach satisfy the time/space reversal test, even when the transitivity is not imposed in the first place. If we use the bilateral FII to generate multilateral index numbers via the Shapley approach, we eventually obtain the EKS index, one of the most widely used multilateral index numbers in statistical agencies, e.g., by Eurostat and OECD in calculating PPPs. If a bilateral Tiirnqvist-Theil index, we obtain the multilateral CCD index. We also used the Shapley approach to obtain the multilateral version of the Vartia/LMDI index. Similarly, the approach can be used for all the additive counterparts of the mentioned indices. We listed all the well-known index numbers and the index numbers developed in this chapter in Table 2-5, along with their sources and characteristics to provide a quick reference for the readers. 51 In terms of the consistencies between multiplicative index numbers and their additive counterparts in terms of the ranking of factors. We have shown that even though the Fisher Ideal Index is considered one of the preferred forms of index numbers, when the number of factors increases from two to many, the multiplicative FII and its additive counterpart, the Shapley/Sun Index, will no longer necessarily provide consistent rankings of the pre-defined factors. Even though the inconsistancy is widely recoganized, it is not yet clarified and proved. We provide a proof for the consistency of the FII and SSI in two-factor decomposition and the inconsistency of the two in three-factor decomposition, which can be further extended to the cases in which the factors are more than three. The Vartia/LMDI index and its additive counterpart will provide consistent order of the pre-defined factors in two-case decomposition even when the number of factors exceeds two, due to the simple relationship between multiplicative Vartia/LMDI index and its additive counterparts. The relationship is shown in equation (1-4), indicating that the ratio between the multiplicative Vartia/LMDI index and its additive counterpart is a constant for each IDA. However, none of the EKS/Shapley numbers we obtained and their additive counterpart can generate a consistent ranking of factors when the number of cases exceeds two, even the rank preserving V artia/LMD I index and its additive counterpart. This study is the first time that the characteristic is pointed out and examined. A compromise approach we found for the EKS/Shapley number based on FII and SSI is to develop upper and lower bounds that are rank preserving. We suggest using adjusted versions of Laspeyres and Paasche indices to bound three-factor FII and use their geometric averages and arithmetic 52 averages to bound the multiplicative and additive EKS/Shapley numbers based on FII and SSI, respectively. This can serve as the starting point of the future researches on the consistencies between multiplicative and additive IDA. We also united both the Laspeyres-based and Divisia-based index numbers under the framework of discrete approximation of Divisia-based index numbers. It showed that the source of difference across the mentioned index numbers lies in the weighting scheme that each index number uses to aggregate the item level change in each factors. The new framework also revealed the linkage between multilateral Laspeyres, Paasche, Fisher Ideal indices and their additive counterparts, which can serve as a starting point to examine their consistencies in the rank of factors. 53 Table 2-5 Summary and Comparison of Index Numbers and IDA Approaches Approach Author Additive or Major Properties Advance over Applicability Multiplicative Previous Fisher Ideal Fisher (1922) Multiplicative Time reversal; Factor Overcome Two factors, Index (Fii) reversal; Zero robust; base/terminal year two cases Proportionality; Exact bias for quadratic aggregator function; Superlative Generalized Siegal (1945), Multiplicative Time reversal; Factor Extended Fii to multi- Multi-factors, Fii Ang (2004), de reversal; Zero robust; factor case, *No two cases Boer (2009) Proportionality longer bounded by Laspeyres and Paasche Index Shapley/Sun Shapley (1957), Additive Time reversal; Factor Overcome Multi-factors, Index (SSI) Sun (1998) reversal; Zero robust; base/terminal year two cases Proportionality; bias; Provide an additive approach for complete decomposition Tiirnqvist- Tornquist Multiplicative Time reversal; Exact for Desecrate Divisia Two factors, Theil index (1936), Theil a homogeneous translog Index two cases (TTI) (1965, 1967) aggregator function; Superlative Approach Author Additive or Major Properties Advance over Applicability MultiJ:!licative Previous V artia Index I Vartia (1976) Multiplicative Time reversal; Factor Consistent in Two factors, (VI) reversal; Zero robust; aggregation; Perfect two cases Consistent in decomposition as in aggregation; Exact for Divisia-based Index addilog aggregator function LMDI Ang, B. W., & Multiplicative Time reversal; Factor Extended VI to multi- Multi-factors, Choi, K. H. reversal; Zero robust; factor case two cases (1997) Consistent in aggregation; AMDI Ang, B. (1994) Multiplicative Time reversal; Factor Provide a Divisia- Multi-factors, reversal; Zero robust; based approach for two cases Consistent in additive aggregation; decomposition EKS Eltetii, 6., & Multiplicative Time reversal; Factor Preserve transitivity in Two factors, Koves, P. reversal; Zero robust; multilateral multi-cases (1964, 1973), Proportionality; decomposition Szulc, B. Transitivity (1964) CCD Caves, D. W., Multiplicative Time reversal; Factor Preserve transitivity in Two factors, Christensen, L. reversal; Zero robust; multilateral multi-cases R., & Diewert, Proportionality; decomposition W. E. (1982) Transitivity Approach Author Additive or Major Properties Advance over Applicability MultiJ:!licative Previous EKS/Shapley This Multiplicative Time reversal; Factor Preserve transitivity in Multi-factors, Number - FII dissertation reversal; Zero robust; multi-factor Multi-cases Proportionality; multilateral Transitivity decomposition EKS/Shapley This Additive Time reversal; Factor Preserve transitivity in Multi-factors, Number - SSI dissertation reversal; Zero robust; multi-factor Multi-cases Proportionality; multilateral Transitivity decomposition EKS/Shapley This Multiplicative Time reversal; Preserve transitivity in Multi-factors, Number-TT! dissertation Transitivity multi-factor Multi-cases multilateral decomposition EKS/Shapley This Multiplicative Time reversal; Factor Preserve transitivity in Multi-factors, Number- dissertation reversal; Zero robust; multi-factor Multi-cases VI/LMDI Proportionality; multilateral Transitivity; Consistent decomposition in Aggregation Adjusted This Multiplicative/ Additive Time reversal; Zero Bound Generalized Multi-factors, Laspeyres dissertation robust; Consistent in FII, SSI; Provide same two cases Index (adjLI) Aggregation ranking of factors Adjusted This Multiplicative/ Additive Time reversal; Zero Bound Generalized Multi-factors, Paasche Index dissertation robust; Consistent in FII, SSI; Provide same two cases (adjPI) Aggregation ranking of factors f v. °' Approach Author Additive or Major Properties Advance over Applicability MultiJ:!licative Previous EKS/Shapley This Multiplicative/ Additive Time reversal; Zero Bound EKS/Shapley Multi-factors, Number- dissertation robust; Transitivity; Number - FII, SSI; Multi-cases adj LI Consistent in Aggregation EKS/Shapley This Multiplicative/ Additive Time reversal; Zero Bound EKS/Shapley Multi-factors, Number- dissertation robust; Transitivity; Number - FII, SSI; Multi-cases adj PI Consistent in Aggregation References Ang, B. 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Identifying and quantitatively measuring the drivers of greenhouse gas (GHG) emissions becomes particularly useful in such case to provide valuable information to guide policy analysis and planning. For example, in assigning the carbon allowance to different entities m vanous geographical areas, policy makers should consider how much em1ss1on 1s attributable to the controllable factors and how much to the uncontrollable factors. Ignoring the differences will impede the effectiveness and fairness of the policy. In addition, the same amount of emission reduction thru different approaches though may have same effects on global warming, may have different impact on the local economy or on the performance of the entity in question. A convenient example is that the emission reduction achieved through output reduction and the emission reduction achieved through energy efficiency can have different implications on the performance of the entity. In another way around, at this point, most of the policies in place are policies aiming at promoting renewable energy in the total energy portfolio, or encouraging energy efficiencies. Identifying and quantifying drivers of the spatial differences in GHG 63 emissions may also help policy makers and planners to target efforts on reducing GHG emissions in a certain area. Index decomposition analysis (IDA) can quantitatively measure the contributions of factors in a certain change. The information can serve many purposes. It can, for example, show how much compansation is necessarity for a group of people when a policy measure causes price level change, or how to allocate observed changes in question to controlable and uncontrolable factors, etc. It can also serve as an evaluation tool for policy makers and planners to compare their policy performance with their peers and serve the many aforementioned purposes. We select emissions in electricity production in the United States as our case study for the following reasons. Firstly, according to EPA, the electricity industry accounted for the largest portion of GHG emitted by industies in the United States from 1990 to 2009 (EPA, 2011). It would be important for policy makers to understand which factor contributes the most to the emissions. Secondly, most of the policies to mitigate the emissions from electricity production are implemented at the state level, and usually focus on one or two factors. The most widely-used factors are fuel mix in electricity generation and fuel efficiencies in electricity conversion. The contributions to C0 2 emissions by fuel mix and the fuel efficiencies in electricity conversion are difficult to measure direcly, while the data on fuel mix, fuel consumption, and emissions from electricity production are easy to obtain. It thus makes the case perfect for index decomposition analysis, as IDA can helps to allocate the emission changes to the factors 64 in which we are interested and will require item level data. In this case study, we applied the multilateral EKS numbers developed in the previous chapter based on FII, SSI, and VI/LMDI to analyze the drivers of C0 2 emissions from electricity generation in the United States as a whole and across states. The analysis can provide us insights on how each state does on C0 2 emissions from electricity generation comparing to its peers and how fuel mix, fuel intensity, and C0 2 emission factors contribute to the difference. 1.2. IDA model In general, the decomposition analysis will be framed by the identity with which the decomposition start. It decides the variable of concern, mostly the variable of energy use or pollutant emissions, and the drivers that we assume can affect its change. Several studies started the decomposition with well-known identities and their adjusted versions, e.g. Kaya identity, and other studies chose variables that are more suitable to their question at hand, as did in this one. Kaya Identity was proposed by Y. Kaya (1990). It explains the national level greenhouse gas emissions as the product of population, per capita income, carbon intensity of energy use, and energy intensity of economic activity. GDP E C C=P*--*--*- p GDP E It is said to be a type of IPAT equation that came out of the debate between Barry Commoner (Commoner et al., 1971), and Paul Ehrlich and John Holdren (Ehrlich & Holdren, 1970). The IPAT equation postulates the environmental impact to be the product of population, affiuence, and technology, where affiuence is measured by GDP 65 per capita and technology by the ratio of impact and GDP (Dietz & Rosa, 1994; Chertow, 2000). Kaya identity is widely used to forecast the GHG emissions in various future scenarios as well as serve as the starting point of decomposition to track the historical trajectory of GHG changes, even though in some of the studies, the decomposition is not expressly referred to as IDA (e.g. Albrecht, et al., 2002). Recent discussions of national level GHG emissions have called for incorporating more drivers into the decomposition (e.g. Rosa & Dietz, 2012). In our case study, as electricity generation is only one sector of the economy and we are interested in the effects of the policies that can affect the C0 2 emissions from electricity generation, we chose to construct identities that suits better for our analysis rather than start with Kaya identity. To define the IDA model, the independent factors we chose are: • Fuel mix in electricity generation, defined as the percentage of electricity generated by fuel type; • Electricity conversion coefficient, defined as the ratio of fuel consumed to the amount of electricity generated by fuel type, measured in physical units 3 ; • Fuel emission coefficient, defined as the C0 2 emissions in unit fuel consumption. 3 \\!hen the fuel and electricity are measured in value terms, the result can differ. For example, two places can have the same energy conversion efficiency in unit terms (e.g. one unit of coal is used to produce one unit of coal-fired electricity), but their energy conversion efficiency may differ in value terms because of differences in price between the two places. Analyzing the energy conversion efficiency in value terms can provide us other insights because price is an important incentive for changing people's behavior. The value perspective is a good approach for future research. 66 Fuel mix 1s designed to provide insights on the policies intended to promote the percentage of renewable energy in electriciy generation. Electricity convers10n coefficient is designed to provide insights on energy efficiency related policies and to compare the efficiencies across states. And fuel emission coefficient is designed to capture the quality variance by fuel type. Our data are from EIA (2011), and we are using the data for 2009, because it is the newest available data when the analysis was performed. In terms of the fuel types, we use the fuel categories in EIA data report, which are coal, petroleum, natural gas, other gases, nuclear, hydroelectric conventional, wind, solar thermal and photovoltaic, wood and wood derived fuels, geothermal, other biomass, pumpted storage, and other. Generally speaking, there are two ways to initiate the identities for energy and emission studies: decomposing the energy or emission level (see, e.g. Hammond & Norman, 2012; Hatzigeorgiou, et al., 2010) or decomposing the energy or emission intensities (see, e.g. Ang, 1994; Balezentis, et al., 2011). The intensity approach bypasses the concerns of scale in decomposition analysis, and thus neglects the effects of scale on energy and emission intensity. The level approach can identify the scale effect, but such treatement can also be a distraction, as the scale effects usually are many times larger than the other effects in empirical analysis (see, e.g. Ang, 1994; Ang & Lee, 1994). In our case study, we chose the emission intensity approach rather than the level one. The emission intensity is defined as the C0 2 emissions embodied in one unit of electricity generated. The intensity approach is chosen because, the amount of C0 2 emissions from 67 electricity generation is not a good variable for policy control and directing our attention to scale can lead to ineffective emission reduction policies 4 . Also, the level of C0 2 emissions from electricity production by states can be highly correlated to the size of the state population and the economic activities by state. Simply comparing the level of emissions may not generate much policy insights. We will perform multilateral decomposition to identify the areas that states can focus on to reduce emissions by using the EKS/Shapley numbers as presented in Section 1.5. We can consider the EKS/Shapley numbers to be the impact of certain factor in each state compared to the avarage. So, if the avarage performance is obtainable, performance below average should be an area of focus. Therefore, we have the following identity as the starting point of the decomposition analysis. QC02 QE (3-1) where, Qco,: Total C0 2 emission from electricity generation; QE: Net generation by state; i: Type of fuels. 4 In theory, electricity generation can be characterized as a natural monopoly due to the cost structure. The level of emissions is not a good variable for policy control in natural monopoly, as the monopoly can reduce output to reduce the emission level, which can lead to a welfare loss. 68 Q Ei: The unit of electricity generated in the state by using fuel i; QF( The unit of fuel i used in electricity generation in the state; Q co 2 i: The unit of C02 emission by the consumption of fuel i in electricity generation. The above design calls for multi-factor multilateral decomposition. We have the options to perform the decomposition analysis using various multilateral EKS/Shapley numbers presented in Table 2-4. As our dataset contains many zero values, we will compute the multilateral EKS/Shapley numbers based on the bilateral Fil, SSI, and Vl/LMDI, which have good ability to handle zero values, in both multiplicative and additive forms. We also use the adjusted Laspeyres and Paasche indices to serve as bounds for the multilateral EKS/Shapley number based on Fil. 2. Results The results are shown in Table 3-1. Table 3-1 Result of Multiplicative and Additive Multilateral EKS/Shapley Numbers (2009 data) Multiplicative decomposition Total 01iginal Fuel Mix Unit Unit State Emission Emission Ratio Fii LMDI LI PI AK 1.3495 0.6327 2.1330 0.9880 0.9344 1.2303 0.7934 AL 1.0309 0.4833 2.1330 0.9779 1.0010 0.9700 0.9858 AR 1.1296 0.5296 2.1330 1.0598 1.0787 1.0185 1.1028 AZ 1.0196 0.4780 2.1330 1.0246 1.0335 0.9678 1.0847 CA 0.6190 0.2902 2.1330 0.5111 0.5430 0.5975 0.4372 co 1.6447 0.7710 2.1330 1.4932 1.5437 1.3809 1.6146 69 Total Unit Original Unit Fuel Mix State Emission Emission Ratio Fil LMDI LI PI CT 0.5500 0.2578 2.1330 0.5676 0.5435 0.5753 0.5600 DC DE FL GA HI IA ID IL IN KS KY LA MA MD ME MI MN MO MS MT NC ND NE NH NJ NM NV NY OH OK OR PA RI SC SD 2.1482 1.8254 1.1240 1.2766 1.6779 1.7677 0.1668 1.0890 2.0314 1.6546 2.0277 1.2477 1.0775 1.2503 0.6150 1.5510 1.3690 1.8038 1.0284 1.4012 1.1681 2.0340 1.4993 0.5826 0.5551 1.8012 1.0349 0.6113 1.8035 1.4772 0.3539 1.1333 0.8816 0.8121 0.9136 1.0071 2.1330 61.8557 3.5196 0.8558 2.1330 1.6750 1.6129 0.5270 2.1330 1.2194 1.1514 0.5985 2.1330 1.2328 1.2467 0.7866 2.1330 2.6838 1.9827 0.8287 2.1330 1.3570 1.4865 0.0782 2.1330 0.1017 0.1032 0.5105 2.1330 0.8838 0.9635 0.9524 2.1330 1.6735 1.8448 0.7757 2.1330 1.3610 1.4421 0.9506 2.1330 1.7616 1.8681 0.5849 2.1330 1.1151 1.0995 0.5051 2.1330 1.1563 1.0967 0.5862 2.1330 1.1185 1.1577 0.2883 2.1330 0.4524 0.4914 0.7271 2.1330 1.3411 1.3996 0.6418 2.1330 1.1313 1.1946 0.8456 2.1330 1.5496 1.6603 0.4821 2.1330 0.9697 1.0025 0.6569 2.1330 1.1331 1.2182 0.5476 2.1330 1.1033 1.1486 0.9536 2.1330 1.0367 1.6588 0.7029 2.1330 1.2438 1.3879 0.2731 2.1330 0.5909 0.5706 0.2602 2.1330 0.5372 0.5268 0.8444 2.1330 1.6873 1.7037 0.4852 2.1330 1.0618 1.0689 0.2866 2.1330 0.5966 0.5777 0.8455 2.1330 1.6531 1.7090 0.6925 2.1330 1.1551 1.3548 0.1659 2.1330 0.3752 0.3840 0.5313 2.1330 1.1190 1.1181 0.4133 2.1330 3.2936 1.5988 0.3807 2.1330 0.8030 0.8066 0.4283 2.1330 0.7345 0.8105 5. 5392 690. 7336 1.6542 1.2521 1.2004 2.4519 1.2409 0.1339 0.8062 1.5989 1.2915 1.7636 1.1084 1.1664 1.0918 0.5909 1.3107 1.0524 1.4031 0.9628 1.1474 1.0283 1.2538 1.1049 0.6058 0.5465 1.5503 1.0386 0.6068 1.5639 1.2473 0.3797 1.0647 1.2273 0.7778 0.6810 1.6960 1.1876 1.2660 2.9377 1.4840 0.0773 0.9689 1. 7517 1.4343 1.7596 1.1219 1.1463 1.1459 0.3463 1.3722 1.2161 1. 7114 0.9766 1.1189 1.1837 0.8572 1.4002 0.5763 0.5281 1.8364 1.0855 0.5866 1. 7473 1.0698 0.3708 1.1760 8.8388 0.8290 0.7922 70 Total Unit Original Unit Fuel Mix State Emission Emission Ratio Fil LMDI LI PI TN 1.1628 0.5452 2.1330 0.9228 1.0501 0.8854 0.9618 TX 1.3061 0.6123 2.1330 1.2174 1.2146 1.1890 1.2466 UT 1.7889 0.8387 2.1330 1.7454 1.7816 1.5976 1.9069 VA 1.1006 0.5160 2.1330 0.9971 0.9706 0.9720 1.0227 VT 0.0019 0.0009 2.1330 0.0054 0.0334 0.0021 0.0136 WA 0.2762 0.1295 2.1330 0.2509 0.2576 0.2590 0.2430 WI 1.5736 0.7377 2.1330 1.3708 1.3807 1.3064 1.4383 WV 1.9867 0.9314 2.1330 1.5318 1.8602 1.5306 1.5329 WY 2.0707 0.9708 2.1330 1.5309 1.8028 1.4627 1.6022 Energy Conversion Ratio C02 Coefficient State Fil LMDI LI PI Fil LMDI LI PI AK 1.3607 1.3533 1.4119 1.3114 1.0038 1.0672 1.1547 0.8726 AL 0.9767 0.9876 0.8962 1.0644 1.0794 1.0429 1.0984 1.0608 AR 1.1285 1.1292 1.0175 1.2517 0.9445 0.9274 0.9364 0.9526 AZ 1.0451 1.0314 0.9505 1.1492 0.9522 0.9565 0.9108 0.9954 CA 0.8788 0.8976 0.7891 0.9786 1.3782 1.2701 1.7176 1.1058 co 1.1233 1.0886 1.0049 1.2556 0.9806 0.9787 0.9156 1.0503 CT 0.9257 0.9315 0.8678 0.9874 1.0467 1.0863 1.0840 1.0107 DC 0.2526 0.8560 0.0226 2.8211 0.1375 0.7130 0.0123 1.5351 DE 0.9695 0.9851 0.9203 1.0214 1.1241 1.1489 1.1263 1.1218 FL 0.8971 0.9122 0.8481 0.9489 1.0275 1.0701 1.0922 0.9667 GA 0.9244 0.9483 0.8430 1.0136 1.1202 1.0798 1.1244 1.1161 HI 0. 