1
Assessing future carbon emissions
through energy modelling:
the relevance of background input data
Supervisor: Matteo Vincenzo Rocco
Author: Giuseppe Andrea Romeo
ID Number: 863163
Academic Year 2018 - 2019
POLITECNICO DI MILANO
SCHOOL OF INDUSTRIAL AND INFORMATION ENGINEERING
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Index
Sommario ... 7
Abstract ... 8
Chapter 1 Introduction ... 9
1.1 Aims and research themes ... 9
1.2 Introduction to energy in Africa ... 10
1.3 Introduction to energy in Sub-Saharan Africa ... 12
1.4 Introduction to Kenya ... 13
Chapter 2 Methods and models ... 14
2.1 Supply and Use Tables ... 14
2.1.1 Starting from the roots: Introduction to Supply – Use framework ... 14
2.1.2 Structure of a Supply table ... 15
2.1.3 Structure of a Use Table ... 16
2.1.4 Transformation into symmetric input-output tables: overview ... 18
2.1.5 Transformation into symmetric input-output tables: calculation procedure .. 21
2.2 Input – Output Analysis ... 23
2.3 Matrix Difference Statistics ... 29
2.4 The Input – Output Models ... 31
2.5 The Hybrid Input – Output framework ... 34
2.6 Update of the base year Input-Output model for future scenarios ... 37
2.7 OSeMOSYS model ... 38
2.8 Linking The IOTs models and the OSeMOSYS model ... 39
Chapter 3 Case study ... 42
3.1 Energy situation in Kenya: background and overview ... 42
3.2 Resource Potential and Limits ... 46
3.2.1 Geothermal ... 46
3.2.2 Hydro ... 48
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3.2.4 Wind ... 50
3.2.5 Solar ... 51
3.2.6 Biomass and Biogas ... 54
3.2.7 Nuclear ... 55
3.3 Scenario definition ... 56
3.3.1 Government of Kenya Scenario ... 56
3.3.2 New Policy Scenario ... 57
3.3.3 All Renewable Scenario ... 58
3.4 Input parameters of OSeMOSYS ... 58
3.4.1 Population growth ... 58
3.4.2 Electrification level ... 59
3.5 OSeMOSYS results useful as input for HIOTs ... 61
3.5.1 Government of Kenya Scenario ... 61
3.5.2 New Policy Scenario ... 63
3.5.3 All Renewable Scenario ... 65
Chapter 4 Results and comments ... 67
4.1 Matrix Difference Statistics results ... 67
4.1.1 Final demand ... 68
4.1.2 Inter-industry transaction matrix ... 69
4.1.3 Total Monetary Output vector ... 70
4.2 Introduction to energy and economic results ... 71
4.3 Total Primary Energy Supply using LBM... 72
4.4 CO2 emissions using LBM ... 74
4.5 CO2 emissions intensity and GDP using LBM ... 76
4.6 Distance in database results: LBM – EORA ... 78
4.6.1 TPES, CO2 emissions, Emissions Intensity and GDP: Government of Kenya Scenario ... 78
4.6.2 TPES, CO2 emissions, Emissions Intensity and GDP: New Policy Scenario ... 80
4.6.3 TPES, CO2 emissions, Emissions Intensity and GDP: All Renewable Scenario .. 82
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References ... 86
List of figures
Figure 1 Number and share of people without access to electricity in Africa ... 12Figure 2 Transformation of supply and use tables to input-output tables ... 20
Figure 3: Supply and Use framework ... 21
Figure 4: Simplified Input - Output Table ... 22
Figure 5: Endogenous and exogenous transactions within the system ... 23
Figure 6: Compact visualization of an IOT ... 26
Figure 7: Coefficients version of an IOT ... 27
Figure 8: Final structure of Leontieff extended model ... 27
Figure 9: Hybrid Input - Output Framework ... 28
Figure 10: Coefficient version of an HIOT ... 35
Figure 11: Graphic representation of relevant parameters for OSeMOSYS ... 39
Figure 12: Kenya energy mix share in 2015 ... 42
Figure 13: Institutional framework of Energy Sector in Kenya ... 43
Figure 14: Historical Electricity Generation by Fuel (IEA, 2015) ... 46
Figure 15: Map of Geothermal areas in Kenya ... 47
Figure 16: Historic Oil consumption in Kenya ... 49
Figure 17: Wind speed map (Global Wind Atlas, 2015) ... 50
Figure 18: Wind Power density (Global Wind Atlas, 2015) ... 51
Figure 19: Yearly average Direct Normal Irradiance in Kenya ... 52
Figure 20: Image showing the ratio KWh over KWpeak installed ... 53
Figure 21: Total Primary Energy Supply by source ... 54
Figure 22: Electricity demand projections in the three scenarios ... 57
Figure 23: Population in Kenya ... 59
Figure 24: Population growth rate in Kenya ... 59
Figure 25: Electricity demand according to GoK, NPS and ARS ... 60
Figure 26: Electrification level trends in GoK, NPS, ARS ... 60
Figure 27: Total Annual Capacity Installed in GoK Scenario ... 62
Figure 28: Electricity Production and GHG emissions according to GoK Scenario ... 62
Figure 29: Annual new capacity Installed in New Policy Scenario ... 64
Figure 30: Electricity production and GHG emissions according to the NPS ... 64
Figure 31: Annual new capacity installed according to All Renewable Scenario ... 66
Figure 32: Electricity production and GHG emissions according to ARS ... 66
Figure 33: Simplified structure of an IOT ... 67
Figure 34: Graphical comparison of the two final demands ... 69
Figure 35: TPES differences GoK Scenario. LBM - EORA ... 79
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Figure 37: CO2 emissions/GDP and GDP. GoK ... 80
Figure 38: Total Primary Energy Supply differences. NPS. LBM – EORA ... 81
Figure 39: CO2 emissions NPS. LBM - EORA ... 81
Figure 40: CO2 emissions/GDP and GDP. NPS ... 82
Figure 41: TPES New Policy Scenario. LBM - EORA ... 83
Figure 42: CO2 emissions All Renewable Scenario. LBM – EORA ... 83
Figure 43: CO2 emission intensity and GDP. All Renewable Scenario ... 84
List of Tables
Table 1: Simplified Supply Table ... 15Table 2: Simplified Use Table ... 17
Table 3: Simplified Supply - Use framework ... 17
Table 4: Summary of Matrix Difference Statistics Indeces ... 31
Table 5: Resume of the step-by-step disaggregation procedure ... 34
Table 6: Endogenous vs Exogenous variables in the integrated model ... 41
Table 7: Installed Capacity by KenGen in Kenya (2017) ... 44
Table 8: Installed Capacity by REA in Kenya (2017) ... 45
Table 9: Installed Capacity by IPPs in Kenya (2017) ... 45
Table 10: Comparison of total final demand of the two models in 2009 ... 68
Table 11: Comparison of final demand of the two models ... 68
Table 12: Inter-industry transaction matrix comparison ... 69
Table 13: Total output vector comparison... 70
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Sommario
La scelta della base di dati è fondamentale per i responsabili politici di una nazione in via di sviluppo. La tesi analizza più scenari e conseguenti implicazioni energetiche applicando una metodologia per disaggregare le tecnologie di generazione di potenza usando due diverse basi di dati. La prima è costruita in loco grazie alla raccolta di dati ed informazioni da numerose istituzioni e compagnie private mentre la seconda è EORA. Un modello energetico (OSeMOSYS) è stato collegato ad un modello macroeconomico (Modello Ibrido Input – Output) per prevedere le future emissioni di diossido di carbonio non dal solo settore energia elettrica ma dall’economia in toto. Il caso studio proposto è un paese in via di sviluppo che vuole rientrare entro il 2030 nella classificazione dei paesi con reddito medio – alto (World Bank). Le implicazioni di questo obiettivo sono varie e dipendono dal percorso di sviluppo seguito dal paese nel prossimo decennio. Tre scenari sono stati applicati variando la produzione totale di energia elettrica e la percentuale della popolazione avente accesso ad elettricità. I risultati ottenuti applicando la metodologia proposta al caso studio in oggetto sono numerosi. Il primo riguarda il livello di emissioni prodotte nel 2030 usando le due basi di dati sotto le stesse ipotesi: l’ordine di grandezza della differenza dei risultati è all’incirca quanto il paese ha emesso globalmente nel 2015. Un'altra importante conclusione riguarda l’importanza del settore energia elettrica in un paese in via di sviluppo. Il settore che emette più gas serra in assoluto nell’economia non è l’industria energia elettrica ma quello dei trasporti, il quale da solo, emette tre volte quello che emette il primo. Dunque, ridurre le emissioni derivanti dalla produzione di energia elettrica è importante ma più interessante è l’importanza delle innovazioni nel settore trasporti, il quale è quello che effettivamente influisce maggiormente sul bilancio globale. In conclusione, futuri sviluppi di questo lavoro potrebbero centrarsi sulla disaggregazione delle tecnologie usate nel settore trasporti così da poter produrre un migliorato strumento per l’abbattimento delle emissioni di gas serra di un paese in via di sviluppo.
