German energy transition and nuclear phase out– Drivers of the changes in
Germany’s energy consumption by industries using structural decomposition analysis
by
ARTUR SCHLENDER Student number: S3515206
University of Groningen Faculty of Economics and Business
MSc International Economics & Business Master Thesis
First supervisor: prof. dr. Erik Dietzenbacher Second supervisor: dr. Dirk Akkermans
Abstract
This study investigates the driving forces in German energy consumption between 2000 and 2014 using structural decomposition analysis (SDA) and applied to global multi-regional Input-Output tables. The analysis consists of two decomposition studies of which the first explains changes in the country’s total energy consumption using five drivers. The second study then uses the three drivers applicable to changes in production’s use of renewable energy, nuclear energy, and other non-renewable energy sources to show whether changes in industrial energy use reflect trends toward energy transition and nuclear phase out. The most important driver for reducing energy use is technological change with -4.49 Exa Joules (EJ), while increases are majorly ascribed to changes in final demands (+3.16 EJ). Trade in intermediate goods (+0.55 EJ) as well as households’ direct consumption (-0.38) have a minor impact. The composition of the energy mix has no effect on total energy consumption. In production, technological changes and final demands also explain most variation. Trade in intermediate goods has as low impact as also found for total energy use. Final demands illustrate best by cumulative changes over the time period for RE (+41.8%) and nuclear energy (+195.1) that the second SDA study confirms the trend toward energy transition. The trend toward phasing out of nuclear power cannot be confirmed by the SDA alone, but by consultation of overall energy use data that shows a decline in reliance on nuclear energy.
Table of Contents
Abstract ... II
Data and Methods ... 6
Structural Decomposition Analysis ... 6
Data Sources ... 8
Deflation and Chaining of the Results ... 10
Empirical Results ... 11
Results on German total energy consumption 2000-2014 ... 11
Drivers of changes in German total energy consumption 2000-2014 ... 15
Driving forces of changes in German energy consumption by industries ... 17
Drivers of the changes in Germany’s energy consumption by industries using structural decomposition analysis
Todays’ and future generations are facing a myriad of challenges that interlink scientific disciplines, which demand a high level of collaboration, involvement as well as foresightedness of stakeholders at global scale. Climate change is a prime example for interdisciplinary communication, for instance between economics, business and environment, and ranges among those issues considered among the biggest global challenges according to the World Economic Forum (2016). With greenhouse gas (GHG) emissions having increased by approximately 80% since 1970, climate hazards such as droughts, storms and unpredictable precipitation are observed more frequently with increasingly devastating outcomes. Further consequences affect all kinds of living species that are threatened through loss in biodiversity, melting of the poles and rising sea levels, just to mention a few. The major reason why we can observe the escalation of the world temperature at unprecedented rates, known as climate change, is the increase in GHG emissions that is majorly linked to energy use.
1990, to derive 20% of EU energy from renewable energies (RE) as well as improving energy efficiency by 20%. How to arrive at these levels is left to the discretion of each individual EU member state, though. Consequently, approaches vary according to each country’s abundance of RE sources together with reliance on all remaining Non-Renewable energy (Non-RE) sources, not including nuclear energy having a particular role in this context that is controversially discussed. Given Germany is a major stakeholder in Europe’s economic performance with lately a share of total EU GDP amounting to roughly 21% in 2017 (European Commission, 2018), and plays a key role in curbing GHG emissions as well as acting as role model to battle climate change. Since 1990 it was able to cut GHG emissions by 22%, which is well above the stipulated UNFCCC target to decrease emissions by 20% until 2020. One of the driving forces that allowed Germany this achievement is energy transition –the reduction of GHG, growing levels of energy efficiency and the increasing use and prioritization of RE sources over Non-RE in satisfying the country’s demand for energy. Further, Germany stipulated the nuclear phase out until 2022 by the Thirteenth Act Amending the Atomic Energy Act of 31 July 2011 to manifest that nuclear disasters at Chernobyl in 1986 and Fukushima in 2011 shall not repeat and future energy demand must be met using different energy sources. Not only the nuclear safety question is subject to debate (Jahn, D., and Korolczuk, S., 2012) but also the permanent storage of nuclear waste at disposal sites, because the degradation process is tedious and radioactive rays are in the long-term detrimental to the environment and its living organisms. This is why energy transition as well as the nuclear phase out play a key role in the long-range agenda for Germany’s desired goals.
Regarding the role of energy transition at global level from an economic point of view, Dietzenbacher, E., Kulionis, V., and Capurro, F., (2019) find that it has a marginal role in explaining changes in energy use although results for the EU are most promising. However, these results apply to the EU only and must be interpreted in a global context, in which trade and global integration in form of slicing up of production steps entailed significant increases in trade volumes (Arto, I. and Dietzenbacher, E. 2014), partially due to lower wages in developing countries (Timmer, M.P., Dietzenbacher, E., Los, B., Stehrer, R., and De Vries, G. J., 2015). The use of energy (Wood et al., 2018) and GHG emissions (Baumol, W. J., Nelson, R. R., & Wolff, E. N.,
nations via convergence (Mc Millan, M., Rodrik, D., & Sepulveda, C., 2017), resulting among others in efficiency gains in production processes and more efficient use of industrial inputs such as energy.
Given the results at global level for the role of energy transition mentioned above, it is pertinent to further delve into analysing Germany’s energy consumption patterns from an economic perspective– a country advocating and leading the movement toward energy transition phasing out of nuclear power, to show whether national results yield a similar picture. On this account, changes in the national use of energy might differ significantly by going into different directions measured by various contributions. Therefore, this research aims to analyse the German changes in total energy use based on Global Input-Output Tables using the World Input-Output Database (WIOD) and performing a Structural Decomposition Analysis (SDA). A second study using three further SDAs will serve to quantify how RE, nuclear energy and Non-RE consumption in German production are steered. As a result, this study will show how each mechanism(driver) contributed to what extent to the changes in German total energy use. Furthermore, special attention is attached to energy use by German industries since they are responsible for the bulk of the country’s energy use (AG Energiebilanzen, 2019). The latter study eventually helps derive the following research question:
“Which drivers have the biggest impact on changes in German energy consumption by industries and do they confirm the country’s trend toward the increasing use of RE proxying energy transition and phasing out of nuclear power?”
Data and Methods Structural Decomposition Analysis
quantify the contribution of slightly different drivers to changes in Germany’s total energy use. These drivers are:
1. Technological changes due to changes in total energy use in production as well as changes in technological coefficients;
2. Changes in the final demands;
3. Changes in the trade in intermediate goods reflecting variation global production fragmentation;
4. Changes in energy transition reflected by the fuel mix consisting of RE, Non-RE, and nuclear energy consumed relative to overall energy consumption in production and directly by households
5. Changes in energy consumed directly by households.
The methodology used for this study is available at appendices B1-B10 and explains in detail the use of IO tables along with the set-up of the two SDA studies.