7239 0.8571 0.5891 0.8895 0.8637 0.9874 0.7879 0.9468 IA 1.2927 1.2345 1.1162 1.4971 1.0077 0.9633 0.9348 1.0863 ID 0.7191 0.6723 0.5700 0.9072 2.2794 2.4030 3.9580 1.3128 IL 1.2275 1.1797 1.0467 1.4396 1.0038 0.9581 0.9435 1.0679 IN 1.0711 1.0375 0.9413 1.2187 1.1333 1.0614 1.0779 1.1915 KS 1.3814 1.3013 1.2488 1.5282 0.8800 0.8817 0.8258 0.9378 KY 1.0337 0.9924 0.9860 1.0838 1.1135 1.0937 1.0590 1.1708 LA 1.2130 1.2107 1.1959 1.2303 0.9225 0.9373 0.9140 0.9310 MA 0.8912 0.9073 0.8372 0.9487 1.0456 1.0828 1.0846 1.0080 MD 0.8978 0.8834 0.8390 0.9607 1.2451 1.2225 1.1867 1.3063 ME 0.6889 0.7794 0.5408 0.8775 1.9736 1.6058 3.3833 1.1512 MI 1.0699 1.0682 0.9646 1.1868 1.0810 1.0375 1.0751 1.0869 71 Energy Conversion Ratio C02 Coefficient State Fil LMDI LI PI Fil LMDI LI PI MN 1.2239 1.1901 1.0697 1.4004 0.9887 0.9629 0.9421 1.0375 MO 1.2489 1.1920 1.0782 1.4465 0.9321 0.9114 0.8566 1.0142 MS 1.2050 1.1776 1.1353 1.2789 0.8802 0.8711 0.8698 0.8907 MT 1.2899 1.2643 1.1776 1.4128 0.9588 0.9098 0.9788 0.9391 NC 0.8817 0.8664 0.8099 0.9598 1.2008 1.1739 1.1019 1.3086 ND 1.4583 1.5200 1.0950 1.9423 1.3454 0.8067 2.1760 0.8318 NE 1.3102 1.2113 1.1116 1.5443 0.9200 0.8918 0.8144 1.0394 NH 0.8653 0.8729 0.8172 0.9161 1.1395 1.1696 1.1969 1.0848 NJ 0.9381 0.9378 0.8780 1.0024 1.1014 1.1235 1.1451 1.0595 NM 1.1406 1.1245 1.0068 1.2921 0.9359 0.9402 0.8768 0.9991 NV 0.9943 0.9782 0.9193 1.0754 0.9803 0.9898 0.9567 1.0045 NY 0.9888 0.9880 0.9278 1.0539 1.0362 1.0711 1.0927 0.9825 OH 0.9331 0.9323 0.8474 1.0275 1.1692 1.1319 1.1028 1.2396 OK 1.2175 1.1813 1.1111 1.3341 1.0503 0.9230 1.1570 0.9535 OR 1.0021 1.0053 0.9713 1.0340 0.9411 0.9168 0.9273 0.9552 PA 0.9459 0.9468 0.8626 1.0372 1.0708 1.0706 1.0319 1.1112 RI 0.5115 0.7398 0.1766 1.4814 0.5233 0.7453 0.1888 1.4501 SC 0.8640 0.8647 0.8049 0.9273 1.1706 1.1643 1.1382 1.2039 SD 1.4071 1.2948 1.2389 1.5982 0.8839 0.8705 0.8141 0.9597 TN 1.0642 0.9945 0.9660 1.1724 1.1841 1.1134 1.0828 1.2949 TX 1.2221 1.2161 1.1759 1.2701 0.8778 0.8842 0.8593 0.8968 UT 0.9776 0.9618 0.8707 1.0977 1.0484 1.0440 0.9655 1.1383 VA 0.8648 0.8742 0.8127 0.9204 1.2764 1.2971 1.2633 1.2895 VT 0.8854 0.2735 0.3285 2.3864 0.4046 0.2113 0.1569 1.0434 WA 1.1454 1.1507 1.1095 1.1824 0.9611 0.9318 0.9942 0.9291 WI 1.1617 1.1693 1.0447 1.2917 0.9882 0.9747 0.9730 1.0037 WV 0.9928 0.9162 0.8848 1.1141 1.3064 1.1657 1.2218 1.3969 WY 1.2124 1.1935 0.9941 1.4787 1.1156 0.9624 1.1390 1.0927 Additive Total unit Original Unit Fuel Mix State emission Emission Difference Fil LMDI LI PI AK AL AR 0.0498 -0.0995 -0.0533 0.6327 0.4833 0.5296 -0.5829 -0.1771 -0.1660 0.0491 -0.4034 -0.5829 -0.0994 -0.0925 -0.0447 -0.1540 -0.5829 -0.0238 -0.0511 -0.0014 -0.0462 72 Total unit Original Unit Fuel Mix State emission Emission Difference Fil LMDI LI PI AZ CA co CT DC DE FL GA HI IA ID IL IN KS KY LA MA MD ME MI MN MO MS MT NC ND NE NH NJ NM NV NY OH OK OR PA -0.1048 -0.2926 0.1882 -0.3250 0.4243 0.2729 -0.0559 0.0156 0.2038 0.2459 -0.5047 -0.0723 0.3695 0.1928 0.3678 0.0021 -0.0777 0.0033 -0.2945 0.1443 0.0589 0.2628 -0.1007 0.0741 -0.0352 0.3707 0.1200 -0.3097 -0.3226 0.2616 -0.0977 -0.2963 0.2627 0.1097 -0.4169 -0.0515 0.4780 0.2902 0.7710 0.2578 1.0071 0.8558 0.5270 0.5985 0.7866 0.8287 0.0782 0.5105 0.9524 0.7757 0.9506 0.5849 0.5051 0.5862 0.2883 0.7271 0.6418 0.8456 0.4821 0.6569 0.5476 0.9536 0.7029 0.2731 0.2602 0.8444 0.4852 0.2866 0.8455 0.6925 0.1659 0.5313 -0.5829 -0.0446 -0.0772 -0.0276 -0.0615 -0.5829 -0.4264 -0.3511 -0.2667 -0.5861 -0.5829 0.2205 0.1797 0.2442 0.1969 -0.5829 -0.2955 -0.3220 -0.2740 -0.3169 -0.5829 0.9253 0.8115 0.7674 1.0833 -0.5829 0.2531 0.2177 0.2746 0.2316 -0.5829 0.0169 -0.0298 0.0600 -0.0263 -0.5829 0.0437 0.0320 0.0811 0.0063 -0.5829 0.4370 0.3091 0.5605 0.3135 -0.5829 0.1921 0.1682 0.2074 0.1768 -0.5829 -1.1371 -0.6309 -0.7322 -1.5420 -0.5829 -0.0872 -0.1058 -0.0706 -0.1037 -0.5829 0.3839 0.3468 0.4351 0.3328 -0.5829 0.1726 0.1419 0.1988 0.1464 -0.5829 0.3826 0.3543 0.4399 0.3253 -0.5829 -0.0271 -0.0528 -0.0015 -0.0527 -0.5829 -0.0067 -0.0540 0.0279 -0.0412 -0.5829 0.0150 -0.0049 0.0450 -0.0150 -0.5829 -0.7069 -0.3910 -0.4308 -0.9830 -0.5829 0.1342 0.1164 0.1807 0.0877 -0.5829 0.0400 0.0127 0.0589 0.0212 -0.5829 0.2901 0.2482 0.3127 0.2676 -0.5829 -0.0722 -0.0984 -0.0249 -0.1196 -0.5829 0.0265 0.0239 -0.5829 0.0062 -0.0121 -0.5829 0.0045 0.2694 -0.5829 0.1445 0.1108 0.0804 -0.0273 0.0290 -0.0165 0.2992 -0.2901 0.1626 0.1264 -0.5829 -0.2989 -0.3085 -0.2704 -0.3274 -0.5829 -0.3216 -0.3364 -0.2897 -0.3535 -0.5829 0.3126 0.2610 0.3310 0.2942 -0.5829 -0.0233 -0.0719 0.0202 -0.0668 -0.5829 -0.2929 -0.3106 -0.2693 -0.3165 -0.5829 0.3000 0.2678 -0.5829 0.0468 0.0816 0.3379 0.2622 0.1689 -0.0753 -0.5829 -0.3806 -0.3881 -0.3662 -0.3950 -0.5829 -0.0027 -0.0298 0.0148 -0.0202 73 Total unit Original Unit Fuel Mix State emission Emission Difference Fil LMDI LI PI RI -0.1696 0.4133 -0.5829 0.1819 0.1397 0.0505 0.3134 SC SD TN TX UT VA VT WA WI WV WY -0.2021 -0.1546 -0.0377 0.0295 0.2558 -0.0669 -0.5820 -0.4534 0.1549 0.3486 0.3879 0.3807 0.4283 0.5452 0.6123 0.8387 0.5160 0.0009 0.1295 0.7377 0.9314 0.9708 -0.5829 -0.1693 -0.1812 -0.1568 -0.1817 -0.5829 -0.1764 -0.1845 -0.1486 -0.2042 -0.5829 -0.0615 -0.0596 -0.0200 -0.1030 -0.5829 0.0435 0.0079 0.0720 0.0150 -0.5829 0.3466 0.2938 0.3792 0.3140 -0.5829 -0.0914 -0.1097 -0.0713 -0.1115 -0.5829 -0.3286 -0.2956 -0.5103 -0.1469 -0.5829 -0.5096 -0.4677 -0.4477 -0.5716 -0.5829 0.1330 0.1058 0.1531 0.1130 -0.5829 0.3546 0.3499 0.4495 0.2597 -0.5829 0.3524 0.3332 0.4052 0.2997 Energy conversion ratio C02 coefficient State Fil LMDI LI PI Fil LMDI LI PI AK 0.2216 0.1716 0.2813 0.1619 0.0054 0.0442 AL -0.0316 -0.0266 -0.0500 -0.0132 0.0314 0.0195 0.1626 -0.1519 0.1477 -0.0849 AR 0.0583 0.0477 0.0476 0.0690 -0.0877 -0.0499 -0.0147 -0.1608 AZ 0.0044 -0.0013 -0.0058 0.0145 -0.0647 -0.0264 -0.0152 -0.1142 CA -0.0967 -0.0453 -0.1416 -0.0517 0.2304 0.1038 0.5196 -0.0588 co 0.0494 0.0298 0.0340 0.0648 -0.0817 -0.0213 -0.0053 -0.1582 CT -0.0453 -0.0353 -0.0728 -0.0179 0.0158 0.0323 DC -0.0469 -0.1271 -0.4081 0.3143 -0.4542 -0.2601 DE -0.0320 -0.0382 -0.0388 -0.0252 0.0518 0.0934 FL -0.0695 -0.0642 -0.0895 -0.0495 -0.0032 0.0382 GA -0.0628 -0.0562 -0.0805 -0.0452 0.0347 0.0398 -0.1627 -0.1059 -0.1640 -0.1613 -0.0706 0.0006 0.1460 0.1141 0.1123 0.1796 -0.0922 -0.0364 -0.3724 -0.1070 -0.4841 -0.2607 1.0048 0.2332 0.0793 -0.0478 -0.4247 -0.4836 0.1190 -0.0153 0.0894 -0.0959 0.1426 -0.0732 0.0325 -0.1736 0.0087 -0.1931 2.2514 -0.2417 HI IA ID IL IN KS 0.0823 0.0657 0.0705 0.0940 -0.0674 -0.0322 -0.0030 -0.1318 0.0083 -0.0089 -0.0059 0.0225 -0.0227 0.0316 0.0781 -0.1236 0.1880 0.1454 0.1783 0.1977 -0.1678 -0.0945 -0.0600 -0.2756 KY -0.0219 -0.0432 0.0014 -0.0451 0.0071 0.0567 0.0773 -0.0632 LA 0.1167 0.0995 0.1389 0.0945 -0.0876 -0.0446 -0.0340 -0.1411 MA -0.0722 -0.0651 -0.0932 -0.0512 0.0012 0.0414 MD -0.0997 -0.1013 -0.0881 -0.1113 0.0880 0.1095 0.0793 -0.0770 0.1457 0.0302 74 Energy conversion ratio C02 coefficient State Fil LMDI LI PI Fil LMDI LI ME -0.3320 -0.1085 -0.4457 -0.2183 0.7444 0.2050 0.0046 0.0497 -0.0170 0.0140 PI 1.6771 -0.1883 0.0870 -0.1211 MI MN MO MS MT 0.0271 0.0139 0.0994 0.0790 0.1244 0.0909 0.0911 0.0744 0.1492 0.1173 0.0796 0.1193 -0.0805 -0.0327 -0.0006 -0.1605 0.0936 0.1553 -0.1518 -0.0763 -0.0381 -0.2655 0.1143 0.0678 -0.1196 -0.0767 -0.0521 -0.1870 0.1375 0.1610 -0.1017 -0.0672 0.0213 -0.2248 NC -0.1100 -0.1091 -0.1016 -0.1185 0.0686 0.0860 0.1668 0.3473 0.1091 -0.1817 0.1243 0.0128 0.9411 -0.7230 ND NE 0.2571 0.2830 0.1249 0.0922 0.1077 0.1422 -0.1494 -0.0829 -0.0586 -0.2401 NH -0.0770 -0.0664 -0.1081 -0.0458 0.0662 0.0652 NJ -0.0428 -0.0326 -0.0674 -0.0182 0.0418 0.0465 0.1561 -0.0237 0.1185 -0.0349 NM 0.0739 0.0530 0.0409 0.1068 -0.1249 -0.0524 -0.0291 -0.2206 NV -0.0223 -0.0199 -0.0261 -0.0185 -0.0521 -0.0059 NY -0.0196 -0.0147 -0.0430 0.0039 0.0162 0.0290 OH -0.0810 -0.0835 -0.0714 -0.0907 0.0436 0.0783 OK 0.1106 0.0857 0.1088 0.1123 -0.0477 -0.0576 0.0113 -0.1155 0.0827 -0.0503 0.1116 -0.0244 0.1222 -0.2176 OR -0.0050 -0.0001 0.0069 -0.0169 -0.0313 -0.0287 -0.0031 -0.0596 PA -0.0503 -0.0540 -0.0637 -0.0370 0.0015 0.0322 0.0563 -0.0534 RI -0.1610 -0.1543 -0.3656 0.0436 -0.1905 -0.1549 -0.3322 -0.0488 -0.0927 -0.0900 -0.1097 -0.0756 0.0598 0.0691 0.1220 -0.0023 SC SD 0.1414 0.1063 0.1734 0.1094 -0.1196 -0.0763 -0.0728 -0.1664 TN -0.0129 -0.0317 -0.0051 -0.0206 0.0366 0.0537 0.0918 -0.0186 TX 0.1204 0.1027 0.1405 0.1003 -0.1345 -0.0812 -0.0637 -0.2052 UT -0.0532 -0.0596 -0.0539 -0.0524 -0.0377 0.0217 VA -0.1014 -0.0967 -0.1100 -0.0929 0.1259 0.1394 0.0289 -0.1042 0.2056 0.0463 VT -0.0964 -0.1335 -0.2649 0.0722 -0.1570 -0.1528 -0.3854 0.0714 WA 0.0479 0.0370 WI 0.0935 0.0747 0.0897 0.0062 0.0083 -0.0227 0.0627 0.1243 -0.0717 -0.0257 WV -0.0901 -0.1030 -0.0449 -0.1353 0.0840 0.1017 WY 0.1253 0.0993 0.0614 0.1893 -0.0899 -0.0445 Source: Calculation based on data from EIA, 2011 0.0646 -0.0479 0.0253 -0.1687 0.1658 0.0023 0.1043 -0.2840 75 3. Interpretation ofresults In Table 3-1 Result of Multiplicative and Additive Multilateral EKS/Shapley Numbers (2009 data), we included the original C0 2 emissions in unit electricity generation in column 2, and calculate its ratio or difference to the EKS/Shapley numbers for the C0 2 emissions in unit electricity generation in column 3. We can see in column 3 that the ratio and difference are all constant and equal to the geometric average and the arithmetic average of the original C0 2 emissions in unit electricity generation, respectively. We can also verify by manipulating the formula that the EKS/Shapley numbers in multiplicative and additive form are equal to the ratio or difference between the original group level indicator by area, in our case, the C0 2 emissions in unit electricity generation by state, and the geometric average or arithmetic average of all original group level indicators, respectively. It is worth mentioning again that the above EKS/Shapley numbers can yield bilateral indices simply by taking the ratio or difference of two EKS/Shapley numbers. The bilateral indices calculated in such a way will satisfy the transitivity criterion. However, as we mentioned in Chapter 2 Section 2.4, the multiplicative and additive EKS/Shapley numbers will not yield consistent order for the factors. Such inconsistency will lead to difficulties in interpreting results, as one index can be a major positive driver according to one decomposition method but a minor positive or even negative driver according to another. 76 A compromised approach is to develop a bound for certain index numbers we are using. From Chapter 2 Section 2.5, we can see that the geometric and arithmetic average for the adjusted Laspeyres and Paasche indices can serve as the bound for the EKS/Shapley number based on FII and SSI, even though we cannot say that one of them will always be the upper or lower bound. However, we can verify that the EKS/Shapley numbers based on VI/LMDI are not always bounded by the geometric and arithmetic average of the adjusted Laspeyres and Paasche indices. So our work of developing the bound for the index numbers is not complete. Developing the true upper and lower bound for all the well-behaved index numbers is an interesting question for future research. 3.1. Interpretation of the additive indices We can see that the total unit emissions (column 1 in Table 3-1) actually are an adjusted version of the original total unit emissions (column 2 in Table 3-1 ). They are the difference or ratio between the original total unit emissions and the arithmetic or geometric average of the original total unit emissions by state. The EKS/Shapley number based on FII and the EKS/Shapley number based on VI/LMDI are the two approaches to allocate the difference or ratio to the three pre-defined factors: fuel mix, energy conversion coefficient, and C0 2 emission coefficient. The Fisher ideal indices, as we explained previously, allocate the changes to factors via a fairness principle, which was elaborated in Fisher (1922). The Log Mean Divisia Index and its additive counterpart, on the other hand, project the difference to a log scale, and use it to allocate the change. Their differences are also explained in detail in Chapter 2. 77 Take California as an example. The additive decomposition result in Table 3-1 can be interpreted as: comparing to the average of unit emissions in electricity generation across the state, California's unit emission is 0.2926 (unit) less. The fuel mix contributed to 0.4264 or 0.3511 (unit) less, according to the Fisher ideal indices and the LMDI indices, respectively; the energy conversion coefficient contributed to 0.0967 or 0.0453 (unit) less; and the C0 2 emission coefficient contributed to 0.2304 or 0.1038 (unit) more. So we see that California's fuel mix is much better than the average in terms of generating relatively lower C02 emissions, and its energy efficiency in electricity generation is slightly better than the average, but the C0 2 emission coefficient, which is designed to represent the qualities of fuels in electricity generation, a slightly worse comparing to the average. At the same time, the arithmetic average of adjusted Laspeyres and Paasche indices set the bound of the EKS/Shapley number based on FIL It serves as an estimate of the range of the indices if some kinds of unfairness are allowed in the indices generation. Take California as an example, the range of its fuel mix indices ranges from -0.5861 to -0.2667, meaning that the unit emission reduction due to the fuel mix in California can range from 0.2667 to 0.5861 less than the average unit emissions of all states. Therefore, we can consider the fuel mix is a good negative driving force of the unit emissions in electricity generation in California. The adjusted Passche Index and Laspeyres Index of C0 2 emission coefficient index of California are -0.0588 to 0.5196, respectively. It suggests that the C0 2 emission coefficient can be a slightly negative driving force or a positive driving force, depending on whether the other factors use the value of California's or the average value of all states. In Table 3-1, 20 states and the District of Columbia have all 78 positive fuel mix index, meaning that for the 21 areas, fuel mix is very likely to be positive drivers for the unit emissions from electricity generation. There are 20 states with all negative fuel mix indices, meaning that the fuel mix in the 20 states contribute negative! y to the unit emissions from electricity generation. Figure 3-1 to Figure 3-3 shows the additive version of the EKS/Shapley numbers for the three factors, in which the vertical line indicates the range set by the EKS/Shapley numbers of the adjusted Laspeyres and Paasche indices. When the whole vertical line is above or below zero, we call the corresponding index to be strictly positive or negative. 1. 5 L5 1.0 1.0 ;t x • .. \ */ x tx • • , :!; • ,"' F<" ,_ "W'~'< 0 < 9 )!1.1; ~ >;~~ 'e! ~:t> = f~~--it;;~' uuvca~o-- ~~~~ ~~2~ ~X %z ~ xzooo• ~~ ~ ·: *)11: >:< ~ ~ )( 0.5 0.5 0.0 0.0 45 45 x f · LO · LO ~ .1.5 -1.5 -2.0 -2.0 Upper Lower o Fisher XL MDI Figure 3-1 Additive EKS/Shapley Number for Fuel 111.lix's Contribution to C02 Emissions from Electricity Generation in the United States 79 0.4 0.4 03 03 l 0.2 0.2 & '" J ... 01 01 -~ - ... x • "'~ <I> ~ . 'j{ .. ...:"' "' " * 7' . 1-0 ' I -4> 0.0 0.0 ~ . ~.f·~·~f'.8 li( ~~~oso=~~X~<ow=%o~~vo~,i-'~~=~~~ ;;~~~~~ ~;~1; -0. l -0. l - ,- ~ ..l'X~:.!<llli::i::!!:l:tx ·:;:x' ~x~~OQ ' , ,~ ~ ... )(. I ' .,, <I> • , -0.2 -0.2 -0.3 -0.3 ' -0.4 -0.4 -0.5 -0.5 -0.6 -0.6 Upper Lower o Fisher X Li.\l!Dl Figure 3-2 Additive EKS/Shapley Numbers for Energy Conversion Coefficient's Contribution to C02Emissions from Electricity Generation in the United States 2.0 +--------1---------------------+ 2.0 1.5 +--------1-----f----------------+ 1.5 1.0 +-------~----1----------------+ 1.0 0.5 +---r-----1-----t-----t-------------+ 0.5 -1.0 -1.0 Upper Lower ofisher XLMDI Figure 3-3 Additive EKS/Shapley Numbers for C02 Emission Coefficient's Contribution to C02 Emissions from Electricity Generation in the United States We can also write the additive decomposition result in Table 3-1 in percentage terms for ease of understanding. We use the arithmetic average of the all the unit emissions by state as the base and present the percentage terms in Table 3-2. The interpretation of Table 3- 80 2 is much simpler than Table 3-1. Again, take the indices for California as an example. The data show that California's unit emission in electricity generation is 50.21% lower than the average unit emissions, in which the fuel mix attributes 73.15% or 60.24% less of the average unit emissions, energy conversion ratio contributes 16.59% or 7.77% less, and the C0 2 emission coefficient attributes to 39.53% or 17.81 % more of the average unit emissions, according to the Fisher ideal decomposition rules, or the log mean Divisia rules, respectively. Table 3--2 Additive Decomposition in Percentage Terms Total Energy conversion unit Fuel Mix ratio State emission Fii LMDI LI PI Fii LMDI AK 8.55% -30.39% -28.49% 8.43% -69.20% 38.02% 29.45% AL -17.08% -17.05% -15.86% -7.67% -26.42% -5.42% -4.56% AR -9.14% -4.09% -8.77% -0.25% -7.93% 10.00% 8.18% AZ -17.99% -7.64% -13.24% -4.73% -10.55% 0.75% -0.22% CA -50.21 % -73.15% -60.24% -45.75% -100.56% -16.59% -7.77% co 32.29% 37.84% 30.83% 41.90% 33.78% 8.47% 5.12% CT -55.76% -50.69% -55.24% -47.02% -54.36% -7.78% -6.06% DC 72.79% 158.76% 139.23% 131.66% 185.86% -8.05% -21.80% DE 46.82% 43.43% 37.35% 47.12% 39.73% -5.49% -6.55% FL -9.59% 2.89% -5.12% 10.30% -4.51 % -11.93% -11.02% GA 2.68% 7.50% 5.49% 13.92% 1.08% -10.78% -9.64% HI 34.96% 74.98% 53.03% 96.16% 53.80% -27.91% -18.17% IA 42.18% 32.96% 28.85% 35.58% 30.34% 25.04% 19.58% ID -86.59% -195.09% -108.23% -125.62% -264.57% -63.89% -18.35% IL -12.41 % -14.95% -18.15% -12.11% -17.79% 14.12% 11.26% IN 63.40% 65.87% 59.51% 74.65% 57.09% 1.43% -1.52% KS 33.08% 29.61% 24.35% 34.10% 25.11% 32.26% 24.95% KY 63.10% 65.64% 60.78% 75.47% 55.81% -3.75% -7.42% LA 0.36% -4.65% -9.06% -0.25% -9.04% 20.03% 17.08% MA -13.33% -1.15% -9.27% 4.78% -7.07% -12.39% -11.16% MD 0.57% 2.57% -0.83% 7.72% -2.57% -17.10% -17.38% 81 Total Energy conversion unit Fuel Mix ratio State emission Fil LMDI LI PI Fil LMDI ME -50.53% -121.29% -67.08% -73.92% -168.66% -56.96% -18.62% MI 24.76% 23.02% 19.97% 31.00% 15.04% 4.66% 2.39% MN 10.11% 6.87% 2.18% 10.11% 3.63% 17.06% 13.55% MO 45.09% 49.78% 42.58% 53.64% 45.92% 21.35% 15.60% MS -17.28% -12.39% -16.89% -4.27% -20.51 % 15.62% 12.76% MT 12.71% 4.55% 4.10% 13.80% -4.69% 25.61% 20.13% NC -6.04% 1.07% -2.08% 4.98% -2.83% -18.88% -18.71% ND 63.60% 0.78% 46.23% 51.33% -49.77% 44.11% 48.55% NE 20.59% 24.79% 19.01% 27.90% 21.68% 21.43% 15.81 % NH -53.14% -51.29% -52.93% -46.40% -56.18% -13.21 % -11.40% NJ -55.35% -55.17% -57.72% -49.70% -60.65% -7.35% -5.60% NM 44.88% 53.63% 44.77% 56.78% 50.48% 12.67% 9.10% NV -16.75% -3.99% -12.33% 3.47% -11.45% -3.83% -3.41 % NY -50.83% -50.25% -53.28% -46.21% -54.30% -3.36% -2.53% OH 45.06% 51.48% 45.95% 57.97% 44.99% -13.90% -14.32% OK 18.82% 8.03% 13.99% 28.98% -12.92% 18.97% 14.71 % OR -71.53% -65.30% -66.59% -62.84% -67.77% -0.86% -0.02% PA -8.84% -0.46% -5.11 % 2.54% -3.46% -8.64% -9.26% RI -29.09% 31.22% 23.96% 8.67% 53.76% -27.62% -26.48% SC -34.68% -29.04% -31.09% -26.91% -31.18% -15.90% -15.45% SD -26.52% -30.26% -31.66% -25.49% -35.03% 24.26% 18.24% TN -6.47% -10.55% -10.23% -3.42% -17.67% -2.21% -5.45% TX 5.05% 7.47% 1.36% 12.36% 2.58% 20.66% 17.62% UT 43.89% 59.47% 50.40% 65.06% 53.88% -9.12% -10.23% VA -11.47% -15.67% -18.81 % -12.23% -19.12% -17.40% -16.59% VT -99.84% -56.38% -50.72% -87.54% -25.21 % -16.53% -22.91% WA -77.79% -87.44% -80.24% -76.80% -98.07% 8.22% 6.35% WI 26.57% 22.83% 18.15% 26.27% 19.38% 16.05% 12.82% WV 59.80% 60.84% 60.03% 77.13% 44.56% -15.46% -17.68% WY 66.55% 60.47% 57.16% 69.52% 51.42% 21.51 % 17.03% Energy conversion ratio C02 coefficient State LI PI Fil LMDI LI PI AK 48.26% 27.77% 0.92% 7.59% 27.90% -26.06% AL -8.57% -2.26% 5.39% 3.35% 25.35% -14.57% 82 Energy conversion ratio C02 coefficient State LI PI Fil LMDI LI PI AR 8.17% 11.83% -15.05% -8.56% -2.52% -27.59% AZ -0.99% 2.49% -11.10% -4.53% -2.60% -19.59% CA -24.30% -8.87% 39.53% 17.81% 89.16% -10.09% co 5.83% 11.11% -14.02% -3.66% -0.91% -27.13% CT -12.49% -3.06% 2.70% 5.54% 13.60% -8.20% DC -70.02% 53.93% -77.92% -44.63% -72.87% -82.97% DE -6.66% -4.33% 8.89% 16.02% 20.41 % -2.63% FL -15.35% -8.50% -0.55% 6.55% 15.34% -16.45% GA -13.81 % -7.76% 5.96% 6.83% 24.47% -12.55% HI -28.14% -27.67% -12.11% 0.10% 5.57% -29.78% IA 19.26% 30.82% -15.82% -6.25% 1.49% -33.12% ID -83.06% -44.72% 172.40% 40.00% 386.27% -41.48% IL 12.10% 16.13% -11.57% -5.52% -0.52% -22.62% IN -1.00% 3.86% -3.90% 5.42% 13.40% -21.20% KS 30.60% 33.92% -28.79% -16.22% -10.29% -47.28% KY 0.23% -7.73% 1.21% 9.73% 13.26% -10.84% LA 23.84% 16.22% -15.02% -7.66% -5.83% -24.22% MA -15.99% -8.78% 0.20% 7.10% 13.61% -13.21 % MD -15.11% -19.09% 15.09% 18.79% 25.00% 5.18% ME -76.46% -37.45% 127.71% 35.17% 287.73% -32.31 % MI 0.79% 8.52% -2.92% 2.40% 14.93% -20.77% MN 13.65% 20.46% -13.82% -5.62% -0.10% -27.53% MO 16.06% 26.65% -26.05% -13.10% -6.54% -45.55% MS 19.62% 11.63% -20.51% -13.16% -8.94% -32.08% MT 23.59% 27.62% -17.45% -11.53% 3.66% -38.56% NC -17.43% -20.32% 11.77% 14.75% 21.33% 2.20% ND 28.63% 59.59% 18.72% -31.18% 161.47% -124.04% NE 18.47% 24.40% -25.63% -14.23% -10.06% -41.20% NH -18.55% -7.86% 11.35% 11.19% 26.78% -4.07% NJ -11.57% -3.13% 7.17% 7.97% 20.33% -5.99% NM 7.02% 18.33% -21.42% -8.99% -5.00% -37.85% NV -4.48% -3.17% -8.94% -1.01% 1.94% -19.81 % NY -7.39% 0.67% 2.78% 4.98% 14.18% -8.63% OH -12.24% -15.56% 7.49% 13.43% 19.15% -4.18% OK 18.67% 19.26% -8.18% -9.88% 20.97% -37.33% OR 1.19% -2.90% -5.38% -4.93% -0.53% -10.23% 83 Energy conversion ratio C02 coefficient State LI PI Fil LMDI LI PI PA -10.92% -6.35% 0.25% 5.53% 9.67% -9.16% RI -62.73% 7.49% -32.69% -26.58% -57.00% -8.37% SC -18.82% -12.97% 10.26% 11.86% 20.92% -0.40% SD 29.75% 18.77% -20.52% -13.09% -12.49% -28.54% TN -0.88% -3.53% 6.28% 9.21% 15.76% -3.19% TX 24.10% 17.22% -23.07% -13.92% -10.93% -35.21 % UT -9.25% -8.99% -6.46% 3.72% 4.96% -17.88% VA -18.87% -15.94% 21.60% 23.92% 35.27% 7.94% VT -45.46% 12.39% -26.94% -26.21% -66.13% 12.25% WA 15.39% 1.06% 1.43% -3.90% 11.08% -8.22% WI 10.76% 21.33% -12.30% -4.40% 4.34% -28.95% WV -7.70% -23.22% 14.42% 17.45% 28.44% 0.39% WY 10.54% 32.48% -15.42% -7.64% 17.89% -48.73% 3.2. Interpretation of the multiplicative indices The multiplicative decomposition result, in general, can be interpreted in a similar way as additive decomposition, though they reflect different assumptions on the relationship between the change being decomposed and the factors involved. Looking at the indices, we can see that the additive decomposition analysis assumes that the change of the dependent variable can be presented as the summation of the indices, each of which represents the change caused by one factor. The multiplicative decomposition, on the other hand, assumes that the growth rate of the dependent variable can be presented as the summation of the indices, each of which can be seen as the growth rate caused by one factor. 84 The implication of the multiplicative decomposition is not as obvious as the additive decomposition. The trick is to take the natural logarithm of the multiplicative results we have obtained in Table 3-1. Then each value can be interpreted as the natural growth rate, or continuously compounded growth rate (CCGR), over the period when the number of time periods for the compounded growth rate approaches positive infinity and the length of the intervals are approaching zero. The relationship between the natural growth rate and the unit emissions or the multiplicative indices can be written as V = 1 * ( 1 + ~) n, r = ln V when n ~ = , in which V represents the unit em1ss1ons or multiplicative indices as we have obtained in Table 3-1, and r represents the natural growth rate, or continuously compounded growth rate (CCGR) of the item 5 . Therefore, we can present the multiplicative data in percentage term as well, and interpret the data in Table 3-1 as the summation of multiple compounded growth rate. We choose the natural logarithm of column 3 in Table 3- 1 as the base, which can be interpret as the average growth rate of C0 2 emissions in unit electricity generations by state. Table 3-3 present the percentage terms of the growth rate relates to the results in Table 3-1. Table 3--3 Percentage ofCCGR to the Average CCGR by States Total Original Fuel Mix Unit Unit Average State Emission Emission CCGR Fii LMDI LI PI AK 39.6% -60.4% 100.0% -1.6% -9.0% 27.4% -30.5% 5 The continuously compounded interest rate (CCIR) formula is commonly written as A =Pert, where A represents the amount after year t, P represents the principle, r represents the continuously compounded interest rate over one year, and t represents the number of years. In our case, noted that rather than looking at the growth over time, we are looking at the "growth" or "change" over space, assuming t=l, and P represents the average performance level, and A represents the level by state, we should obtain the CCGR in our case defined similarly as the CCIR. 85 Total Original Fuel Mix Unit Unit Average State Emission Emission CCGR Fil LMDI LI AL AR AZ CA co CT DC DE FL GA HI IA ID IL IN KS KY LA MA MD ME MI MN MO MS MT NC ND NE NH NJ NM NV NY OH OK 4.0% 16.1% 2.6% -63.3% 65.7% -78.9% 100.9% 79.4% 15.4% 32.2% 68.3% 75.2% -236.4% 11.3% 93.6% 66.5% 93.3% 29.2% 9.8% 29.5% -64.2% -96.0% -83.9% -97.4% -163.3% -34.3% -178.9% 0.9% -20.6% -84.6% -67.8% -31.7% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% -3.0% 7.7% 3.2% -88.6% 52.9% -74.8% 544.5% 68.1% 26.2% 27.6% 130.3% 0.1% 10.0% 4.4% -80.6% 57.3% -80.5% 166.1% 63.1% 18.6% 29.1% 90.3% -24.8% -336.4% 100.0% 40.3% 52.3% 100.0% -301.7% -299.8% -88.7% 100.0% -16.3% -6.4% 100.0% 68.0% -33.5% 100.0% 40.7% -6.7% 100.0% 74.7% -70.8% 100.0% 14.4% -90.2% 100.0% 19.2% -70.5% -164.2% 100.0% 14.8% 100.0% -104.7% -4.9% 80.8% 48.3% 82.5% 12.5% 12.2% 19.3% -93.8% 57.9% -42.1% 100.0% 38.7% 44.4% 41.5% -58.5% 100.0% 16.3% 23.5% 77.9% -22.1% 100.0% 57.8% 66.9% 3.7% -96.3% 100.0% -4.1% 0.3% 44.5% -55.5% 100.0% 16.5% 26.1% 20.5% -79.5% 100.0% 13.0% 18.3% 93.7% -6.3% 100.0% 4.8% 66.8% 53.5% -46.5% 100.0% 28.8% 43.3% -71.3% -171.3% 100.0% -69.5% -74.1% -77.7% -177.7% 100.0% -82.0% -84.6% 77.7% -22.3% 100.0% 69.1% 70.3% 4.5% -95.5% 100.0% 7.9% 8.8% -65.0% -165.0% 100.0% -68.2% -72.4% 77.8% -22.2% 100.0% 66.4% 70.7% 51.5% -48.5% 100.0% 19.0% 40.1% -4.0% 2.4% -4.3% -68.0% 42.6% -73.0% 226.0% 66.4% 29.7% 24.1% 118.4% 28.5% -265.4% -28.4% 62.0% 33.8% 74.9% 13.6% 20.3% PI -1.9% 12.9% 10.7% -109.2% 63.2% -76.5% 863.0% 69.7% 22.7% 31.1% 142.3% 52.1% -337.9% -4.2% 74.0% 47.6% 74.6% 15.2% 18.0% 11.6% 18.0% -69.4% -140.0% 35.7% 41.8% 6.7% 25.8% 44.7% 70.9% -5.0% -3.1% 18.2% 14.8% 3.7% 22.3% 29.9% -20.3% 13.2% 