A benchmark ecological stock-flow-consistent input-output model for Denmark

Thomsen, Simon Fløj; Raza, Hamid; Byrialsen, Mikael Randrup Working Paper A benchmark ecological stock-flow-consistent input-output model for Denmark FMM Working Paper, No. 114 Provided in Cooperation with: Macroeconomic Policy Institute (IMK) at the Hans Boeckler Foundation Suggested Citation: Thomsen, Simon Fløj; Raza, Hamid; Byrialsen, Mikael Randrup (2025) : A benchmark ecological stock-flow-consistent input-output model for Denmark, FMM Working Paper, No. 114, Hans-Böckler-Stiftung, Macroeconomic Policy Institute (IMK), Forum for Macroeconomics and Macroeconomic Policies (FMM), Düsseldorf This Version is available at: https://hdl.handle.net/10419/324479 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/legalcode.de FMM WORKING PAPER No. 114 • February 2025 • Hans-Böckler-Stiftung A BENCHMARK ECOLOGICAL STOCK -FLOW-CONSISTENT INPUT -OUTPUT MODEL FOR DENMARK Simon Fløj Thomsen, Hamid Raza, Mikael Randrup Byrialsen 1 ABSTRACT This paper aims to develop an ecological macroeconomic model for the Danish economy that can link the economic and financial system with some key aspects of the climate. To do so, we combine Stock-flow-Consistent approach (SFC) with Input-Output tables (IO) to build a hybrid model, which we call Ecological Stock-Flow-Consistent Input-Output model (E-SFCIO). Most parameters of the model are estimated using time series data from 1995 to 2019, after which, we carry out simulations. We find that the model (with some minor adjustments) can replicate the dynamics of our key variables pertaining to the economy, financial system, and climate. To further validate the model, we analyse the response of the economy to various shocks, finding that it can capture the stylised facts. The model offers a foundation for providing a reasonable assessment of the climate policies to the relevant stakeholders. ————————— 1 Aalborg University Business School, Aalborg University, Denmark. Corresponding author is Simon Fløj Thomsen email: [email protected]. 1 A benchmark Ecological Stock-Flow-Consistent Input-Output model for Denmark Simon Fløj Thomsen∗ Hamid Raza∗ Mikael Randrup Byrialsen∗ Abstract This paper aims to develop an ecological macroeconomic model for the Danish economy that can link the economic and financial system with some key aspects of the climate. To do so, we combine Stock-flow-Consistent approach (SFC) with Input-Output tables (IO) to build a hybrid model, which we call Ecological Stock-Flow-Consistent Input-Output model (E-SFC-IO). Most parameters of the model are estimated using time series data from 1995 to 2019, after which, we carry out simulations. We find that the model (with some minor adjustments) can replicate the dynamics of our key variables pertaining to the economy, financial system, and climate. To further validate the model, we analyse the response of the economy to various shocks, finding that it can capture the stylised facts. The model offers a foundation for providing a reasonable assessment of the climate policies to the relevant stakeholders. Key words: Empirical Stock Flow consistent models, Input-Output modelling, Ecological macroeconomics, Denmark. JEL-codes: E12, E17, F41, L16. ∗ Aalborg University Business School, Aalborg University, Denmark. Corresponding author is Simon Fløj Thomsen email: [email protected]. ∗ Aalborg University Business School, Aalborg University, Denmark, [email protected] ∗ Aalborg University Business School, Aalborg University, Denmark, [email protected] 2 1. Introduction In recent years, the issue of green transition and sustainable development has played a central part in shaping national policies. The challenges inherent in the path towards green transition have garnered considerable attention from various research disciplines, ranging from scientific research - testing new technologies - to social sciences, examining the complex and multifaceted interactions between society and environmental sustainability. Within this discourse, significant emphasis is placed on the interplay between economic factors and climate targets – the understanding of which remains incomplete due to the complex nature of this relationship. As such, policymakers are striving to improve their understanding of the economic costs associated with climate policies. Denmark, like several other countries, is faced with similar challenges. The country has set ambitious targets for reducing greenhouse gas emissions, aiming for a 70% reduction by 2030 compared to 1990 levels, surpassing the European climate law's target of 55%. However, current measures are projected to achieve only a 63.1% reduction by 2030, resulting in a shortfall of 6.9%, equivalent to 5.5 million tons of CO2E (DEA 2023). There is a clear lack of consensus amongst various stakeholders on how to achieve these targets and whether cutting emissions at a faster rate is economically feasible. To guide policy decisions on this matter, the Danish government relies, at least partly, on the insights of the Green Reform Model (Kirk et al. 2024), which is the workhorse for studying the interaction between climate and the Danish economy. This model is built on the principles of computable general equilibrium (CGE), featuring profit maximisation by producers (firms) and utility maximisation by consumers (households). The model is supply-driven, consisting of 52 production industries and 26 energy types (Kirk et al. 2024).1 While the model provides a very detailed description of the real economic activity, the question of whether this description is a realistic representation of the economy is subject to discussion. However, a notable shortcoming of this model is its failure of providing a realistic representation of the financial aspects of the economy, something that is considered to be quite crucial in this discussion (Pollitt and Mercure 2019). The financial system, through ad hoc assumptions, is simplified to the extent that it is almost irrelevant. This invites the same criticism that post-Keynesians have directed at supply-side models in general (Lavoie and Godley 2001; Godley and Lavoie 2006). 1 Firms, while adhering to a generic CES (Constant Elasticity of Substitution) production function, optimize between two complementary inputs namely, capital and energy. 3 In this paper, we aim to develop an ecological macroeconomic model that can link the economic and financial system with some key aspects of the climate. Our main goal is to provide a holistic overview of the issue using a model that, apart from capturing the stylized facts, is capable of evaluating the economic and financial risks associated with climate policies of socio-economic nature. To link the economy, environment and the financial system, we combine Stock-flowConsistent approach (SFC) with Input-Output tables (IO) to build a hybrid model, which we call Ecological Stock-Flow-Consistent Input-Output model (E-SFCIO). The integration of these two approaches allows us to connect final demand with supply and inputs of the firms. A key element of our model is the inclusion of a financial market; sectoral wealth and debt are modelled in more detail, providing a more nuanced understanding of who is paying for the green transition. When solving the model, most parameters are estimated using time series data from 1995 to 2019, after which, we carry out simulations, finding that the model is capable of replicating the dynamics of our key variables pertaining to the economy, financial system, and climate. To further validate the model, we analyse the response of the economy to various shocks, finding that it can capture the stylised facts of the Danish economy. We believe our proposed model will serve as a foundation for providing a reasonable assessment of the climate policies to the relevant stakeholders. Our model structure is based on a social accounting matrix where the most relevant transactions are registered (intermediate and final consumption, income and tax payments, transfers, etc.) on a whom-to-whom basis with a coherent representation of their corresponding financial transactions and environmental impacts. The detailed representation of the social and economic structure enables the analysis of the impact of climate policies on income and wealth distribution - an aspect that, striking as it may seem, is beyond the scope of many macroeconomic models. Moreover, it allows to design and test fine-tuned sector-specific (or industry-specific) policies. Furthermore, the explicit modeling of the main financial assets and liabilities of the key sectors of the economy allow for a coherent description of the multiple ways of financing climate policies, as well as the risks inherent in their implementation. Our model, strongly influenced by post-Keynesian theory, is built on the notion of demand-led growth and excludes discount rates and damage functions. Its main focus will be the testing of the feasibility and joint coherence of multiple climate policies, but not the estimation of the feedback effects from the environment to the economy.2 2 The neglect of feedback effects does not imply that they are considered unimportant. Rather, the scope of this project is to build a first version of an E-SFCIO for Denmark. Once this model is running and producing reliable results it will 4 The remainder of the paper is organized as follows. In section 2, we provide a brief overview of the Danish climate targets. In section 3, we offer a background discussion of the type of model developed in this paper. In section 4, will provide a detailed description of the databank constructed for the model. In section 5, we present the model equations and the overall structure of the model. In section 6, we carry out model evaluation, comparing the model simulations with observed data. In the same section, we show how the model response as we perform 3 simple shocks to the model. Section 7 concludes this paper. 2. The Danish Climate goals Over the last decade, sustainable development and green transition have been at the heart of policy discussions. In 2015, 196 countries around the world joined the Paris Agreements with the aim of reducing the emission of greenhouse gases (GHG) significantly in such a way that the 2°C target (of atmospheric temperature increase above pre-industrial levels) is met by 2050 (UNFCCC 2015). In 2020, the Danish Parliament signed the Climate Law, according to which the emission of GHG must be lowered by 50% in 2025 and by 70% in 2030 (compared to the level in 1990 which was approx. 78 million tons3). This target is more ambitious than the target set by the European climate law, which aims for a 55% reduction in GHG emissions by 2030 compared to 1990 levels. Furthermore, the Danish climate law, in line with the European climate law, has set a long-term goal of making the country climate-neutral (i.e., net GHG emissions equal to zero) by 2050 (EPRS 2021). Apart from its own national targets, Denmark has an obligation of reducing emissions in specific sectors not included in the ETS (Emission Trading System) as part of the EU targets for 2030. More specifically, the 2023 revised version of EU’s Effort Sharing Regulation (ESR) in 2023 obliges Denmark to reduce GHG emissions in non-ETS sectors – comprising agriculture, transport (excl. aviation), building heating, small industries, and waste – by 50% collectively in 2030 (compared to 2005 levels). be possible to move to a second stage, where the feedback effects are incorporated into the model. It is worth mentioning that there is no scientific consensus about how these feedback effects should be modeled, which drives us to conclude that the investigation of these phenomena constitutes a research project on its own. 3 Here, the estimate is based on net emissions within the Danish territory (excl. Greenland and Faroe Islands) and includes LULUCF. 