Numerous research papers at national levels demonstrate how the focus of SDA can vary depending on the research question one investigates. SDA in the case of Australia (Wood, 2009; He, H., C.J. Reynolds, L. Li and J. Boland, 2019), India (Mukhopadhyay, K., & Chakraborty, D.,
1999), Brazil (Wachsmann, U., Wood, R., Lenzen, M., & Schaeffer, R.2009), South Korea (Lim, H. J., Yoo, S. H., & Kwak, S. J., 2009), or for European member states (Alcantara, V., & Duarte, R., 2004) such as Portugal (Guevara, Z., & Rodrigues, J. F., 2016), the Netherlands (De Haan, M., 2001) Czech Republic (Weinzettel, J., and Kovanda, J., 2011) show how SDA allow for numerous approaches to quantify changes in a variable of interest at different geographical levels. These key variables may be energy consumption changes, changes in industrial CO2 emissions, air emissions per se, changes in water consumption, etc. This is where this investigation will be linked up to with focus on energy consumption and changes in shares of RE, nuclear energy and Non-RE used in production.
use and emissions in a specific economic sector (Su, B. and Ang, B. W., 2012). In contrast, SDA involves more data and is primarily used by Input-Output analysts, whose objective is to assess the changes in energy consumption as a whole that can be a region, country or even the entire world. Further, using the IDA also bears limitations such as less detailed decomposition of economic production structure (Hoekstra, R. & van den Bergh, J. C. J. M., 2003) or it fails to analyse the interdependencies of different economic sectors (Feng, K., Siu, Y. L., Guan, D. & Hubacek, K., 2012). Another disadvantage vis-à-vis the SDA is its incapability to distinguish between intermediate and final consumption being reason why indirect impacts of changes in final consumption cannot be captured. Given these limitations, this study will employ SDA, since it allows to make inferences about economy wide and sector specific changes of energy in economic structure, final demand components and categories. Furthermore, it allows for evaluation of direct and indirect effects along the entire supply chain across upstream and downstream industries (Miller, R. E. and Blair, P. D., 2009), which assists in highlighting interdependencies between sectors and consequently overcomes static features of Input-Output models (Feng, K., Davis, S. J., Sun, L., & Hubacek, K., 2015).
Data Sources
2019). A detailed comparison of databases can be consulted in Tukker and Dietzenbacher (2013). For this reason, numerous studies have been carried out to assess the merits and back draws of each database by studying and comparing their outcomes (Arto, I., J.M. Rueda-Cantuche and G.P. Peters, 2014; Inomata, S. and Owen, A., 2014; Moran, D. and Wood, R., 2014; Owen, A., Steen-Olsen, K., Barrett, J., Wiedmann T. and Lenzen, M., 2014; Owen, A., Wood, R., Barrett, J., and Evans, A., 2016; Wieland, H., Giljum, S., Bruckner, M., Owen, A., and Wood, R., 2018). As Dietzenbacher et al. (2019) sum up, differences are marginal at global scale and also in terms of contributions expressed in percentages. For convenience, this study uses the WIOD given that other databases do not provide substantial benefits from their use and simply because the energy data this study grounds upon has been harmonized with the sector specifications of the WIOD (Kulionis, 2018).
As stated above, the WIOD 2016 release, henceforth WIOD16, is available at www.wiod.org (for a technical explanation, see Dietzenbacher et al., (2013) and a user guide, Timmer et al., (2015) and is utilized in combination with the energy use data of Kulionis (2018) to conduct the SDA for the time-period 2000-2014. The WIOD16 encompasses data on 44 countries with 28 EU member states and fifteen additional economies, namely Australia, Brazil, Canada, China, India, Indonesia, Japan, Mexico, Norway, Russia, South Korea, Switzerland, Taiwan, Turkey, and the United States. The last country called Rest of the World (RoW) is an estimated aggregate of the non-covered parts of the world that are crucial to include when assessing global MRIO (Timmer et al., 2015). In total, there are 56 industries available for each country that are harmonized and classified according to the guidelines of the International Standard Industrial Classification revision 4 (ISIC Rev. 4) (United Nations Statistics Division, 2009) and also comply with the SNA 2008 (United Nations Statistics Division, 2008). The data in the WIOD16 is available in previous year’s prices and does not include data on environmental accounts such as energy use data.
partially more aggregated than the energy classifications of the International Energy Agency (IEA)–the institution addressing most topics related to the full spectrum of energy issues to its mission nowadays. Given Kulionis’ energy data (2018) refers to the IEA standard, an overview of WIOD16 energy product correspondence is given in table 1.
Deflation and Chaining of the Results
The deflation process of all physical quantities that are measured in this study are in Terra Joules (TJ = 1012), or Exa Joules (EJ = 1018) ensures that results, using WIOD IO tables in monetary units, are not affected by price effects. They represent a potential bias usually resulting from the computation of input coefficients (e.g. RE use per industrial output in USD in PJ) or other linkages between physical entities such as energy, water or land use, to mention a few, and money units. WIOD provides users with an adequate solution to overcome this issue by using data in constant prices or in other words, prices of the previous year. The aforementioned inflation effect can be illustrated taking a simple example: suppose we have 5 Kilo Joules of RE input for 5000 USD of output in industry y in year t0. In the subsequent year; the economy experiences higher rates of inflation entailing increasing prices whilst production processes and total outputs remain the same. The RE input coefficient in t0 for industry y accounted for 1/1000 RE per unit of industrial output. Due to inflation between year t0 and t+1, we can observe a price increase of for instance 15%. As a result, monetary values in IO tables also increase by 15% and the input coefficients are altered. RE inputs decrease by 1/ 13.5 equalling 7.4 %. The adjusted RE input coefficients imply that RE use decreased or production gained in efficiency, whereas physical input units remained the same. WIOD IO tables are available in current prices of the year in question and previous year’s prices that allow for deflation to obtain changes expressed in physical units. The deflation procedure is, however, problematic when the base year and the one of interest are non-consecutive, but parted by several years in-between. In this case, properties of both years’ basket of goods might differ gradually, particularly if countries are very different, and the monetary values in constant prices are biased. WIOD’s IO tables were treated using a double deflation method with the drawback of potentially cumulating biases in the value added when using previous year’s prices (see Diet Dietzenbacher, E., and Hoen, A. R., 1998, 1999). Hence, deflating over longer periods using the double deflation method is not recommended (Dietzenbacher et al., 2019).
physical units e.g. RE consumption between two years. These volume changes are also computed between all other years of the time period observed. In order to display volume changes throughout the time period, this study uses De Haan’s (2001) method to chain the volume changes that is further explained in Part IX – Chaining of results of chapter 3.4 Methodology.
Empirical Results
This study analysed five drivers in the German energy mix used in production and directly by households over the time period 2000-2014. The first sub-chapter will briefly describe how the analysis illustrates Germany’s changes in energy consumed in production and directly by households as well as their aggregate. Afterwards, the results of the first SDA study with the performance of each driver are displayed in the next sub-section, followed by the last sub-section that is dedicated to the second SDA study on changes of RE, nuclear energy and Non-RE use due to drivers in Germany’s production.