44.4% -66.2% -72.8% -79.8% -84.3% 57.9% 80.2% 5.0% 10.8% -65.9% -70.4% 59.0% 73.7% 29.2% 8.9% 86 Total Original Fuel Mix Unit Unit Average State Emission Emission CCGR Fil LMDI LI PI OR PA RI SC SD TN TX UT VA VT WA WI WV WY -137.1% -237.1% 100.0% -129.4% -126.3% 16.5% -16.6% -27.5% -11.9% 19.9% 35.3% 76.8% 12.7% -825.2% -169.9% 59.8% 90.6% 96.1% -83.5% 100.0% -116.6% 100.0% -127.5% 100.0% -111.9% 100.0% -80.1% 100.0% -64.7% 100.0% -23.2% 100.0% 14.8% 157.3% -29.0% -40.7% -10.6% 26.0% 73.5% 14.7% 61.9% -28.4% -27.7% 6.5% 25.7% 76.2% -87.3% -925.2% -269.9% 100.0% -0.4% -3.9% 100.0% -689.7% -448.8% 100.0% -182.5% -179.1% -40.2% 100.0% -9.4% 100.0% -3.9% 100.0% 41.6% 56.3% 56.2% 42.6% 81.9% 77.8% -127.8% -130.9% 8.3% 27.0% -33.2% -50.7% -16.1% 22.8% 61.8% -3.7% -812.5% -178.3% 35.3% 56.2% 50.2% 21.4% 287.7% -24.8% -30.7% -5.1% 29.1% 85.2% 3.0% -566.9% -186.8% 48.0% 56.4% 62.2% Energy Conversion Ratio C02 Coefficient State Fil LMDI LI PI Fil LMDI LI PI AK 40.7% 39.9% 45.5% 35.8% 0.5% 8.6% 19.0% -18.0% AL -3.1% -1.6% -14.5% 8.2% 10.1% 5.5% 12.4% 7.8% AR 16.0% 16.0% 2.3% 29.6% -7.5% -10.0% -8.7% -6.4% AZ 5.8% 4.1% -6.7% 18.4% -6.5% -5.9% -12.3% -0.6% CA -17.1% -14.3% -31.3% -2.9% 42.3% 31.6% 71.4% 13.3% co 15.3% 11.2% 0.6% 30.0% -2.6% -2.8% -11.6% 6.5% CT DC DE FL GA HI IA ID IL IN KS -10.2% -181.6% -4.1% -14.3% -10.4% -42.7% 33.9% -43.5% 27.1% 9.1% 42.7% -9.4% -18.7% -1.7% 6.0% -20.5% -500.1% 136.9% -261.9% -2.0% -12.1% -7.0% -20.4% 27.8% -52.4% 21.8% 4.9% 34.8% -11.0% 2.8% 15.4% -21.8% -6.9% 3.6% -22.5% 1.8% 15.0% -69.9% -15.5% -19.3% 14.5% 53.3% 1.0% -74.2% -12.9% 108.8% 6.0% 48.1% 0.5% -8.0% 26.1% 16.5% 29.3% 56.0% -16.9% 10.9% 10.6% 1.4% -44.7% -580.5% 56.6% 18.3% 8.9% 10.1% -1.7% -4.9% 115.7% -5.7% 7.9% -16.6% 15.7% 15.2% 11.6% -4.5% 15.5% 14.5% -31.5% -7.2% -8.9% 10.9% 181.6% 35.9% -7.7% 8.7% 9.9% 23.1% -25.3% -8.5% 87 Energy Conversion Ratio C02 Coefficient State Fil LMDI LI PI Fil LMDI LI PI KY 4.4% -1.0% -1.9% 10.6% 14.2% 11.8% 7.6% 20.8% LA 25.5% 25.2% 23.6% 27.4% -10.7% -8.6% -11.9% -9.4% MA -15.2% -12.8% -23.5% -7.0% 5.9% 10.5% 10.7% 1.1% MD -14.2% -16.4% -23.2% -5.3% 28.9% 26.5% 22.6% 35.3% ME -49.2% -32.9% -81.1% -17.3% 89.7% 62.5% 160.9% 18.6% MI 8.9% 8.7% -4.8% 22.6% 10.3% 4.9% 9.6% 11.0% MN 26.7% 23.0% 8.9% 44.4% -1.5% -5.0% -7.9% 4.9% MO 29.3% 23.2% 9.9% 48.7% -9.3% -12.2% -20.4% 1.9% MS MT 24.6% 33.6% 21.6% 31.0% 16.8% 32.5% -16.8% -18.2% -18.4% -15.3% 21.6% 45.6% -5.6% -12.5% -2.8% -8.3% NC -16.6% -18.9% -27.8% -5.4% 24.2% 21.2% 12.8% 35.5% ND 49.8% 55.3% 12.0% 87.6% 39.2% -28.4% 102.6% -24.3% NE 35.7% 25.3% 14.0% 57.4% -11.0% -15.1% -27.1% 5.1% NH -19.1% -17.9% -26.6% -11.6% 17.2% 20.7% 23.7% 10.7% NJ -8.4% -8.5% -17.2% 0.3% 12.8% 15.4% 17.9% 7.6% NM 17.4% 15.5% 0.9% 33.8% -8.7% -8.1% -17.4% -0.1% NV -0.8% -2.9% -11.1% 9.6% -2.6% -1.4% -5.8% 0.6% NY -1.5% -1.6% -9.9% 6.9% 4.7% 9.1% 11.7% -2.3% OH -9.1% -9.2% -21.9% 3.6% 20.6% 16.4% 12.9% 28.4% OK 26.0% 22.0% 13.9% 38.1% 6.5% -10.6% 19.2% -6.3% OR 0.3% 0.7% -3.8% 4.4% -8.0% -11.5% -10.0% -6.1% PA -7.3% -7.2% -19.5% 4.8% 9.0% 9.0% 4.1% 13.9% RI -88.5% -39.8% -228.9% 51.9% -85.5% -38.8% -220.0% 49.1% SC -19.3% -19.2% -28.6% -10.0% 20.8% 20.1% 17.1% 24.5% SD 45.1% 34.1% 28.3% 61.9% -16.3% -18.3% -27.1% -5.4% TN 8.2% -0.7% -4.6% 21.0% 22.3% 14.2% 10.5% 34.1% TX UT 26.5% -3.0% 25.8% 21.4% 31.6% -17.2% -16.2% -20.0% -14.4% -5.1% -18.3% 12.3% 6.2% 5.7% -4.6% 17.1% VA -19.2% -17.7% -27.4% -11.0% 32.2% 34.3% 30.9% 33.6% VT -16.1% -171.1% -146.9% 114.8% -119.4% -205.2% -244.5% 5.6% WA WI WV WY 17.9% 18.5% 13.7% 22.1% -5.2% 19.8% 20.6% 5.8% 33.8% -1.6% -0.9% -11.6% -16.2% 14.3% 35.3% 25.4% 23.3% -0.8% 51.6% 14.4% -9.3% -3.4% 20.2% -5.1% -0.8% -9.7% -3.6% 0.5% 26.4% 44.1% 17.2% 11.7% 88 Take California as the example. The results presented in Table 3-3 can be interpreted as: the continuously compounded growth rate (CCGR) of the C0 2 emissions in unit electricity generation in California is 63.3% less than the average CCGR of the C0 2 emissions across the states in the United States. The 63.3% can be considered the summation of the effect on the growth rate caused by three factors: fuel mix, energy conversion coefficient, and C0 2 emission coefficient. The fuel mix contributes to 86.6% or 80.6% less than the average CCGR; the energy conversion coefficient contributes to 17.1% or 14.3% less; and the C0 2 emission coefficient contributes to 42.34% or 31.56%, according to the multiplicative EKS/Shapley numbers based on bilateral FII and LMDI, respectively. We can also identify the items that are strictly higher or lower than the average with the bound established by the natural logarithm of the geometric mean of the adjusted Laspeyres and Paasche indices. There are 30 states plus the District of Columbia with all positive percentages in fuel mix, meaning that, for these areas, fuel mix contributes to a more than average growth rate of C0 2 emissions in unit electricity generation. There are 13 states with all negative percentages in fuel mix, meaning that fuel mix in the 13 states contributes to a less than average growth rate of C0 2 emissions in unit electricity generation. The same analysis can be done for the percentages of energy conversion coefficient. There are 19 states with all positive percentages in Table 3-3, indicating their more than average C0 2 growth rate related to energy conversion coefficient, and 12 states with all negative percentages, indicating their less than average C0 2 growth rate related to energy conversion coefficient. For C0 2 emission coefficient, there are 21 states with 89 all positive percentages, and 12 states with all negative percentages, indicating their more and less than average growth rate linked to C0 2 emission coefficient, respectively. Table 3-4 summarized all the states in which each of the factors are considered to be the drivers that contribute strictly more or less than average to the C0 2 emissions in unit electricity generation according to the indices calculated in Table 3-1. Table 3-4 States with Factors being Positive or Negative Drivers Energy Conversion Fuel Mix Coefficient C0 2 Coefficient Additive Multiplicative Additive Multiplicative Additive Multiplicative + + + + + + co AL AR CA AK AL AK CA MD AR AL AR DC AR co CT AR CA AR CT NC AZ CA AZ DE AZ DC ID co CT co FL VA co CT HI GA CA DE IL IA DE IA HI WV DC DE KS HI CT FL ME IL FL IL ID IL GA LA IA ID GA NH KS GA KS MA KS ID MS IN IL HI NJ LA HI LA MD LA IN MT KS LA IA NY MI ID MN ME MN KY NM KY ME IN OR MN MA MO NC MO MA OR MI MS KS SC MO MD MS NH MS MD SD MN NH KY SD MS ME MT SC NE ME TX MO NJ LA VT MT NC ND VA NM MI WA NE NY MA WA ND NH NE OR NC NM OR MD NE NJ NM RI NH OH SC MI NM NV OK SD NJ RI SD MN OK OH SD TX OH TX TN MO SD PA TX PA UT VA MT TX SC WA SC WI VT NC WA TN WI TN WV WA NE WI UT VA WY NM WY VA WV NV WV OH OK 90 Fuel Mix Additive Multiplicative + + PA RI TX UT WI WV WY Energy Conversion Coefficient Additive Multiplicative + + 3 .3. The outliers and differences between index numbers C0 2 Coefficient Additive Multiplicative + + We see that a few states have extremely large or small indexes. Examples include multiplicative FII and PI of fuel mix for DC and multiplicative FII and PI of fuel mix for VT as indicated in Table 3-1, and additive indexes for DC and ID as indicated in Table 3-2. In order to get a better understanding on what the index number captures, we went back to the dataset to see how the energy profile of the outlier states differ from the rest. Looking at the energy profile of electricity generation in DC in 2009, we see that unlike the other states, DC's electricity was solely produced by petroleum, as indicated in EIA's statistics, which gave it a disadvantaged fuel mix compared to other states. The disadvantage was captured in both the multiplicative and additive fuel mix indexes for DC. On the other hand, as we see that DC's C0 2 emissions from unit electricity generation was only about twice the average level, we can expect that DC was doing much better than the average in energy conversion efficiency and fuel C0 2 coefficient. It 91 was the case and was captured in the energy convers10n efficiency index and C0 2 coefficient index, as expected. Another outlier in multiplicative decomposition is VT. The fuel mix, fuel electricity ratio, and C0 2 emission coefficient indexes are all significantly lower than the indexes for other states. One reason is that the C0 2 emissions from unit electricity generation in VT were much lower than the rest of the states in 2009. Also, looking at the energy profile in VT's electricity generation, we can see that the majority of the electricity in VT was produced by nuclear (>70%) and conventional hydro (20% ), both are clean energies with little environmental impacts. Also, the fuel C0 2 emission coefficients of the petroleum and natural gas were moderately better in VT than the others, and VT had no coal-fired electricity. Additive decomposition also indicated several outliers. Looking at ID's energy profile, we can see that about 80% of the electricity in ID was conventional hydroelectricity and about 12% was produced by natural gas. The fuel mix index indicates that ID's fuel mix was significantly better than the average. The area that ID didn't perform well is the fuel C0 2 coefficient. It is because that the coal C0 2 coefficient in ID was much worse than the average. Even though the percentage of coal-fired electricity in ID was only 0.63%, the fuel C0 2 emission coefficient index still captured its impact. In Table 3-1 and Table 3-2, we see large variations across indexes obtained by different approaches for several states. For the Laspeyres index and Paasche index, the explanation of the differences is quite intuitive. The source of their differences is the selection of the 92 value for all other independent variables, one chooses the value in the base scenario and the other chooses the value in the compare scenario. For the two well-behaved index numbers, FII and VI/LMDI, intuitively, we can say that FII splits the identity based on the fairness principle while VI/LMDI splits the identity by transforming the change into a log-scale. To better explain the difference between the two, we write both of them in the form of discrete Divisia approximation as in Table 2-1 for the case. To simplify the notation, we write equation (3-1) as v = I V; = If; * P; * C; i i where, V;: C0 2 in unit electricity generation by fuel type i; f;: Percentage of electricity generated by fuel type i; p;: Fuel electricity conversion ratio of fuel type i. c;: C0 2 coefficient of fuel type i; Without losing the generality, we look at the index of fuel mix only. The fuel mix index in discrete Divisia form can be written as In F = If= 1 s; *In;,:, i = 1, ... , N, and the weighing scheme in VI/LMDI and FII are: L(f,1p1c1 f,opoco) ·(VI/LMDI) = ; ; ; , ; ; ; s, ("" f,1 1 1 "\' f,O 0 D) L ~i i Pi Ci 1~i i Pi Ci ·(Fl/)=-* ;P;C;, ;P;C; ;P;C;, ;P;C; 2 [ L(f,1 1 1 f,o 1 1) L(f,1 o o f,o o o) l s, 3 . 1 1 1 . 0 1 1 + . 1 0 0 . 0 0 0 L(I,f; P;C;,Lif; P;c;) L(I,f; P;C;,L,f; P;c;) 1 [ L(f, 1 o 1 f,o o 1) L(f,1 o 1 f,o o 1) l i Pi Ci, i Pi Ci i Pi Ci, i Pi Ci +3* . 1 0 1 . 0 0 1 + . 1 0 1 . 0 0 1 L(I,f; P; C; ,I, f; P; C;) L(I,f; P; C; ,I,f; P; C;) 93 y-x where L(x,y) = 1 1 for x =/= y; and L(x,y) = x for x = y ny- nx It is the differences in the weighting scheme or aggregation scheme that caused the variations in the index numbers. Intuitively, the FII considered a series of cases in which the values of base case and compare case are free to choose, while VI/LMDI only considered the cases that actually happens, which are the base case and the compare case, in the computation. 4. Policy implications The above results can help policy makers and planners identify the areas that can lead to C0 2 emission reductions. The indices showing larger than average emissions identified the areas which policy makers and planners should focus on. For example, Colorado is identified by both of the additive and multiplicative decompositions to have a fuel mix that contributed to larger than average C0 2 emissions in unit electricity generation. If we consider that an average fuel mix is obtainable, Colorado should really focus on improving its fuel mix to reduce C0 2 emissions. Please note that we calculated the average level of C0 2 emission in unit electricity generation in our study, which is shown in column 4 in Table 3-1, but we did not calculate the average levels of C0 2 emissions change in unit electricity generation attributed to each of the pre-defined factors. Based on the definition of index numbers, we can consider the EKS/Shapley number for each of the pre-defined factors as the ratio or difference between the C0 2 emissions change in unit electricity generation attributed to the factor in question in the state and that for all 94 states. It is an indirect way of obtaining the ratio and difference to the averages. Instead, if we were to start with the percentages of electricity by fuel types by states, the average level of fuel mix would be difficult to obtain, which makes the comparison to the means difficult. For example, we may have two sets of fuel mix for comparison: one includes 50% of coal, 30% of natural gas, and 20% of renewables, and the other includes 60% of coal, 10% of natural gas, and 30% of renewables. Adding the numbers up will always give us one hundred percent and as coal is more C0 2 intensive than natural gas and renewables are less, when their percentages all go up, it is difficult to say whether one set of fuel mix contribute to more or less of the C0 2 emissions than the other set without ID A. IDA is a valuable tool to reveal how the drivers contribute to a change in a quantitative manner. In our case, we obtained the direction and magnitude of the contribution to the change of C0 2 emissions in unit electricity generation of three drivers: fuel mix, fuel electricity conversion efficiency, and C0 2 emission factors. IDA alone cannot automatically generate policy recommendations but it provides data for further policy analysis. For example, we can combine the data on fuel mix contributed C0 2 emissions in electricity generation with RPS (Renewable Portfolio Standard) data to yield insights on whether RPS has contributed to the C0 2 emission changes by improving fuel mix. We can also combine the data of C0 2 emissions attributed to fuel conversion efficiency with financial and performance data on energy efficiency policies to see whether the two are directly related. 95 A complete framework of using IDA for policy analysis is not yet developed. Siegel et al. (1995) presented a framework based on a social accounting matrix to link SDA with the sources of growth and then linked the sources of growth to development policies. His framework provided an ex ante perspective of using SDA to assist policy analysis (Rose & Casler, 1996). A similar strategy can be used to develop a framework of IDA for policy analysis. This will be a worthwile topic for future research. To start, we provide a few policy examples that relate to the three factors in our IDA model in Table 3-5. We selected them from Rose & Wei (2011) and Nelson et al. (2014), which are two comprehansive studies of climate action plans on their macroeconomic impacts, institutional structures, and cost of implementation. They can be a good selection of policies for states to remedy their shortcomings as identified in Table 3-4 and can also serve as the starting point for future policy analysis. Table 3-5 Policies and Factors Factor Fuel Mix Electricity Conversion Factor C02 Emission Factor Policy Examples Renewable Portfolio Standard Nuclear Power Expand low-GHG fuels Power plant efficiency improvements CHP systems Develop low-GHG fuels 2 Landfill gas-to-energy 3 C02 capture and storage Source: Adapted form Rose & Wei (2011); Nelson et al. (2014). 96 We will also point out several technical concerns of using IDA for policy analysis. The first is the disagreement between the additive decomposition and multiplicative decomposition. We are not able to suggest which one of them is superior. We can only say that they postulate how the effects of the pre-defined factors would be added up to the change of dependent variables differently. The additive decomposition assumes that the summation of the change caused by the pre-defined factors would be equal to the change of dependent variables; and the multiplicative decomposition assumes that the summation of the continuously compounded growth rate caused by the pre-defined factors are equal to the continuously compounded growth rate of the dependent variables. If we have no better reason to reject one approach over another, a conservative approach is to keep both in mind even though they yield different results. Another critical consideration is the accuracy of the results. In order to answer the question, we developed upper and lower bounds for the multilateral EKS/Shapley numbers that used Fisher ideal indices as the bilateral building block. In general, as Laspeyres and Paasche indices are bounds for FII, we adjusted the Laspeyres and Paasche indices to make them suit the multi-factor cases and use their geometric and arithmetic averages across the states to bind the multilateral EKS/Shapley numbers. Similar to the two-factor bilateral case, we can see that when a factor in one state differs greatly from the others, the range set by the upper and lower bound becomes larger. For example, the fuel mix in DC differs greatly from the rest of the states, and the range indicated by the upper and lower bounds is very large. Note that FII is a "mix" of Laspeyres index and Paasche index, in which the two are mixed at equal weights, the range indicated by the 97 adjusted Laspeyres index and the adjusted Paasche index can also be seen as the sensitivity range of FII when certain unequal weights are allowed. When the range set by the upper and lower bound is small, it may indicate that, even ifthe unequal weights may suit the practical situation better, using FII in IDA still will give us fairly good result. While a state has different status relates to one factor compared to the others, the range indicated by the adjusted Laspeyres index and the adjusted Paasche index becomes large. At present, there is no index number that is similar to FII but can allow unequal weights, but the upper and lower bounds may be able to indicate the range of values for such unequal-weighted index numbers. Also, the bounds we developed do not bound Vartia/LMDI index. 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Drivers of Green Job Change in the United States: A Temporal Two-Stage IDA "Green Jobs" is an often used term in the popular press and government reports, especially since the Great Recession began in late 2007 and the high unemployment rate became a major concern of policy makers. Whether the investment in environment- related areas through renewables and energy efficiency can generate more jobs and promote economic growth is a hotly debated issue in the United States. Proponents state that such investment can not only help environment and increase the U.S. energy independence, but also promote green jobs to absorb the excess labor due to the recessed economy. Opponents, on the other hand, believe that investing in so-called "green industry" can only have a limited or even a negative impact on employment and that such investment may not be the best way to cure unemployment. To clarify the issue, it would be valuable to analyze what constitute green jobs, determine the driving forces of green jobs change, and compare green jobs with similar non-green jobs. In this chapter, we will use IDA with the newly generated data on green jobs over time published by the U.S. Bureau of Labor Statistics (BLS) to conduct the analysis. Several challenges remain in the analysis of green jobs and we will try to tackle some of them. Firstly, "green jobs" is a very loose term. Though it is often used, there is no widely accepted definition of the term. Secondly, the ambiguities in definition lead to troubles in green job measurement and data collection, and, at this point, only very limited data on green jobs are available. Thirdly, employment changes usually will be affected by many factors, such as changes in the total economic output, economic 101 structure, labor productivity, and so on. The amount of green jobs changes will also be affected by such factors, and attributing all the green job change to the economy becoming greener can be misleading. We will discuss such challenges one by one in the chapter. In this chapter, we will firstly discuss the definitions of green jobs, its measurements, and implications for policy evaluation and then use a two-stage Index Decomposition Analysis (IDA) to analyze the drivers of green jobs over time in the United States. The rationale is to clarify what green job means first, and then analyze what drivers its change and whether the change is what we expected. However, we can only perform the analysis subject to the available data. It is the first time an IDA is applied in green jobs analysis and the first time a two-stage IDA is applied in the literature. 1. Definition of Green Job 1.1. Vacancy vs. Employment To define green jobs, it is valuable to examine the definition of jobs and employment and where the "green" comes into play. "Job" is usually a loose term as well. It can refer to vacancies created by new establishments that are to be filled or vacancies that are filled by workers. To differentiate the two, the labor market literatures often use vacancies and employment to represent the two situations (see, e.g. Blanchard & Diamond, 1989, Davis & Haltiwanger, 1992). Vacancy usually refers to created but unfilled positions via the expansion of existing establishments, the creation of new establishments, or the separation of workers and existing positions. When a vacancy becomes available, the 102 company can choose to freeze it, cancel it, or post it onto labor market to find potential matches. Employment happens when an unemployed person fills a vacancy. The process of generating green jobs should not be different from the generation of other jobs: a vacancy should be created, posted, and matched to yield a valid employment opportunity. To be green, the position should have certain functionality relates to greener environment and/or activities that lead to green products and services, and/or contributes to the greening process. A job vacancy can be classified to be green as long as the designed functionality or potential activities can be termed green. But a green vacancy will not yield any potential environmental and/or ecological benefits until a worker is hired, even though adding vacancies will likely have positive implications in the labor market and for policy makers. Green employment, defined as a green vacancy being filled, can deliver both environmental and/or ecological benefits, as well as labor market benefits. Due to the different implications to the environment and the labor market of green vacancies and green employments, we would suggest to differentiate the two, especially in the analysis of environmental policy impacts to the labor market and vice versa. For example, the investment in environmental friendly industries and establishments may generate green vacancies, but those vacancies may not become employment immediately if there are obstacles in the matching process and/or the desired skills are in a temporary shortage. In such cases, using green employment as a measure of how many positions are 103 created by the investment m green industries and by environmental policies can be misleading. Most of the green job definitions either do not differentiate the two or simply focus on one type of definition. And most of the data on green jobs cannot generate a full picture of the dynamics of labor market. The best available data on green jobs are the green goods and services survey by the Bureau of Labor Statistics (BLS), which focuses on green employment only. Also, as the Green Goods and Services (GGS) program is eliminated due to the budget cuts in 2013, we only have two years of data on green employment. That said, it is valuable to point out the differences of green vacancies and green employment, and the possible short-comings of the analysis using the limited data on green employment. We will come back to the point later in the chapter. 