5 While assessing Denmark’s path towards green transition, the Danish Energy Agency (DEA) and Danish Council on Climate Change (DCCC 2023, 2024)4 in their assessments have repeatedly underscored the significant challenges that Denmark faces in achieving both its national as well as EU targets. According to 2022 statistics, the net domestic emission was 43.3 million tons, suggesting a 41.7% reduction compared to the 1990s. The country still needs a significant reduction of approximately 20 million tons in the remaining period to meet the 2030 national target. A recent assessment by DEA (2023) indicates that Denmark will most likely miss its targets unless significant reductions in agriculture and transport sectors are achieved, as both of these sectors collectively contribute to more than half of the total net emissions.5 More specifically, with the current measures in place, it is projected that Denmark will achieve 63.1 percent reduction by 2030 (leaving a gap of 6.9 percent, which corresponds to 5.5 million tons of CO2). To close the remaining gap, the government has recently reached an agreement including taxation on CO2equivelant (CO2E) emissions emitted by the agricultural sector starting from 2030. How such policies will affect the economy, are the type of questions, we would like to address using our model. 3. Combining Stock-flow models with Input-Output tables Stock-Flow Consistent models gained a lot of attention after the publication of Godley and Lavoie (2006), and more so after the 2008 crisis. The approach offers a consistent methodology that relates stocks and flows by way of social accounting and flow-of-fund matrices. Since the traditional national accounts are now complemented by the new System of Environmental-Economic Accounting (SEEA) data, this makes SFC approach a natural candidate for the integration of environmental issues into the economic models. The SFC and IO frameworks have independently co-existed for a long time, but the approach of integrating the two is a recent development. While the standalone SFC framework offers a comprehensive perspective on economic and financial dynamics, the integration of IO is particularly useful for addressing pressing climate-related issues. This combined SFC-IO methodology presents a promising research avenue and is increasingly attracting attention within the field of ecological economics. The number of existing studies using SFC-IO approach is very limited. Most studies in this regard have used SFC-IO setup to build either fully or partly theoretical models (see, e.g., Berg et al 2015; Naqvi 2015; Jackson & Jackson 2021; 4 The Danish Council on Climate Change (DCCC) is assigned with the task of advising the government on achieving its intended targets. 5 According to 2022 statistics, agriculture contribute 27% and transport contribute 29% to the total net GHG emissions in CO2 equivalents. 6 Dunz et al. 2021).6 Full-fledged empirical models based on SFC-IO approach for individual countries are still in the making. At the time of this writing, several projects are under development while only a very small number of studies are currently available in the literature (Valdecantos 2021).7 Thus, our work is also a contribution to the emerging literature in ecological macroeconomics. We extend the existing SFC framework in three ways: i) by integrating a full Input-Output (IO) table into the modeling framework, ii) by integrating environmental aspects (such as energy usage and supply by each industry) into the analysis, and iii) by introducing a relationship between energy usage (in physical units) and economic activity while capturing the resulting GHG emissions. We now procced to providing a formal description of the steps involved in constructing this model as well as the overall structure of the model. In our presentation, we reserve the term “sector” to describe institutional sectors of the economy namely, households, non-financial corporations, financial corporation, government, and rest of the world. We use the term “industry” to describe different industries involved in production. 4. Data requirements for the model In this section, we will describe the construction of the databank used in E-SFCIO model for Denmark. For the industry level, we use the annual input-output data, and for the sectoral level, we use the annual national accounts (including both transactions and balance sheets). To implement ecological aspects into the model, we also include energy and emission accounts for the Danish economy. 4.1. Input-Output data We use IO data from Statistics Denmark for the period 1995-2019 and divide the production sector into nine industries (see appendix 8.1 for more information about the industries). In Table 1, we provide a general representation of IO flows used in our model. The inter-industry flows are captured via a 9 by 9 matrix. The final demand block consists of consumption, public consumption, investment, change in inventories8, and exports. Households’ consumption basket consists of a wide range of products, where a detailed classification is carried out for the food products. The final 6 In the Life cycle assessment literature (LCA) there has also been theoretical contributions combining the Input-output analysis with Stock-Flow Consistent modelling (Almeida et al. 2022). 7 Ongoing projects include empirical SFC-IO models for countries like Greece, Italy, Argentina, and others. 8 To simplify the model, we have added the acquisitions less disposals of valuables to the change in inventories. Both variables are held exogenous within the model and will enter the same equations whereas it will not impact any results. 7 demand flows are captured via a 11 by 9 matrix. We have classified the IO table into different blocks, each representing a matrix. Understanding the dimensions of these different blocks will play a crucial role in understanding the equations in this paper. We encourage the reader to take a moment to fully understand the blocks (highlighted in different colours) and their dimensions. Table 1: Input-Output Matrix (general representation) We now move from a general representation of the IO matrix to the specific case of Denmark. Table 2 is a representation of an IO-table using Danish data (in nominal values) for 2019. When moving across the table horizontally, the flows represent the production of each industry. For example, the first row shows the production of agricultural sector. Note that each industry engages in two types of production, i) production of products sold as intermediate goods to other industries (which are used as inputs in production), and ii) production of final products sold to various institutional sectors (incl. rest of the world), determining final demand. If we move vertically down the table (or read the table from top to bottom), the entries (with the exception of gross operating surplus and mixed income) represent the costs of domestic industry associated with production. For example, the first column of the table shows the cost of production in the agricultural industry. The cost of the industry consists of three categories, i) domestic and imported inputs, ii) production and value added taxes, and iii) compensation of employees. The difference between the total value of production and costs, gives us the gross operating surplus. This will be explained in more detail, when presenting the model equations in section 5. 14 In a static setup, the relationship between final demand 𝑭𝑭𝒅𝒅𝒅𝒅𝒅𝒅,𝒕𝒕 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 and production 𝒑𝒑𝒑𝒑𝒅𝒅𝒅𝒅𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 would require the calculation of the Leontief inverse,14 but since we use a dynamic setup, we can simply use equation 4 in combination with equation 5d to calculate total production for each industry, which for industry n will result in equation 6 presented in section 5.1.1. 4.2. Transaction-Flow-Matrix from a sectoral perspective Before we move further into the data requirements of the model, we find it important to first provide an overview of the transaction flows from the perspective of institutional sectors in the economy (aka Transaction-Flow-Matrix - TFM). Our model consists of 5 institutional sectors namely, households, non-financial corporations (NFC), financial corporations (FC), government, and the rest of the world (ROW). Table 4: Transaction-Flow-Matrix It is important to highlight that the national accounts, which provide the basis for a full empirical model, can be presented at both industry and sectoral level. When describing production in the model structure, we use the industry-level accounts (discussed in section 4.1), but when explaining the TFM in Table 4, we choose to use the presentation from the sectoral perspective. The reason is that data for variables below gross operating surplus and mixed income, such as financial income or changes in financial transactions, is unavailable at industrial level. Consequently, the current model 14 In a static input-output model one should obtain the Leontief inverse to relate domestic final demand (𝑭𝑭𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐) to domestic production (𝒑𝒑𝒑𝒑𝒅𝒅𝒅𝒅𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐). This can be done using the following equation: �𝑰𝑰𝟗𝟗−𝑨𝑨𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐�−𝟐𝟐∗𝑭𝑭𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝒊𝒊𝟐𝟐𝟐𝟐= 𝒑𝒑𝒑𝒑𝒅𝒅𝒅𝒅𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐. Where �𝑰𝑰𝟕𝟕−𝑨𝑨𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐�−𝟐𝟐 is referred to as the Leontief inverse (𝑳𝑳𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐−𝟐𝟐). 15 can explain the rows below gross operating surplus only at a sectoral level. For example, the model will only explain net lending (surplus/deficit) at a sectoral level but not at an industrial level. We now provide an explanation of how industries and sectors are connected. Note that entries above the gross operating surplus are obtained from the IO table whereas flows below the gross operating surplus are obtained from the national accounts at a sectoral level. To establish a connection between industries (IO data) and institutional sectors (sectoral national accounts), we use gross operating surplus as a binding flow. This requires identifying, what share of industrial profits (from production) falls under which sectors; in this regard, we use the 2016 matrix of industry by sector provided by Statistics Denmark (DST 2021), which contains the share of gross value added (GVA) from each industry allocated to the corresponding institutional sectors. For example, the matrix suggests that two-thirds (approx. 66.7 percent) of the GVA from the agricultural industry belongs to the households, one-third (approx. 33.3 percent) belongs to the NFC, whereas none belongs to the other sectors. Therefore, it is assumed that two-thirds of the gross operating surplus from the agricultural industry is owned by the household sector, whereas the remaining belongs to the NFC. This implicitly suggests that two-thirds of both the total production (which includes the sale of final consumption goods) and the total costs (part of which include paying wages) related to the agricultural industry belong to the household sector. However, to keep the presentation of TFM simple, entries in relation to consumption (as an income) and wages (as an expense) are not explicitly included for the household block. To get the weights for each of the 9 industries, we calculate a weighted average of the shares obtained from the matrix of industry by sector, using the level of gross operating surplus for each industry (more information about the estimation of these shares are provided in appendix 8.2).15 It is important to highlight that the allocation of gross operating surplus (which we at the industry level call profits) to other institutional sectors should not be confused with dividend payouts against equity holdings; that mechanism is separately captured in our framework as will be discussed. After transforming gross operating surplus and mixed income (profits) from an industry to sectoral level, we now focus on sector-specific income and expenses. Here, we rely on the sectoral national accounts data presented by Statistics Denmark. This includes sectoral saving, which is used for 15 An alternative approach is to calculate exogenous shares of total profits received by the household, the government sector, financial corporations, and non-financial corporations based on the sectoral data and then divide out total gross operating surplus using these shares. A problem that might arise following this approach is if agricultural increase profits this will lead to an increase in total profits and based on the exogenous shares profits obtained by the sectors will increase. In reality, an increase in agriculture industry profits should only increase the profits obtained by the household sector and non-financial corporations following the shares obtained from the Matrix of industry by sectors. 