Results on German total energy consumption 2000-2014
Table 1 gives an overview of the German energy consumption in production measured in Exa Joules and distinguished by RE, nuclear energy, Non-RE and total energy consumption. The results for EJ use indicate that RE use increased while consumption of nuclear, Non-RE and total energy consumption decreased. Percentagewise, however, the results are slightly different for Non-RE and total energy use that show a growing share in total energy consumption relative to Germany’s total energy consumption. Regarding RE use, the share of RE indicates that German industries consumed roughly 25 % more of RE relative to total German RE use compared to 2000 when RE consumption was by and large balanced between consumption in production and directly by households. This confirms once again that energy consumption growth by industries and as share of total energy consumption has a substantially bigger role in total energy consumption when comparing to households’ direct energy use. The share of nuclear energy use remains logically at 100.0% because German households are no direct consumers of nuclear energy.
These trends are in line with growing motivation to further energy transition and reducing reliance upon nuclear power, that are also reflected by the 2000-2014 growth rates. Energy efficiency may play a key role to explain the overall smaller energy growth rates as well as for Non-RE use together with the aforementioned trends regarding RE and nuclear power use. Yet, one notes that RE consumption growth rates decreased especially for the second sub-period implying that its role relative to total energy consumption growth may have lessened. Nevertheless, this can be also due to overall smaller energy growth rates that substantially determines RE growth rates, too.
Table 1 Overview of total German energy consumption in production and changes, 2000-2014
EJ use confirm the trends seen in production, with RE use increasing while consumption of Non-RE and total energy consumption decreased.
Nuclear energy consumption does not figure in the table given German households do not directly use this energy carrier that is only employed by industries. Percentagewise, the results constitute the second side to the same coin referring to German production. The RE share directly consumed by households obviously decreased, whereas those of Non-RE and total energy consumed by households decreased.
Table 2 Overview of total German energy directly consumed by households and changes, 2000-2014
consumption growth that is increasing when one compares the two sub-periods. Yet, this growth rate must be interpreted together with changes in RE EJ of total RE consumption. This share in German total RE consumption decreased by -27 % indicating that RE use in production grows much faster in total volumes. Hence, inferences that can be made based only on the RE growth rate for households are relaxed.
Table 3 shows the overall trend for Germany’s total energy consumption over the time period 2000-2014 with the distinction of the energy mix into RE, nuclear energy, and Non-RE consumption as well as their aggregate for both, production and direct consumption by households. The results sum up the results for production and households, that are growing EJ use of RE and declining consumption of nuclear energy, Non-RE and, consequently, an overall decline in the German energy use. This result is not surprising due to moderate population growth and more efficient use of energy. Although RE becomes more important, the bulk of the energy consumption still originates from Non-RE carriers. Nuclear energy obviously became less important with a use in 2014 inferior to RE. That is, one can confirm that consumption patterns indicate the direction toward the set goals of energy transition and the phasing out of nuclear energy. Further, total energy use declines that can be majorly attributed to technological change or more economical energy consumption by industries or directly by households that also applied to more countries
(Voigt, S., De Cian, E., Schymura, M., and Verdolini, E., 2014) and also at global scale (Dietzenbacher et al., 2019).
Table 3 Overview of total German energy consumption in production, directly by households and changes, 2000-2014
Drivers of changes in German total energy consumption 2000-2014
This study analysed five drivers to the changes in German energy consumption in production and directly by households that are subject to changes illustrated by the SDA throughout the covered time period. Given the research question at hand: “Which drivers have the biggest impact on changes in German energy consumption by industries and do they confirm the country’s trend toward the increasing use of RE proxying energy transition and phasing out of nuclear power?” this sub-section provides insights to each driver’s long-run effect to explain changes in Germany’s energy use.
in final demands as well as changes in households’ direct energy consumption. The fifth driver, changes due to the composition of the energy mix, logically does not affect total energy consumption, which is why it does not figure in the figure. On the contrary, the changes and shares in the three kinds of energies referred to throughout the study are majorly determined by changes in total energy consumption. Therefore, a separate analysis is dedicated to these results and discussed in the next sub-chapter “Driving forces of changes in Germany’s energy consumption by industries”. Furthermore, the change in the total energy consumption figures here as well to show how all drivers all together affect changes in energy consumption.
this is twofold given international production fragmentation, providing industries with inputs further spreads over time and gains in importance regarding trade. This is also found by Jacobsen, H., (2000) on Denmark that implies changes in international trade structure have potential to raise demand in domestic energy. In reference to figure 1, the contributions of trade in intermediate goods to changes in total energy consumption declined and remained low starting from 2010 until 2014, which may be partially also explained by this. On the other hand, production abroad of inputs for industries that are imported come along with energy consumption elsewhere, that otherwise would have taken place locally. Consequently, imports and exports for the most part cancel out each other, because they solely substitute energy use at foreign and vice versa (Dietzenbacher et al., 2019), which also confirmed by Jacobsen (2000). At last, households’ direct energy consumption had small explanatory power over changes in total energy consumption (-0.38 EJ) and showed minor variation over the time period.
Figure 1: Changes in Germany’s total energy consumption by drivers, 2000-2014 in previous year’s prices
Driving forces of changes in German energy consumption by industries
2000-2014 in order to answer the research question. The method used to conduct this analysis is described in detail together with an example of how the results were calculated in appendix B9. The analysis consists of three additional SDAs for RE, nuclear energy and Non-RE consumption by industries and how their changes between years are driven by technological change, trade in intermediate goods, and final demands.
When turning to variation within years, the picture is scattered and patterns are not easy to identify. Striking are the changes in year 2003 as well as for the time period 2012-2014 when technological change explains most deviation in energy use. Trade in intermediate goods explains best variations in 2003, 2006, and 2011. The last driver logically explains most changes for the period of the economic recession between 2008 and 2009 as well as for 2003.
The results for cumulative variation based on each energy type separately are available in appendix C2 and indicate that the biggest additive effect on RE and Non-RE consumption is due to technological changes. These findings are consistent with the results displayed in table 1, because most RE and Non-RE is consumed by industries for which efficiency gains and more economical use of inputs is a key motivation in production. Variation in RE use indicates in this case growing demand for RE; and change in Non-RE is linked to less Non-RE consumption or more efficient use of inputs and technological progress. In turn, cumulative changes in nuclear energy are mostly driven by final demands in production that had by far the biggest explanatory power over changes in nuclear power. This may be interpreted again together with the results for total energy consumption in table 1, that point toward phasing out of nuclear power illustrated by continuously decreasing demand in nuclear energy that can be seen especially in the recent time period (2011-2014).
Conclusion
Changes in Germany’s total energy consumption are negative (-1.59) and mostly driven by technological changes (-4.93 EJ) and final demands (+3.16 EJ) followed by trade in intermediate goods having a moderate effect (+0.55 EJ) as well as variation in households’ direct energy (-0.38). No effect was found for composition of energy use referring to the three energy categories, given total energy use drives their consumption and not the other way around.
At production level, additive percentagewise changes in RE use are mostly driven by final demands (+38.5%) and technological change (-20.7%) that also drive most variation in nuclear energy by (+195.1%) and (+124.1%), respectively. Thus, final demands have best steering power over changes in RE consumption by industries given their increase also levels their share in total energy. In contrast, the trend for nuclear power phase out cannot be confirmed alone by the SDA that shows no declining use of nuclear power, but by consulting results on total energy use in production. These results confirm trends indicating the weakening role of nuclear power in industries’ energy use. Finally, the research question can be answered positively, that RE as well as nuclear use patterns in production confirm Germany’s trend toward energy transition and nuclear phase out.