1.2. Meaning of Green 1.2.1. Scope Next, we discuss what constitutes of being "green". "Green" in this context, rather than having a scientific purpose, is more like an idea that has been implanted in people's mind to represent certain expectations and concerns. It may be valuable to explore where the idea of green came from. The demands of becoming green correspond to a half-century- long environmental movement that reflects the deep concern over the relationship of human-beings and nature. The movement was joined with many streams of beliefs, including the conservation of nature, the defense of own space, deep ecology, saving the planet, and green politics, using the terms in Castells (2004). The conservation of nature marked the origins of the grassroots environmental movement started in the early 104 twentieth century in the United States (Castells, 2004). Organizations such as the Sierra Club and the Audubon Society identify themselves as nature lovers to fight against the uncontrolled development and unresponsive bureaucracies to preserve the wildness and the planet (Castells, 2004). Local communities also were quickly mobilized under the notion of"Not in my Back Yard" to protect their space from the intrusion of undesirable uses and pollutants (Castells, 2004). The "Not in my Back Yard" movement can be seen as the response of the conflict between residents' right to quality of life and businesses' interest. While it is believed that trade-offs can be made between the two parties to resolve the conflict, the movement also reflects the concerns over the maturity of institutions and equity involving low-income and/or minorities communities. The concern over the environment and that we only have one planet also triggered global environmental protection actions. The United Nations Environment Program (UNEP) was created in 1972 after the Stockholm UN conference on the human development, representing a tangible institutional outcome of the environmental movements (McCormick, 1991). Most of the international organizations, such as the World Bank and OECD, also developed environmental related policies by 1980 (McCormick, 1991). It also reflects that some of the environmental issues can go beyond certain geographical and/or jurisdictional boundaries and will require large-scale cooperation. If we consider the abovementioned three approaches to protect the environment concern about trade-off between development and nature, the deep-ecology movement reflects the idea of protecting the environment for its own sake. It claims that non-human life 105 represents values that are independent of human purposes. Such view not only expanded the scope of the environmental movement toward ecology but also acknowledged that the utilitarian perspective toward environment protection is limited. In addition, as a science-based movement, the environmental movement connects closely with science and technology developments. The scope of green also evolved over time to contain the contemporary environmental and ecological issues associated with the science and technology development, for instance, climate change, the use of nuclear energy, and so on. Bramwell (1994) has described the environmental movement as "the revolt of science against science that occurred towards the end of the 19th century in Europe and North America." The development of science and technology has freed people from labor and brought the standards of living to a new level, while the excessive and uncontrolled development posed challenges to the environment at the same time. Scientific methods and approaches are used to reveal such damages and to propose environmental friendly alternatives. Most of the major environmental groups in the world have their own science and technology capabilities to analyze the possible impacts and solutions for environmental deterioration and to distribute information to the public. The International Panel of Climate Change (IPCC) is a good example of the scientific bodies organized for environmental protection. It was established in 1988 by UNEP and the World Meteorological Organization (WMO) to serve as the reviewers and distributors of recent scientific, technological, and socio-economic information regarding climate change. 106 In sum, we can see that the scope of green, inherited from the half-century long environmental movement, constitutes the conservation of nature, pollution reduction, justice towards the poor and minorities, protection of the ecological system, and has evolved over time to contain the contemporary environmental and ecological issues revealed and/or caused by the science and technology development. The scope of green also covers both the instrumental perspective towards the environment and ecology, which mostly deals with the trade-off between development and environment protection, and the deep-ecology perspective, which worships the value of nature that is independent of human use. However, the former perspective of green is more practical and is often adopted in implementation. 1.2.2. The means of becoming green Now we discuss being green given the parameters of current social and economic conditions and the trade-off with development. The ultimate or ideal status of being green can represent a state in which environmental and ecological stocks are not being depleted. Our current strategies include the reduction of activities that are proven to have negative effects on environment, development of measures to restore the environmental resources, and measures to constrain the anthropogenic environmental damage to the communities. To be more specific, such approaches include but are not limited to the following: • Development of energy efficiency measures • Development and use of renewable energies 107 • Conservation of natural resources, such as water, forest, land, and so on • Recycling and/or reduction of wastes • Proper treatment and reduction of pollutants • Restore and preserve of ecosystems and biodiversity • Adjustment of economic structures to use less energy, produce less waste, while keeping the same level of output, growth rate, and/or the standard of living We can see in the following section that the some of the definitions of green jobs proposed by government agencies define the green jobs by the functionality of the position and that such functionalities are related to the means of becoming green mentioned above. It is not right or wrong to define green jobs based on the scope of being green or the means of being green. The latter is often used or at least applied in green job statistics as the level of being green, and how it affects employment or vice versa is hard to measure directly. With the science and technology development, the means of becoming green may not be valid in the future. Definition of green, especially the one based on the means of getting green, and the measures of green based on it, should then be updated regularly to avoid misunderstanding. In addition, the definition of green based on means is vulnerable to the influences of other factors. For example, say, we can define the green jobs as the employment in directly delivering energy efficient end product and services, and ideally, we will evaluate the measure of green jobs while holding all other things unchanged. Such ceteris paribus condition is not always easy to satisfy. In reality, the investment in energy efficient product and services can lead to the increase, decrease, or no change in green employment in the same industry and/or in economy wide. It is 108 uncertain, as the other factors, for instance, the economic structure and total economic output, can affect green employment as well. On the other hand, if we observe green employment growth, we cannot be sure that the economy is turning green as well. The green employment can increase due to economic output increases even if the economy is not becoming greener. In the second part of the chapter, we will use index decomposition analysis to reveal how green jobs are affected by different drivers. In addition, in terms of measuring green jobs, it is necessary to identify whether both the full-time and part-time positions are/should be counted. If we consider that green jobs should be long-lasting, then only the full-time positions should be counted. However, part-time positions can provide benefits such as financial assistance and on-the-job trainings, and thus should be counted by the statistics when financial assistance to the family and training are concerned as well as job security. Secondly, the boundary of the job function does not always comply with the elements in being green and/or means of becoming green. For example, a job can contributes to both renewable energy, and ordinary pollution and greenhouse gas emission reduction. When two surveys are done to account for the green jobs in renewable energy and pollution reduction, respectively, one job can be recorded twice when the two survey results are added up for the total numbers of green jobs. These are some of the challenges in green job measurement that will surely affect data quality. In selecting the dataset on green jobs in this study, we will select the one that is less adversely affected by the issues mentioned above. 109 1.3. Compare major definitions and measurements of green jobs Many definitions of "Green Jobs" are proposed by various government agencies. The Green Jobs Act of 2007 in the United States authorizes up to $125 million in funding for labor training programs at the national and labor level for job growth in green industries. The programs are administrated by the Department of Labor (DOL). Bureau of Labor Statistics (BLS) under DOL provides the following definitions of green job for data collection purposes (BLS, 2010). Two types of jobs are considered green job: a) Jobs in businesses that produce goods or provide services that benefit the environment or conserve natural resources; b) Jobs in which workers' duties involve making their establishment's production processes more environmentally friendly or use fewer natural resources. The two types of jobs are not mutually exclusive. BLS acknowledges that double-counting can occur when the two definitions are used to count green jobs in practice. And in the green job statistics, BLS specified the following five groups to be counted that a green job can fall into. They are: 1) energy from renewable sources; 2) energy efficiency; 3) pollution reduction and removal, greenhouse gas reduction, and recycling and reuse; 4) natural resources conservation; and 5) environmental compliance, education and training, and public awareness. Following the BLS definition, U.S. Environmental Protection Agency (EPA) classifies clean energy jobs as a subset of green jobs that relates to: energy efficiency, renewable energy, and clean combined heat and power (CHP) (CA Employment Development Department, 2011). Following its definition of green jobs, BLS adopts two approaches to count them in its data collection activities. For counting green jobs relating to the end-product, BLS 110 prepares a list of 6-digit North American Industry Classification System (NAICS) industries and classifies the ones with green goods and services. This approach is used in Green goods and services (GGS) survey that is conducted by the BLS Quarterly Census of Employment and Wages (QCEW) program. 333 industries are selected out of the 1,192 industries under the detailed NAICS system, and only the employment directly associated with the production of green goods and services are counted (BLS, 2010). When measuring the green jobs using the process approach, green jobs are counted when the workers on job spend more than half of their time involved in green technologies and practices, regardless of the end product and service. While the first approach may only involve the accounting of jobs in several industries, the second approach can involve the accounting of jobs of all industries except private households. In addition, we can see that BLS 's first definition of green job follows an end-product approach, meaning that whether a job can be counted as green job depends on its direct end product. No matter what the occupation is, as long as the end products and services are classified as green, the position will be counted as a green job. The second definition follows a process approach, and the jobs that can make the practices more environmental friendly are counted as green jobs. Jobs belonging to such a category include: research and development in renewable energy, energy conservation, pollution control, and natural resource conservation. Following the second definition, occupations may have certain impacts on whether the jobs will be counted as green or not. 111 The states in the United States also developed their own definition of green jobs. A list of working definisions of green industries and green jobs can be found in various papers and reports (e.g. Furchtgott-Roth ,2012; CA Employment Development Department, 2011). Several states, such as Arizona, Idaho, Maryland, and others simply adopted the BLS definision, while states such as Maryland, Virginia, Louisiana, Pennsylvania, Oregon, New Jersey, California and others have developed their own green job definision (Furchtgott-Roth, 2012). That said, the state's definision of green jobs may not differ with BLS 's greatly. Most of the definisions covers the categories identified by BLS - renewable energy, energy efficiency, pollution reduction and management, natural resources conservation, and environmental compliance and trainings. Other definitions of green jobs are also proposed and used in other countries and by international organizations. In a report by OECD, green job was defined as "jobs that contribute to protecting the environment and reducing the harmful effects human activity has on it (mitigation), or to helping to better cope with current climate change conditions (adaptation)" (OECD/Martinez-Fernandez, et al, 2010; p. 21). The report, at the same time, acknowledges that green job is a fuzzy word and the "green" is a matter of degree that can change over time because of innovation and technology development. Several other examples of definition include: UNEP: Green jobs are defined as work in agricultural, manufacturing, research and development (R&D), administrative, and service activities that contribute substantially to preserving or restoring environmental quality. Specifically, but not exclusively, this includes jobs that help to protect ecosystems and biodiversity; reduce energy, materials, and water consumption through high-efficiency strategies; de carbonize the economy; and minimize or altogether avoid generation of all forms of 112 waste and pollution. But green jobs, as we argue below, also need to be good jobs that meet longstanding demands and goals of the labor movement, i.e., adequate wages, safe working conditions, and worker rights, including the right to organize labor unions (UNEP, 2008a; p. 3). US White House Task Force on the Middle Class: Green jobs involve some tasks associated with improving the environment, including reducing carbon emissions and creating and/or using energy more efficiently; they provide a sustainable family wage, health and retirement benefits, and decent working conditions; and they should be available to diverse workers from across the spectrum of race, gender and ethnicity (Middle Class Task Force, 2009; p. 5). In the aforementioned OECD report on green jobs, the consequences of the activities on job are emphasized. The scope of green jobs thus is expanded to cover those jobs that can affect the "demand" side of the economy and those can help to adapt to the consequences of"not green". We can see that there are several key elements regarding the definition of green jobs based on the above analysis and the definitions proposed and used by government agencies. Such elements include the differentiation of vacancies and employment, the elements m the scope of green, including the conservation of nature, the pollution reduction, the justice towards the low-income and minorities, the protection of the ecological system, and the considerations of science and technology development overtime, and/or the specifying of means of being green, and whether the scope of being green includes adaptation to the environment. We summarize the major elements in green job definitions in Table 4-1. 113 Table 4--1 Green Job Definitions Comparison White House BLS End- Task Product Force on and BLS the Services Process Middle Approach Approach OECD UNEP Class Scope of Green Nature conservation y y y y y Pollution reduction y y y y y Balanced development N N N N N Protect the ecological system N N y y N Change with technology N N y N N Disaster mitigation and adaptation N N Y* N N Low-income and minorities N N N N N Carbon emission reduction N N y y y Means of Being Green Promote energy efficiency y y NIA y y Renewable energy development y y NIA N N Control pollution and waste y y NIA y y Education and training y y NIA N N Ecosystems Protection N N NIA y N Economic structure change N N NIA N N Industries specific y N NIA y N Characteristics of jobs Specify vacancies and employment N N N N N Only count full-time positions N N NIA NIA NIA Decent wage jobs? NIA NIA NIA y y Equality in employment process NIA NIA NIA y y Measurement available? y y N N N Prone to double counting N y NIA NIA NIA *Climate change related only 1.4. The definition and measure of green job used in this study As we need to use green job statistics to conduct further analysis, we use the following principles to select green job definitions and measures in our study. Firstly, the green job 114 definition should cover most of the elements mentioned in the scope of green and/or the means of being green in Table 4-1. Secondly, a valid measurement methodology should be developed and/or the statistics on green job as defined should be available. And thirdly, the methodology should be less prone to double-counting, and more consistent with the other economic statistics provided by other government agencies. We found that the best available dataset on green job statistics is the Green Goods and Services Survey (GGS) data that was published by BLS. The survey was done following the BLS green job definition of the end-product and services approach. Its advantage is that the statistical methods provide a valid basis of green job accounting. It complies with the employment and economic statistics of other government agencies, such as the Bureau of Economic Analysis, and is less prone to double counting compared to the BLS green job definition of the process approach. The short-coming of using the above dataset is that it focuses on employment only, while the vacancies can also have strong labor market implications. Also, the dataset does not contain occupation related data so we won't know how or whether the green job change is affected by occupation change. We will hold the occupation issue apart for a while and discuss it at the very end of the chapter. 115 2. Decomposition analysis for employment change in the United States 2.1. The Index Decomposition Analysis model Index decomposition analysis (IDA) can reveal the contributions of pre-defined factors to a certain change. It usually starts with an identity that expresses the relationship between the set of pre-defined factors and the group level indicator whose changes are of interest. We select four factors that can affect green-employment change. They are 1) the share of green job within an industry, 2) structure of the economy, 3) labor productivity, and 4) total economic output. As total employment is the summation of green-employment and non-green-employment, we can start with the identity with total employment and further decompose it for green-employment and non-green employment, or start with the green- employment and non-green employment independently and aggregate the indices together for total employment, as long as the index number formulas we use are consistent in aggregation. For the total employment, green-employment, and non-green employment in K industries in the United States, we start with the identity in equation ( 4- 1). K t t t , '\' Emp; Emp; VA; , Emp = L Emp' * VA' *VA'* VA i=l [ [ Kt t t Kt t t L Emp 9 .; Emp; VA; , L Empng.i Emp; VA; , = *--*--*VA+ *--*--*VA Emp' VA' VA' Emp' VA' VA' ' i=l [ [ i=l [ [ i = l, ... ,K (4-1) where • Emp': Total employment in the United States in year t • Em pf: Employment by industry in year t 116 • Emp~,i: Green employment by industry in year t • Emp~ 9 ,;: Non-green employment by industry in year t • V Af: Value-added by industry in year t • VA : Value-added of the whole economy, used as the measure of economic • volume t EmPgi Empf : Percentage of green employment in the total employment by industry in yeart Emp~ i • ~· : Percentage of non-green employment in the total employment by industry Em pi in year t The above two should add up to one. Empt • --,': Employment per value added, used in the analysis as the proxy of labor VAi productivity by industry in year t t • ~ ~~: Share of value added by industry, used as the measure of economic structure in yeart We can use both of the additive decomposition and the multiplicative decomposition model to perform the analysis. As the Vartia/LMDI index is the only index that is consistent in aggregation and decomposes perfectly, we use the Vartia index to perform the decomposition 6 . It is also worth noting that the additive counterpart ofVartia/LMDI 6 Vartia proposed Vartia index (as Vartia Index I) in his 1976 paper in which he proposed the term "consistent in aggregation" and proved that the Tbrnqvist-Theil index number is not consistent in aggregation (Vartia, 1976). Consistent in aggregation requires the index numbers to be as same in the situation when we apply the index number formula on a group of items as in the situation when we apply the index number formula on the subset of the group of items and then use the same index number formula 117 index is not consistent in aggregation, so we will use the multiplicative decomposition only in this section. We will discuss the consistency in aggregation later in this chapter. The decomposition of equation ( 4-1) can be written as: Emp 1 · E 1 VA 1 Emp 1 · E 1 VA 1 "<'K g.i* mp;* __ ;*VAl+"<'K ng.i* mp;* __ ;*VAl Emp 1 Lr=l Emp' VA' VA' Lr=l Emp' VA' VA' ln--=ln i i i i Emp° K Emp 9 °.; Emp 0 VA° K Emp~ 9 .; Emp 0 VA 0 "' * __ , * __ , * VA 0 + "' * __ , * __ , * VA 0 Li=l Emp' VA' VA' Li=l Emp' VA' VA' [ [ [ [ = lnGEmp + lnlEmp + lnSEmp +In VEmp = w 19 * lnGEmpg + w 29 * lnlEmpg + w 39 * lnSEmpg + w 49 *In VEmpg +Wing * lnGEmPng + Wzng * lnlEmPng + W3ng * lnSEmPng + W4ng * ln VEmPng, i = 1, ... ,K (4-2) where • GEmp, GEmp 9 , GEmPng: Index for the share of the specific type (green, non-green) of employment in the total employment within industries, respectively; • LEmp, LEmp 9 , LEmPng: Labor productivity index for the total employment, green employment, and non-green employment, respectively; • SEmp, SEmp 9 ,SEmpn 9 : Economic structure index for the total employment, green employment, and non-green employment, respectively; • VEmp, VEmPg' VEmPng: Economic volume index for the total employment, green employment, and non-green employment, respectively; • w 1 ,j E {1g,1ng,2g,2ng,3g,3ng,4g,4ng}: Weight to aggregate indices for green employment and non-green employment to the corresponding indices for to aggregate the subset index numbers to yield the group index number. LMDI is the multi-factor version of Vartia Index applied in energy and emission decomposition studies (see, e.g. Ang, 1997). Vartia/LMDI index is consistent in aggregation and decomposes perfectly, while Fisher Ideal Index, Shapley/Sun Index, and Tornqvist-Theil Index are not consistent in aggregation (see, e.g. Ang, 2001; Ang, 2004). 