16 capital formation (investments) and other capital transfers;16 if a sector’s savings are not enough to meet its investment expenditures and other capital transfers, the sector will run into a (sectoral) deficit, which is reported by the row called net lending in the TFM. This deficit is covered by adjustments in the balance sheet as shown by the rows below net lending, representing the changes in eight net financial stocks namely gold, deposits, securities, loans, equities, insurances, derivatives, and trade credits. The structure of the balance sheet, although not explicitly presented, is obvious from the lower part of TFM. The net value of each financial stock is calculated as the difference between the asset and liability of the same financial stock. When calculating the change in net financial wealth (as shown by the last row of the TFM), we also account for re-evaluations of the stock of net financial stocks, represented by the 8 rows just above the net financial wealth. 4.2.1. Net financial income One crucial aspect for the sectoral data is the calculation of rates of return for the 4 types of income on financial assets (reported in the rows under the gross operating surplus) being: net interest payments denoted by NINT, net income on other investments (related to pension and insurances) denoted by NOIR, net income on net equities denoted by NDIV, and finally income on net FDI denoted by NFDI. A crucial step in calculating these rates of returns is to ensure that incomes on financial assets in the TFM (4 income streams in our case) are linked to the holdings of financial stocks (8 financial stocks in our case). To clearly establish a link in this regard and to simplify the structure of the model, we rely on certain assumptions.17 First, we assume that the rate of return on a given financial stock is the same across institutional sectors, e.g., the interest rate on loans is the same for all sectors. This raises the question of which sector’s stocks and flows should be used to calculate the rates, which motivates our second assumption; it can be argued that, since financial corporations serve as financial intermediators, this sector should be used to calculate the rates of returns on financial stocks. In appendix 8.3, we present a detailed description of how these different rates of returns are calculated, which determine the 4 types of net financial income presented in the TFM. We now proceed to presenting the data used in the environmental block of the model. 16 Here, we use exogenous shares to divide the total nominal investments across the sectors. 17 Our assumptions are mostly dictated by the lack of transparency in the data. 17 4.3. Environmental data We use a mix of data sources for the environmental variables. For the energy supply and use, we collect all data from Statistics Denmark. For emissions, we have chosen to use a combination of the data from GreenREFORM model and Statistics Denmark. The appealing feature of the emission data used in GreenREFORM is that we can relate a specific type of emissions to a specific type of energy usage. In the following sections, we present this in further detail, starting with the energy accounts from Statistics Denmark. 4.3.1. Energy Accounts For the energy accounts used in our analysis, we consider 21 different types of end-use energy products supplied and used in the economy. This data is crucial for understanding the direct energy usage patterns across different economic units, providing clear insights into which energy sources are most utilized by each industry. Table 5 provides an overview of the Danish energy accounts in 2019, expressed in physical units. Table 5: Energy supply and usage in 2019 by each industry (in million Gigajoules) Note: Coil (crude oil), Oilp: Oil products), RefG (Refinery gas), GasT (Gasoline for transportation), FGas (jet fuel), FGasBunk (Jet fuel bunkered), DieT (Diesel for transportation), DietTBunk (Diesel for transportation - bunkered), NGasExt (Natural gas extraction), NGasCons (Natural gas consumption – incl. city gas), CC (coal and smoke), Waste (Waste), RE (Renewable energy), Straw (Straw), FW (Firewood and wood chips), WP (wood pellets), BioG (Biogas), BBB (Biodiesel, bioethanol and bio-oil), El (electricity), DHeat (District heat). For each of the 21 energy types, we have both supply and usage data for each industry, represented by the first nine rows in each block. Specifically for energy supply, energy can be imported or 18 produced using accessible inputs in the form of waste or renewable energy (e.g., wind or solar power). In the usage block, energy can be exported for use outside Denmark, consumed by households, or lost due to distribution losses. If there is an excess supply (usage) of a specific energy type, this will increase (lower) the inventories of that energy type (see the row “Change in inventories”). As a result, total energy usage equals total energy supply for each industry. Although we have both the supply and usage data at an industrial level, in most cases, we cannot see what fraction of the total energy used by an economic unit is supplied by a specific supplier. We can only establish partial links based on our abductive reasoning of the energy accounts, which could be useful in interpreting the results. For instance, from a consumption point of view, the ‘energy producing and refineries’ industry shows a high consumption of crude oil (328.7 million gigajoules), indicating its substantial reliance on the mining industry. Whereas, from a production point of view, this industry serves as the sole provider of natural gas for consumption and the biggest provider of district heating, the latter being the largest source of energy for the household sector used in heating residential units. Thus, the household sector, for its energy consumption, appear to have a strong direct dependence on energy producing and refineries industry. Unfortunately, we do not have the full information to transparently link each and every unit of energy between suppliers and users. This limitation, along with the absence of energy prices required to convert physical units to monetary units, prevents us from integrating energy accounts in the IO setup presented earlier. Nonetheless, it is important to emphasise that the costs (revenue) associated with using (selling) energy as an intermediate good are implicit in the IO table. In this version of the model, we simply aim to establish a relationship between energy usage (in physical units) and economic activity while capturing the resulting GHG emissions. A more realistic extension of the model will require accounting for the price of each energy type, converting physical units to monetary units, and then integrating energy accounts in the IO setup. 4.3.2. Emission Accounts We collect data on six types of emissions: carbon dioxide (CO2), nitrous oxide (N2O), methane (CH4), sulfur hexafluoride (SF6), perfluorocarbons (PFC), and hydrofluorocarbons (HFC). These emissions are later used to calculate the CO2-equivalent measure (CO2E). As mentioned, we use a mix of data sources for the emissions data. For CO2, N2O, and CH4, we use data from the GreenREFORM model databank (Svarer et al., 2024). In contrast, we use data from Statistics Denmark for SF6, PFC, and HFC. The choice of data source depends on how the emission type is produced. Since CO2, N2O, and CH4 are emitted both in relation to energy usage and 19 independently of it, the detailed setup of the GreenREFORM model databank allows us to disaggregate energy-related emissions down to specific energy types. In the table below, we present this disaggregation for CO2 emissions related to energy: 18 Table 6: CO2 emissions related to energy usage As detailed emissions data from the GreenREFORM database are only available up until 2017, we construct new emissions data for 2018 and 2019, assuming the same relationship between energy usage and emissions as in 2017 (since energy data is available for 2018 and 2019). This will become clearer in section 5.4.2, where energy-specific emissions coefficients are calculated. For SF6, PFC, and HFC emissions, which are unrelated to energy usage, it is neither necessary nor possible to disaggregate these emissions into the format of Table 6. This data is available for the entire time period, and no further operations are required. This concludes the data requirements for the model, which relies on national accounting data at both the industry and sectoral levels, along with emissions and energy data. In the next section, we introduce the structure of the model. 5. The model structure The model has four major blocks, i) the domestic production block, describing total production, production costs, and profits for the domestic industries, ii) the aggregate (or final) demand block, providing a detailed description of the drivers of aggregate demand. Since the model is demanddriven, this block to a large degree determines industrial production (or the supply side), which is presented in the production block. iii) the stock-flow consistency block, in which we model the 18 This data was published together with the presentation of the green reform model used to evaluate environmental regulations of the agricultural industry in Denmark (Svarer et al. 2024). Duo to inconsistency with energy used and emissions for wood pills for the agricultural industry, we have modified the databank by setting emission for the agricultural sector associated with wood pellets to 0. This only occurs in 1995, 2000, and 2003 and the highest absolute value being 4.37E-13. 20 financial aspects of each institutional sector to capture the interdependence between real and financial spheres of the economy, while ensuring there are no leakages in the system, and iv) the environmental block, where we model the types of energies used in the production process and also capture the resulting GHG emissions of each industry and the economy as a whole. 5.1. Production components 5.1.1. Production We can formally show the accounting identity used to calculate total production. As mentioned in section 4.1.2, we use a dynamic setup where we rely on a single equation (see equation 4), according to which, total domestic production in fixed prices is defined as follows: 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=�𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑖𝑖 9 𝑖𝑖=1 +�𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 +𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢+𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢+Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑝𝑝𝑝𝑝𝑚𝑚,𝑡𝑡 𝑖𝑖+𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢(equation 6a) In the above equation, ∑𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑖𝑖 9𝑖𝑖=1 represents the sum of inputs (or total intermediate goods) sold by the domestic industry n to the domestic industry i (where i=1,2,3,…,9). That is, it represents the sum across columns (representing sales) while holding the row fixed for an industry n. For example, if we take the row that represents the agricultural sector, the sum of column 1 (left) to column 9 (right) will represent the total intermediate goods sold by the agricultural sector. The term ∑𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 in the equation represents consumption of different types of goods (p) offered by industry n. In other words, this represents the sum across the columns (representing sales of different good types) in the household consumption block while holding the row fixed for an industry n. The remaining elements of equation 6a, given by 𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢,𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢,Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑝𝑝𝑝𝑝𝑚𝑚,𝑡𝑡 𝑖𝑖, and 𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 represent the production of industry n (everything in deflated values with base year 2010) for the purpose of public spending, investment, changes in inventories, and exports, respectively.19 By including equation 5d (𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢= 𝑎𝑎𝑡𝑡𝑖𝑖 𝑢𝑢∗𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢) in the model we take into account the indirect effect of changes in real production on required inputs. It is important to highlight that this relationship is modelled using the deflated variables. If this relationship was captured using nominal values, an increase in prices for final consumption goods in industry n would result in an increase in 19 From total production, we can derive the sales within each industry by deducting the change in inventories from the production 𝑠𝑠𝑎𝑎𝑠𝑠𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢−Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢. If industry n produces more than what is sold, the change in inventories will be positive, whereas a negative value indicates that goods produced in previous years were sold in the current period, lowering the value if the inventories. Since changes in inventories are relatively small and treated as exogenous, we do not distinguish between sales and production. 