Nevertheless, this study bears some limitations that can be found in the methodology with its elements used to usually perform Input-Output analyses, the use of data as well as the tools used to run the computations. These are for instance the computation of the Leontief inverse using Matlab, given the inverse computation of singular matrices such as the input coefficients matrix B possibly can yield inaccurate results. Further, using the WIOD16 energy data to consolidate RE, and Non-RE (all remaining non-Renewable energy carriers except nuclear energy) use also consists of the energy product Waste, that includes renewable as well as non-renewable municipal waste. This represents a minor bias, because the data cannot be further disentangled. Considering the study’s results, especially the first decomposition study for drivers of total energy use might be biased, given some variations such as in 2003 are lacking of logical explanation.
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Xu, Y., and Dietzenbacher, E. (2014). A structural decomposition analysis of the emissions embodied in trade. Ecological Economics, 101, 10-20.
Appendix A
Table A1 WIOD 2016 and IEA energy product correspondence
Appendix B1
The global multiregional input-output (GMRIO) framework:
This methodology follows the work of Dietzenbacher et al. (2019) primarily using the approaches of Arto and Dietzenbacher (2014) as well as Xu and Dietzenbacher (2014), and is used as backbone for the subsequent SDA. However, it differs in its analysis, in the first instance, by focusing rather on the total energy consumption by industries and directly by households. In a second step, changes in RE, nuclear energy and Non-RE consumption are quantified in production and linked to drivers steering total energy consumption. An SDA’s aim is to illustrate how changes in the variable of interest, which is German total energy consumption in this study together with RE, nuclear energy, and Non-RE use in production in the second study, can be divided into the effects of each driver of this very key variable, that is for instance change in RE consumption by industries. As the research question states are particularly the drivers of the changes in RE and nuclear energy key variants and derived from the first SDA on total energy. As a result, the methodology helps identify which driver has the biggest effect on changes in total energy consumption as well as for RE and nuclear energy use by industries. Thus, most important drivers of variation in production’s RE use have biggest explanatory power over energy transition and changes in industries’ nuclear energy use reflects nuclear phaseout, respectively.
The GMRIO Tables have a structure of 𝐼 countries of which each comprises 𝑖 industries.1 The 𝐼𝑖 × 𝐼𝑖 matrix 𝐘 of intermediate deliveries, the 𝐼𝑖 × 𝐼 matrix 𝐅 of final demands as well as the 𝐼𝑖-element output vector 𝐰 are (in partitioned form) given by:
𝐘 = [ 𝐘11 ⋯ ⋮ ⋱ 𝐘1𝐶 ⋮ ⋯ 𝐘1𝐼 ⋰ ⋮ 𝐘𝐶1 ⋯ 𝐘𝐶𝐶 ⋯ 𝐘𝐶𝐼 ⋮ ⋰ 𝐘𝐼1 ⋯ ⋮ 𝐘𝐼𝐶 ⋱ ⋮ ⋯ 𝐘𝐼𝐼] , 𝐅 = [ 𝐟11 ⋯ ⋮ ⋱ 𝐟1𝐶 ⋮ ⋯ 𝐟1𝐼 ⋰ ⋮ 𝐟𝐶1 ⋯ 𝐟𝐶𝐶 ⋯ 𝐟𝐶𝐼 ⋮ ⋰ 𝐟𝐼1 ⋯ ⋮ 𝐟𝐼𝐶 ⋱ ⋮ ⋯ 𝐟𝐼𝐼] , 𝐰 = ( 𝐰1 ⋮ 𝐰𝐶 ⋮ 𝐰𝐼 )
1 A thorough distinction of matrices, vectors, scalars is denoted as follows: Bold capital letters are assigned to matrices
(e.g. Y or 𝐘𝑅𝑆), bold lower case letters (e.g. w or 𝐰𝑅) are vectors, and scalars are in italics (e.g. i, 𝑤𝑘𝐶, or 𝑦𝑗𝑘𝐶𝑁). The
last two particularities are an apostrophe indicating a transposition (e.g. 𝐰′ or (𝐰𝑅)′) as well as a circumflex (or “hat”)
In this framework, element 𝑦𝑗𝑘𝐶𝑁 of the 𝑖 × 𝑖 matrix 𝐘𝐶𝑁 provides the monetary value in million dollars of intermediate inputs from industry 𝑗 in 𝐶 to industry k in country 𝑁. Element 𝑓𝑗𝐶𝑁of the i-element vector 𝐟𝐶𝑁yields the deliveries from industry j in country C for final consumption in country N. The matrix F encompasses all final demand categories such as final consumption expenditure by households, consumption expenditure by non-profit organization, expenditures by government, gross fixed capital formation as well as changes in inventories and valuables. The element 𝑤𝑗𝐶 of the i-element in the vector 𝐰𝐶 yields the output of industry j in country C. The 𝐼𝑖 accounting equations are given by 𝐰 = 𝐘𝐩𝐼𝑖+ 𝐅𝐩𝐼, where 𝐩𝐼𝑖 is the Ii-element summation vector consisting of ones.