118 total employment. For Vartia/LMDI indices, w 19 = w 29 = w 39 = w 49 = L(EmpJ, Emp2)/L(Emp1, Emp 0 ) and W1ng = Wzng = W3ng = W4ng = Also, the indices of employment share, labor productivity, economic structure, and economic volume for the total employment, green employment, and non-green employment can be calculated directly by using Vartia/LMDI index formulas below. Emp} EmpJ = n lE(G,L,S,V) i = 1, ... , K;j E {total,g, ng}; l E {G, L,S, V} Emp 1 · Empf total V A~total l,) XG· = Empf total XL = VA~ total ,xf1 = VA 1 v VA 1 Emp 0 . Empf total V Af total , xi,J =-- l,) l,) VA 0 l,) Empf total V Af total VA 0 l a, _ L(Empt 1 ,Emp~i) _ wJ - ( 1 1) ,L(a,b)- a-b L Emp 1 ,Emp 1 lna-lnb' when a= b (4-3) when a* b In which the definition of variables are the same as in equation ( 4-1) and ( 4-2) 2.2. Data Sources and Refinements We adopted the first definition from BLS in our research, which defines green job by the end-product by industry. Therefore, in our research, green jobs are defined as the jobs that relate to the product or services that benefit the environment and/or conserve natural resources, including the related research and development, and installation and maintenance services. Data relating to the green job, as defined above, are collected 119 through the BLS's Green Goods and Services (GGS) survey. In the survey, jobs fall into one or more of the following categories are counted: energy generated from renewables; products and services that improve energy efficiency; products and services that reduce or eliminate pollutants (including greenhouse gases) and waste materials or waste water; products and services that conserve natural resources, including forestry, land, soil, water, wildlife, and storm water management. The jobs relates to the compliance of environmental regulation, environmental education and training are also included in the scope of green jobs. Based on the Green Goods and Services Industry List published by BLS in May, 2012, of the 1083 industries classified by six-digit NAICS code, 60 have end-products or services that relate to energy from renewable sources, 132 relate to energy efficiency, 122 relate to pollution and waste reduction and removal, 74 relate to natural resources conservation, and 45 relate to environmental compliance, training and education. In total, excluding the industries that fall into two or more categories, there are 325 industries that generate green jobs. BLS publishes green job data from the GGS survey in 2010 and 2011 (BLS, 2012). We obtained the data of value-added by industry from BEA (BEA, 2013). As BEA data is published by using 2002 NAICS code and the GGS survey used 2012 NAICS code, we transferred the BEA industries by using 2012 NAICS code and matched it with the GGS survey sector scheme. Also, as BEA's sector scheme is more aggregated, we only used the 3-digit or 2-digit NAICS code for the GGS data and sector scheme, whichever is better matched to BEA's sectors, excluding double-counting. Table 4-2 presents the common sector scheme that we used in the computation. We used the 120 following approaches to handle the inconsistencies in BLS GGS data and to fit it to the BEA sector scheme. It means that the BEA sector scheme is the final sector scheme we used in the computation. Please note that, to avoid double-counting, either the aggregated sector or the relating disaggregated sectors are included in the BEA sectors in the study, but not both. When there is no corresponding sector in BLS' s green goods and services sectors, these sectors do not contain green employment, and we can fill in zeroes for them in the dataset. Examples are oil and gas extraction, mining and its support activities, and so on. When an aggregated sector is found in BE A's sectors but none of its disaggregated sectors exists in BEA's sectors, we simply add up the amount in all the disaggregated sectors found in BLS 's GGS sectors and map the aggregate. If an aggregated sector and some of its disaggregated sectors in BE A's sectors are found in BLS 's GGS sectors but not all of the disaggregated sectors are found, we map the existing BLS's GGS sectors and allocate the remaining portion (if any) to the other disaggregated sectors in the BEA sector scheme. Examples are the Farms (111-112) sector and Forestry, fishing, and related activities (113-115) sector in BEA sectors, and 11, 21 Natural resources and mining, 111 Crop production in BLS GGS sectors. In the above case, the amount in 111 Crop production is allocated to Farms (111-112) and the remaining portion, which is the difference between 11, 21 Natural resources and mining and 111 Crop productions in BLS GGS sectors, is allocated to Forestry, fishing, and related activities (113-115) sector in BEA sectors. Another example is the disaggregated transportation sectors in BEA sectors ( 481000 to 493000) and the 48-49 Transportation and warehousing sector in BLS GGS sectors. In 121 such case, the difference between 48-49 Transportation and warehousing sector and the sum of 483 Water transportation and 485 Transit and ground passenger transportation is allocated to the other sectors based on their counts of six-digit green sectors in the Green Goods and Services Industry List published by BLS in May, 2012. Our final data refinement handles the inconsistencies between the green employment published in the aggregated sectors and their related disaggregated sectors. We consider that the sum of green employment in all the disaggregated sectors should be equal to the amount shown in the corresponding aggregated sector. However, this is not always the case in the published GGS data. Other than the data treatment mentioned above, when all the disaggregated sectors do not add up to the related aggregated sector, the amount in the disaggregated sectors will be increased or decreased proportionally to match the data shown in the aggregated sector. Table 4--2 BLS GGS Sectors Scheme Mapped to BEA Sectors Industry Code 110000 111-112 113-115 210000 BEA SECTORS (Sector scheme used in IDA computation) Farms Forestry, fishing, and related activities 211000 Oil and gas extraction 212000 Mining, except oil and gas 213000 Support activities for mining 220000 Utilities 230000 Construction 31-33 321000 Wood products 327000 Nonmetallic mineral products 330000 331000 Primary metals BLS GGS Industry 11,21 Natural resources and mining 111 Crop production 22 Utilities 23 Construction 31-33 Manufacturing 321 Wood product mfg. 327 Nonmetallic mineral product mfg. 33 Durable goods 331 Primary metal mfg. 122 Industry Code 332000 333000 BEA SECTORS (Sector scheme used in IDA computation) Fabricated metal products Machinery 334000 Computer and electronic products Electrical equipment, appliances, and 335000 336000 3361- 3363 3364- 3369 337000 339000 31-32 components Motor vehicles, bodies and trailers, and parts Other transportation equipment Furniture and related products Miscellaneous manufacturing Food and beverage and tobacco 311000 products 312000 313000 BLS_GGS_Industry 332 Fabricated metal product mfg. 333 Machinery mfg. 334 Computer and electronic product mfg. 335 Electrical equipment and appliance mfg. 336 Transportation equipment mfg. 337 Furniture and related product mfg. 314000 Textile mills and textile product mills 314 Textile product mills 315000 Apparel and leather and allied products 316000 322000 323000 324000 325000 326000 Paper products Printing and related support activities Petroleum and coal products Chemical products Plastics and rubber products 420000 Wholesale trade 44-45 Retail trade 48-49 481000 Air transportation 482000 Rail transportation 483000 Water transportation 484000 Truck transportation Transit and ground passenger 485000 transportation 486000 Pipeline transportation Other transportation and support 487000 activities 488000 492000 322 Paper mfg. 324 Petroleum and coal products mfg. 325 Chemical mfg. 326 Plastics and rubber products mfg. 423 Merchant wholesalers, durable goods 453 Miscellaneous store retailers 48-49 Transportation and warehousing 483 Water transportation 485 Transit and ground passenger transportation 123 Industry Code 493000 510000 BEA SECTORS (Sector scheme used in IDA computation) Warehousing and storage Publishing industries (includes 511000 software) 516000 Motion picture and sound recording 512000 industries 515000 Broadcasting and telecommunications 517000 518000 519000 52-53 520000 521000 522000 Information and data processing services Federal Reserve banks, credit intermediation, and related activities Securities, commodity contracts, and BLS_GGS_Industry 511 Publishing industries, except Internet 515 Broadcasting, except Internet 52,53 Financial activities 5 2 Finance and insurance 523 Securities, commodity contracts, 523000 investments investments 524000 Insurance carriers and related activities Funds, trusts, and other financial 525000 vehicles 530000 531000 Real estate Rental and leasing services and lessors 532000 of intangible assets 533000 54-55-56 540000 541100 Legal services Computer systems design and related 541500 services Miscellaneous professional, scientific, 541200 and technical services 541300 541400 541600 54-55-56 Professional and business services 54 Professional and Technical Services 5415 Computer systems design and related services 5413 Architectural and engineering services 5414 Specialized design services 5416 Management and technical consulting services 124 Industry Code 541700 541800 541900 BEA SECTORS (Sector scheme used in IDA computation) Management of companies and 5 50000 enterprises 560000 561000 Administrative and support services Waste management and remediation 562000 services 600000 610000 Educational services 620000 621000 Ambulatory health care services Hospitals and nursing and residential 622000 care facilities 623000 624000 Social assistance 700000 BLS_GGS_Industry 5417 Scientific research and development services 55 Management of companies and enterprises 56 Administrative and waste services 561 Administrative and support services 562 Waste management and remediation services 6 Educational services, health care, and social assistance 61,62 Education and health services 710000 71, 72 Leisure and hospitality 711000 Performing arts, spectator sports, 712000 museums, and related activities Amusements, gambling, and recreation 713000 industries 720000 721000 Accommodation 722000 Food services and drinking places 810000 Other services, except government 920000 General government 2.3. Results and interpretations 712 Museums, historical sites, zoos, and parks 81 Other services, except public administration 92 Public administration To facilitate the interpretation and to check and show the robustness of Vartia/LMDI indices, we also calculated other well-behaved multiplicative and additive indices, 125 including Fisher ideal indices and its additive counterparts, the Shapley/Sun indices, and the additive counterpart of Vartia/LMDI indices. The decomposition results are shown in Table 4-3. We can see that the four approaches yield quite consistent results. Green employment at the national level increased 158,374 positions between 2010 and 2011. According to the Shapley/Sun decomposition, among those positions, labor productivity contributed to a decrease of about 20,461 jobs, the share of green products and services contributed to an increase of about 112,484 jobs, economic structure a decrease of 957 jobs, and economic volume an increase of 65,394 jobs. The additive Vartia/LMDI decomposition gave similar results. The share of green products and services was the largest positive driver of green job increase, and the economic volume was the second largest positive driver. Labor productivity and economic structure are the two modest negative drivers. Table 4-3 Vartia/LMDI Indices for Green-employment, Non-green employment, and Total Employment in the United States, 2010 to 2011 (2010 =base) Green Employment Base case (thousand people) 3125.152 Compare case (thousand people) 3283.525 Fisher Ideal Shapley Vartia Additive Index Number Decomposition Index (Fil) Value Index LMDI Total Value Change (Ratio or Difference) 1.0507 158.3737 1.0217 158.3737 Labor productivity (reciprocal) 0.9936 -20.4614 0.9972 -20.4206 Green employment share 1.0357 112.4835 1.0154 112.5152 Economic structure 1.0003 0.9572 1.0001 0.9626 Economic volume 1.0206 65.3944 1.0089 65.3165 Residuals 1.0000 0.0000 1.0000 0.0000 126 Fisher Ideal Shapley Vartia Additive Percentage or Log Percentage Index (Fil) Value Index LMDI Total Value Change (Ratio or Difference) 100.00% 100.00% 100.00% 100.00% Labor productivity (reciprocal) -12.90% -12.92% -12.89% -12.89% Green employment share 70.99% 71.02% 71.04% 71.04% Economic structure 0.63% 0.60% 0.61% 0.61% Economic volume 41.27% 41.29% 41.24% 41.24% Residuals 0.00% 0.00% 0.00% 0.00% Non-Green Employment Base case (thousand people) 101157.848 Compare case (thousand people) 102807.475 Fisher Ideal Shapley Vartia Additive Index Number Decomposition Index (Fil) Value Index LMDI Total Value Change (Ratio or Difference) 1.0163 1649.6263 1.0070 1649.6263 Labor productivity (reciprocal) 0.9918 -836.3021 0.9965 -835.0407 Non-green employment share 0.9989 -112.4835 0.9995 -112.4759 Fisher Ideal Shapley Vartia Additive Index Number Decomposition Index (Fil) Value Index LMDI Economic structure 1.0051 517.2847 1.0022 516.5816 Economic volume 1.0206 2081.1272 1.0089 2080.5612 Residuals 1.0000 0.0000 1.0000 0.0000 Fisher Ideal Shapley Vartia Additive Percentage or Log Percentage Index (Fil) Value Index LMDI Total Value Change (Ratio or Difference) 100.00% 100.00% 100.00% 100.00% Labor productivity (reciprocal) -50.65% -50.70% -50.53% -50.62% Green employment share -6.82% -6.82% -6.82% -6.82% Economic structure 31.34% 31.36% 31.24% 31.32% Economic volume 126.13% 126.16% 126.11% 126.12% Residuals 0.00% 0.00% 0.00% 0.00% 127 Total Employment Base case (thousand people) 104283.000 Compare case (thousand people) 106091.000 Fisher Ideal Shapley Vartia Additive Index Number Decomposition Index (Fil) Value Index LMDI Total Value Change (Ratio or Difference) 1.0173 1808.0000 1.0075 1808.0000 Labor productivity (reciprocal) 0.9919 -856.7635 0.9964 -855.4547 Green employment share 1.0000 0.0000 1.0000 0.0000 Economic structure 1.0049 518.2419 1.0022 517.5052 Economic volume 1.0206 2146.5216 1.0089 2145.9496 Residuals 1.0000 0.0000 1.0000 0.0000 Fisher Ideal Shapley Vartia Additive Percentage or Log Percentage Index (Fil) Value Index LMDI Total Value Change (Ratio or Difference) 100.00% 100.00% 100.00% 100.00% Labor productivity (reciprocal) -47.35% -47.39% -48.33% -47.31% Green employment share 0.00% 0.00% 0.00% 0.00% Economic structure 28.65% 28.66% 29.30% 28.62% Economic volume 118.70% 118.72% 119.03% 118.69% Residuals 0.00% 0.00% 0.00% 0.00% The green job share being the largest driver in the growth of green jobs indicates that green job change is largely driven by the increased share of green products and/or services in industries, represented by the ratio of revenue from green products and services to the total revenue of the industry. There can be many reasons for the increased revenue share from the green products and services. It is possible that the public is favoring green products and services other than the non-green ones in 2011. And it is also possible that establishments start to reap more revenues associated with green products and services in the second year of the survey. However, the possibility of simple 128 accounting change is not excluded, when companies categorize more revenue as green other than non-green in 2011. Such symbolic accounting manipulation can happen when there are external incentives for more green jobs. Accordingly, we see that the share of non-green employment became the negative drivers for the change in non-green employment. In the total of about 1,649,626 employment increase in non-green jobs, the non-green share in industry caused about 112,484 employment decreases. The second largest positive driver for green-employment increase is economic volume, the level of economic activity as measured by the value-added of the whole economy. It indicates that the economic recovery/expansion has helped to create more jobs. Economic volume change is expected to drive up the employment of both green jobs and non-green jobs. As we see in the decomposition results, the economic volume attributed to about 65,394 gains in green employment, and about 2,081,127 gains in non-green employment. The growth rate relates to economic volume, which are indicated by the multiplicative economic volume indices, are consistent across the green, non-green, and total employment. Economic structure change has little impact on green job growth between 2010 and 2011. This agrees with our understanding of structure changes, which typically happen gradually and can show significant impact only in the long-run. However, by looking at the multiplicative economic structure indices for green employment, non-green employment, and total employment, we do see that the economic structure is a relatively larger positive driving force for the non-green employment than for the green 129 employment. It indicates that, in general, we do not see that the economic structure in the United States is turning greener from 2010 to 2011. As the economic structure change turned out to be a minor positive driven force for green and non-green employment, we can see that the economic structure in general may have become slightly labor intensive between 2010 and 2011 in the United States. And the non-green industries may have experienced faster job growth than the green industries due to economic structure change. Labor productivity contributes to a minor decrease in green employment and non-green employment. It complies with our understanding that the increase in labor productivity will lead to employment decrease. According to our decomposition result, labor productivity contributed to about 20,461 decreases in green employment, and 836,302 decreases in non-green employment. And the continuously compounded rate of decreasing in green employment relates to labor productivity is smaller than that in non green employment, meaning that the labor productivity increase is faster in non-green employment than in green employment. The result agrees with our estimations of employment change due to labor productivity change when the green-employment share is increasing. It is possible as, for example, renewable energies tend to be more labor intensive than non-renewable energies. And many scholars pointed out that many low skilled positions are created in renewable energy related industries. Such increasing in low-skilled positions and the low-skilled employment can contribute to the slowing down of labor productivity increase or even labor productivity decrease. On the other hand, while the non-green industries and/or non-green shares in industries are shrinking because of the growth of green industries and/or green shares in industries, non-green 130 employment will start to decrease. We can assume that the less productive jobs will be eliminated sooner than the more productive ones in non-green industries. It thus causes the labor productivity increase in the non-green industries to be faster than in green industries. In general, we revealed how the four pre-defined factors, green or non-green share of employment within industry, economic structure, economic volume, and labor productivity, contribute to the change in green employment, non-green employment, and total employment change between 2010 and 2011 in the United States via index decomposition analysis. Economic volume is a positive driver to both the increase in green employment and non-green employment. It also caused identical growth rate in the green and non-green employment, which agrees with our assumption that while all the other conditions be held constant, economic volume should have similar effects on green and non-green employment. Economic structure and labor productivity are minor positive and negative drivers to both of the green and non-green employment, respectively, even though the growth rates caused by the economic structure change and the labor productivity change in the two types of employment differ from each other. The economic structure and labor productivity both contribute to greater change in non-green employment than in green employment. 131 3. Occupation and wage in green job change The occupation-related data on green job from the Occupational Employment and Wages in Green Goods and Services (GGS-OCC) data was published by BLS to provide occupational employment and wage information (BLS, 2012). The occupational employment and wage data are aggregated to establishments that receive all, a portion, or none of their revenue from green goods and services. However, BLS only published the occupational data on November, 2011, so that we cannot fit the occupational data into the previous index decomposition model. But the dataset is valuable still as it can provide us the occupation and wage related data on green jobs. According to the GGS-OCC occupation data, the hourly mean and median wages, and the annual mean and median wages in the establishments that receive all of their revenue from green products and services are lower than that of the establishments that receive part or none of their revenue from green products and services. The mean wage differences can be caused by the wage level change in a single occupation, the occupation structure for the kind of establishments in the economy, and the industry structures for the kind of establishments in the economy. We can use a three-factor decomposition analysis to reveal the factors that affect mean wage difference between the establishments with all of their revenue from green products and services and the establishments with none of their revenue from green products and services, and between the establishments with a portion of their revenue from green products and services and the establishments with none of their revenue from green products and services. Such decomposition analysis can help policy makers gain insights on how the wage might be affected by the 132 increasing mix of revenues from green products and services and also help business to develop their strategies. We start the decomposition with the following identity: AveW= Emp· · Emp; W, .. * f,J *-- '·1 Emp; Emp ' i=l, ... ,K;j=l, ... ,O (4-4) where • AveW: Mean hourly or annual wage of the establishments with no, a portion, or all of their revenue from green products and services; • W;,J: Hourly or annual wage by industry and by occupations; • Emp;f Employment by industry and by occupations; • Emp;: Employment by industry; • Emp: Total employment of the establishments with none, a portion, or all of their revenue from green products and services, respectively. We conduct the two decomposition analyses below, firstly by companng the establishments with all of their revenue from green products and services to establishments with none of their revenue from green products and services with the latter as the base, and secondly by comparing the establishments with a portion of their revenue from green products and services to establishments with none of their revenue from green products and services, with the latter as the base. We obtain the data from BLS (2012). Table 4-4 to Table 4-7 presented the decomposition results. 