21 inputs from other industries (∑𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑖𝑖 9𝑖𝑖=1 ). We can now compute total production (𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢) in nominal terms, using the price indices in Table 3 as follows. 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=�𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑖𝑖 9 𝑖𝑖=1 +�𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 +𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢+𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢+Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢+𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 (equation 7a) where 𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑖𝑖= 𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑖𝑖∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is nominal intermediate goods sold by industry n to other industries, ∑𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 =∑𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 ∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is nominal private consumption of goods, 𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗ 𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is nominal government consumption of goods produced by a domestic industry n, 𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢= 𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is nominal investment using goods of a domestic industry n, Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢= Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is the nominal change in inventories, and 𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is the nominal exports of goods by a domestic industry n. 5.1.2. Cost of production To estimate the costs of a specific domestic industry, we can move vertically down the IO table (see Table 2), where all the entries, except gross operating surplus and mixed income, represent the costs associated with production. The total cost of production (𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑 𝑢𝑢) for a domestic industry n in nominal terms is determined as follows: 𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=�𝑍𝑍 𝑡𝑡𝑖𝑖 𝑢𝑢 9 𝑖𝑖=1 +𝑍𝑍𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢+𝑍𝑍𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 +𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢+𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢+𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑢𝑢 +𝑊𝑊𝑡𝑡𝑢𝑢 (equation 8) where ∑𝑍𝑍 𝑡𝑡𝑖𝑖 𝑢𝑢 9𝑖𝑖=1 represents total inputs purchased by industry n (incl. both domestic and imported inputs). That is, each type of input (e.g., agricultural input) can be divided into domestic and imported input as follows: 𝑍𝑍 𝑡𝑡𝑖𝑖 𝑢𝑢=𝑍𝑍 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 + 𝑍𝑍 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 (equation 9a) �𝑍𝑍 𝑡𝑡𝑖𝑖 𝑢𝑢 9 𝑖𝑖=1 = �𝑍𝑍 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢+ �𝑍𝑍 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 9 𝑖𝑖=1 9 𝑖𝑖=1 (equation 9b) Here, ∑𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 9𝑖𝑖=1 is the cost of domestic inputs purchased by industry n from domestic industry i at time t. The term ∑𝑍𝑍𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢9𝑖𝑖=1 denotes the sum of inputs purchased by industry n from foreign industries at time t. Note that the notation 𝑍𝑍𝑡𝑡𝑖𝑖 𝑢𝑢 is the sum across rows i (where i = 1,2,3,…,9) while holding a 22 column n fixed, which gives us inputs as costs for an industry n. For example, to calculate total domestic inputs purchased by the agricultural sector, we choose the column, representing the agricultural sector, and then take sum of row 1 (top) to row 9 (bottom). Note that the notation 𝑍𝑍𝑡𝑡𝑖𝑖 𝑢𝑢 in equation 8 is different from the notation 𝑍𝑍𝑡𝑡𝑢𝑢 𝑖𝑖 denoting inputs as sales in equation 7 (which was the sum across columns i while holding a row n fixed). In the rest of the presentation, 𝑍𝑍𝑡𝑡𝑖𝑖 𝑢𝑢 will represent costs of inputs for an industry n whereas 𝑍𝑍𝑡𝑡𝑢𝑢 𝑖𝑖 will represent sales of an industry n, in both cases with industry i as the counterpart. For the remaining notations in equation 8, 𝑍𝑍𝑢𝑢𝑖𝑖𝑑𝑑𝑝𝑝,𝑡𝑡 𝑢𝑢 denotes the unspecified imports used, 𝑍𝑍𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 represents the import duties paid, 𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢 denotes the commodity taxes, 𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢 denotes the value added taxes, 𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑢𝑢denotes other production taxes, and 𝑊𝑊𝑡𝑡𝑢𝑢 denotes the wage bill paid by industry n. The costs related to 𝑍𝑍𝑢𝑢𝑖𝑖𝑑𝑑𝑝𝑝,𝑡𝑡 𝑢𝑢 and 𝑍𝑍𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 will be addressed in section 5.2.6, where we discuss imports, while the remaining costs will be covered now as we begin modeling the various taxes associated with production. In this context, commodity taxes, value-added taxes, and other production taxes are calculated using an exogenous time-varying rate for each industry. For commodity taxes in each industry (𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢), we multiply domestically purchased inputs by the corresponding tax rate as follows: 𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢=� �𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 9 𝑖𝑖=1 �∗𝐶𝐶𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑢𝑢 (equation 10) Using the same strategy, we calculate value added taxes (𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢) by multiplying the domestically purchased inputs with the corresponding tax rate as follows: 𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢=� �𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 9 𝑖𝑖=1 �∗𝑉𝑉𝑉𝑉𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑢𝑢 (equation 11) Regarding other production taxes paid by the 9 industries (𝑃𝑃𝑉𝑉𝑃𝑃𝑡𝑡𝑢𝑢), we distinguish between environmental taxes (𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢) and non-environmental taxes (𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢). The identity representing total other production taxes can be represented as follows: 𝑃𝑃𝑉𝑉𝑃𝑃𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢= 𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢+𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢 (equation 12) To compute non-environmental (net) other production taxes, we use an exogenous rate based on total inputs used from domestic production. This can be expressed as follows: 23 𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢=� �𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 9 𝑖𝑖=1 �∗𝐼𝐼𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑢𝑢 (equation 13) The environmental taxes (𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢) are determined endogenously in the model and will be further discussed in section 5.4.3 (equation 144a). The final component of industry specific costs is the wage bill 𝑊𝑊𝑡𝑡𝑢𝑢 paid to workers by the nine industries. Here we multiply the wage rate 𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡𝑢𝑢 with the number of employees in each industry: 𝑊𝑊𝑡𝑡𝑢𝑢=𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡𝑢𝑢∗𝑉𝑉𝑀𝑀𝑃𝑃𝑡𝑡𝑢𝑢 (equation 14) If the total nominal value of production (in equation 7) of an industry are higher than its nominal costs (in equation 8), the industry will have a positive mixed income and gross operating surplus (or profits), which is represented in the last row of the value-added block. This identity can be represented as follows: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢=𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢− 𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 (equation 15) where 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢 in equation 15 represents the profit (gross operating surplus and mixed income) of industry n. For example, the gross operating surplus and mixed income for the agricultural industry is 21.5 billion DKK in 2019 (see Table 2), which is equivalent to the difference between total production measured as the sum of the first row and the total costs measured by the sum of the first column (excluding the gross operating surplus and mixed income itself). The calculations of profits as a residual ensures that we have a full account of production in the IO framework where total output of a given industry n equal its total outlays (e.g., total output and outlays for agriculture sector are 77.232). 5.1.3. The labour market: Prices, wages, and employment For price setting at an industry level, we follow a standard pricing mechanism often used within the Post-Keynsian literature (Harris 1974, Asimakopulos 1975, Godley and Lavoie 2006). We assume that producers have some degree of market power (or monopoly) and can therefore set prices above the unit cost of production. This approach to price setting is realistic when applied at an industrial level, since products across the industries are not close substitutes. To estimate the price within each industry, we assume the price for a product offered by industry n is a function of a mark-up over unit cost of production as follows: 30 𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 (equation 26b) 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 (equation 26c) 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 (equation 26d) Where 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 represents total household consumption of goods produced by the domestic industry whereas 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 represents the total household consumption of imported goods. The share of imported goods in the Danish consumer basket is quite stable around 10 percent over the last decade. To include taxes paid on final consumption we calculate exogenous tax rates based on the observed data. All final demand components are taxed through both commodity and value added taxes associated with each good type p: 𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑝𝑝=𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑐𝑐𝑑𝑑𝑢𝑢𝑐𝑐,𝑝𝑝∗𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝 (equation 27a) 𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑝𝑝=𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑐𝑐𝑑𝑑𝑢𝑢𝑐𝑐,𝑝𝑝∗𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝 (equation 27b) The term 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝 in equation 27a and 27b represents consumption of the households for each good type p. Thus, 𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑝𝑝 is the commodity taxes and 𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑝𝑝 the value added taxes paid on the consumption of each good type p. To calculate total commodity taxes and value added taxes on consumption, we can take the sum across the good types in the consumption block as follows: 𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑝𝑝 7 𝑝𝑝=1 (equation 28a) 𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑝𝑝 7 𝑝𝑝=1 (equation 28b) 5.2.2. Investments To estimate investment, we follow the approach of what is also known as the post-Kaleckian Bhaduri and Marglin (1990) model. According to this approach, investment is defined as a function of capacity utilization and profit share. The rate of capacity utilization is constructed as the ratio of 31 real