The input coefficients of the matrix dimension 𝐼𝑖 × 𝐼𝑖 can be described as 𝐁 = 𝐘𝐰̂−1, meaning that 𝐁𝐶𝑁 = 𝐘𝐶𝑁(𝐰̂𝑁)−1 or 𝑏𝑗𝑘𝐶𝑁 = 𝑦𝑗𝑘𝐶𝑁/𝑤𝑘𝑁. This yields the intermediate deliveries per unit of the receiving industry’s output. Subsequently, we can substitute 𝐘𝐩𝐼𝑖 = 𝐁𝐰 in the accounting equations that yields 𝐰 = 𝐁𝐰 + 𝐅𝐩𝐼 and can be expressed as
𝐰 = (𝐈 − 𝐁)−1𝐅𝐩𝐼 = 𝐋𝐅𝐩𝐼 (1)
, with the 𝐼𝑖 × 𝐼𝑖 matrix 𝐋 ≡ (𝐈 − 𝐁)−1 describing the Leontief inverse, that – in its partitioned form – can be noted as
𝐋 = [ 𝐋11 ⋯ ⋮ ⋱ 𝐋1𝐶 ⋮ ⋯ 𝐋1𝐼 ⋰ ⋮ 𝐋𝐶1 ⋯ 𝐋𝐶𝐶 ⋯ 𝐋𝐶𝐼 ⋮ ⋰ 𝐋𝐼1 ⋯ ⋮ 𝐋𝐼𝑅 ⋱ ⋮ ⋯ 𝐋𝐼𝐼]
Energy consumption by industry can be written as
that can be also written as
𝐠̅ = 𝐠 + 𝐠̈ + 𝐠̃
, with 𝐠̅ describing an 𝐼𝑖 –element vector with element 𝑔̅𝑗𝐶of the vector 𝐠̅𝐶 that yields the total energy consumption in country C for each industry j. Similarly, vector g gives the RE consumption in country C for each industry j. In the same fashion, vector 𝐠̈ describes nuclear energy consumption and vector 𝐠̃ yields the total Non-RE consumption for each industry j. In regards to direct energy used by households, we can write
𝐡̅ = ( ℎ̅1 ⋮ ℎ̅𝐶 ⋮ ℎ̅𝐼) , 𝐡𝐚 = ( ℎ1 ⋮ ℎ𝐶 ⋮ ℎ𝐼) , 𝐡𝐚̈ = ( ℎ̈1 ⋮ ℎ̈𝐶 ⋮ ℎ̈𝐼) , and 𝐡𝐚̃ = ( ℎ̃1 ⋮ ℎ̃𝐶 ⋮ ℎ̃𝐼)
that can be also written as
𝐡̅ = 𝐡 + 𝐡̈ + 𝐡̃
, with 𝐡̅ being an I-element vector and element ℎ̅𝐶 showing total energy consumed directly by households in country C. Similarly, vector h describes RE consumed directly by households. In the same fashion, vectors 𝐡̈ and 𝐡̃ being I-element vectors with elements ℎ̈𝐶 and ℎ̃𝐶 giving total nuclear energy and Non-RE consumed directly by households in country C, respectively. Ultimately, all energy consumption can be noted as
𝐞̅ = ( 𝑒̅1 ⋮ 𝑒̅𝐶 ⋮ 𝑒̅𝐼) , 𝐞 = ( 𝑒1 ⋮ 𝑒𝐶 ⋮ 𝑒𝐼) , 𝐞̈ = ( 𝑒̈1 ⋮ 𝑒̈𝐶 ⋮ 𝑒̈𝐼) , and 𝐞̃ = ( 𝑒̃1 ⋮ 𝑒̃𝐶 ⋮ 𝑒̃𝐼)
𝐞̅ = 𝐞 + 𝐞̈ + 𝐞̃
, with 𝐞̅ being an 𝐼-element vector and element 𝑒̅𝐶giving all energy consumed in country C. This element sums up the total energy consumed in both, production and households. This can be also noted as,
𝑒̅𝐶 = 𝐩𝑖′𝐠̅𝐶 = ∑ 𝑔̅𝑗𝐶 𝑗
+ ℎ̅𝐶 (2)
This can be also noted as
𝐞̅ = 𝐏𝐠̅ + 𝐡̅ (3)
with matrix 𝐏 of the dimension 𝐼 × 𝐼𝑖 that can be noted as
𝐏 = [ 𝐩𝑖′ ⋯ ⋮ ⋱ 0 ⋮ ⋯ 0 ⋰ ⋮ 0 ⋯ 𝐩𝑖′ ⋯ 0 ⋮ ⋰ 0 ⋯ ⋮ 0 ⋱ ⋮ ⋯ 𝐩𝑖′]
Similarly, as equations (2) and (3), vector 𝐞 gives all consumption of RE in equation (4), vector 𝐞̈ describes all consumption of nuclear energy in equation (5) as does also vector 𝐞̃ for Non-RE in equation (6), respectively.
𝐞 = 𝐏𝐠 + 𝐡 (4)
𝐞̈ = 𝐏𝐠̈ + 𝐡̈ (5)
Appendix B2 Part IV – Renewable energy consumption in production
The formula for RE input coefficients can be noted as
𝐱 = 𝐰̂−1𝐠 = ( 𝐱1 ⋮ 𝐱𝐶 ⋮ 𝐱𝐼) = ( (𝐰̂1)−1𝐠1 ⋮ (𝐰̂𝐶)−1𝐠𝐶 ⋮ (𝐰̂𝐼)−1𝐠𝐼) (7)
or alternatively, 𝑥𝑗𝐶 = 𝑔𝑗𝐶/𝑤𝑗𝐶 showing RE consumption in industry j in country C per unit of industry j’s output. In a second step, the proportion of RE consumption relative to total energy consumption can be expressed as a share that is
𝑥𝑗𝐶 = 𝑔𝑗 𝐶 𝑤𝑗𝐶 = 𝑔𝑗𝐶 𝑔̅𝑗𝐶 𝑔̅𝑗𝐶 𝑤𝑗𝐶 = 𝑡𝑗 𝐶𝑥̅ 𝑗𝐶 (8)
, with 𝑡𝑗𝐶 describing RE consumption as a proportion of total energy consumption in industry j in country C and 𝑥̅𝑗𝐶 denoting the input coefficient for total energy consumption (i.e. the total energy consumption in industry j in country C per unit of industry j’s output).
Thus, we can deduct from equation (7) that 𝐠 = 𝐱̂𝐰 and 𝐏𝐠 in (4) can also be noted as
𝐏𝐠 = [ 𝐩𝑖′ ⋯ ⋮ ⋱ 0 ⋮ ⋯ 0 ⋰ ⋮ 0 ⋯ 𝐩𝑖′ ⋯ 0 ⋮ ⋰ 0 ⋯ ⋮ 0 ⋱ ⋮ ⋯ 𝐩𝑖′] 𝐱̂𝐰 = [ (𝐱1)′ ⋯ ⋮ ⋱ 0 ⋮ ⋯ 0 ⋰ ⋮ 0 ⋯ (𝐱𝐶)′ ⋯ 0 ⋮ ⋰ 0 ⋯ ⋮ 0 ⋱ ⋮ ⋯ (𝐱𝐼)′] 𝐰 = 𝐗𝐰 (10)
multiplied by the input coefficient vector w, which yields the RE input coefficients matrix 𝐗𝐰. From equation (9) follows in matrix notation
𝐓 = [ (𝐭1)′ ⋯ ⋮ ⋱ 0 ⋮ ⋯ 0 ⋰ ⋮ 0 ⋯ (𝐭𝐶)′ ⋯ 0 ⋮ ⋰ 0 ⋯ ⋮ 0 ⋱ ⋮ ⋯ (𝐭𝐼)′] , and 𝐗 = [ (𝐱1)′ ⋯ ⋮ ⋱ 0 ⋮ ⋯ 0 ⋰ ⋮ 0 ⋯ (𝐱𝐶)′ ⋯ 0 ⋮ ⋰ 0 ⋯ ⋮ 0 ⋱ ⋮ ⋯ (𝐱𝐼)′] (11)
, where 𝐓 with the dimension 𝐼 × 𝐼𝑖 gives the matrix of RE consumption as a share of total energy consumption in country C. Matrix X with the dimension 𝐼 × 𝐼𝑖 gives the share of RE consumed relative to total energy consumed in country C of which the latter, namely 𝐗̅ is defined in the same way as X, but for total energy consumption in country C. Subsequently, we use equation (9) again and describe the formula as 𝐗 = 𝐓⨂𝐗̅, with ⨂ indicating the Hadamard or Schur product that performs an element-wise multiplication of two matrices yielding a new matrix as a result.