133 Table 4--4 Drivers of Annual Wage Change between All-green firms and Non-green firms, Non-green firms= Base Annual Wage in Non-green Finns 58526 Annual Wage in All-green Finns 47918 Index Number Decomposition Fil SSI VI Total Value Change (Ratio or Difference) 0.8187 -10608 0.8187 Annual Wage Level 0.9834 -923 0.9659 Occupation Structure 0.7318 -18987 0.9018 Industry Structure 1.1378 9302 0.9449 Residuals 1.0000 0 0.9948 Table 4--5 Drivers of Annual Wage Change between Mixed-green firms and Non green firms, Non-green firms= base Annual Wage in Non-green Finns 58526 Annual Wage in Mixed-green Firms 54500 Index Number Decomposition Fil SSI VI Total Value Change (Ratio or Difference) 0.9312 -4026 0.9312 Annual Wage Level 1.0014 68 1.0004 Occupation Structure 0.9658 -1961 0.9786 Industry Structure 0.9629 -2133 0.9514 Residuals 1.0000 0 0.9997 Table 4--6 Drivers of Hourly Wage Change between All-green firms and Non-green firms, Non-green firms= base Hourly Wage in Non-green Finns 27.00 Hourly Wage in All-green Finns 22.96 Index Number Decomposition Fil SSI VI Total Value Change (Ratio or Difference) 0.8505 -4.0356 0.8505 Hourly Wage Level 0.9877 -0.3023 0.9744 Occupation Structure 0.7329 -9.0169 0.8982 Industry Structure 1.1750 5.2836 0.9697 Residuals 1.0000 0.0000 1.0022 134 Table 4--7 Drivers of Hourly Wage Change between Mixed-green firms and Non green firms, Non-green firms= base Hourly Wage in Non-green Finns 27.00 Hourll'. Wage in Mixed-green Finns 22.09 Index Number Decomposition Fil SSI VI Total Value Change (Ratio or Difference) 0.8183 -4.9058 0.8183 Hourly Wage Level 0.9882 -0.3000 0.9883 Occupation Structure 0.9664 -0.8028 0.9794 Industry Structure 0.8568 -3.8030 0.8458 Residuals 1.0000 0.0000 0.9994 We see that the annual wage and hourly wage in the establishments with no revenue from green products and services are higher than the wage in the establishments with all or a portion of revenue from green products and services. When we decompose the difference in average annual and hourly wage, we can see that for the all-green firms, wage and occupation structure are negative drivers of the wage increase, meaning that the all-green firms may have more lower-paid occupations comparing to the no-green firms, and for similar occupation and industry, the wage offered by the all-green firms is in general lower than the wage offered by the no-green firms. The trend is consistent in both the annual wages and hourly wages. We also see that industry structure is a positive driving force for the wage difference from non-green firms to all-green firms, meaning that the all-green firms are in general more likely to locate in high-paid industries. Industry structure being the positive driving force for wages from non-green firms to all-green firms is also consistent for both of the annual and hourly wages. In the comparison between the mixed-green firms and non-green firms, the non-green firms also have higher annual and hourly wages. But the driving factors show different 135 patterns in annual and hourly wages. We see that the annual wage level of mixed-green firms is higher than the annual wage level of non-green firms, while the hourly wage level of mixed-green firms is lower than the hourly wage level of non-green firms. And occupation structure and the industry structure are all negative driving forces for the wage change from non-green firms to mixed-green firms, meaning that the mixed-green firms are more likely to have a larger percentage of low-wage occupations and locate in lower-paid industries. In general, the wage level of green jobs is not quite encouragmg according to the decomposition results. Compared to the wage level of non-green firms, the annual wage level in all-green firms, and the hourly wage level in all-green and mixed-green firms all decrease. A possible interpretation is that workers are willing to accept lower-wages when the firms generate green products and services because of their good public image and/or bright economic prospects, given the assumption that the economy is turning green. Another interpretation is that, combined with our decomposition on labor productivity in Section 2, it is possible that faster growing labor productivity in non-green employment contributes to higher wages in non-green firms. 4. Conclusion In this chapter, we used index decomposition analysis to examine the drivers of green employment and the wage differences in firms with different portions of their revenues coming from green goods and services. We began by presenting the challenges in the 136 study of green jobs, including the ambiguities in the definition and the influences on green job statistics such as economic output change, labor productivity change, and so on. We pointed out the implications of specifying green vacancies and green employment in green job definition; we also examined the major perspectives in the environmental movement to reveal the main themes in the scope of green. After identifying the major elements in the scope and means of becoming green and common challenges in measuring green jobs, we compared the several green job definitions proposed by government agencies. We selected the green employment statistics from Green Goods and Services Survey by the Bureau of Labor Statistics as the main dataset for our analysis because it is the best available dataset on green jobs statistics when the study is performed and is less prone to double-counting comparing to the dataset on Green Technologies and Practices by BLS, which is based on the process approach definition of green jobs. We performed a two-stage index decomposition analysis on the employment change from 2010 to 2011 to reveal the drivers in green employment and how such driving forces differ with those in non-green employment and in the total employment. The four pre defined driving forces we have chosen for the decomposition are economic volume (or economic output), labor productivity, industry structure, and green/non-green employment share within the industry. We found that green employment share and the economic output change are the two major positive drivers for green employment increase from 2010 to 2011, economic structure has positive but limited impact on green employment increase, and labor productivity is the major negative driving forces for 137 green employment increase. Comparing the decomposition results with non-green employment, we found that economic output is a positive driving force for green and non-green employment and the implied continuously compounded growth rates are identical. Labor productivity causes a faster decrease of non-green employment comparing than green employment. And economic structure causes faster increase of non-green employment than green employment. In the last section, we examined whether green jobs are high-paid jobs. We examined the driving forces for the average wage difference among firms with all revenue, a portion of their revenue, and no revenue from green goods and services. We calculate the annual and hourly wage level for the three kinds of firms by eliminating the effects of occupation structure and industry structure. The results indicate that the wage levels in the all-green and mixed-green firms are lower than the non-green firms with the exception of annual wage level in mixed-green firms. It indicates that even though we have positive green employment growth, the wage level in such positions are in general lower and such employment contains a larger percentage of low-paid occupations. It is possible that the higher wages in non-green firms is caused by faster-increased labor productivity and/or that the workers are willing to accept lower wages to work in firms that produce green goods and services. It would be valuable to examine why the employment and wage pattern differs between green jobs and non-green jobs in a more comprehensive way, and this can be the topic for future research. 138 References Ang, B. W. (2004). Decomposition analysis for policymaking in energy: which is the preferred method? Energy Policy, 32, 1131-1139. Ang, B. W., & Choi, K. H. (1997). Decomposition of Aggregate Energy and Gas Emission Intensities for Industry: A Refined Divisia Index Method. The Energy Journal, 18(3 ), 59-73. Ang, B. W., & Liu, F. (2001). A New Energy Decomposition Method: Perfect in Decomposition and Consistent in Aggregation. Energy, 26, 537-548. Blanchard, 0., & Diamond, P. (1989). The Beveridge Curve. Brookings Papers on Economic Activity, 20(1 ), 1-60. BEA. (2013). Industry Economic Accounts. from Bureau of Economic Analysis: http://www.bea.gov/industry/xls/GDPbyind _VA_ NAICS _ 1998-2012.xls BLS. (2010). Technical Note. 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The elusive and expensive green job. Energy Economics, 34, S43-S52. 139 McCormick, J. (1991). Reclaiming Paradise: The Global Environmental Movement. Indiana University Press. OECD/Martinez-Fernandez, C., Hinojosa, C., & Miranda, G. (2010). Green jobs and skills: the local labour market implications of addressing climate change. OECD, CFE/LEED. Retrieved from www.oecd.org/dataoecd/54/43/44683169.pdf?conte 140 Chapter 5. Drivers of C0 2 Emissions in Electricity Generation in China: A Multi-temporal Multilateral IDA In this chapter, we use index decomposition analysis to identify the drivers of changes in C0 2 emissions from electricity generation in China over time and over space. According to the latest World Bank data, China surpassed the United States in 2006 to become the largest C0 2 emitter in the world, and its per capita C0 2 emissions surpassed the world average in 2006 (World Bank, 2013a; World Bank, 2013b). Electricity is one of the major sectors contributing to C0 2 emissions (Zhang et al., 2013), and most of the electricity generation in China still depends on coal. A few decomposition studies have been performed on the C0 2 emissions from electricity generation in China over time (Zhang et al., 2013; Malla, 2009). China is a large country with regional disparities in population, natural resource endowment, and economic development. In recent years, there is an increasing interest in analyzing the regional variations of the driving forces of C0 2 emissions in China (see, e.g. Yang, et al., 2013; Tian, et al., 2011). In this chapter, we make the first attempt to analyze the provincial level C0 2 emission drivers and compare them across spaces using multilateral index numbers as presented in Chapter 2. The chapter is organized as three sections. In the first section, we will describe the status of C0 2 emissions from electricity generation in China and the factors that can affect the emissions. In the second section, we will present the index decomposition model, the results, and their interpretations. In the last section, we will summarize and present the policy implications. 141 1. C0 2 emissions from electricity generation in China Even though China has published its trial version guidelines for provincial level carbon inventories (NDRC, 2011) and started pilot projects and researches to finalize the guidance (NDRC, 2012), when we performed the study, there was no publicly available data on C0 2 emissions from electricity generation by provinces over time in China. We therefore calculated the emissions by using the best data available to compare how C0 2 emissions from electricity generation vary over time and over space. We used the method suggested by the IPCC with the formula shown in equation 5-1. IPCC suggested three tiers of methods for calculating the national carbon inventory, with tier 1 method requiring the least amount of lower level location and technology specific data. Tier 1 method is the one we chose due to data limitations. It is based on "fuel combustion from national energy statistics and default emission factors" (IPCC, 2006), which is simplified compared to the method proposed by the National Development and Reform Commission (NDRC) of the People's Republic of China. That said, it is the most appropriate one given our data limitations and can still well illustrate how different factors affect the change in C0 2 emissions in electricity generaiton. When the tier 1 method is applied at the provincial level, our calculation is based on fuel combustion from provincial level energy statistics, together with country-specific emission factors. where E; = L Fu * E ~ j (5-1) E;: The C0 2 emissions from electricity generation in province i 142 F;,J: The type j fuel that is used in electricity generation in in province i E Fj: The nationwide emission factor for fuel j We obtained the provincial level fuel consumption data in electricity generation from 2006 to 2009 from the provincial level energy balance tables published in China Energy Statistic Yearbooks. The energy balance tables publish fuel consumption data in most of the energy consumption activities, including electricity generation. They are available for almost all provincial level jurisdictions in China, other than Xizang and the Special Administrative Regions (SARs), which consists of the Hongkong SAR and the Macau SAR. The fuel types that are included in the calculation are raw coal, clearned coal, other washed coal, briquettes, coke, coke oven gas, other gas, crude oil, gasoline, kerosene, diesel oil, fuel oil, LPG, refinery gas, natural gas, other petroleum products, and other coking products. The energy balance tables provide the fuel consumptions m electricity generation m physical units. In order to calculate the C0 2 emissions from fuel combustion, we firstly converted the physical units to common energy units using net calorific values (NCVs) as suggested by IPCC (IPCC, 2006). IPCC has published two sets of paremeters for calculating the NCVs of fuels. The first set is published in IPCC Third Assessment Report - Climate Change 2001: Mitigation (IPCC, 2001), in which NCVs for crude oil, coal, and natural gas are country specific. The second set is published in the Energy Volume in 2006 IPCC Guidelines for National Greenhouse Gas Inventories (IPCC, 2006), in which the NCV s for more detailed fuel types are provided but none of them are country specific. The National Development and Reform Commission (NDRC) of China 143 has also published national standards for defaut NCV s by fuel types (NDRC , 2008). The fourth data source we found is the multiple years Energy Balances of Non-OECD Countries published by the International Energy Agency (IEA) (IEA, 2006-2012). We summarized the four sets of NCVs in Table 5-1, in which only IEA publishes country- specific time series NCV s. In the time series NCV s for China, we see that the data for coal varies in 2004 and 2005. We selected the NCV s from the four datasets based on the following principles. We gave the first priority to time series country specific data, second priority to country specific data, and last to data that can use as default for any country any time. The selection principle applies later when we were choosing data from differet sources to calculate effective emission factors for each type of fuels too. Table 5-2 presents the net calorific value used in this study. Table 5-1 Net Calorific Values, Various Sources (TJ/Gg) IPCC IPCC Climate 2006 Change Carbon China 2001 Inventory NDRC IEA 2010 2009 2008 2007 Coal Total 20.94 Raw Coal* 25.80 20.91 21.21 21.25 21.25 21.25 Cleaned Coal** 26.70 26.34 24.15 26.75 26.75 26.75 Other Washed Coal*** 26.70 8.36 21.21 21.25 21.25 21.25 Briquettes**** 20.70 10.45 Coke 28.20 28.44 26.80 26.80 26.80 26.80 Coke Oven Gas 38.70 1 17.35 Other Gas Petroleum Products Total Crude Oil 41.88 42.30 41.82 144 IPCC IPCC Climate 2006 Change Carbon China 2001 Inventory NDRC IEA 2010 2009 2008 2007 Gasoline 44.81 44.30 43.07 41.87 41.87 41.87 41.87 Kerosene 43.76 44.10 43.07 Diesel Oil 43.34 43.00 42.65 Fuel Oil 40.20 40.40 41.82 LPG 47.32 47.30 50.18 Refinery Gas 48.16 49.50 1 46.06 Natural Gas 48.00 2 37.24 Other Petroleum Products 40.20 40.20 Other Coking Products 28.20 IEA 2006 2005 2004 2003 2002 2001 2000 Coal Total Raw Coal 21.25 21.25 22.43 20.94 20.94 20.94 20.94 Cleaned Coal 26.75 26.75 26.75 26.75 26.75 26.75 26.75 Other Washed Coal 21.25 21.25 22.43 20.94 20.94 20.94 20.94 Briquettes 8.37 8.37 8.37 8.37 8.37 8.37 Coke 26.80 26.80 26.80 26.80 26.80 26.80 26.80 Coke Oven Gas Other Gas Petroleum Products Total Crude Oil 41.87 41.87 41.87 41.87 41.87 41.87 41.87 Gasoline Kerosene Diesel Oil Fuel Oil LPG Refinery Gas Natural Gas Other Petroleum Products Other Coking Products 1. uncertainty range: expert judgement 145 *Use the value of other bituminous coal as in IPCC and IEA; **Use the value of anthracite as in IPCC and coking coal as in IEA; ***Use the value of other bituminous coal as in IPCC and IEA; ****Use the value of brown coal briquettes as in IPCC and sub-bituminous coal as in IEA Source: IPCC, 2001; IPCC, 2006; China National Development and Reform Commission, 2011; International Energy Agency, 2006-2012 Table 5-2 Net Calorific Values used in the Study (TJ/Gg or TJ/10 6 *M 3 ) 2009 2008 2007 2006 Raw Coal 21.25 21.25 21.25 21.25 Cleaned Coal 26.75 26.75 26.75 26.75 Other Washed Coal 21.25 21.25 21.25 21.25 Briquettes 10.45 10.45 10.45 10.45 Coke 26.80 26.80 26.80 26.80 Coke Oven Gas 17.35 17.35 17.35 17.35 Other Gas 16.08 16.08 16.08 16.08 Crude Oil 41.87 41.87 41.87 41.87 Gasoline 43.07 43.07 43.07 43.07 Kerosene 43.07 43.07 43.07 43.07 Diesel Oil 42.65 42.65 42.65 42.65 Fuel Oil 41.82 41.82 41.82 41.82 LPG 50.18 50.18 50.18 50.18 Refinery Gas 46.06 46.06 46.06 46.06 Natural Gas 37.24 37.24 37.24 37.24 Other Petroleum Products 40.20 40.20 40.20 40.20 Other Coking Products 28.20 28.20 28.20 28.20 Due to data limitations, we were unable to obtain provincial level emission factors for each type of fuels. In our analysis, we calculated the countrywide emission factors by each type of fuels and used them as the default emission factors for all provinces. The countrywide emission factors by fuel type are calculated based on equation 5-2. 146 where E Fj: The nationwide emission factor for fuel j CJ: The carbon content for fuel j OJ: The carbon oxidation factor for fuel j M: The molecular weight ratio of carbon dioxide to carbon ( 44/12) Table 5~3 shows the default carbon content and default carbon oxidation factors published by IPCC and China NDRC. We also presented the calculated effective C0 2 emission factor based on the IPCC 2006 and China NDRC data in the table. In our calculation, we relied mostly on the China NDRC data based emission factors, only when the data are not available for certain type of fuels, such as Kerosene, we used IPCC 2006 data based emission factors. Table 5-3 Carbon Content, Carbon Oxidation Factor, and C0 2 Emission Factors by Fuel Type, Various Sources IPCC 2006 China C02 C02 Carbon Carbon Emission Carbon Carbon Emission Content Oxidation Factor Content Oxidation Factor {~/GJ) factor (kg/TJ) {~/GJ) factor {~/TJ) Raw Coal 26.53 0.93 90813 Cleaned Coal 25.41 0.98 91307 Other Washed Coal 25.41 0.98 91307 Briquettes 33.56 0.90 110748 Coke 29.42 0.93 100322 Coke Oven Gas 13.58 0.98* 48797 Other Gas 147 IPCC 2006 China C02 C02 Carbon Carbon Emission Carbon Carbon Emission Content Oxidation Factor Content Oxidation Factor {ki?/GJ) factor (kg/TJ) {ki?/GJ) factor {ki?/TJ) Crude Oil 20.00 1.00 73333 20.08 0.98 72154 Gasoline 19.10 1.00 70033 18.90 0.98 67914 Kerosene 19.50 1.00 71500 0.98 0 Diesel Oil 20.20 1.00 74067 20.20 0.98 72585 Fuel Oil 21.10 1.00 77367 21.10 0.98 75819 LPG 17.20 1.00 63067 0.98 0 Refinery Gas 15.70 1.00 57567 18.20 0.98 65399 Natural Gas 15.30 1.00 56100 15.32 0.99 55612 Other Petroleum Products 20.00 1.00 73333 20.00 0.98 71867 Other Coking Products 0.93 The C0 2 emissions from electricity generation by province can thus be calculated by using the provincial level energy consumption data in common energy units and the C0 2 emission factors as calculated above. We present the result in Figure 5-1. The C0 2 emissions from electricity generation by provinces show veriations over space in terms of the annual level of C0 2 emissions, and over time in terms of the C0 2 emission growth rate. We can see that in general, the C0 2 emission from electricity generation goes up regularly year after year in most of the provinces. A few exceptions are Guangdong, Sichuan, Hubei, Hunan, and Beijing, whose C0 2 emissions from electricity generation started to decrease in 2009 or before. We can also see the variations across the provinces change over the years. For example, Hebei produced more C0 2 emissions from electricity generations in 2006 than Inner Mogolia and the pattern reversed since 2007. 148 Million Ions C02 300 250 200 ISO >- 1 00 Figure 5-1 C02 Emissions from Electricity Generation by Province in China, 2006- 2009 The COi emissions in electricity generation by province over time can be influenced by many factors. The factors may include the increasing demand in electricity consumption, the change in electricity distribution across provinces, the change in electricity generation efficiency, the change in the fuel structure in electricity generation, and so on. We will discuss the change of the elements that affect the emissions in electricity generation in the following section and discuss how each change attributes to the emissions in electricity generation in the next section. 2. Index decomposition analysis of the emission drivers 2.1. Index decomposition analysis design 2.1.1. Variables and model selection In this section, we discussed the selection of factors for explaining COi emissions change from electricity generation and the multiplicative and additive decomposition approaches. 149 • 1006 • 2007 • 2008 • 1009 We selected the explanatory variables based on the policies in which we are interested, the factors that can be affected by the policies, and the data availabilities. We identified the following factors that can affect C0 2 emissions growth over the years by provinces: population, per capita electricity consumption, the flow of electricity between provinces, and fuel use in electricity generation. For fuel use, ideally, we would use fuel conversion efficiency, fuel quality, fuel structure, and fuel emission factors to describe how the fuel use contributes to the C0 2 emission growth in electricity generation. It would lead us to a seven-factor decomposition model that includes: population, per capita electricity consumption, flow of electricity between provinces, fuel conversion efficiency, fuel quality, fuel structure, and fuel emission factors as the explanatory factors. For example, equation 5-3 is an identity we can use as the starting point of the decomposition: "' , F;' C;' E' E' F' L.i Fs, * F' * F' Et= Net *_s_*...l!...*....:.....* si i NC' E' E' F' s p s (5- 3) where E': Total C02 emissions from electricity generation in year t NC': Total number of retail customers served in the state in year t Ef: Total retail sale in the state in year t E~: Total net generation in the state in year t E~,: Total net generation in the state from fuel type i in year t Fs': Total fuel use in electricity generation in standard coal in year t 150 F 5 ~: Type i fuel used in electricity generation in standard coal in year t F{: Type i fuel consumed in electricity generation in the state in year t C{: C0 2 emitted from electricity generation from fuel type i in the state in year t Using the above equation as the starting point, we can conduct seven-factor index number decomposition over time and over space. In the right side of equation 5-3, from left to right, the seven explanatory factors are the population or scale effect, the electricity consumption per customer, location factor of electricity generation, fuel efficiencies in electricity generation, structure of fuel use in electricity generation, fuel quality, and C0 2 emission factors for the kind of fuel. They are represented by either a number or a vector. The first four factors, population or scale effect, the electricity consumption per customer, location factor, and fuel efficiencies in electricity generation, are represented by the population by provinces over time, the ratio of electricity consumption to population, the ratio of electricity generation to electricity consumption, and the ratio of fuel use aggregate in standard coal to electricity generation aggregate, respectively. The last three factors, structure of fuel use in electricity generation, fuel quality, and C0 2 emission factors for the kind of fuel, are each represented by a vector, in which each element represents the percentage of each type of fuel in the measure of standard coal in the total fuel use in electricity generation, the conversion factor of each type of fuel in physical measures to standard coal measures, and the C0 2 emission factors for each type of fuel in physical measures, respectively. Even though equation 5-3 is a rather comprehensive identity formula that contains many factors, we have to compromise the comprehensiveness due to data availability. That said, 151 the method and procedure to obtain index numbers presented in this paper can be equally applied whenever the missing data become available. As our limited data did not include any variations over time or over space, we can expect that the last two factors will turn out to have no contribution to the final change of C0 2 emissions from electricity generation over time and over space. This does not mean that the fuel quality and the C0 2 emission factor by fuel type are constant over time and over space. The fuel quality and the C0 2 emission factors by fuel type are important factors that can affect the C0 2 emissions in electricity generation and will be addressed in future research. For the above reason, we will only analyze the first five factors from now on in our paper. There are two ways to conduct the decomposition over time and over space. The first is to decompose the changes over time in C0 2 emissions in electricity generation by each province and then compare the significance of the contribution of the factors over space. This approach complies with a continuously compounded growth model as discussed in Chapter 3. The second approach is to decompose the changes over space and then compare the spatial variations over time. These two decomposition approaches usually will not yield the same results. Same results can be obtained in rare cases, as did in this one. In our case, only the fuel structure data is a vector by fuel type, meaning that we cannot factor out the scalar when multiplying the vector by a scalar. This property is called the proportionality test and can often be presented in equation 5-4: (5-4) where 152 X M,1,0 ( 1 0 1 1 1 1 0). Th . d b " " . h" h J x 1 ,x 1 , ... ,A*XJ,xJ, ... xM,xM. e 1n ex num er ior iactor J, w 1c 1s a function of xJ, j = 1, ... , M; t = 1,0 A: The scalar for vector xf For the superlative index number that satisfies the proportionality test, such as Fisher ideal index number, given our data characteristics, the over time I over space decomposition and the over space I over time decomposition yielded the same result. In our paper, as the starting point, we use Fisher ideal index number as the base for our over space over time and over time over space decomposition. 