Parole chiave: modelli energetici; base di dati; differenze statistiche di matrici; Analisi Input – Output; OSeMOSYS;
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Abstract
Database choice is crucial for policy makers. This thesis analyzes multiple scenarios and selected implications while applying a methodology for disaggregating electricity power sector using two different databases. The first one is a locally built model that was produced gathering information from a number of local data providers while the second one is EORA. An energy model (OSeMOSYS) was linked to a macro-economic model (Hybrid Input – Output Model) in order to figure out the future carbon emission not of the power sector only but of the economy as a whole. The case study proposed is a developing country whose target is to enter in the upper-middle-income economy classification of the World Bank by 2030: Kenya. The implications of this objective are various and depend on the development path that the country will follow in the next decade. Three scenarios were applied to the country’s economy while different electricity demands and energy access levels were explored. The interesting outcomes from applying the proposed methodology to the case study are numerous. The first one regards the emission levels predicted in 2030 using the two databases under the same assumptions: the rough order of magnitude of difference is about the actual GHG emissions of Kenya in the year 2015. Another important conclusion regards the relevance of electricity sector in this developing country. The principal absolute emitter in Kenya is not the power generation sector but the transport one which alone emits three times the level of electricity sector. This is a fundamental finding and also one of the most relevant sources of distance between the two databases. Hence, decarbonizing power sector mix is important but more interesting is the focus on innovations required in the transport sector which actually drive global emissions of the country. In conclusion, future developments of this work should further investigate innovation in transport sector and hence disaggregation of this economic industry if the objective is providing a influent tool for the abatement of GHG harmful emissions.
Key words: energy models; databases; matrix difference statistics; Input – Output Analysis; OSeMOSYS;
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Chapter 1
Introduction
This chapter introduces the problems and the research questions addressed in this manuscript. First objectives and research themes are highlighted, then an overview of Africa’s main challenges is provided along with a brief introduction of Kenya current situation.
1.1 Aims and research themes
The idea for this thesis project came up during an ongoing collaboration between Politecnico di Milano and Technical University of Kenya (TU-K). The collaboration between the two institutions started with the objective of informing people and give access to a sound knowledge in the technical area of research.
In fact, Kenya is one of the fastest developing countries located in sub-Saharan Africa. It has experienced a 50% economic growth, increasing by 45% its energy demand in the last 10 years. Nairobi has a crucial role in this scenario since it reflects big effects of this development path on environmental impact accelerated by rapid urbanization.
The aim of this thesis is to provide a deep energy analysis of the country. Investigating critical material and energy flows it will be possible to understand more in detail the energy metabolism of the country. One way of tackling the problem of increasing energy demand is to understand embodied energy in the industries that characterize the economy. This turns out to be really important to identify energy hotspots (points/processes along the supply chain that shows the highest resource consumptions to be sustained). Therefore, the main goal is to promote energy efficiency improvements in the most energy demanding sectors of the Kenyan economy. The final purpose is to provide the government with a powerful tool for help policy makers facing increased energy demand, population and economic growth occurring within the country till 2030. The overarching aim of this study is to evaluate the future impact of electricity generation sector in Kenya.
The aim will be met by undertaking research under the following themes:
Research theme 1 (RT1): Calculating the difference between a locally built database and EORA database.
First, the common set of sectors covered by the Kenyan database and EORA are identified and then their CO2 emissions are calculated using each database. Yet from this starting
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point a key issue is highlighted: if every SRIO1 database calculates different CO
2 emission
levels, how can policy makers be confident that the results are useful? Results from one model shouldn’t be trusted by hard, but rather they should be carefully compared with others using different approaches so that validation of the findings could be verified. Research theme 2 (RT2): Determining whether results produced by each database are statistically similar to each other.
This research theme will focus on discovering the distance between two databases. The analysis will identify if there are particular elements of the database that are substantially different between two IO models. RT2 uses as metric of comparison matrix difference statistics (MDS). This is further used as method for understanding the SIOT2 database
differences.
Research theme 3 (RT3): Determining actual CO2 emission level in Kenya and, under three different scenarios, predicting future ones till the year 2030.
RT3 represents the application of the methodology proposed in the thesis. It uses an optimization model that maximizes final demand constraint to the total electricity output, that is exogenously given, while optimizing allocation of resources among different producing sectors. The point is to underline the importance of energy mix in a developing economy that must face not only energy related challenges but also several other issues simultaneously like poverty reduction, improved education, improved water access and so on. RT3 brings together multiple information to provide a final estimation of how emission levels and GDP growth will vary under pre-defined assumptions.
1.2 Introduction to energy in Africa
One out of every five people on earth has no access to electricity. Energy access is a fundamental problem that must be tackled as soon as possible from governments, institutions and through international cooperation between countries. Access to energy is a key imperative to improve quality of life and to attain an upper middle-income economy by the year 2030 for Kenya. Lack of access to electricity services dramatically undermines all productive sector of the country, consequently inhibiting economic development.