At last, we can use equation (1) and substitute as follows
𝐏𝐠 = 𝐗𝐰 = (𝐓⨂𝐗̅)𝐰 = (𝐓⨂𝐗̅)𝐋𝐅𝐩𝐼 (12)
Appendix B3
Part IV – Nuclear energy consumption in production The formula for nuclear input coefficients can be noted as
𝐱̈ = 𝐰̂−1𝐠̈ = ( 𝐱̈1 ⋮ 𝐱̈𝐶 ⋮ 𝐱̈𝐼 ) = ( (𝐰̂1)−1𝐠̈1 ⋮ (𝐰̂𝐶)−1𝐠̈𝐶 ⋮ (𝐰̂𝐼)−1𝐠̈𝐼 ) (13)
nuclear energy consumed as a proportion of the total energy consumption in country C.
At last, we can use again equation (1) and substitute as follows
𝐏𝐠̈ = 𝐗̈𝐰 = (𝐓̈⨂𝐗̅)𝐰 = (𝐓̈⨂𝐗̅)𝐋𝐅𝐩𝐼 (14)
Appendix B4 Part IV – Non-RE consumption in production
The formula for nuclear input coefficients can be noted as
𝐱̃ = 𝐰̂−1𝐠̃ = ( 𝐱̃1 ⋮ 𝐱̃𝐶 ⋮ 𝐱̃𝐼) = ( (𝐰̂1)−1𝐠̃1 ⋮ (𝐰̂𝐶)−1𝐠̃𝐶 ⋮ (𝐰̂𝐼)−1𝐠̃𝐼) (15)
The rationale that is used to determine matrices 𝐓 and 𝐓̈ also yields matrix 𝐓̃, which describes Non-RE consumed as a share of the total energy consumption in country C.
At last, we can use again equation (1) and substitute as follows
𝐏𝐠̃ = 𝐗̃𝐰 = (𝐓̃⨂𝐗̅)𝐰 = (𝐓̃⨂𝐗̅)𝐋𝐅𝐩𝐼 (16)
Summing all energy decomposition shares 𝐓, 𝐓̈ , and 𝐓̃, this gives
Appendix B5
Part V – Direct consumption of RE, Non-RE and nuclear energy by households
Given equation (1), direct energy consumption by households can be also decomposed by their share of RE, nuclear energy as well as Non-RE relative to their total energy consumption. This can be expressed as summation of three shares that are
ℎ𝐶 ℎ̅𝐶
+
ℎ̈𝐶 ℎ̅𝐶+
ℎ̃𝐶 ℎ̅𝐶= 𝑟
𝐶+ 𝑟̈
𝐶+ 𝑟̃
𝐶= 1
(17) For country C, total energy used directly by households is partitioned into:a)
𝑟, the RE share relative to total energy consumed directly by households
b)
𝑟̈, the nuclear energy share relative to total energy consumed directly by households
c)𝑟̃, the Non-RE share relative to total energy consumed directly by households
By way of conclusion, we can now write our decomposition for total energy consumption per country as indicated by equation (1) with the 𝐼-element vector 𝐞̅ as
𝐞̅ = 𝐏𝐠̅ + 𝐡̅ = (((𝐓 + 𝐓̈ + 𝐓
̃ )⨂𝐗̅) 𝐋𝐅𝐩
𝐼) + ((𝐫̂ + 𝐫̈̂ + 𝐫̃̂)𝐡̅)
(18)Similarly, we can write for RE, nuclear energy as well as Non-RE
𝐞 = 𝐏𝐠 + 𝐡 = ((𝐓⨂𝐗
̅)𝐋𝐅𝐩
𝐼) + 𝐫̂𝐡̅
(19a)𝐞̈ = 𝐏𝐠̈ + 𝐡̈ = ((𝐓̈⨂𝐗
̅)𝐋𝐅𝐩
𝐼) + 𝐫̈̂𝐡̅
(19b)𝐞̃ = 𝐏𝐠̃ + 𝐡
̃ = ((𝐓̃⨂𝐗̅)𝐋𝐅𝐩
𝐼) + 𝐫̃̂𝐡̅
(19c)So far, the methodology founds on the following ten elements:
• the 𝐼 × 𝐼𝑖 matrix 𝐗̅ with element 𝑥̅𝑗𝐶 indicating the input coefficient for total energy use (i.e. the total use of energy in industry j in country C per unit of industry j’s output);
• the 𝐼 × 𝐼𝑖 matrix 𝐓 with element 𝑡𝑗𝐶 indicating the RE consumption as a share of total energy used in industry j in country C;
• the 𝐼 × 𝐼𝑖 matrix 𝐓̈ with element 𝑡̈𝑗𝐶 indicating the nuclear energy consumption as a share of total energy used in industry j in country C;
• the 𝐼 × 𝐼𝑖 matrix 𝐓̃ with elements 𝑡̃𝑗𝐶 indicating the Non-RE consumption as a share of total energy used in industry j in country C;
• the 𝐼 × 𝐼𝑖 matrix 𝐋 (the Leontief inverse) with elements 𝑙𝑗𝑘𝐶𝑁 indicating the amount of output that needs to be produced in industry j in country C to satisfy one unit of final demand for product k from country N;
• the 𝐼 × 𝐼𝑖 matrix 𝐅 encompassing all final demands with deliveries from industry j in country C for final demands in country N;
• the 𝐼-element vector 𝐫 with elements 𝑟 describing the share of renewable energy in the total energy consumed directly by households;
• the 𝐼-element vector 𝐫̈ with elements 𝑟̈indicating the total nuclear energy directly consumed by households as a share of their total energy consumption;
• the 𝐼-element vector 𝐫̃ with elements 𝑟̃ indicating the total Non-RE consumed directly by households as a share of their total energy consumption;
• the 𝐼-element vector 𝐡̅ with element ℎ̅ showing total energy consumed directly by households in country C.
Appendix B6
Part VI – Decomposition Forms
households’ direct use ((𝐫̂ + 𝐫̈̂ + 𝐫̃̂)𝐡̅). In this framework, the change in the use of energy can be split into changes in the contribution of total energy consumption Δ𝐗̅ in 𝐗̅, the shares of RE, nuclear energy, and Non-RE consumption as Δ𝐓 in 𝐓, Δ𝐓̈ in 𝐓̈, and Δ𝐓̃ in 𝐓̃, and so forth. This is yet only one option for decomposing according to the SDA methodology. Dietzenbacher and Los (1998) find that the unweighted average is a suitable means to cope with this problem and show that it can be obtained by taking the average of two polar forms. Referring to the study at hand, the changes of total energy use denoted by equation (18) 𝐞̅ = 𝐏𝐠̅ + 𝐡̅ = (((𝐓 + 𝐓̈ + 𝐓̃ )⨂𝐗̅) 𝐋𝐅𝐩𝐼) + ((𝐫̂ + 𝐫̈̂ + 𝐫̃̂)𝐡̅) can be decomposed for the changes in each of its determinants over time. For example, Δ𝐓 = 𝐓1− 𝐓0describes the changes in RE based upon two points in time. From this follows the first polar decomposition for total energy use that we label with the subscript 𝑎 when we consider the country level.
So far, we referred to 𝐅𝐩𝐼 and 𝐅𝐩𝐶, but henceforth we note the determinant final demands by way of simplicity as F for the polar decomposition although it is still included in the computation process.