GDP (𝑦𝑦𝑡𝑡) to the real stock of capital (𝑘𝑘𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). Profit share (𝑝𝑝𝑠𝑠𝑡𝑡) is defined as the ratio of gross operating surplus to GDP. The estimated equation gives us the following: Δln(𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡)= 1.8∗∗∗Δln �𝑑𝑑𝑡𝑡−1 𝑘𝑘𝑡𝑡−1 𝑁𝑁𝑁𝑁𝑁𝑁�−0.09∗∗∗ln(𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡−1 𝑡𝑡𝑑𝑑𝑡𝑡)+ 1.42∗∗∗ 𝑝𝑝𝑠𝑠𝑡𝑡−1 (equation 29) According to the estimates, aggregate investment, in the short run, is driven by the rate of capacity utilization whereas in the long run, it is driven by the profit share. Note that our measure of total investments includes both domestic and imported goods used in capital formation (but excludes value-added taxes and commodity taxes for now). We then use investment shares (𝜆𝜆𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢) to divide investment spending on the basis of industries, supplying goods used in investments. 𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑢𝑢=𝜆𝜆𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢∗𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 (equation 30a) We can then divide investment in each industry into investment spending using domestic products and imported products. We use an import share (𝜙𝜙𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢) calculated for each industry: 𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=�1−𝜙𝜙𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢�∗𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑢𝑢 (equation 30b) 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢=�𝜙𝜙𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢�∗𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑢𝑢 (equation 30c) To convert real investments into nominal, we use the corresponding price deflators for domestic and foreign industries as follows: 𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equation 31a) 𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (equation 31b) Lastly, we aggregate investment across industries for both nominal and real terms: 𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 32a) 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 32b) 𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 32c) 32 𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 32d) We can finally use exogenously calculated tax rates, to calculate the commodity taxes and value added taxes associated with domestically produced investment products. 𝐼𝐼𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 ∗𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 33a) 𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 ∗𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 33b) 5.2.3. Change in inventories Changes in inventories are determined exogenously within the model. We choose to keep it exogenous in real values. The following equations describe real inventories, including domestic and 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 and import related 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =� Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9𝑢𝑢=1 (equation 34a) Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =� Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9𝑢𝑢=1 (equation 34b) Nominal inventories are partly endogenous in a sense that they are affected by (endogenous) domestic producer prices (𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢). Inventories in nominal terms can be represented as follows: Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equation 35) As a result, the total change in inventories in nominal values are also calculated within the model: Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 36) Finally, taxes pertaining to inventories are exogenous and are calculated within the model as follows: Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣𝑟𝑟𝑢𝑢𝑡𝑡∗Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 37a) Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣𝑟𝑟𝑢𝑢𝑡𝑡∗Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 37b) 33 5.2.4. Government spending Government spending, like changes in inventories, is also treated as exogenous in real values. Final government consumption of imported (𝑔𝑔𝑝𝑝𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡) and domestic goods (𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 ) in real terms are computed as follows: 𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =�𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9𝑢𝑢=1 (equation 38a) 𝑔𝑔𝑝𝑝𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =�𝑔𝑔𝑝𝑝𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9𝑢𝑢=1 (equation 38b) Again, as domestic prices can change in the model, so can the nominal value of government spending: 𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equation 39) We can then calculate the total government spending in nominal values as follows: 𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =�𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9𝑢𝑢=1 (equation 40) Finally, the commodity and value added taxes pertaining to government consumption are computed as follows: 𝐺𝐺𝑃𝑃𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑎𝑎𝑑𝑑𝑣𝑣 ∗𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 41a) 𝐺𝐺𝑃𝑃𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑎𝑎𝑑𝑑𝑣𝑣 ∗𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 41b) For completeness, we have chosen to present equations related to the changes in inventories and government spending, even though they are not necessary for running the model. It is important for the reader to note that these two variables will only change in nominal terms and only for domestic industries. 5.2.5. Exports We determine the total exports for each of the nine industries using a variant of the Armington model. Our exports in each industry are determined by price competitiveness and global demand. We can express the exports equation in log-linear form as follows: ln �𝑥𝑥𝑡𝑡𝑢𝑢 𝑚𝑚𝑡𝑡𝑢𝑢∗�= α 0 𝑢𝑢+ α 1𝑢𝑢∗ln(𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡−1 𝑢𝑢)+𝑎𝑎𝑝𝑝𝑗𝑗𝑐𝑐,𝑡𝑡 𝑢𝑢 (equation 42) 34 where 𝑚𝑚𝑡𝑡𝑢𝑢∗is the global demand (or imports) for the type of goods produced by n type of industries across the globe. For example, when estimating the exports for the agricultural sector, 𝑥𝑥𝑡𝑡𝑢𝑢 represents exports of Danish agricultural industry whereas 𝑚𝑚𝑡𝑡𝑢𝑢∗ represents the global demand for agricultural products. Thus, the left-hand side of equation 42 represents the share of Danish exports to total world imports within each specific industry. To calculate the share of Danish exports in the global market, we use the BACI-dataset providing import and export values amongst countries in the world at a product-level.28 α 1𝑢𝑢 captures the export elasticities to movements in real exchange rate 𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑢𝑢. Real exchange rate for each industry is a proxy for international competitiveness, defined as follows: 𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑢𝑢=𝑥𝑥𝑝𝑝𝑡𝑡𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (equation 43) where 𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is the domestic price of industry n, 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 is the price of imports of industry n, both price indices are calculated in Danish currency whereas we do not need to consider the nominal exchange rate. To find the export elasticities (represented by α 1𝑢𝑢), we use estimates found by Kronborg, Poulsen, and Kastrup (2020) who derive export elasticities using the BACI-dataset for the Danish economy. As the BACI-dataset does not include exports for all industries, we use an average export elasticity for the Danish economy in the mining and financial corporation industries. The vector of the export elasticities pertaining to each industry is presented in the table below:29 28 As the BACI-dataset does not include products for all industries included by Denmark statistics, we use an average export share for the whole Danish economy based on all products in the BACI-dataset. 29 As we perform the aggregation to match the 9 industries in this paper, we use export within each industry to calculate a weighted average. 35 Table 7: Export elasticities The negative values of the parameter(s) α 1𝑢𝑢 imply that an increase (decrease) in the domestic price in industry 𝑖𝑖 will appreciate (depreciate) the real exchange rate, which in turn will lower (raise) exports of industry n.30 We set the constant ( α 0 𝑢𝑢) to match the logarithmic value of the first observation in the market share for each industry. Finally, we include an adjustment term (𝑎𝑎𝑝𝑝𝑗𝑗𝑐𝑐,𝑡𝑡 𝑢𝑢), which captures the effects of variables other than the real exchange rate. As the price elasticities presented by Kronborg, Poulsen, and Kastrup (2020) are based on micro data (with the goal of finding a causal relationship between relative prices and exports), these estimates are found to be theoretically intuitive, but poorly fitting the aggregate data. Leaving out the adjustment terms would therefore create large discrepancies compared to the observed data which could be problematic in the model simulations. An alternative approach is to obtain these elasticities using aggregate data. This approach, however, did not work in our case, as the estimates (using aggregate data) were found to be non-sensical due to small sample size. We believe it is crucial that the export elasticities have realistic signs and magnitudes, therefore, we make a strategic decision of using theoretically intuitive elasticities based on Danish micro data. After estimating the export share for each industry, we multiply the market share ( 𝑐𝑐𝑡𝑡𝑖𝑖 𝑑𝑑𝑡𝑡𝑖𝑖∗) with the corresponding denominator (𝑚𝑚𝑡𝑡𝑢𝑢∗) to obtain exports of each industry in levels (𝑥𝑥𝑡𝑡𝑢𝑢). 30 We use elasticities whereas an export elasticity of -5.13 for the agriculture industry implies that a 1% increase in the real exchange rate for this industry lowers its export by 5.13%. 36 Once we have the total value of exports for each industry, we split this value into two categories, i) goods that are domestically produced and exported, and ii) goods that are first imported and then exported by the domestic industry. We use exogenous shares (𝜙𝜙𝑐𝑐,𝑡𝑡 𝑢𝑢 and 1−𝜙𝜙𝑐𝑐,𝑡𝑡 𝑢𝑢) based on the observed data in the Input-Output table (Table 2) to split exports: 𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=�1−𝜙𝜙𝑐𝑐,𝑡𝑡 𝑢𝑢�∗𝑥𝑥𝑡𝑡𝑢𝑢 (equation 44a) 𝑥𝑥𝑑𝑑,𝑡𝑡 𝑢𝑢=�𝜙𝜙𝑐𝑐,𝑡𝑡 𝑢𝑢�∗𝑥𝑥𝑡𝑡𝑢𝑢 (equation 44b) where 𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 represents goods that are domestically produced and exported, and 𝑥𝑥𝑑𝑑,𝑡𝑡 𝑢𝑢 represents goods that are first imported by industry n and then simply exported. We can use the corresponding price deflators to convert exports from real into nominal values: 𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equation 45a) 𝑋𝑋𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑥𝑥𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (equation 45b) To compute total exports for the Danish economy, we simply sum each type of exports across the industries as follows: 𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 46a) 𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 46b) 𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 46c) 𝑋𝑋𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑋𝑋𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 46d) where 𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 denote total (real) exports of goods that are domestically produced and 𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 denote exports of goods, which first enter the economy as imports.31 In the above set of equations, the notations in capital letters represent nominal values. 31 Note that an increase in exports as a result of real exchange rate depreciation will proportionately increase those imports which are linked to exports. 