Energy is not a basic need, however it is an enabler of all sectors of development. As Yemane et al. sustain, while the availability of electricity by itself is not a panacea for the economic and social problems facing Africa, the supply of electricity is nevertheless
1 SRIO: Single Region Input – Output 2 SIOT: Symmetric Input – Output Table
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believed to be a necessary requirement for the economic and social development of Africa [1]. Having modern energy unlocks access to improved healthcare, improved education and improved economic opportunities resulting in even a longer life. While to those that do not have energy, it is a major constraint on their social and economic development. Pasten and Santamarina [2] sustain that energy access has a key role on development of a nation. The factors that account to define the quality of life include:
• Improved Water Access: Proportion of the population using improved drinking water sources, such as public tap, tube well, and protected springs.
• Life Expectancy at Birth: The number of years a newborn infant would live if the mortality patterns at the time of birth prevail throughout the individual’s life. • Infant Mortality Rate: The number of infants that die before reaching one year of
age, per 1000 live births in a given year.
• Mean Years of Schooling: Lifetime number of years of education received by individuals aged 25 and older.
They conclude that electrification level and energy consumption per capita do influence quality of life, especially in developing countries. Yet, to this day, one out of five people still lacks access to modern electricity and approximately 3 billion people in the world rely on wood, coal, charcoal or animal waste for cooking and heating.
On September 25th 2015, countries adopted a set of goals to end poverty, protect the planet and ensure prosperity for all as part of a new sustainable development agenda. Each goal has specific targets to be achieved over the next 15 years.
The goal number 7 of the Sustainable Development Goals focuses on “Ensure access to affordable, reliable, sustainable and modern energy for all”.
This goal identifies the following items to be respected by 2030:
• ensure universal access to affordable, reliable and modern energy services; • increase substantially the share of renewable energy in the global energy mix; • double the global rate of improvement in energy efficiency;
• enhance international cooperation to facilitate access to clean energy research and technology, including renewable energy, energy efficiency and advanced and cleaner fossil-fuel technology, and promote investment in energy infrastructures; • expand infrastructure and upgrade technology for supplying modern and sustainable energy services for all in developing countries, in particular least developed ones, small island developing States, and land-locked developing countries, in accordance with their respective programs of support.
Improved energy access often comes with a high cost. Especially in developing countries the large use of cheap fossil fuel-based power plant leads to high environmental and social
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impacts. Though, a focus on how energy is provided, what are the sources employed and how the energy supply-chain develops are of paramount importance to guarantee the sustainability of the underlined goal.
1.3 Introduction to energy in Sub-Saharan Africa
Sub-Saharan Africa has more people living without access to electricity than any other world region – more than 620 million people, and nearly half of the global total (Figure 1). It is also the only region in the world where the number of people living without electricity is increasing, as rapid population growth is outpacing the many positive efforts to provide them access. In 37 sub-Saharan countries the number of people without electricity has increased since 2000 while the regional total rose by around 100 million people. On a more positive note, about 145 million people gained access to electricity since 2000, led by Nigeria, Ethiopia, South Africa, Ghana, Cameroon and Mozambique. Overall, the electricity access rate for sub-Saharan Africa has improved from 23% in 2000 to 32% in 2012 [3].
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1.4 Introduction to Kenya
In Kenya the situation is slightly different with respect to the rest of East Africa. In 2016, access to electricity was available to 56 percent of the population, while over 80 percent of Kenyans relied on traditional use of biomass as primary source of energy for cooking and heating [4].
These facts make urgent the application of sound policies oriented at improving water and energy access while fostering economic development, ensuring decent life conditions for the highest possible percentage of the population. In order to tackle these problems, it is important to start acting as soon as possible with powerful instruments to first detect and then predict while correcting numerous aspects of future progresses of this country. One of these instruments is macro-economic modelling. A well-established framework is the one introduced by Leontief in the 30s usually referred as Input – Output framework. Concerning energy modelling, in order to be able to understand the impact of future electricity generation mixes on the national economy, OSeMOSYS represents a powerful solution. The choice has fallen on these two models since for both of them a dataset was available in the base year considered for the study.
In the following chapters a link between the two models will be proposed and applied and implications on the background economy of future electricity scenarios are going to be discussed deeply.
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Chapter 2
Methods and models
Abstract This chapter gives a brief description of the methods used to build the model applied in this project work, including their general mathematical expression. A comprehensive explanation of the Input – Output basic framework and an overall presentation of the models are given. A more detailed explanation of how the techniques have been employed to specifically understand the differences between the analyzed databases is provided later on in dedicated sections (Chap. 3 and 4).
2.1 Supply and Use Tables
2.1.1 Starting from the roots: Introduction to Supply – Use framework
Supply – Use Tables and Input – Output Tables offer a detailed portrait of a country. Actually, they provide a deep analysis of different aspects, allowing to fully characterize a complex system: from the process of production, through the use of goods and services (products) towards the income generated in that production [5]. Despite the required efforts, this approach leads to a wide range of benefits. In fact, Supply - Use Tables (SUTs further on) provide a consistent framework for balancing national accounts. As far as the core of the accounting system is concerned, they create noticeable effects on quality and stability of statistical results. Supply – Use Tables in combination with Input – Output Tables constitute the appropriate basis for many different types of analysis of a country, such as environmentally extended Input - Output analysis and social – economic accounting.
The supply and use framework enables detailed investigation of industries and products through a breakdown of the production account, the goods and services account and the generation of income account. These tables show the structure of the costs of production (input structure) and income generated in the production process (value added structure), the flow of goods and services produced within the country (output structure), and the flows of goods and services with the rest of the world (import structure). The underlying assumption is that industries use commodities to make commodities [6]. How “industries use commodities” is shown in the Use matrix while how “industries make commodities” is revealed by the Make (also said to be Supply) matrix.
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2.1.2 Structure of a Supply table
A Supply table shows the supply of goods and services by product and by type of supplier, distinguishing supply by domestic industries and imports from those of other countries. In the case considered, imports were treated as they were produced by the analyzed national economy. Input structure of imports hence is treated as the one of products produced by the country itself. The production matrix (supply matrix) shows the domestic output of industries by products. So, in this matrix it is possible to recognize how industries supply goods and services to produce products.
Table 1: Simplified Supply Table
Primary (main) activities of industries are reported on the diagonal of the production matrix while secondary activities of industries are reported off the diagonal. As each industry can produce not only products characteristic for that industry but also other products, the production matrix of domestic output has not only data entries on the main diagonal. The production of products representing the core business of an industry is called primary output, while all the rest secondary output. As an example, referring to the industry Petroleum products, production of biodiesel may be considered as primary activity. However, biodiesel production is manufactured with the help of alkali hydroxide whose homogeneous catalysis gives rise to some technological problems: a massive amount of wastewater, soap formation and glycerol [7]. These are the so called
byproducts: something produced in a usually industrial or biological process in addition
to the principal product3.
In order to distinguish between primary and secondary output of an industry, a relation between industries and products has to be defined based on the criteria of industrial origin. A hierarchy of primary and secondary product of industries is provided by European Classification system [5].