2.1.2. Five-factor FII decomposition As discussed in Chapter 2, we can choose vanous well-behaved index numbers to perform decomposition analysis. Many authors have discussed the pros and cons of each index numbers approaches and suggested that, in terms of policy making, among those well behaved index numbers, the choice really is a matter of taste (see, e.g. Ang, 2004). In our research, we follow the following principles of choosing index number formulas and finally chose FII to perform our decomposition in this chapter. We choose only among the well-behaved index numbers and choose the index number formula based on our data characteristics and availabilities. For example, if our data contain many zeroes, we may not choose the Tiirnqvist-Theil index number, as it has poor abilities to handle zero values. In our case, our dataset does contain many zero values, especially for the data on fuel structures. For this reason, the Tiirnqvist-Theil index number, even though it is one of the superlative index numbers, will not suit our needs. In addition, we can also 153 see that for majority of the factors, the data across items are the same. The reason is that we use many provincial level characteristics, such as population, total electricity consumption, and so on. Ideally, we would have, for example, electricity generation and consumption data by fuel type for each province. But as described in the previous section, such data are only available at a low level of detail, so we can only use the aggregate level data to perform the decomposition. In our case, the proportionality characteristic, as one of the desirable characteristics, can simplify the complicated Fisher Ideal Index in multi-factor cases and the choice of decomposition sequence of time and space. As FII also has other superior characteristics, e.g. ease to handle zero values, perfect in decomposition, etc., we use FII and FII-based multilateral index numbers to perform our decomposition. Equation 4-5 shows the five-factor bilateral/bi-period Fisher Ideal Index formula. Starting · h h ·d · · F 1 2 1 vt - ""N t - ""N ITM t · - 1 M· · - wit t e 1 entity 1n ormu a - , - Lii=l vi - Lii=l J=l x 1 ,i, J - , ... , , l - 1, ... N; t = 1, ... , T, the five-factor bilateral/bi-period Fisher Ideal Index formula can be presented in equation 5-5. (5-5) In which S represents a binary permutation of a vector including five elements, each of which take on the value T or T-1, and r represents the number of permutations that are equal to year T in vector t. Equation 5-5 is the five-factors generalized FII, which was presented in Siegel (1945) and De Boer (2009). 154 2.2. Decomposition results and interpretation 2.2.1. Drivers of C0 2 emissions growth rates over time To simplify the interpretation of results, we use the continuously compounded growth rate (CCGR) rather than the multiplicative index number to represent the change in C0 2 emissions, in which the CCGRs are simply the natural logarithm of multiplicative index numbers. The CCGRs perspective to interpret the multiplicative index numbers is presented in Chapter 3. The CCGRs of the C0 2 emissions from electricity generation over time are shown in Figure 5-2 and the average growth rate and the standard deviation of the CCGRs are shown in Table 5-4. Figure 5-2 mapped the CCGRs of the total C02 emissions, and the CCGRs of C02 emissions attributed to each driver by province over time on many grayscale maps of China, the darker the color, the faster the increase in C0 2 emissions. Table 5-4 Growth Rate of C0 2 Emissions from Electricity Generation over Time, Average and Standard Deviations by Factors, 2006 to 2009 ...., ""d (.) t'rj ""d t"'" t'rj "zj "zj ~ 0 0 - ('t> 0 =~ = "Cj = ('t> '"i l"'.i ('t> ~ e. rlJ. ~ (.) ~ l"'.i - - - ..... ;· (.) rn ~ s :l. ~ .... 0 = 0 ..... l"'.i "Cj d .... "Cj ;::'.'. .... = l"'.i = 0 = ..... ~ ..... "zj ~ ~ l"'.i .... ~ ('t> = s ~ '"i l"'.i rlJ. '"i ..... .... ('t> 0 s '"i 2006-2007 0.1321 0.0066 0.1302 0.0000 -0.0099 0.0052 Average 2007-2008 0.1334 0.0082 0.0532 0.0042 0.0533 0.0145 2008-2009 0.0572 0.0067 0.0592 0.0037 -0.0077 -0.0046 Standard 2006-2007 0.0942 0.0081 0.0408 0.0453 0.0865 0.0219 Deviations 2007-2008 0.0881 0.0094 0.0367 0.0506 0.0795 0.0400 2008-2009 0.1090 0.0108 0.0363 0.0441 0.0826 0.0409 155 2006-2007 2007-2008 2008-2009 (a) (b) (c) Population Effect (d) (e) (f) (g) (h) (i) 156 2006-2007 Location Factor (j) (m) Fuel Stmcture (p) ~ -0.23---0.11 - -0.11-0 • a.-0.12 •012-0.24 . 0. 24-- N/A 2007-2008 2008-2009 (k) (l) (n) (o) (q) (r) Figure 5-2 Growth Rates ofC~ Emissions from Electricity Generation over Time Attributed to Five Drivers by Province, 2006 to 2009 157 According to Table 5-4, the C0 2 emission growth rate decreased significantly from 2008 to 2009, compared to the C0 2 emissions growth rate from 2006 to 2008. This decrease is mainly attributed to the improved fuel conversion efficiencies and fuel structure with average CCGRs of -0.0077 and -0.0046 from 2008 to 2009, respectively. The finding complies with the dominant view that the increased energy intensity, which is reflected in the index of fuel conversion efficiency in our model, contributes to the decrease of C0 2 emissions in China over time (see, e.g. Zhang, et al., 2009; Wang, et al., 2005). At the average level, population continues to be a minor but positive driver of C0 2 emissions growth from 2006 to 2009; per capita electricity consumption was a dominant positive driver of C0 2 emission growth from 2006 to 2009, but its force decreased in 2008. The effects of location factor were minor but positive from 2007 to 2009, and the effects of fuel structure were minor but started to become negative from 2008 to 2009. We also computed the space-specific CCGRs of C0 2 em1ss10ns and the portions of space-specific CCGRs that were attributed to each driver by province. In this case, the CCGRs of C0 2 emissions over time over space and over space over time are the same using EKS/Shapley number based on bilateral Fisher Ideal Index. We thus provide a simplified interpretation of the CCGRs ofC0 2 emissions over time over space and treat it as the space-specific CCGRs. Figure 5-3 maps the space-specific CCGRs. It gives us a straightforward visual on how the growth rates of C0 2 emissions from electricity generation vary from province to province and how the variations were associated with the five factors. We used many grayscale maps of China to illustrate the direction and the 158 magnitude of the space-specific CCGRs and the portion of CCGRs attributed to each driver by province, the darker the gray, the faster increase in C0 2 emissions. Based on the average CCGRs presented in Table 5-4, C0 2 emission growths have slowed down from 2008 to 2009. The deceleration of C0 2 growth happened mostly in the provinces in the middle and southeast of China, according to Figure 5-2 (c). For the provinces that turned lighter in Figure 5-2 ( c) from 2008 to 2009, we see significant improvement in fuel conversion efficiency, as shown in Figure 5-2 ( o ). For the provinces that show positive growth of C0 2 emission from electricity generation in 2009, we see significant positive contribution from fuel conversion efficiencies and fuel structures, as shown in Figure 5-2 (o) and Figure 5-2 (r) and most of the areas that show positive C0 2 emission growth locates in the northern part of China. Looking at the contributions of factors over time, we see the following patterns in the C0 2 emissions attributed to population: 1) The average CCGRs of C0 2 emissions attributed to population continues to be positive over time, meaning that population continues to be a positive driver of C0 2 emissions growth over time on a chained basis; 2) Even though the average trend applies at most of the provincial levels, there are a few exceptions. Figure 5-2 (f) shows the growth rates of C0 2 emissions from electricity generation over time attributed to population change. Even though most of the areas in China are medium gray from 2006 to 2009, meaning that population change led to an increase in C0 2 emission growth, the color ofSichuan is light gray on Figure 5-2 (d), (e), and (f), meaning that population continues to lead to C0 2 decrease from 2006 to 2009 in 159 Sichuan. A few other provinces, Henan, Hubei, Anhui, Heilongjiang, and Jilin, have population as a negative driver of C0 2 emission growth from time to time. Per capita electricity consumption also is a positive driver of C0 2 emission growth over time and its force decreased in 2008 with CCGRs of 0.0066, 0.0082, and 0.0067 over the years. Most of the regions in China had per capital electricity consumption as a positive driver for C0 2 emission growth except Guangdong, Shanghai, Ningxia, and Shanxi. Fuel conversion efficiency was the main negative driver of C0 2 emission growth in the period of 2006 to 2007, and 2008 to 2009. Even though many provinces have improved their fuel conversion efficiency and decreased the C0 2 emission growth associated with it, many other provinces have fuel conversion efficiency as positive drivers of C0 2 emission growth. Out of the 30 provinces, autonomous municipalities, and directly-administered district, 13 of them had fuel conversion efficiency as positive driver of C0 2 emission growth in the period of2006 to 2007, 22 of them in the period of2007 to 2008, and 15 of them in the period of 2008 to 2009. The regions with fuel conversion efficiency as the positive driver tend to locate in the northern part of China. Fuel structure was a minor positive driver of C0 2 emissions growth in the period of 2006 to 2007, and 2007 to 2008, and minor negative driver of C0 2 emission growth in the period of 2008 to 2009. Most of the provinces, autonomous municipalities, and directly administered district did not have a consistent pattern of fuel structure being the positive or negative driver of C0 2 emission growth. Only Guangdong and Ningxia continues to have fuel structure as negative driver of C0 2 emission growth over time. 160 2.2.2. Drivers of space-specific growth rates of C0 2 emissions Provinces are subject to two levels of forces, one affects all provinces and the other affects the individual province only. The former type of force can be linked to national level policy, economic conditions that are not controlled by a single one province, etc. on the other hand, provinces in China have their sovereignty and special natural endowments that are crucial for C0 2 emissions. So separating the space-specific CCGRs from the CCGRs over time presented in the previous section may provide policy makers more insights on the drivers of C0 2 emission changes. The simplest way to obtain the space specific growth rate is by subtracting the average growth rate from the total growth rate, which is done in the study. As mentioned before, the simple way coincides with the over space over time multilateral EKS/Shapley numbers based on bilateral Fisher Ideal Index due to the proportionality property and the data pattern in this case. The disparities in the decomposition over time then over space and decomposition over space then over time in general cases can be the topic of future research. Eight provmces, directly administered municipalities, and autonomous reg10ns had population as a positive (larger than average) driver from 2006 to 2009, as shown in Figure 5-3 ( d), ( e ), and (f): Beijing, Guangdong, Guangxi, Hainan, Ningxia, Shanghai, Tianjin, and Xinjiang. Beijing, Tianjin, and Shanghai are three of the four directly administered municipalities in China. Directly administered municipalities usually are the political, business, and cultural centers of China and tend to have large population mcrease, which might explain their larger than average increase in population and therefore larger than average population associated emission growth. 161 For per capita electricity consumption, five areas have it as negative driver for C0 2 emission growth from 2006 to 2009, as shown in Figure 5-3 (g), (h), and (i): Beijing, Guangdong, Liaoning, Shanghai, Tianjin, and Zhejiang. Seven areas have it as positive driver for C0 2 emission growth from 2006 to 2009: Anhui, Guangxi, Hainan, Jiangxi, Qinghai, Xinjiang, and Yunnan. In the period from 2007 to 2008, we can see that the majority of the areas that have C0 2 emission increase have the per capita electricity consumption as a positive driver of C0 2 emission growth; and the majority of the areas that have C0 2 emission decrease have the per capita electricity consumption as the negative driver of C0 2 emission growth. However, this pattern between the C0 2 emission change over time and the contributions of per capita electricity consumption over time are not significant in the period from 2006 to 2007 and from 2008 to 2009. For fuel conversion efficiencies, the majority of the areas that have C0 2 increase from 2006 to 2007 have it as a positive driver ofC0 2 growth and the majority of the areas that have C0 2 decrease from 2006 to 2007 have it as negative driver. This pattern continued in the periods from 2007 to 2008 but became less significant. The pattern for fuel structures and location factor across spaces are not significant in our case. We can see that in the periods from 2007 to 2008 and from 2008 to 2009, the areas in the central part of China were more likely to have location factor as a positive driver of C0 2 emissions. Also, we can see that more areas in the periods from 2008 to 2009 had fuel structures as a positive driving force of C0 2 emissions. 162 We presented the coITelation between the total space specific CCGRs of C02 emission growth and the amount attributed to each factors in Table 5-5. As observed earlier, the fuel conversion efficiency correlates highly with the total CCGRs of C02 emissions. Population used to coITelate slightly negatively with the total CCGRs but the coITelation became weaker in the pe1iod from 2008 to 2009. The coITelation between the CCGRs and per capita electricity consumption became weaker too. But the coITelation between CCGRs and location factor and fuel structure became stronger over time. 200~2007 2007-2008 2008-2009 (a) (b) (c) Po ulation Effect (d) (e) (f) 163 2006-2007 2007-2008 2008-2009 (g) (h) (i) Local Quotient (j) 0) (m) (n) (o) 164 2006-2007 Fuel Structure (p) ~ -0 .25--0.12 - -0.12-0 • 0-0.os .0.08-0.16 . 0.16- N/A 2007-2008 2008-2009 (q) (r) Figure 5-3 Space-specific Gt·owth Rate of C0 2 Emissions from Electricity Generation over Time Attributed to Five Drivers by Provinces, 2006 to 2009 Table 5-5 Correlations between Total Growth Rate of C0 2 Emissions and the Attributions by Factors, 2006 to 2009 2006-2007 2007-2008 2008-2009 Total CCGRs 1.0000 1.0000 1.0000 Population -0.3422 -0.2547 0.0096 Per Capita Electricity Consumption 0.3721 0.3679 0.2458 Local Quotient 0.2050 0.2779 0.3743 Fuel Conversion Efficiency 0.8268 0.5347 0.8122 Fuel Structure 0.0473 0.4980 0.3567 3. Conclusion and policy implications ht this chapter, we examined the drivers of C0 2 emissions from electricity generation at the provincial level in China We used the generalized Fii based chained and multilateral 165 index numbers to decompose C0 2 emission changes over time and over space according to five different drivers: population, per capita electricity consumption, location factor, fuel efficiency, and fuel structure, from 2006 to 2009. We found the following trends in C0 2 emissions from electricity generation from 2006 to 2009 and its drivers: • C0 2 emissions from electricity generation are increasing over the years but the growth slowed down from 2008 to 2009. • At the average level, population continued to be a minor positive driver for C0 2 emission growth from 2006 to 2009. Per capita electricity consumption continued to be a strong positive driver for C0 2 emission growth from 2006 to 2009, especially in the period from 2006 to 2007. C0 2 emission growth attributed to per capita electricity consumption slowed down in 2008. • Fuel conversion efficiency was one of the major negative driving forces of C0 2 emission growth other than in the period from 2007 to 2008. Fuel structure was a minor positive driven force of C0 2 emission growth from 2006 to 2008 and became a minor negative driven force from 2008 to 2009. Other than the temporal trend of driving forces on average, we can also see spatial variations of the drivers. Even though on average, population is a positive driving force of C0 2 emission growth, Sichuan had population as a negative driver for C0 2 emission growth over the entire period, and most of the directly administered municipalities and autonomous regions had larger than average growth in population-driven C0 2 emissions. Areas in the middle and southeast China showed C0 2 emission decreases in 2008 and 166 2009, which were associated with the improved fuel conversion efficiencies. At the same time, the areas in the northern part of China had a relatively greater growth rate of C0 2 emissions from electricity generation, which was mainly contributed by fuel conversion efficiencies and fuel structures. The imbalanced development in China, the development policies, and the national economic conditions may all have contributed to the variations in C0 2 emissions from electricity generation. According to the decomposition result, changes in C0 2 emissions were largely driven by populations in the large and developed cities. Typical examples are Beijing and Shanghai, which are the two most developed cities with large population in China. With China's rapid economic development and its regional development policy, most of the provinces, especially those in the West, are quickly catching up. The policy of developing the West was originated in the idea of two general development strategies proposed by Deng Xiaoping in the 1980s. Deng proposed to develop the coastal areas first, and to develop the central and the west part of China when a certain development stage is reached in the coastal areas. In 1999, President Jiang suggested that it was the time to start to develop the West (Yeung, 2004). The areas that are covered in the development strategy include Chongqing, Sichuan, Guizhou, Yunnan, Xizang, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang, Inner Mongolia, and Guangxi. We see from the decomposition result that the southwest region in China has larger than average C0 2 emission growth in electricity generation, contributed primarily by per 167 capita electricity consumption from 2008 to 2009. In contrast, the relatively well- developed eastern and coastal regions in China have lower than average C0 2 emission growth in electricity generation contributed by per capita electricity consumption. There are two possible explanations for the difference. The first is that the rich regions "outsource" the C0 2 emissions from electricity to the poor regions by importing electricity, and the second is that when personal income reached a certain level, per capita C0 2 emissions from electricity consumption stabilizes 7 . We lean towards the latter explanation as the difference between rich regions and poor regions in location factor attributed C0 2 emissions from electricity generation was not significant. The location factor was designed to capture the contribution of electricity imports and exports across provinces to the C0 2 emissions from electricity generation. The decrease in C0 2 emissions from 2008 to 2009 due to fuel conversion efficiency and fuel structure may correspond with the policies of promoting renewable energy and increased energy efficiencies as described in the Eleventh Five-Year Plan for energy development in China. The Tenth Five-Year Plan for energy development in China, which covers energy planning from 2001 to 2005, has recognized the energy structure, 7 In practice, for example, the residents with extremely low income at the starting point may purchase new electrical appliances when their per capita income level increased to a certain level; and the residents with high per capita income level may already have made the purchase and will favor new enviromnental friendly but more expensive electrical appliances in re-purchasing decisions, thus stabilizes the C0 2 emissions from electricity consumption. The taste and behavior variation of rich and poor consumers with income level change can contribute to the rise and stabilization of C0 2 emissions with per capita income level change. In theory, the relationship between the emissions and income level is summarized in Enviromnental Kuznets Curve (EKC), which postulates the relationship between enviromnental degradation indicator and per capita income as an inverted U-shaped curve. J\1any studies have been conducted on testifying the existence of EKC in both the context of developed countries and developing countries, and scholars hold different views toward its existence (see, e.g. Selden & Song, 1994; Stem, 2004; Jalil & Mahmud, 2009). 