37 Finally, we can calculate commodity and value added taxes associated with domestically produced nominal exports: 𝑋𝑋𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑐𝑐∗𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 47a) 𝑋𝑋𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑐𝑐∗𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 47b) 5.2.6. Imports To model imports, we first estimate imports at an industrial level, followed by the estimation of imports in the final demand block. We start by determining the fraction of imports used as inputs in the industries. Recall that in equation 5d, we calculated total inputs using technical coefficients, these inputs consisted of both domestic and imported inputs used in production (also see equation 5c). To isolate the value of imported inputs, we use the share of imports (𝜙𝜙𝑧𝑧,𝑡𝑡 𝑖𝑖 𝑢𝑢) in the total inputs and multiply it with total inputs (𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢) as follows: 32 𝑧𝑧𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢=𝜙𝜙𝑧𝑧,𝑡𝑡 𝑖𝑖 𝑢𝑢∗𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢 (equation 48a) 𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢=�1−𝜙𝜙𝑧𝑧,𝑡𝑡 𝑖𝑖 𝑢𝑢�∗𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢 (equation 48b) where 𝑧𝑧𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 is the value of imported inputs and 𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢 is the value of inputs produced domestically. We can calculate these inputs in nominal terms by using the corresponding price deflators. 𝑍𝑍𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢=𝑧𝑧𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢∗𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (equation 48c) 𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢=𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑖𝑖 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equation 48d) From the IO data, we know that a fraction of imported inputs cannot be categorized using the Danish industry definitions - this is classified as unspecified imports. To determine unspecified imports, we assume a linear relationship between unspecified imports and total production of the domestic industry. 𝑧𝑧𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢=𝛾𝛾𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 (equation 49a) where 𝛾𝛾𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 is the (exogenous) share of unspecified imports in total production. We can also calculate the unspecified imports in nominal values as follows: 32 Note that 𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢 is the real value of equation 2a. 38 𝑍𝑍𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑧𝑧𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑚𝑚𝑢𝑢𝑖𝑖𝑑𝑑 (equation 49b) We now focus on endogenizing the share of imports 𝜙𝜙𝑧𝑧,𝑡𝑡 𝑖𝑖 𝑢𝑢 introduced in equation 48a-b. We assume that the share of imported inputs for each industry is partly driven by the real exchange rate. To determine import elasticities, we follow a simple strategy, known as the “rule of two” where the import elasticity of an industry is assumed to be half the export elasticity.33 This approach is also adopted by the GreenREFORM model (Kirk and Hansen 2023). The main argument is that domestic residents, for a variety of reasons, have a preference for domestically produced goods even if they tend to be more expensive. The functional form of this relationship can be represented as follows: ln(𝜙𝜙𝑧𝑧,𝑡𝑡 𝑖𝑖 𝑢𝑢) = 𝛽𝛽0𝑧𝑧𝑖𝑖 𝑖𝑖+𝛽𝛽1𝑧𝑧𝑖𝑖∗𝑠𝑠𝑖𝑖(𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑢𝑢)+𝑎𝑎𝑝𝑝𝑗𝑗𝜙𝜙,𝑡𝑡 𝑢𝑢 (equation 50) In the above equation, 𝛽𝛽0𝑧𝑧𝑖𝑖 𝑖𝑖 is a constant taking the log of the starting value for the import share (𝜙𝜙𝑧𝑧,𝑡𝑡 𝑖𝑖 𝑢𝑢), and 𝛽𝛽1𝑧𝑧𝑖𝑖 represents the import elasticity (shown in table 8). We find that our computed elasticities are theoretically intuitive and within a justifiable range, when compared with a recent empirical study; Kastrup et al. (2023) use Danish industrial data to estimate import elasticities, finding the macro elasticity to be 1.84, whereas the implied macro elasticity in our case (using weighted average of elasticities across the industries) is around 2.34 Finally, we have an exogenous determined adjustment term capturing other relevant effects than the real exchange rate �𝑎𝑎𝑝𝑝𝑗𝑗𝜙𝜙,𝑡𝑡 𝑢𝑢�.35 33 In general, the rule of two is found to have strong empirical support, e.g., Feenstra et al. (2018) show that the “rule of two” cannot be rejected for almost 80% of all product types. 34 In general, these elasticities tend to vary a lot in the empirical literature. For example, Temere (2017) find that the estimated elasticities using micro data for Denmark ranges between -1.14 and -32.65 with an overall mean of -6.15 and a median of -4.45. Imbs and Mejean (2009) for the US data find elasticities across industries range from 3.1 to 28 with a standard deviation of 4.9. 35 Like in the case of exports, the import elasticity is based on micro data estimations whereas the simulated import of inputs for each industry will fit the observed data poorly if the adjustment term is not included. We do this to not underestimate the import elasticities which is usually the case when using aggregate data (Kronborg, Poulsen, and Kastrup (2020)). 39 Table 8: Import elasticities (Industry) We now focus on imports associated with the final demand block. Focusing on household consumption, we first classify the consumer basket into domestic and imported goods. Since households’ consumption basket consists of 7 types of goods, we carry out the classification for all 7 types. Recall the set of equations 20a-20b, where the proportion of good type (p) in the consumer basket imported from abroad was given by: 𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝=�𝜙𝜙𝑐𝑐,𝑡𝑡 𝑝𝑝�∗𝑐𝑐𝑡𝑡𝑝𝑝. Whereas the proportion of good type (p) in the consumer basket domestically produced was given by: 𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝=�1−𝜙𝜙𝑐𝑐,𝑡𝑡 𝑝𝑝�∗𝑐𝑐𝑡𝑡𝑝𝑝. Thus by endogenizing 𝜙𝜙𝑐𝑐,𝑡𝑡 𝑝𝑝, we can model the substitution effects between household consumption of domestic and foreign goods. To do so, we model 𝜙𝜙𝑐𝑐,𝑡𝑡 𝑝𝑝 as a function of the relative prices. We can represent this relationship as follows: ln(𝜙𝜙𝑐𝑐,𝑡𝑡 𝑝𝑝) = 𝛽𝛽0𝑐𝑐𝑝𝑝+𝛽𝛽1𝑐𝑐𝑝𝑝∗ln (𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑝𝑝) (equation 51) The parameter 𝛽𝛽1𝑐𝑐𝑝𝑝, estimated via OLS, captures the elasticity of substitution between domestic and imported goods.36 The estimates of the import elasticities associated with the 7 product types are presented in table 9 where the highest elasticity is observed for Meat products. 36 In contrast to equation 50 and 42 the import elasticities of final consumption presented in equation 51 are estimated using OLS on aggregated consumption data. As a result, the fitted values will be able to match the observed data and we do not include any adjustment term. 46 dividends (𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), income on other investments (𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), and retained earnings on FDI (𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). Finally, we also account for net other current transfers received (𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). We can now calculate the disposable income of the non-financial corporations (𝑌𝑌𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) by subtracting income taxes paid by the non-financial corporations (𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) as follows: 𝑌𝑌𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (equation 59b) Following the definition in the national accounts, the savings equation of non-financial firms (𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) is represented as follows: 𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (equation 60) NFC sector spends a part of its savings on investment (𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), covering changes in inventories, acquisition and disposals of non-produced non-financial assets43 (𝐼𝐼𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), and other capital transfers (𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). Therefore, we can subtract these flows from savings, and calculate net balance (or sectoral balance): 𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (equation 61) A positive (negative) net balance, reflecting a surplus (deficit), implies that the sector is spending less (more) than its income. We now focus on the vertical consistency of the TFM, for which we need to describe how the resultant surplus is spent or, in the case of a deficit, how it is financed. This requires specifying the financial aspects of the sector which includes the accumulation of financial assets. As we specify how net lending (whether positive or negative) affects the accumulation of financial assets, we also describe the steps and assumptions used to ensure that sectoral balance (or net lending in equation 61) equates financial balance. In other words, we specify how net lending (whether positive or negative) affects the accumulation of financial assets. We start by defining the financial net lending (or financial balance) as follows: 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (equation 62) where 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 denotes the financial balance, which is equal to the sum of (net) transactions associated with gold (gold is only relevant for the financial corporations and ROW), deposits 43 Non-produced non-financial assets refer to assets that have not been produced but have economic value and can be owned or exchanged. These assets include natural resources, contracts, licenses, etc., as well as other intangible assets. 47 (𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶), securities (𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶), loans (𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶), equities (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶), insurance/tech. reserves (𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶), financial derivatives (𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶), and trade credits (𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶). Note that the net transaction linked to each financial stock is computed as the transaction related to the accumulation of a financial asset (which is an outflow for purchasing a financial asset) minus the transaction related to the liability of that asset (which is an inflow representing sources of funding). To provide an overview of the balance sheet, we can calculate the financial net wealth (𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) as follows: 𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (equation 63) Financial net wealth is the sum of net deposits (𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), securities (𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), loans (𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), equities (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), insurance/tech. reserves (𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), financial derivatives (𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), and trade credits (𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). Note that notations used for net financial stocks are distinguished from net financial transactions as the former include “tr” in the subscript. At this point, one can proceed to modelling each financial stock included in equation 63. If there are k number of financial stocks, one approach is to model a maximum of k-1 stocks and treat the last financial asset as a residual. For simplification, we choose to only model net loans (or business credit) of firms while treating other financial stocks as exogenous. The functional form of the equation determining the demand for loans is represented as follows: �𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 𝐾𝐾𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 �= 0.26∗∗∗+ 0.28∗∗�𝐼𝐼𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶 𝐶𝐶𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶�−2.11∗∗∗𝑝𝑝𝑡𝑡−1 𝐿𝐿𝐶𝐶𝑉𝑉 (equation 64) equation 64 states that loan to capital ratio depends positively on investment to savings ratio �𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝑁𝑁 𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝑁𝑁� and negatively on interest rate. The intuition is that investment in excess of savings, is partly financed through loans. Moreover, an increase in the cost of borrowing (represented by interest rate on loans) will lower the demand for loans. After endogenizing the stock of loans, we can use the change in stock of loans to determine loan transactions using the accounting identity expressed as follows: 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (equation 65) where 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 represents the stock revaluations (treated as exogenous), Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 the change in the stock of loans, and 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 is the transaction of loans. 