In order to fill in the SUTs, the relationships between industries and characteristic products does not have to be elaborated specifically since the applied European
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classifications (NACE4 and CPA5) are already structured upon that principle. Furthermore,
the classifications show this relationship directly in their coding system.
Moreover, concerning the Supply and Use Tables, the classification of products can be more detailed than the classification of industries. In this case the Supply and Use system is rectangular meaning that there are more products than industries. Only if the classification of products is as detailed as the classification of the industries, the system has a square format. As an example, the output of the dairy industry could be separately shown in the SUTs for the products of processed milk, butter, yoghurt, and cheese or only as one aggregate product for all Dairy Products. In the analyzed case, the two classifications were homogeneous among the two databases: same number of industries and products was adopted.
2.1.3 Structure of a Use Table
The Use Table is a product-by-industry based table with products and components of value added in the rows and industries, categories of final uses and imports in the columns. A Use Table (Table 2) shows the use of goods and services by product and by type of use, i.e. as intermediate consumption by industry, final consumption, gross capital formation or exports. Thus, a Use table shows how industries use the commodities in the economy. Furthermore, the table implements the components of value added by industry, i.e. compensation of employees, other taxes less subsidies on production, consumption of fixed capital and net operating surplus.
The table of intermediate use shows the intermediate consumption by products and by industry, the table of final uses shows the uses of products for final consumption, gross capital formation and exports, and the table of value added shows the components of value added by industry. Totals over the columns of intermediate and final uses show total use by products, totals over the rows of the intermediate table and the value-added table identify total inputs by industries [5]. It is possible to visualize better these information in the Table 2.
The columns in the use table reflect the cost structure of each specific industry. The intermediate consumption table thus identifies goods and services that are necessary to produce the primary and secondary outputs of industries.
This table has many more entries than the output matrix as some products are required in many industries to produce their output. For example, electricity is a product that is required in more or less all industries. On the other hand, there are certain products that are only being required in one or few industries. An example is crude oil which is only used in refineries.
4 NACE: Nomenclature générale des activités économiques 5 CPA: Statistical classification of products by activity
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Table 2: Simplified Use Table
Between Supply and Use Tables, two types of identities hold. In the Supply Table (Table 1) and the Use Table (Table 2) total output by industries is equal to total input by industries and total supply by products is equal to total use by products.
As in the Supply Table, the classification of products in the intermediate and final use tables can be more detailed than the classification of industries. However, the same level of detail for products and industries is used for the use table as well as for the supply table in both the analyzed databases.
The Supply Table and Use Table can be integrated in one unique framework. The simplified version of the Supply and Use system is shown in Table 3. In this combined form, the two main identities of the system can be clearly seen. Here, the production matrix (product by industry table: read “product” as input and “industry” as output) has been transposed to the corresponding make matrix (industry by product table: read “industry” as input and “product” as output) and the import column of the supply table to a row vector.
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As mentioned above, for both industries and products, the following identities can be observed:
• Output by industry = Input by industry
• Total supply by product = Total use by product.
Each industry output is equal to the sum of intermediate consumption plus value added. For each product, supply (output plus imports) equals the sum of intermediate consumption, final consumption, gross capital formation and exports.
2.1.4 Transformation into symmetric input-output tables: overview
Once the two databases are set as the one in Table 3 some assumptions are needed to transform the SUTs6 into SIOTs7. This is a crucial step and it is done because the symmetric
IO8 framework is much more useful as it is more flexible to be applied both for
environmental and energy analyses.
First of all, it is important to understand the intermediate consumption table. It shows for each industry the use of goods and services needed to produce the primary and the secondary outputs of an industry. For analytical purposes, assumptions about the relations between inputs and outputs are required, leaving aside the stream of production of the outputs (either primary or secondary). For the transformation of SUTs into symmetric IOTs, various assumptions have to be made and in some cases adjustments are required.
In order to perform the transformation an hypotesis must be formulated and one of these models can be applied to both databases so that a unique starting point is defined. The following four basic assumptions [5] are going to be analyzed:
Product by product input-output tables
• Product technology assumption (Model A).
Each product is produced in its own specific way, irrespective of the industry where it is produced.
• Industry technology assumption (Model B).
Each industry has its own specific way of production, irrespective of its product mix.
6 SUTs: Supply – Use Tables
7 SIOTs: Symmetric Input – Output Tables 8 IO: Input – Output
19 Industry by industry input-output tables
• Fixed industry sales structure assumption (Model C).
Each industry has its own specific sales structure, irrespective of its product mix. • Fixed product sales structure assumption (Model D).
Each product has its own specific sales structure, irrespective of the industry where it is produced.
The first two assumptions can be applied to compile product by product input-output tables. The product technology assumption (Model A) assumes that each product has its specific technology, irrespective of the productive industry. The industry technology assumption (Model B) assumes that each industry has its specific technology (in terms of inputs), irrespective of its product mix. These assumptions can also be applied simultaneously by implementing a hybrid technology assumption.
The transformation of SUTs to symmetric industry by industry IOTs is based on assumptions about the sales structure. The fixed industry sales structure assumption (Model C) assumes that each industry has its own specific sales structure, irrespective of its product mix. The fixed product sales structure assumption (Model D) assumes that each product has its own specific sales structure, irrespective of the industry where it is produced.
The selection of the appropriate type of IOTs (product by product vs. industry by industry) depends on the specific objective of the analysis: on the one hand the supply and use system offers a flexible solution, on the other hand industry by industry input-output tables are closer to statistical sources and actual market transactions. Product by product input-output tables are considered to be more homogenous in terms of cost structures and production activities.
The transformation of supply and use tables to input-output tables is visualized in Figure 2.
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Figure 2 Transformation of supply and use tables to input-output tables
The two selected databases were transformed into SIOTs using the Industry technology assumption (Model B). This was done since the purpose of the analysis is to have a focus on the industries that then are going to be used for the energy analysis. It is important to underline that for energy purposes this is the best choice since the commodity “electricity” for instance is produced in its own specific way of production, irrespective of the power plant that is producing it: the production mix does not affect the commodity production which, in this specific case, is a reasonable assumption.
The transformation procedure converts the product by industry system of the supply and use tables into a product by product system or industry by industry system. In the analyzed case, since the two databases use the same classification among products and industries (i.e.: number of industries = number of products) it is possible to infer that industries and products coincide in a one to one classification. From now on hence, the terms “industry” and “product” can be used indifferently due to the motivation given above.
In the case of an input-output table, the two types of identities in the supply and use system are now reduced to one type of identity. It is typical for symmetric input-output tables that for each product or industry input equals output and total supply equals total uses. These two equalities can be visualized in Figure 3.