168 rather than the conflict between the development and energy supply, as the main problem in China's energy planning (people.com.en, 2001). The energy development strategy in the Tenth Five-Year Plan was described as: "Without compromising energy security, we should make optimizing energy structure the top priority of the future energy plan; at the same time, we should make efforts to increase energy efficiency, protect the ecological environment, and accelerate the development of the west (people.com.en, 2001)". The Eleventh Five-Year Plan, which covers energy planning from 2006 to 2010, confirms the focus on improving energy structure and energy savings. The period examined in our analysis covers four years in the Eleventh Five-Year Plan. Based on the results, we can see that China on average has made progress on energy efficiency and fuel structure, and the improvement on the two factors contributed to the decreased C0 2 emission growth from electricity generation. Some scholars have illustrated the changes in C0 2 em1ss1ons as the race between consumption and fuel conversion efficiencies (see, e.g. Peters et al., 2007). lf we look at the drivers of C0 2 emissions at the provincial level, however, we can observe different patterns of the drivers. For some, per capita electricity consumption is the main positive driving force, and fuel conversion efficiency is the main negative one. For some of the most developed areas in China, population, instead of per capita electricity consumption, became the major positive driver of C0 2 emission growth. In addition to fuel conversion efficiency, fuel structure, or sometimes the location factor, became the main negative force. Examples are Beijing, Guangdong, and Tianjin in the period of 2008 to 2009. Different development stages across provinces may come into play in terms of C0 2 169 emission growth. C0 2 emissions attributed to per capita electricity consumption in more developed regions tend to grow slower than that in the less developed regions. If the main goal of policy is to reduce C0 2 emission growth, policy makers may consider tailoring the emission reduction policy to local conditions and focus on the critical areas of C0 2 emission reduction as identified in the index decomposition analysis. We should also consider the possibility of affecting C0 2 emissions growth through different development strategies. That said, index decomposition analysis can serve as a valuable heuristic tool upon which concrete policy recommendations can be formulated. The main purpose of the Index Decomposition Analysis here is to provide the direction and magnitude of C0 2 emission changes associated with the defined drivers. It can direct the attention of policy makers and planners to the critical areas of C0 2 emission changes. For example, the space-specific CCGRs of C0 2 emission changes, as presented in Figure 5-3, can help the officials at the provincial level to identify how the changes in population, per capita electricity consumption, the imports and exports of electricity, fuel conversion efficiency, and fuel structure contribute to the C0 2 emission changes from electricity generation, compared to the average level. The analysis here, however, may not be able to establish causal relationships between the C0 2 emission change and the changes in population, per capita electricity consumption, imports and exports of electricity, fuel conversion efficiency, and fuel structures for deriving policy solution. We consider that, at the very least, index decomposition analysis should be grounded in the existing economic theories to establish causal relationships 170 between the explained and explanatory variables. Index decomposition analysis itself does not establish causal relationships and can only provide few policy recommendations. Other technological, behavioral, and institutional factors should also be considered for effective policy making. Such analysis is limited to date in index decomposition analysis applied in the field of energy and emission studies. But the needs of incorporating those factors are recognized in the field (see, e.g. Rosa & Dietz, 2012). Tremendous efforts, however, have been made in grounding the index number analysis into the neoclassical economic theory in the study of wealth and income (see, e.g. Samuelson & Swamy, 1974; Diewert, 1976; van Veelen & van de Weide, 2008), and in fact, the economic approach of deriving index numbers are based on neoclassical economic theory. In the energy and emission studies, most of the work of grounding the decomposition analysis into the economic theories was initiated in structural decomposition analysis (see, e.g. Rose & Chen, 1991; Siegel et al., 1995), which is similar to index decomposition analysis but in the context of input-output models and able to distinguish between direct and indirect effects. Siegel et al. (1995) have provided a framework for extending SDA for policy analysis based on a social accounting matrix. His framework linked SDA to the sources of growth and then linked development policies with the sources of growth, thus provide an ex ante perspective of using SDA to perform policy analysis (Rose & Casler, 1996). The comprehensive framework of policy analysis using IDA and the grounding in economic theory is still under-developed. Even though in this chapter, we made the attempt to identify the sources of C0 2 emission change and link the sources to a few development policies in China, the analysis is ad hoc. A comprehensive framework as the 171 one presented in Siegel et al. (1995) and grounding IDA into economic theory could yield a solid foundation for the extension to policy analysis and would be a worthwhile topic for future research. 172 References Ang, B. W. (1994). Decomposition oflndustrial Energy Consumption: The Energy Intensity Approach. Energy Economics, 16(3), 163-174. Ang, B. W. (2004a). A generalized Fisher index approach to energy decomposition analysis. Energy Economics, 26(5), 757-763. Ang, B. W. (2004b ). Decomposition analysis for policymaking in energy: which is the preferred method? Energy Policy, 32, 1131-1139. Ang, B. W., & Choi, K. H. (1997). Decomposition of Aggregate Energy and Gas Emission Intensities for Industry: A Refined Divisia Index Method. The Energy Journal, 18(3 ), 59-73. 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Index numbers, in general, are quantitative measures of a variable of interest at the macro level. Starting from an identity that formalizes the relationship between the dependent and independent variables and the multiplicative or additive relationship between indexes and the change in dependent variable, IDA generates index numbers by aggregating the micro level independent variable changes using a weighing scheme. We can also see IDA as an approach to split an identity or decouple one independent variable from the others. While the identity tells us the total change in the dependent variable that is caused by all the independent variables, IDA tells us how much each of the independent variable contributes. The oldest and most-studied index numbers are price index and quantity index, which can be obtained by two-factor IDA. The development and application of index numbers in wealth and income studies were later carried out and extended in the study of energy use and pollutant emissions. In the literature, IDA usually is used exclusively to represent the latter extensions of index numbers theory. Even though IDA is a widely-used tool in studying the drivers of energy use and pollutant emissions, several theoretical and technical issues remained unresolved and constrained its further use in policy analysis. We tackled some of them and pointed out the others for future research. Our first contribution is the development of multi-factor multilateral IDA, which can generate transitive index numbers for the study of regional 177 disparities. Multilateral index numbers are proven to be useful in two-factor multilateral decompositions in the regional comparisons of price levels and quantity levels, e.g. Purchasing Power Parity (PPP), yet the multi-factor multilateral index numbers are not previously developed. As the number of factors for policy analysis usually exceeds two, multi-factor multilateral index number is necessary to deliver the critical piece of information. Another reason that the bilateral IDA cannot be extended to the multilateral cases without adjustments is the requirement of transitivity, which ensures that all two area comparisons are meaningful and consistent with each other. Not only is there no transitive multilateral IDA in the current literature, there is no proposed general approach to extend bilateral IDAs to multilateral IDAs. We filled the gap in the literature by linking the Shapley value and multilateral index numbers. We suggested a universal approach to obtain multilateral index numbers by using the Shapley value. The trick is to obtain the Shapley values for all regions being compared together and use the obtained value to construct multilateral index numbers. When the bilateral index numbers are used to construct the marginal contribution, the approach can lead to the corresponding multilateral index numbers. We have shown the case of Fisher Ideal index to EKS index, Tiirnqvist-Theil index to CCD index, and the Vartia Index (VI)/LMDI to its multilateral counterpart. We hope that the link discovered between the Shapley value and multilateral index numbers can connect the separate pieces of knowledge together and generate wide possibilities for future research. 178 Another unresolved puzzle in IDA methodology involves the introduction of additive decompositions. Additive decompositions and multiplicative decompositions are considered two equivalent approaches to identify the drivers in energy use and pollutant emissions, though additive decompositions are not often used in the study of wealth and income. Scholars in IDA have developed additive counterparts for all well-behaved multiplicative index numbers. For example, Shapley/Sun indexes (SSI) for Fisher Ideal index (FII), additive log mean Divisia Index (LMDI) for multiplicative LMDI, additive arithmetic mean Divisia Index (AMDI) for multiplicative Tiirnqvist-Theil index (TTI)/ AMDI. Only VI/LMDI provides consistent rankings of factors between itself and its additive counterpart, and only in two-case decompositions. The inconsistency can cause confusion in policy analysis and hurt the value of IDA as a quantitative tool of identifying and measuring the drivers of a certain change. We tackled the aforementioned inconsistencies from two angles, both of which reside the possibilities of future researches. Our first approach is to explicitly write the connections of the two in mathematical formulas and examine the linkage. We used the log transformation function proposed in Vartia (1976) to link the Laspeyres, Paasche, Fisher Ideal indexes and their additive counterparts. Therefore we can easily see that Laspeyres and Paasche indexes are rank-preserving but the Fisher Ideal Index is not, and why. Our other approach is to develop rank-preserving upper and lower bounds for the inconsistent index numbers. The practical consideration is to get an idea on how bad the inconsistency can be before we find a solid solution. We did so by developing sensitivity ranges for FII and its additive counterpart in multi-factor and multilateral cases in Chapter 2 and for the 179 case study in Chapter 3. Future research can be developed around the linkage between common statistical indicators, e.g. variance, and the inconsistencies between multilateral and additive index numbers, and the implications for policy analysis. We also proposed a comprehensive framework to unite all the widely-used index numbers. The united framework, compared to the previous dichotomy of Laspeyres based and Divisia-based index numbers, can better explain the differences across the index numbers. We used the log-transformation function to write Laspeyres, Paasche, and Fisher Ideal index numbers in the form of discrete approximation of Divisia index numbers and identified that their variations lie in the weighting schemes that are used to aggregate the value. Future research can be developed under the new framework in examining the essence of the weighting schemes and comparing index numbers in terms of their applicability for various policy analysis purposes. To illustrate the use of multifactor multilateral index numbers, we applied it in analyzing the drivers of C0 2 emissions from electricity generation by state in the United States. The multifactor multilateral FII, LMDI, their additive counterparts, and the upper and lower bounds of FII are used to measure how the variations across states in fuel mix, energy conversion, and C0 2 emission coefficient of fuels contributed to the spatial change in C0 2 emission from electricity generation in 2009. To be conservative, we call a factor strictly positive, if it is identified by all multiplicative index numbers, including the bounds, to be more than one, and by all additive index numbers, including the bounds, to be more than zero, and a factor strictly negative, if it is identified by all multiplicative to 180 be less than one and all additive to be less than zero. We therefore produced a whole picture of how each state does on the three aspects compared to its peers. Via the multifactor multilateral IDA, we separated the spatial variations in C0 2 emissions in electricity generation to three parts: the variations in emissions that are attributed to the changes in fuel mix, to the change in fuel electricity conversion efficiencies, and to the changes in fuel C0 2 emission coefficient. The spatial variation in each driver's contribution indicated by the multifactor multilateral index number can serve many purposes. It can be a starting point for local policies to remedy the excessive emissions. Combining it with local knowledge and the cost of policy implementation, policies can be carefully crafted to target the driver and reduce the emissions in a cost effective manner. It can also present the status quo in C0 2 emissions from electricity generation by states to the national level policy makers in a simple way. To broaden application ofIDA, we extended its use to a new field in Chapter 4. We used a multi-temporal two-stage IDA to study the green employment change and its drivers. Not only the chapter demonstrated the versatility of IDA for various kinds of policy issues, it also provided an innovative two-stage approach to conduct the decomposition. As "green job" is a fuzzy word, we firstly evaluated all its definitions provided by major governmental agencies and then chose a definition provided by the U.S. Bureau of Labor Statistics (BLS) and the corresponding dataset to conduct the analysis. A two-stage LMDI decomposition is used to analyze how the employment change from 2010 to 2011 in the U.S. was influenced by four factors: green/non-green job share within 181 an industry, economic structure, labor productivity, and total economic output of the U.S. economy. The results indicated that green job share was the largest positive driver of green job increase from 2010 to 2011 in the United States. Economic volume, which has positive effects on both green and non-green jobs, was the second largest driver of green job increase from 2010 to 2011. Economic structure, however, had little impact on the change of green and non-green jobs. As one element in green job definition was that green jobs should also be adequately paid jobs, we therefore conducted an analysis on wage levels to see whether workers were paid more or less by working in the companies that provide green goods and services than in the companies that do not. The result indicated that, eliminating the occupational and industrial influences, the annual wage level in all-green firms and the hourly wage level in both all-green and mixed green firms were lower than the wage levels in non green firms. The result suggests that green jobs were not necessarily be higher paid jobs, at least compared to similar positions in the companies that have no revenue from green products and services. However, we should also point out that we only examined the wage levels for firms at one point of time due to data limitations. It thus provided no information on the growth rate of the wage levels. Future researches can be developed along similar lines but with more comprehensive datasets. Rather than estimating the variations across space at one single point of time or over time for a single entity, we can also use ID A to obtain how the spatial variations change over time or how the growth rate associated to each driver varies across space. Therefore we 182 may also shed light on the historical route of the spatial variations. We made the attempt in chapter 5 by performing a multilateral and multi-temporal IDA on the drivers of C0 2 emissions from electricity generation by province in China based on a balanced panel data. In rare cases, as in Chapter 5, the sequence of decomposition over time and over space does not make any difference in terms of the results. In Chapter 5, we first obtained the drivers of the change over time in C0 2 emissions from electricity generation by province, and then delineated each driver to the portion that is associated with a general trend and the portion that is space-specific. We found that even though the C0 2 emissions from electricity generation in China continued to grow from 2006 to 2009, its growth rates slowed down in 2008, which was mostly contributed by the changes in fuel conversion efficiency and fuel structure. Per capita electricity consumption continued to be major positive driver and population minor positive driver of C0 2 emissions growth, which offset the environmental gain from the improved fuel efficiency and structure. That said, we also see spatial variations in the directions and magnitude of the drivers. For example, Beijing continued to have negative growth rate of C0 2 emissions from electricity generation over time, which was mainly driven by two of the three factors from time to time: the location factor, fuel conversion efficiencies, and fuel structure, but was offset continuously by the increased population. Also, the southwest region in China tended to have larger positive contributions by per capita electricity consumption to C0 2 emissions growth than the well-developed eastern and coastal regions. All of these helped us to identify the general trend and spatial variations in C0 2 emissions growth and can be 183 informative to policy makers in designing national and provincial level environmental policies. In general, IDA is a valuable tool to generate index numbers that represents the direction and magnitude of the drivers of a change. In this dissertation, we presented the tool in a systematic way and filled some gaps in the literature that can hinder its applications in policy analysis. We also extended the use of IDA to the new field of green jobs. Similar as most of the quantitative models and tools for policy analysis, the models and tools are subject to data availabilities and do not develop policy recommendations, though they are indispensable part of the analysis. Our three case studies in Chapter 3 to Chapter 5 illustrated how we might use IDA to analyze the drivers of spatial variations or temporal changes of an indicator and to yield a dynamic picture of the drivers by combining both IDA over time and IDA over space. Similar as how widely the price index and quantity index is used in policy analysis, the potential ofIDA is limitless. In Table 6-1, we provided some possible ways that IDA can be used to assist policy analysis. The list can be extended when the case studies developed. At present, most of the IDAs are used for ad hoc policy analysis. It will be helpful ifthere is a comprehensive framework of using IDA for policy analysis. Such a framework is not yet developed but can be a worthwhile topic for future research. We should mention that such a framework was proposed in Structural Decomposition Analysis (SDA), which can be seen as an alternative of IDA. SDA is based on the more extensive requirements 184 Input-Output Tables and has the advantage of differentiating the direct and indirect impacts (see, Rose & Casler, 1996). A comprehensive SDA framework for policy analysis was proposed by Siegel et al (1995) to link the development policies with the indexes and transformed the traditional ex post SDA to ex ante. Similar work on IDA can be beneficial. Table 6--1 Example Use ofIDA to Assist Policy Analysis Index Numbers Price Index & Quantity Index Energy use and pollutant emissions index Green employment and wage index Ways IDA Can Inform Policy Analysis Widely used for obtain cost of living, purchasing power of money, and other types of index numbers. Adjust long-term contracts and/or contracts over space Track the price and quantity change at the macro level Certain index numbers can be used in forecasting Can be used in analyzing productivity change Identify how each driver affects emissions in climate change negotiation Compare how emissions and energy use are affected over time I over space Separate the combined effects for better understanding the mechanism of change Separate the combined effects for compensation Separate the combined effects for policy evaluation Track the change in energy use and pollutant emissions Identify the driver of green employment change Decide the amount of government subsidies for green investment, e.g. to compensate the wage difference in green firms Inform policy implementation strategy of turning firms green, e.g. non-green to mixed-green to green, or non-green to green 185 Consolidated Bibliography Albrecht, J., Francois, D., & Schoors, K. (2002). 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Abstract (if available)
Abstract
This dissertation examines the theoretical roots of index decomposition analysis (IDA), fills in some key gaps, extends this method, and applies it to three cases to provide policy and planning insights. IDA is a widely used tool in energy use and pollutant emissions studies to estimate the directions and magnitude of the driving forces of a change in a key economic variable. The usefulness of index decomposition analysis resides in the fact that policy makers and planners sometimes need a way to distinguish how one factor affects a certain change of interest at the macro level when the change is a combined effect of multiple factors on a group of items. IDA can separate the contributions of drivers to the explained variable change and can aggregate the effects at the group level. Therefore, it provides a quantitative way to reveal the significance of drivers to a change and can help policy makers and planners develop remedies where necessary. ❧ This dissertation consists of six chapters. The theoretical foundation and nearly a century of studies on index numbers were summarized briefly in Chapter 1 and in detail in Chapter 2. Chapter 1 also describes how this dissertation is organized. By reviewing the history and recent developments in index numbers and IDA, I identified several remaining issues and proposed a new approach to generate multi-factor multilateral index numbers. I discussed the issue of consistencies in the ranking of factors between multiplicative IDAs and their additive counterparts. I also united both the widely-used Laspeyres-based and Divisia-based index numbers under the framework of discrete approximation of Divisia index, which has the advantage to identify the source of differences across index numbers and to reveal the link between the multiplicative index numbers and their additive counterparts. ❧ Index numbers were first studied in the field of wealth and income to obtain the price level and quantity level changes between multiple time periods and/or areas. Major contributions include the derivation of index number formulas/approaches, the meaning of index numbers, and their connections with economic theory (see, e.g. Fisher, 1922
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Asset Metadata
Creator
Zhou, Jie
(author)
Core Title
Measuring the drivers of economic, energy, and environmental changes: an index decomposition analysis
School
School of Policy, Planning and Development
Degree
Doctor of Policy, Planning & Development
Degree Program
Policy, Planning, and Development
Defense Date
05/23/2014
Publisher
University of Southern California
(original),
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(digital)
Tag
EKS index,environmental changes,Fisher ideal index,index decomposition analysis,LMDI,multilateral index,OAI-PMH Harvest,Shapley value
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English
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Electronically uploaded by the author
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Rose, Adam Z. (
committee chair
), Nugent, Jeffrey B. (
committee member
), Tang, Shui Yan (
committee member
)
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jiezhou@usc.edu,jzhou615@gmail.com
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https://doi.org/10.25549/usctheses-c3-472989
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University of Southern California Dissertations and Theses
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The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
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Tags
EKS index
environmental changes
Fisher ideal index
index decomposition analysis
LMDI
multilateral index
Shapley value