48 While treating other financial stocks as exogenous, we can describe the accounting identities to show their evolution over time. This is done by adding the net transactions and net re-evaluations to the last years stock of the net financial asset: 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (equation 66) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (equation 67) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (equation 68) 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (equation 69) where NSEC represents net stock of securities, NINSU represents net stock of insurance and pensions, NDERV represents the net stock of derivatives, and NTCRED represents the net stock of trade credits. Note that notations for transactions and revaluations pertaining to each of the financial stock are distinguished by using subscripts tr and rv, respectively. In the above set of equations, for each financial stock, we can see that when current transactions and revaluations are added to the past value of a financial stock, we get the present value of the financial stock. In other words, changes in the value of a financial stock can occur for only two reasons, i.e., new transactions and revaluations. We are now left with two financial stocks namely equities and deposits. Regarding equities, we assume that the stock market is demand-driven in a sense that new equities issued by non-financial corporations equal the demand for equities from other sectors. This relationship is captured in equation 70a as follows: 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=−�𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (equation 70a) where the transactions pertaining to the supply of equities by NFC is denoted by 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶, which is equal to the collective demand for equities by other sectors, given by the sum of the transactions of equities by households (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻), financial corporations (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶), government (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺), and rest of the world (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅). This implies that the net stock of equities (representing a liability) for NFC equals the sum of the net stock of equities (representing assets) of other sectors: 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (equation 70b) To ensure that sectoral balance (or net lending in equation 61) equates financial balance in equation 62, we treat one financial stock, namely deposits, as residuals, which in this case should be defined as follows: 49 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 −(𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶) (equation 71a) Note that we include an extra adjustment term 𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 to account for the small discrepancy between financial net lending (𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) and net lending (𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) present in the published data. Like other financial stocks, we treat stock revaluations of deposits as exogenous, and can show that the stock of deposits evolves according to equation 71b: 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (equation 71b) This completes the description of how the balance sheet of NFC sector is related to the real side of the economy. While holding the rest of the financial stocks exogenous, we have modeled two main sources of funds: issuing equities and securing loans. We now proceed to discussing the income and financial aspects of the household sector. 5.3.2. Households We start by describing the computation of income for the household sector. The major source of household income takes the form of labour income share (wages), paid by the NFC. First, we define the total amount of wages paid by the NFC sector as the sum of all wages paid by the nine industries: 𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=�𝑊𝑊𝑡𝑡𝑢𝑢 9 𝑢𝑢=1 (equation 72a) We know that a small fraction of workers employed by the NFC sector is foreign labour. Therefore, we can subtract wages paid to non-residents from the total wages in equation 66a, the resultant of which will give us wages paid to domestic households. This calculation is carried out in equation 66b below: 𝑊𝑊𝑡𝑡𝐻𝐻= 𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝑊𝑊𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 (equation 72b) Where 𝑊𝑊𝑡𝑡𝐻𝐻 represents wages received by the household sector and 𝑊𝑊𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 denotes wages paid to foreign labour. We can now calculate the net income received by households (𝑌𝑌𝑡𝑡𝐻𝐻) as follows: 𝑌𝑌𝑡𝑡𝐻𝐻=𝐵𝐵2𝑡𝑡𝐻𝐻+𝑊𝑊𝑡𝑡𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝐻𝐻+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝐻𝐻−𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡 𝐻𝐻 +𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻 (equation 73a) 50 Households income consists of various income types: gross operating surplus received by households is denoted by (𝐵𝐵2𝑡𝑡𝐻𝐻), wages are denoted by (𝑊𝑊𝑡𝑡𝐻𝐻), net income received on financial stocks (𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻,𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻,𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝐻𝐻,𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝐻𝐻), social benefits received (𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡 𝐻𝐻), and net other current transfers (𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻) and finally we deduct social contributions paid (𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡 𝐻𝐻). By subtracting income taxes from net income received by households (𝑌𝑌𝑡𝑡𝐻𝐻), we can calculate the disposable income for households: 𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻=𝑌𝑌𝑡𝑡𝐻𝐻−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝐻𝐻 (equation 73b) We can now calculate household savings by subtracting aggregate private consumption (𝐶𝐶𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎) and adjusting for pension savings (𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡𝑎𝑎𝑑𝑑𝑗𝑗), which is a part of household savings (𝐶𝐶𝑡𝑡𝐻𝐻), but are not accessible for consumption as they are placed in pension funds. 𝐶𝐶𝑡𝑡𝐻𝐻=𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻−𝐶𝐶𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎+𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡𝑎𝑎𝑑𝑑𝑗𝑗 (equation 74) We can then calculate the net lending (or sectoral balance) for the household sector: 𝐼𝐼𝐿𝐿𝑡𝑡𝐻𝐻=𝐶𝐶𝑡𝑡𝐻𝐻−𝐼𝐼𝑡𝑡𝐻𝐻−Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻−𝐼𝐼𝑃𝑃𝑡𝑡𝐻𝐻−𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻 (equation 75) where 𝐼𝐼𝑡𝑡𝐻𝐻 denotes household investment, 𝐼𝐼𝑃𝑃𝑡𝑡𝐻𝐻 denotes transactions pertaining to the acquisition and disposal of non-produced non-financial assets (such as natural resources, contracts, licences, etc.), and 𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻 denotes other capital transfers. We now focus on modeling the financial side of households, where we roughly follow the same approach as for non-financial corporations. First, we define the equation for financial balance: 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 (equation 76) where 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝐻𝐻 is the net lending, determined by net transactions pertaining to various financial assets. 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 denotes transaction related to deposits, 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 denotes transactions related to securities, 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 represents loan transactions, 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 denotes transactions related to insurance and pensions, 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 denotes transactions related to derivates, and 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 denotes transactions related to trade credits. We now define the financial net wealth of the households as follows: 51 𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐻𝐻 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐻𝐻 (equation 77) 𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝐻𝐻 is the financial net wealth, determined by the net value of the financial stocks on the balance sheet of households. For the household sector, we endogenies two financial stocks, which constitute a significant portion of the balance sheet. On the asset side, we model equities endogenously, whereas on the liability side, we model loans endogenously. To model equities, we first define a variable, equity to wealth ratio, representing the share of net equities to total financial wealth in the previous period. 𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻=�𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐻𝐻−𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡−1 𝐻𝐻� (equation 78a) Following the intuition of Tobins portfolio theory, which has now become a well-integrated part of the stock-flow consistent models, we assume that the share of equity in the financial wealth of households partly depends on the rate of return associated with equities.44 The specific functional form of the estimated equation is represented as follows: Δ𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻= 0.33∗Δ𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1 𝐻𝐻+ 0.060Δ�𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡−1 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡−1 𝐻𝐻� 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−2 𝐻𝐻−0.18𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1 𝐻𝐻 + 0.10∗�𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡−2 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡−2 𝐻𝐻� 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−3 𝐻𝐻 (equation 78b) The estimates imply that an increase in the return on equity will increase the share of equities in the wealth formulation. This is found to be the case both in the short-run and long-run. The intercept (0.063) can be interpreted as capturing the share of equities in wealth that is not dependent on the rate of return associated with equities. We can use the estimated share in equation 78b to calculate net equities held by the household as follows: 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐻𝐻=𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻∗𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡−1 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (equation 78c) The estimated stock value in equation 78c is then used to determine the transactions for equities (while treating the revaluations of equities as exogenous): 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻=Δ𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐻𝐻−𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (equation 78d) 44 Here we use a different rate of return compared to the dividend rate calculate in appendix 8.3. The rate used in equation 78b only focus on the household sector and furthermore includes the re-evaluations. For equities, the reevaluations seem to be an important aspect in determining demand, whereas we include this in the rate of return. 