• Total supply by product = Total use by product • Total input by product = Total output by product
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2.1.5 Transformation into symmetric input-output tables: calculation procedure
In the previous section an overview of SUTs and IOTs structure was provided. Here it is explained how the transformation is done using matrix algebra and equations.Figure 3: Supply and Use framework
•
𝐔(𝑝 𝑥 𝑖) = [𝑢
𝑖𝑗]
, Use Matrix •𝐕(𝑖 𝑥 𝑝) = [𝑣
𝑖𝑗], Supply Matrix
•
𝐞(𝑝 𝑥 1) = [𝑒
𝑗], Final demand vector
•𝐪(𝑝 𝑥 1) = [𝑞
𝑖], Total use of products
•
𝐱(𝑖 𝑥 1) = [𝑥
𝑗], Total output of industries
•
𝐡(1 𝑥 𝑖) = [ℎ
𝑗], value added
Products Industries Final demand Total outputs
Pr o d u ct s Use of products by industry
U
Sales of products to final demand e Total use of products q In d u st ri es Supply of products by industry V Total output of industries x Value added h To ta l in p u ts Total supply of products q' Total input of industries x'22
To transform a SUT table to a I-by-I SIOT, two additional matrices need to be calculated in order to generate
Z,
the product by product matrix for intermediates. These are:𝐁 = 𝐔𝐱̂
-1 (1)𝐃 = 𝐕𝐪
̂
-1 (2)𝐁
represents the input requirements for products per unit of output of an industry.𝐃
represents the market share coefficients of the make table [6]. Each column of𝐃
show what is the percentage of total amount of commodity j produced by industry i. Note that the column sum of𝐃
is unity.In order to generate the inter-industry transaction matrix in a canonical symmetric input-output table it is necessary to multiply
𝐁
and𝐃
to obtain𝐙
𝐈= 𝐃𝐁𝐱̂
(3)While to obtain the final demand by industry
𝐟
, the matrix𝐃
must be post-multiplied by𝐞:
𝐟 = 𝐃𝐞
(4)Figure 4: Simplified Input - Output Table
Industries Final demand Total outputs
In d u st ri es Inter-industry transaction matrix Z Sales of industries to final demand f Total output of industries x Value added h To ta l in p u ts Total input x'
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2.2 Input – Output Analysis
Input – Output Analysis (IOA) is the analytical framework originally developed in late 1930s by Wassily Leontief in order to analyze and understand the interdependence of industries within a given economy. During last decades, original IOA framework have been modified and developed in order to extend its evaluation to Environmental Impact Analysis. Given a system with n productive processes it is possible to connect each other by endogenous9 transactions of goods and services xij and exogenous10 transactions of
resources 𝐫𝐤𝐢. Each productive process need to satisfy an exogenously defined final demand 𝐟𝐢.
Each of these n productive processes will give a part of its production as an intermediate input for the other n – 1 processes. This can be stated in the following equation:
𝑥𝑖 = 𝑥𝑖1+ ⋯ + 𝑥𝑖𝑗+ ⋯ + 𝑥𝑖𝑛+ 𝑓𝑖 (5)
This relation is valid for each of the n productive processes:
1 11 1j 1n 1 i i1 ij in i n n1 nj nn n x = x + + x + + x f x = x + + x + + x f x = x + + x + + x f + + + (6)
This can be visualized in the following figure.
Figure 5: Endogenous and exogenous transactions within the system
9 Endogenous variable: dependent variable generated within a model
10 Exogenous variable: its value is independent from other variables in the system
System boundary Process 1 Process i Process n f1 fi fn rk1 rki rkn x1n,n1 x1i,i1 xin,ni x11 xnn xii
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Therefore, it is possible to rewrite the system analyzed in a matrix form, as usually done in common IO application.
• x (n x 1) is the total production vector. It is constituted by the n elements calculated through the previous equation
• f (n x 1) is the final demand vector
• Z (n x n) is the endogenous transaction matrix. The elements of Z are
x
ij • i (n x 1) is the row vector used to sum up the rows.The introduced expression can be synthetized in:
𝑥𝑖 = ∑ 𝑥𝑖𝑗+ 𝑛
𝑗=1
𝑓𝑖 (7)
And further in:
𝐱 = 𝐙𝐢 + 𝐟 (8)
To introduce the canonical Leontief Model a new parameter must be defined: the technical coefficient matrix 𝐀(𝑛 × 𝑛). The element 𝑎𝑖𝑗 in the 𝐀 matrix represents the output flows from process ith to process jth required to produce one single unit of the jth product.
𝐀(𝑛 × 𝑛) = 𝐙𝐱̂−𝟏 with: 𝑎𝑖𝑗= 𝑥𝑖𝑗
𝑥𝑗 (9)
The expression can be written as:
𝐱 = 𝐀𝐱̂𝐢 + 𝐟 → 𝐱 = 𝐀𝐱 + 𝐟 (10)
Working out this equation it is possible to obtain the canonical form the relation that in IOA links total output vector 𝐱 with final demand 𝐟 :
25 • I (n x n) is the identity matrix;
• A (n x n) is the technical coefficient matrix. It represents the amount of input produced by ith sector and consumed by jth necessary to the production • L (n x n) is the Leontief inverse matrix. It is the core of the Input-Output Analysis.
Each element of this matrix represents the embodied (direct and indirect) amount of ith product required by the jth process to satisfy one unit of jth product as final demand.
This equation represents the Leontief Production Model and explicitly accounts for the relation between final demand and total production. In order to account also for 𝐫𝐤𝐢, the exogenous transactions directly related with the ith process, it is necessary to introduce a new matrix: the exogenous transaction matrix 𝐑.
• 𝐑 (m x n) is the exogenous transaction matrix. Every row of the matrix is expressed in physical unit (J, hours, ktonCO2) and represents the total amount of
resources/emissions directly requested/emitted by each of the j processes present in the matrix. Every column represents all the exogenous resources/emissions directly requested/emitted by the jth process.
In order to create a coefficient version of 𝐑, it is necessary to multiply it by the inverse of the total production vector:
𝐁 = 𝐑𝐱̂−𝟏 with: 𝑏𝑘𝑗 = 𝑟𝑘𝑗
𝑥𝑗 (12)
In this way we obtain 𝐁. 𝐁 (m x n) is the intervention coefficient matrix, representing the amount of the kth direct exogenous transaction caused by the production of one unit of jth product. This 𝐁 of course is different from the market share coefficient matrix previously defined.
𝐞 = [(𝐈 − 𝐀)𝐓]−𝟏 𝐁𝐓= (𝐋 𝐁)𝐓= (𝐁 𝐋)𝐓 (13) e (n x m) is the specific embodied exogenous resources matrix. In this matrix an important information is hold: it represents the embodied exogenous resources per unit of final demand.The last equality holds for a property of the transposed matrix.
Thus, if 𝐞 is pre-multiplied by 𝐟̂, the diagonalized final demand, it is possible to obtain 𝐄.
𝐄 = 𝐟̂ 𝐞 = 𝐟̂ (𝐁 𝐋)𝐓 (14)
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Notice that elements of total embodied exogenous resource matrix 𝐄 obviously differ from the elements of the exogenous transaction matrix 𝐑: indeed, matrix 𝐄 can be interpreted as the allocation of exogenous transactions among final demand products while 𝐑 represents the total amount of resources/emissions directly requested/emitted by each of the j processes present in it.