Δ𝐞̅𝑎= ((Δ𝐓 + Δ𝐓̈ + Δ𝐓̃)⨂𝐗̅1𝐋1𝐅1) + ((𝐓0+ 𝐓̈0+ 𝐓̃0)⨂Δ𝐗̅ 𝐋1𝐅1) +
((𝐓0 + 𝐓̈0+ 𝐓̃0)) ⨂𝐗̅0(Δ𝐋)𝐅1+ ((𝐓0+ 𝐓̈0+ 𝐓̃0)) ⨂𝐗̅0𝐋0 (Δ𝐅) +(Δ𝐫̂ + Δ𝐫̈̂ + Δ𝐫̃̂)𝐡̅1+ (𝐫̂0+ 𝐫̈̂0+ 𝐫̃̂0)Δ𝐡̅
In a next step, we can denote the second polar decomposition for RE consumption that is labelled by the subscript 𝑏 that can be derived in the same way as the one above
Δ𝐞̅𝑏 = ((Δ𝐓 + Δ𝐓̈ + Δ𝐓̃)⨂𝐗̅0𝐋0𝐅0) + ((𝐓1+ 𝐓̈1+ 𝐓̃1)⨂Δ𝐗̅ 𝐋0𝐅0) +
((𝐓1+ 𝐓̈1+ 𝐓̃1)) ⨂𝐗̅1(Δ𝐋)𝐅0+ ((𝐓1+ 𝐓̈1+ 𝐓̃1)) ⨂𝐗̅1𝐋1 (Δ𝐅) +(Δ𝐫̂ + Δ𝐫̈̂ + Δ𝐫̃̂)𝐡̅0 + (𝐫̂1+ 𝐫̈̂1+ 𝐫̃̂1)Δ𝐡̅
In the last step, we can calculate the average of the two polar decompositions by
Having performed the decompositions for changes in total energy use, we can now write the SDA for the second study on the changes in the consumption of the three types of energy sources in production, based on equations 12, 14, and 16 that use the terms 𝐏𝐠, 𝐏𝐠̈, and 𝐏𝐠̃.
Δ𝐠𝑎 = ((Δ𝐭⨂𝐠̅1)′𝐏′+ (𝐭
0⨂Δ𝐠̅)′𝐏′)
In a next step, we can denote the second polar decomposition that is labelled by the subscript 𝑏 that can be derived in the same way as the one above
Δ𝐠𝑎 = ((Δ𝐭⨂𝐠̅0)′𝐏′+ (𝐭
1⨂Δ𝐠̅)′𝐏′)
In the following, we can calculate the average of the two polar decompositions
Δ𝐠 = 𝐠1 − 𝐠0 = (𝐠𝑎+ 𝐠𝑏)/2
In the same fashion, we perform the decompositions for 𝐠̈, nuclear energy and 𝐠̃, Non-RE, equations 14, and 16, respectively.
Appendix B7
Part VII– Technological and trade structure contributions
Given energy transition largely goes hand in hand with technological progress, it seems adequate to further split up our equation (18) in regard to changes in its technological as well as trade structure components. The former denotes for instance the use of less inputs in order to produce the same output whereas the latter describes a shift in the origin of the input, for instance a different country, whilst maintaining the amount of inputs and produced output. The division into the changes in the technological and trade-related components can be performed using the change in the Leontief inverse (Δ𝐋) that proxies changes in the input coefficients of the matrix B. This break down procedure of the changes in the input coefficients into its two contributors follows Oosterhaven and van der Linden (1997) and requires in the first instance to formulate Δ𝐋 like Δ𝐁
For the first polar equation Δ𝐞̅𝑎 ((𝐓0 + 𝐓̈0+ 𝐓̃0)) ⨂𝐗̅0(Δ𝐋)𝐅1the initial changes in the contribution of L, is substituted by 𝐋0(∆𝐁)𝐋1 that subsequently gives
((𝐓0+ 𝐓̈0 + 𝐓̃0)) ⨂𝐗̅0(Δ𝐋)𝐅1 = ((𝐓0+ 𝐓̈0 + 𝐓̃0)) ⨂𝐗̅0𝐋0(∆𝐁)𝐋1𝐅1 (21a)
For the second polar equation Δ𝐞̅𝑏 the replace ∆𝐋 by 𝐋1(∆𝐁)𝐋0 in ((𝐓1+ 𝐓̈1+ 𝐓̃1)) ⨂𝐗̅1(Δ𝐋)𝐅0 which gives
((𝐓1+ 𝐓̈1+ 𝐓̃1)) ⨂𝐗̅1(Δ𝐋)𝐅0 = ((𝐓1+ 𝐓̈1 + 𝐓̃1)) ⨂𝐗̅1𝐋1(∆𝐁)𝐋0𝐅0 (21b)
Given we want to split up the technological as well as trade-related components of the Leontief inverse, the two contributions have to be expressed in matrix notation with their respective coefficients that are described in matrices V, and Q. These are noted as
𝐕 = [ 𝐕1 ⋯ ⋮ ⋱ 𝐕𝑁 ⋮ ⋯ 𝐕𝐼 ⋰ ⋮ 𝐕1 ⋯ 𝐕𝑁 ⋯ 𝐕𝐼 ⋮ ⋰ 𝐕1 ⋯ ⋮ 𝐕𝑁 ⋱ ⋮ ⋯ 𝐕𝐼] where 𝐕𝐶 = ∑ 𝐁𝐶𝑁
𝐶 with its element 𝑣𝑗𝑘1𝑁 = 𝑣𝑗𝑘2𝑁 = ⋯ = 𝑣𝑗𝑘𝐶𝑁 = ∑ 𝑏𝐶 𝑗𝑘𝐶𝑁 yielding the total amount of input of good j (i.e. irrespective of the inputs’ origin country C) per unit of output of good k in country N. The share of this amount stemming from country C is described by 𝑞𝑗𝑘𝐶𝑁 = 𝑏𝑗𝑘𝐶𝑁/𝑣𝑗𝑘𝐶𝑁 = 𝑏𝑗𝑘𝐶𝑁/ ∑ 𝑏𝐶 𝑗𝑘𝐶𝑁. Note that these shares denote import shares when 𝐶 ≠ 𝑁. Hence, we can write
𝐁 = 𝐐⨂𝐕
At last, the deviation in the technical and trade-related input coefficients can be decomposed as
Δ𝐁 =1
2(Δ𝐐)⨂(𝐕1+ 𝐕0) + 1
2(𝐐1+ 𝐐0)⨂(Δ𝐕) (22)
Appendix B8
Part VIII– Final SDA form for seven determinants of change in total energy consumption
Using the two polar decomposition method taking their average which is reflected by Δ𝐞̅ = 𝐞̅1− 𝐞̅0 = (𝐞̅𝑎+ 𝐞̅𝑏)/2 , we now can write
Δ𝐞̅ = 1 2((Δ𝐓 + Δ𝐓̈ + Δ𝐓̃)⨂𝐗̅1𝐋1𝐅1) + 1 2((Δ𝐓 + Δ𝐓̈ + Δ𝐓̃)⨂𝐗̅0𝐋0𝐅0) + (23a) 1 2((𝐓0+ 𝐓̈0+ 𝐓̃0)⨂Δ𝐗̅ 𝐋1𝐅1) + 1 2((𝐓1+ 𝐓̈1+ 𝐓̃1)⨂Δ𝐗̅ 𝐋0𝐅0) + (23b) 1 4((𝐓0+ 𝐓̈0+ 𝐓̃0)) ⨂𝐗̅0𝐋0(Δ𝐐)⨂(𝐕1+ 𝐕0)𝐋1𝐅1+ 1 4((𝐓1+ 𝐓̈1+ 𝐓̃1)) ⨂𝐗̅1𝐋1(Δ𝐐)⨂(𝐕1+ 𝐕0)𝐋0𝐅0+ (23c) 1 4((𝐓0+ 𝐓̈0+ 𝐓̃0)) ⨂𝐗̅0𝐋0(𝐐1+ 𝐐0)⨂(Δ𝐕)𝐋1𝐅1+ 1 4((𝐓1+ 𝐓̈1+ 𝐓̃1)) ⨂𝐗̅1𝐋1(𝐐1+ 𝐐0)⨂(Δ𝐕)𝐋0𝐅0+ (23d) 1 2((𝐓0+ 𝐓̈0+ 𝐓̃0)) ⨂𝐗̅0𝐋0 (Δ𝐅) + 1 2((𝐓1+ 𝐓̈1+ 𝐓̃1)) ⨂𝐗̅1𝐋1 (Δ𝐅) + (23e) 1 2(Δ𝐫̂ + Δ𝐫̈̂ + Δ𝐫̃̂)𝐡̅1+ 1 2(Δ𝐫̂ + Δ𝐫̈̂ + Δ𝐫̃̂)𝐡̅0+ (23f) 1 2(𝐫̂0+ 𝐫̈̂0+ 𝐫̃̂0)Δ𝐡̅ + 1 2(𝐫̂1+ 𝐫̈̂1+ 𝐫̃̂1)Δ𝐡̅ (23g)