However resources as energy [J], CO2 emissions [kton] and hours [h] are conservative
quantities, meaning that no matter how the allocation of them is spread among 𝐱 or 𝐟, the total request/emission must be the same. That is, the sum of all the resources/emissions directly requested/emitted by the entire system must be equal to the sum of the resources/emissions directly and indirectly requested/emitted by the final demand of products. In term of matrices this translates in:
{ 𝐑𝑚×𝑛⋅ 𝐢𝑛×1= 𝐑𝐭𝐨𝐭(𝑚 × 1)
[𝐢1×𝑛⋅ 𝐄𝑛×𝑚]𝐓= 𝐄𝐭𝐨𝐭(𝑚 × 1) (15)
𝐑𝐭𝐨𝐭= 𝐄𝐭𝐨𝐭 (16)
All the matrices computed can be visualized in the following figures.
Figure 6: Compact visualization of an IOT
From / To 1 … n Final demand Total production Process 1 Endogenous transactions matrix 𝐙(𝑛 × 𝑛) 𝐟(𝑛 × 1) 𝐱(𝑛 × 1) … Process n Resource 1 Exogenous transactions matrix 𝐑(𝑚 × 𝑛) … Resource m
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Figure 7: Coefficients version of an IOT
Figure 8: Final structure of Leontieff extended model
The Input-Output model of a generic productive system is primarily used to quantify the amount of exogenous transactions embodied in each product of the system, through the application of production model previously shown. However, the IO table can be further manipulated to deal with impact problems.
Impact models treat IO shocks. Two types of shocks can be imagined to be applied to national economies. First one would be a sudden change in national final demand. The model then reveals how a change in the final demand of the system respectively affects its total production and total embodied exogenous transactions using the following equations: 𝚫𝐱 = 𝐋𝚫𝐟 (17) 𝚫𝐄 = 𝚫𝐟̂(𝐁𝐋)𝚻 (18) From / To 1 … n Final demand Total production Process 1 Technical coefficients matrix 𝐀(𝑛 × 𝑛) = 𝐙𝐱̂−𝟏 𝐟(𝑛 × 1) 𝐱(𝑛 × 1) … Process n Resource 1 Intervention coefficients matrix 𝐁(𝑚 × 𝑛) = 𝐑𝐱̂−𝟏 … Resource m
Processes Resources Resources From / To 1 … n 1 … m 1 … m Process 1
Leontief inverse matrix 𝐋 = (𝐈 − 𝐀)−𝟏 Specific embodied exogenous transactions matrix 𝐞 = (𝐁𝐋)𝐓 Total embodied exogenous transactions matrix 𝐄 = 𝐟̂𝐞 … Process n Total Total embodied exogenous transactions vector 𝐄𝐭𝐨𝐭= 𝐢(1 × 𝑛)𝐄
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The hypothesis underlying these calculations is that direct technical coefficient matrix 𝐀 does not change.
The second shock that can be imagined is the one applied to technologies. Changes in technology of one or more productive processes of a same system result in a change in technical coefficients matrix from 𝐀 to 𝐀̅, and input coefficients matrix from 𝐁 to 𝐁̅. This leads to the following relations:
𝚫𝐱 = (𝐋 − 𝐋̄ )𝐟 (19)
𝚫𝐄 = 𝐟̂[(𝐁𝐋)𝚻− (𝐁̄𝐋̄ )𝚻] (20)
The hypothesis underlying these calculations is that final demand 𝐟 does not change. In the proposed model the first approach was used to introduce IO shocks.
When IOA is applied to national economies it is important to understand that these tables come with a certain level of aggregation (NACE, SNA etc.). However, if the objective of the research is to underline the impact of technology change it is often necessary to disaggregate the original table and produce a new one which explicitly accounts for it. As Lenzen [8] sustains, it is superior for environmental analysis to disaggregate the IO table, even if only partial information exists for the disaggregation. This led to Hybrid Input-Output Analysis.
Figure 9: Hybrid Input - Output Framework System transactions National Transactions (supply chains) 1 … n 1 … s 1 1 Downstream cutoff Upstream cutoff National final demand National total production System final demand System total production National exogenous transactions System exogenous transactions 1 … s 1 … n 1 … m
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The system represented in Figure 9 is a simplified structure of a national economy. In principle every national economy can be represented with a hybrid IOT provided the proper amount of information needed to disaggregate the interested sectors.
It is called hybrid since the foreground system (in yellow) is usually represented in physical units while the background system (in grey) is described by monetary values. Mathematical formulation is similar to the one previously showed but attention must be paid to the not uniform units used across the IOT. In this formulation rows must be homogeneous (i.e. background system rows must be in monetary units and foreground system ones must be in physical units).
Equations describing the system are the following ones:
𝐱𝐇= 𝐙𝐇𝐢 + 𝐟𝐇 (21)
𝐑𝐇= [𝐑𝐍 𝐑𝐒] (22)
In Figure 9 it is possible to highlight two important matrices: 𝐂𝐍𝐒 and 𝐂𝐒𝐍. These two matrices are the core of the HIOA. 𝐂𝐍𝐒 is called upstream cutoff matrix and it represents the flows of goods and services from the economy to the analyzed sectors belonging to the foreground system. 𝐂𝐒𝐍 is usually called downstream cutoff matrix and it represents the flows of goods and services from the sectors belonging the foreground system to the economy. Usually the time frame in which these analyses are performed is one year as national IOTs are normally compiled yearly.
2.3 Matrix Difference Statistics
Once the HIOT has been defined matrix difference statistics can be used to statistically compare the two databases considered. In order to understand the difference between two databases a number of techniques can be used. Here, notation provided by Gallego and Lenzen [9][10], cact and csup is overcomed since no database is considered to give
superior results with respect to the other. The EORA database is not considered to produce superior result with respect to the locally built one nor viceversa. This means that the similarity tests used must be commutative and calculate the same result regardless of which IO system is chosen as cact or csup [11]. The Chi-squared statistic is an example of a
comparison test which calculates different results if the variables are interchanged, and thus it was not used in this analysis.
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After surveying the literature, and excluding methods that were non-commutative or directly correlated to other methods, the following four matrix comparison statistics were selected to measures matrix similarity:
1. The mean absolute deviation (MAD) (MABS in Harringan et al 1980)
𝑀𝐴𝐷 = 1 (𝑚𝑛)∙ ∑ ∑|𝑐𝑎,𝑖𝑗− 𝑐𝑏,𝑖𝑗| 𝑛 𝑗=1 𝑚 𝑖=1 (23)
2. The mean squared deviation (MSD)
𝑀𝑆𝐷 = 1 (𝑚𝑛)∙ ∑ ∑(𝑐𝑎,𝑖𝑗− 𝑐𝑏,𝑖𝑗) 2 𝑛 𝑗=1 𝑚 𝑖=1 (24)
3. The Isard Romanoff Similarity Index (DSIM)
𝐷𝑆𝐼𝑀 = 1 (𝑚𝑛)∙ ∑ ∑ (|𝑐𝑎,𝑖𝑗− 𝑐𝑏,𝑖𝑗|) (𝑐𝑎,𝑖𝑗+ 𝑐𝑏,𝑖𝑗) 𝑛 𝑗=1 𝑚 𝑖=1 (25) 4. R-squared (RSQ) 𝑅𝑆𝑄 = [ ∑ ∑ (𝑐𝑎,𝑖𝑗− 𝑐𝑎,𝑖𝑗) ∙ (𝑐𝑏,𝑖𝑗− 𝑐𝑏,𝑖𝑗) 𝑛 𝑗=1 𝑚 𝑖=1 (∑𝑚𝑖=1∑𝑛𝑗=1(𝑐𝑎,𝑖𝑗− 𝑐𝑎,𝑖𝑗) 2 ∙ ∑𝑚𝑖=1∑𝑛𝑗=1(𝑐𝑏,𝑖𝑗− 𝑐𝑏,𝑖𝑗) 2 )1/2 ] 2 (26)
Each index represents a different facet of similarity. The first three indices are described as distance measures and concern with cell-by-cell deviations between two matrices. The MAD calculates the mean of all of the absolute distance between each corresponding cell in the two matrices. This index does not discriminate between deviations from small and large elements meaning that the overall result is not influenced more if a couple of cells shows 1000 units distance while another couple shows another 1000 units distance. The overall result just remains unaffected. Another important aspect to be remarked regarding this index is that cells containing smaller values may tend to show smaller differences.
The MSD calculates the mean of the squared of all the differences between each corresponding cell in the two matrices, meaning large deviations will count more towards overall distance evaluation. This index emphasizes the effect of differences between cells
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containing larger values, meaning that cells containing larger values will tend to show larger differences.
In contrast, the DSIM calculates the mean of proportional differences between each corresponding cell in the two matrices.
RSQ is a goodness of fit measure and calculates how well the set of values in each matrix correlate to one another. If the second matrix is a multiple of the first, or the product of the first matrix plus a scalar, RSQ is one in both cases because there is perfect correlation. Table 4 summarizes the matrix difference statistics employed in this study.
Type of measure Name Authors Notes
Distance measure
MAD Günlük-Senesen and Bates (1988), Harrigan et al. (1980)
A low value means the matrices are similar MSD Günlük-Senesen and Bates
(1988)
A low value means the matrices are similar DSIM Gallego and Lenzen (2006),
Harrigan et al. (1980)
A low value means the matrices are similar
Goodness of fit RSQ Knudsen and Fotheringham (1986)
An RSQ value of 0 indicates no correlation
between the two matrices, whereas a value
of 1 suggests perfect correlation Table 4: Summary of Matrix Difference Statistics Indices
2.4 The Input – Output Models
In order to operate a correct analysis of Kenya’s economy, two databases were chosen to be compared. The first one will be called “locally built IOT” and the second one is EORA. EORA was chosen since it was the only reliable provider that had a SUT for Kenya for the selected baseyear. It is important to underline that building an IOT is a complicated and laborious task that requires a lot of time and efforts to be completed. This is why usually updated tables comes with one or two years lag with respect to the analyzed year. Kenya SIOT was regionally built following the steps described in previous section starting from the locally built SUT using an 81 sector ISIC rev4 classification. In this table Electricity is separated with respect to the other economic industries though a proper division for the energy analysis that was done ex-ante. A currency conversion is applied to convert local currency into US dollars: from Kenyan Shillings (KSH) to USD.
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EORA maintains the sector aggregations and the SUT structure of the original data. This database takes known raw data and uses them as constraints in an optimization algorithm. The optimization routine is used to estimate missing data, such as the off-diagonal elements of intermediate transaction matrix, imports and, generally, to balance the model. Some of the constraint data is likely to conflict, yielding no solution. The EORA reconciliation algorithm uses standard deviations to decide how much the raw data values are permitted to vary in finding a solution table that satisfies every constraint. A table for the year 2000 is generated and this table is known as the initial estimate [12], [13]. Tables for the year 1999 and earlier, and the year 2001 and later, are generated using the initial estimate with new sets of constraint data collected for that year. EORA takes emissions data from the IEA and uses the territorial principle to allocate between resident’s direct emissions and industrial emissions [11]. EORA SUT for the year 2009 is provided with a 51 sectorial aggregation following the ISIC rev4 classification. Also in this database the commodity “Electricity” is disaggregated with respect to the rest of the economy. A harmonization of sectors using the principle of the smallest common denominator must be performed if the goal is to operate a one-to-one industry comparison between the two databases. Since the two classifications are different, they must be homogenized using a superior aggregation. This is done following the ISIC rev4 division[14]. Thus, at the end of the harmonization process, the two IOTs show the same level of sectorial aggregation. Since the two databases have the same structure but different hypotheses at the root, they show considerable differences that can be attributed to several sources: balancing procedures, misclassification of data, incorrect currency conversion and so on. One of the aims of this thesis (RT1) is to figure out what are the main elements that contribute to global distance between the two databases using the methods explained above.
Another aim of this thesis (RT3) is to understand the impact of different energy mix on future CO2 emissions for Kenya using different databases and provide the government
with a tool able to quantitively assess the problem of GHG emission regulation.
In order to reach this goal, the industry “Electricity” used in the two databases is too aggregated. A disaggregation procedure is needed to extract the different production technologies and make explicit the link between energy mix and CO2 emitted. Keeping the
sector aggregated would translate in considering an average technology that would be used to produce electricity rather than specifying which technologies are actually used in the energy mix and hence what are the sources of pollution emission directly caused by the power sector of the country.
A functional disaggregation methodology of the “Electricity” sector was proposed by Lindner [15] who disaggregated Chinese electricity industry and Algarin [16].
First step consists in separating “Electricity” sector into its main components: “Transmission and Distribution” and “Power Generation” sectors. This is done using the
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share of total investments done in the two subsectors for the base line year. Same hypothesis was applied to both models so that a fair comparison can be performed. The summation of the values of technical coefficients of the new sectors must be the same of the one characterizing the “Electricity” industry, according to the following equations:
∑ 𝑎𝑖,𝑗 = 𝑎𝑖 𝑗 (27) ∑ 𝑎𝑖,𝑗 = 𝑎𝑗 𝑖 (28)
First equation refers to column disaggregation rule while the second refers to row disaggregation rule. Once this first disaggregation is done, the Power Generation sector is further separated into the detailed power generation technologies that compose the energy mix of the country. Particular attention must be paid now on new columns and new rows as they must be treated differently. As already said in the previous section the coefficient 𝑎𝑖,𝑗 represents the flows of goods and services that comes from the ith sector going to the jth sector. Thus, when disaggregating columns, the interest is put on how the ith sector provide goods and services to the jth column. These flows are characterized by Operation and Maintenance costs share among the producing power sectors. This share varies every year since the variable costs associated to the fuel vary. This is considered into column disaggregation. Value added separation is also done according to column disaggregation.