These seven contributions can be consolidated into five drivers as follows:
• technological changes consisting of changes ∆𝐗̅ in the input coefficients for total energy use (23a), as well as changes Δ𝐕 in technology coefficients (23d);
• changes in the international trade integration based on production fragmentation measured by changes Δ𝐐 in the import shares of intermediate inputs (23c);
• changes in the final demands Δ𝐅 (23e);
• changes in energy inputs consisting of changes Δ𝐓, Δ𝐓̈, and Δ𝐓̃ in the share of RE, nuclear
energy, and Non-RE consumption relative total energy use in production (23a) as well as energy input changes Δ𝐫, Δ𝐫̈, andΔ𝐫̃ directly used by households (23f);
Appendix B9
Part IX– Final SDA form for two determinants of change in RE, nuclear energy, and Non-RE consumption in production
Using the two polar decomposition method taking their average which is reflected byΔ𝐠 = 𝐠1− 𝐠0 = (𝐠𝑎+ 𝐠𝑏)/2, we now can write
Δ𝐠 = 1 2(Δ𝐭⨂𝐠̅1) ′𝐏′+ 1 2(Δ𝐭⨂𝐠̅0) ′𝐏′+ (24a) 1 2(𝐭0⨂Δ𝐠̅)′𝐏′ + 1 2(𝐭1⨂Δ𝐠̅)′𝐏′ (24b)
The same type of SDA is also used for to calculate Δ𝐠̈ as well as Δ𝐠̃ Δ𝐠̈ = 1 2(Δ𝐭̈⨂𝐠̅1) ′𝐏′+ 1 2(Δ𝐭̈⨂𝐠̅0) ′𝐏′+ (25a) 1 2(𝐭̈0⨂Δ𝐠̅)′𝐏′ + 1 2(𝐭̈1⨂Δ𝐠̅)′𝐏′ (25b) Δ𝐠̃ = 1 2(Δ𝐭̃⨂𝐠̅1) ′𝐏′+ 1 2(Δ𝐭̃⨂𝐠̅0) ′𝐏′+ (26a) 1 2(𝐭̃0⨂Δ𝐠̅)′𝐏′ + 1 2(𝐭̃̈1⨂Δ𝐠̅)′𝐏′ (26b)
As a result, we obtain two contributions for each of the three SDAs can be consolidated into two types of drivers:
• changes in energy shares consisting of changes Δ𝐭, Δ𝐭̈, and Δ𝐭̃ that drive changes in total RE, nuclear energy, and Non-RE consumption in production (24a, 25a, and 26a);
• changes in total energy consumption Δ𝐠̅ in production driving total RE, nuclear energy, and Non-RE use (24b, 25b, and 26b);
in this study that steer changes in production. At last, we can quantify how much each of the three drivers explains deviation in total RE, nuclear energy, and Non-RE use in production. This can be illustrated using the following example: suppose that Δ𝐠̅, which is total energy consumption in production are driven by 60% due to final demands, that are insights gained through the first SDA study on changes in total energy use due to drivers. Changes in Δ𝐭 , the share in RE in total energy consumption by industries drives Δ𝐠, the total RE energy consumption in production by 30%. The last is assumption that Δ𝐠̅, total energy consumption in production, drive Δ𝐠, RE consumption in production by 20%. Thus, we can deduct that final demands drive Δ𝐠 by 12% given the 20% changes in Δ𝐠 due to changes Δ𝐠̅ can be substituted into the 60% changes in Δ𝐠̅ driven by final demands. This exercise can is equally performed for all three drivers in regards to other types of energy sources and displayed in appendix C1 together with the cumulative results in appendix C2.
Appendix B10 Part X – Chaining of results
For the time-period covered in this study ranging from 2000-2014, the WIOD GMRIO provides data in current (CU) as well as previous year’s prices (PYP). According to the Arto and Dietzenbacher approach (2014), we can chain the results in their physical unit or volume changes. This is done by taking a variable (e.g. the RE input in TJ per million US Dollars of output) in PYP for y1 that gives 𝑎𝑦1𝑃𝑌𝑃 and the same variable, but in year y0 in current prices, in order to obtain the changes between both years
∆𝑎𝑦1−𝑦0 = 𝑎𝑦1𝑃𝑌𝑃− 𝑎𝑦0𝐶𝑈𝑅
As a result, we obtain volume changes given that the variable is expressed in same prices in both cases. In an analogous manner, the volume changes can be obtained between y2 and y1
∆𝑎𝑦2−𝑦1 = 𝑎𝑦2𝑃𝑌𝑃− 𝑎𝑦1𝐶𝑈𝑅
At last we can calculate the difference between years y0 to y2 that can be expressed as chaining of results for both previous operations
∆𝑎𝑦2−𝑦0 = ∆𝑎𝑦2−𝑦1+ ∆𝑎𝑦1−𝑦0 = (𝑎𝑦2𝑃𝑌𝑃− 𝑎
Appendix C
Table C1 Changes in RE, nuclear energy, and Non-RE consumption in production due to drivers of changes in total industrial energy consumption, 2000-2014
Table C2 Cumulative changes in absolute percent in RE, nuclear energy, and Non-RE consumption in production due to drivers of changes in total industrial
energy consumption, 2000-2014
Appendix D Matlab script for computations of analysis for 2000-2014