When disaggregating rows instead, the focus is put on how the new power generation technologies provide goods and services (mainly intermediate use for industries) to the column sectors. Rows disaggregation is performed thanks to the shares given by the OSeMOSYS model, that changes according to years and scenarios considered. Each productive sector and the final demand vector are assumed to consume electricity using the same national energy mix. A resume of the step-by-step disaggregation process is provided in the following table (Table 5).
34 Step 1 Step 2 Electricity Transmission and Distribution Power Generation Technology 1 … Power Generation Technology n
Table 5: Resume of the step-by-step disaggregation procedure
From now on, the term “new sectors” is used to indicate Transmission and Distribution and the n power generation technology sectors, while the term “common sectors” indicates the sectors present in the national economy excluding the new sectors.
2.5 The Hybrid Input – Output framework
At this point two IOTs are formed. Both of them show the same sectorial classification and the same currency. However they both have the new sectors showed in monetary term, though an average price for electricity is applied on the base year to both of the model to convert new rows into physical units such as GWh or TWh. Once all the steps described in the previous subchapter and average price of electricity were applied, the framework with which it is possible to work with is described in the following figure (Figure 10). Two different Hybrid Input Output Tables are created which have the following structure:
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Figure 10: Coefficient version of an HIOT
𝐀𝟎= [ 𝐀𝐍 𝐂𝐔
𝐂𝐃 𝐀𝐄]; 𝐟𝟎 = [ 𝐟𝐍
𝐟𝐄]; 𝐛𝟎 = [𝐛𝐍 𝐛𝐄]; (29)
Given n as the total number of sectors of the national economy, s as the number of energy technologies plus Transmission and Distribution (new sectors) and m as the number of exogenous transactions it is possible to distinguish:
• 𝐀𝟎 is a n x n matrix. Each element 𝑎𝑖,𝑗 represents the flow of goods and services
coming from ith sector going to the jth sector per unit of jth sector output. This matrix is a coefficient-dimensional matrix composed by four sub-matrices:
o 𝐀𝐍 is a (n-s) x (n-s) matrix. Here flows from common sectors within
common sectors are represented, thus the matrix is homogeneous in terms of unit of measurements and the coefficients are measured in [𝑈𝑆𝐷
𝑈𝑆𝐷]
Industries New sectors Final demand Total outputs
In d u st ri es National technical coefficient matrix AN
New sectors upstream
cutoff coefficient matrix
CU National final demand fN National total output of industries xN N ew s ec to rs
New sectors downstream
cutoff coefficient matrix
CD
New sectors technical
coefficient matrix AE New sectors final demand fE New sectors total output xE
National value added
hN
New sectors value added
hE
National exogenous
resource coefficient matrix
bN
New sector exogenous
resource coefficient matrix
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o 𝐂𝐔 is a (n-s) x s matrix. Here flows from common sectors to new sectors
are represented. The elements in this matrix represent the flows of goods and services of non-energy sectors to the new sectors per unit of new sectors total output. Hence the matrix is no longer homogeneous in terms of unit of measurements: coefficients here are measured in [𝑈𝑆𝐷
𝐺𝑊ℎ].
o 𝐂𝐃 is a s x (n-s) matrix. Here flows from new sectors to common sectors
are represented. The elements in this matrix represent the amount of electricity consumed by common sectors per unit of common sectors output. Also this matrix is no longer homogeneous in terms of unit of measurements. Elements in this matrix are measured in [𝐺𝑊ℎ𝑈𝑆𝐷].
o 𝐀𝐄 is a s x s matrix. Here flows from new sectors to new sectors are represented, hence this matrix is homogeneous in terms of unit of measurements. Here, coefficients are measured in [𝐺𝑊ℎ𝐺𝑊ℎ] and represent the amount of electricity consumed by each new sector per unit of electricity produced by new sectors.
• 𝐟𝟎 (n x 1) is the hybrid final demand vector. It is composed by the common sector final demand 𝐟𝐍 (n-s) x 1, measured in [𝑈𝑆𝐷] and the final demand of electricity 𝐟𝐄 s x 1, measured in [𝐺𝑊ℎ]. This parameter will be deeply analyzed in the following chapter.
• 𝐛𝟎 (m x n) is the hybrid intervention coefficient matrix. Its elements represent the amount of direct resources/emissions adsorbed/released per unit of production.
Once these matrices are characterized for both IOTs, Leontief production model can be applied as described in the following equations:
𝐱𝟎 = (𝐈 − 𝐀𝟎)−𝟏∙ 𝐟𝟎= 𝐋𝟎∙ 𝐟𝟎 (30)
𝐑𝟎= 𝐛𝟎∙ 𝐱 ̂𝟎 (30)
𝐱𝟎 (n x 1) is the hybrid total output vector while 𝐑𝟎 (m x n) is the total exogenous resource
matrix: this represents the total amount of resources/emissions adsorbed/released by each sector.
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2.6 Update of the base year Input-Output model for future scenarios
As mentioned before 𝐂𝐔, 𝐂𝐃 and 𝐀𝐄 matrices are the ones containing the coefficient relation between common sectors and new sectors. It is important to well define the model at the base year so that it is possible to update it when applying future energy scenarios, hence the matrices 𝐂𝐔, 𝐂𝐃 and 𝐀𝐄 must be carefoully defined and updated. At this point it is important to recall the definition of a generic direct technical coefficient 𝑎𝑖𝑗, since it is useful for the analysis of the following paragraph. The coefficient is called direct because only direct flow of goods and services are captured by this variable.
𝑎𝑖𝑗 = 𝑧𝑖𝑗
𝑥𝑗 (30)
This 𝑎𝑖𝑗 represents the intermediate output of the ith sector per unit of jth sector output, referring to Figure 7 structure.
Upstream cutoff matrix 𝐂𝐔 constains the share of O&M costs split between power generation technologies. The total stream of intermediate output coming from common sectors to new sectors constitues the flow to be split among the specific generation technologies chosen for the analysis. This flow must be divided by the total output of each sector to obtain the coefficients contained in 𝐂𝐔. They vary according the year and the scenario considered. However, 𝐂𝐔 is very difficult to be estimated as information for disaggregation should be found in national financial reports, government investment patterns and private companies data. Being on field collecting these kind of data helped the author in this task but an approximation at the end must be done. These coefficients were estimated based on raw data and information gathered on field for the scenario definition developed.
Downstream cutoff matrix 𝐂𝐃 is intrinsically different from 𝐂𝐔 due to its definition and meaning. Elements in 𝐂𝐃 represents the way in which common sectors consume electricity coming from the new sectors per unit of output of jth common sector. These coefficients vary from year to year and according to the scenario considered.
𝐀𝐄 is the technical coefficient matrix that regulates the flow of electricity within power generation technologies. This matrix also changes from year to year and according to the scenario considered as electricity input required to produce one unit of electricity output varies considering different technologies. The author decided to split the original 𝑎𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦,𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 using a diagonal matrix. This means that each power generation technology uses as intermediate input only power coming from the same electricity generation technology.