52 To endogenies household loans, we first define the ratio of loans to disposable income.45 𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻=�−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻 𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻� (equation 79a) We assume this ratio is positively influenced by investment and negatively influenced by the cost of the loan, represented by the interest rate on the loan. The estimated functional form of this relationship is given by equation 79b: 𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻= 0.91∗∗∗𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1+ 2.28∗∗∗�𝐼𝐼𝑡𝑡𝐻𝐻 𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻�−0.31𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉−0.37∗∗∗𝑃𝑃2016 (equation 79b) We can use the estimated share from equation 79b to calculate the stock of loans held by the household sector as follows: 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻=−𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻∗𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻 (equation 79c) The stock value in equation 79c is then used to determine the transactions for loans (while treating the revaluations of loans as exogenous): 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻=Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (equation 79d) To ensure that sectoral balance of the household sector equates its financial balance, we again treat deposits, as residuals, which in this case should be defined as follows: 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻=𝐼𝐼𝐿𝐿𝑡𝑡𝐻𝐻+𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝐻𝐻−(𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻 +𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻) (equation 80a) Here, again, we include an adjustment term 𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝐻𝐻 to capture discrepancies between net lending and financial balance in the published statistics. The transaction data on deposits can be used to determine the stock of deposits for the households (𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝐻𝐻) while treating revaluations as exogenous: 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (equation 80b) The remaining financial assets on the balance sheet of the households are exogenously determined; these financial stocks evolve as follows: 45 We multiply the ratio by -1 as households only have loans as liabilities, whereas the net loans are negative. 53 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐻𝐻=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (equation 81) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝐻𝐻=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (equation 82) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (equation 83) 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐻𝐻=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (equation 84) The identities in the above set of equations have the same intuition as discussed earlier in the case of NFC. That is, when current transactions and revaluations are added to the past value of a financial stock, we get the present value of the financial stock. This completes the description of the factors influencing households balance sheet in our model. To sum-up, for the household sector, we have modeled two financial stocks namely equities (assets) and loans (liabilities); both collectively constitute a substantial portion of the households balance sheet. In the next, we discuss the role of financial corporations. 5.3.3. Financial corporations We first define the income of financial corporations. Using the definition of net income presented in section 4.2.1 and appendix 8.3 we can calculate the income received by the financial sector (𝑌𝑌𝑡𝑡𝑁𝑁𝐶𝐶) using the following identity: 𝑌𝑌𝑡𝑡𝑁𝑁𝐶𝐶=𝐵𝐵2𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑁𝑁𝐶𝐶+𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶−𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶 (equation 85a) The income consists of various flows: gross operating surplus (𝐵𝐵2𝑡𝑡𝑁𝑁𝐶𝐶), net income on financial assets (𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶,𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶,𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑁𝑁𝐶𝐶,𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑁𝑁𝐶𝐶), social contributions received (𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶), and net other current transfers (𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶). Finally, we subtract social benefits paid (𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶) to compute net income. By subtracting taxes from net income, we can compute disposable income as follows: 𝑌𝑌𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶=𝑌𝑌𝑡𝑡𝑁𝑁𝐶𝐶−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝑁𝑁𝐶𝐶 (equation 85b) We can now calculate the savings of the financial corporations, which requires adjusting net disposable income for flows pertaining to pensions. The saving identity of the financial corporations can be presented as follows: 𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶=𝑌𝑌𝑃𝑃𝑁𝑁𝐶𝐶−𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡𝑎𝑎𝑑𝑑𝑗𝑗 (equation 86) 54 Note that the pension deductions from the income of financial corporations are, in turn, received by the households (𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡𝑎𝑎𝑑𝑑𝑗𝑗), as was shown in the savings equation for the household sector (see equation 74). We can calculate the net lending of the financial corporations using the same set-up as before: 𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝐶𝐶=𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶−𝐼𝐼𝑡𝑡𝑁𝑁𝐶𝐶−Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶−𝐼𝐼𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶−𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶 (equation 87) Focusing on the financial aspects of the sector, we can calculate the financial net lending as follows: 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 (equation 88) where 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝐶𝐶 is the financial balance which, by definition, is equal to the sum of net transactions associated with each financial stock. The only additional transaction is related to the acquisition or sale of gold denoted by 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶. We can now define the net financial wealth (representing the net value of the financial balance sheet) of the financial sector as follows: 𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶 (equation 89) We assume that financial corporations clear the market for deposits, loans, insurance, and derivatives. Thus, we can write: 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (equation 90) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (equation 91) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (equation 92) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (equation 93) Using the transactions in the above set of equations, we can determine the value of each financial stock as follows: 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (equation 94) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (equation 95) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (equation 96) 55 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (equation 97) To ensure consistency between sectoral balance (equation 87) and financial balance (equation 88), we model net transactions of securities as a residual: 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝑁𝑁𝐶𝐶 −(𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶) (equation 98) Using the transactions of securities in equation 98, we can define the evolution of net stock of securities over time as follows: 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (equation 99) We are now left with two financial stocks on the balance sheets of financial corporations, gold reserves and the net stock of trade credits. These two financial stocks are assumed to be fully exogenous and are given by the following equations: 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (equation 100) 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (equation 101) This concludes the factors in the balance sheet of the financial corporations. To sum-up, the main role of this sector is to clear the market for deposits, loans, insurance, and derivatives in the model. In the following, we describe the income and financial aspects of the government sector. 5.3.4. Government The main income received by the government sector is taxes, this includes commodity taxes, value added taxes, other production taxes, and import duties paid by each industry. To calculate the total taxes paid to the government, we take the sum of different taxes across industries and the final demand components. 𝐶𝐶𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢 9 𝑢𝑢=1 +𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐺𝐺𝑃𝑃𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡+𝐼𝐼𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝑋𝑋𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 102a) 𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢 9 𝑢𝑢=1 +𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐺𝐺𝑃𝑃𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝑋𝑋𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 102b) 𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑃𝑃𝑉𝑉𝑃𝑃𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (equation 102c) 62 We endogenize the energy used by households using a linear relationship between energy used and domestic consumption. This relationship is expressed in equation 132: 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝐻𝐻=𝑃𝑃𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻∗𝑐𝑐𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 (equation 132) We use the difference between total energy usage and total energy supply, to calculate the change in energy inventories as follows: 𝐼𝐼𝑖𝑖𝑖𝑖𝑃𝑃𝑟𝑟𝑠𝑠𝑡𝑡𝑎𝑎,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸= 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 −𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (equation 133) Unfortunately, the stock values of these inventories are not available for our sample, therefore we set the starting stock value to zero in the first period of the sample with changes in this stock being defined as: 𝐼𝐼𝑖𝑖𝑖𝑖𝑡𝑡𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸=𝐼𝐼𝑖𝑖𝑖𝑖𝑡𝑡−1 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸+𝐼𝐼𝑖𝑖𝑖𝑖𝑃𝑃𝑟𝑟𝑠𝑠𝑡𝑡𝑎𝑎,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸 (equation 134) We now focus on energy reserves available in the economy. There are two energy reserves in Denmark: Crude oil (𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡 𝑎𝑎𝑗𝑗 ) and Natural gas extracted (𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡 𝑎𝑎𝑗𝑗 ). The data on these reserves is measured in m3 and Nm3, but we convert them to gigajoules to fit the energy usage and supply accounts. For conversions, we use the conversion rates presented in the annual reports by the Danish energy agency. It can be shown that the reserves for crude oil and natural gas evolve according to the following equations:51 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡 𝑎𝑎𝑗𝑗 =𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 −�𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡−1 𝑢𝑢 9 𝑢𝑢=1 + 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 (equation 135a) 𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡 𝑎𝑎𝑗𝑗 =𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 −�𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑟𝑟𝑐𝑐𝑡𝑡𝑝𝑝,𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡−1 𝑢𝑢 9 𝑢𝑢=1 +𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 (equation 135b) In the above set of equations, 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡 𝑎𝑎𝑗𝑗 and 𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡 𝑎𝑎𝑗𝑗 are the opening stocks of crude oil and natural gas. These energy reserves will deplete over time depending on the pace of extractions, which in turn, depends on the demand for these type of energies; the extraction of crude oil is denoted by ∑𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑢𝑢,𝑡𝑡−1 𝑐𝑐𝑢𝑢𝑝𝑝 9𝑢𝑢=1 and the extraction of natural gas is denoted by ∑𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑟𝑟𝑐𝑐𝑡𝑡𝑝𝑝,𝑢𝑢,𝑡𝑡−1 𝑐𝑐𝑢𝑢𝑝𝑝 9𝑢𝑢=1 . 51 Supply data for crude oil and natural gas matches closely with the production data for crude oil and natural gas reserves provided by the Danish energy agency for oil and gas reserves in Denmark. Therefore, we assume that domestic supply data from Statistics Denmark shows how much oil and gas is produced/extracted from the oil and gas reserves. Thereby the rest of the data is consistent with consumption and use data also used from Statistics Denmark. 63 New discoveries of reserves or revaluations are added to the existing stocks, captured by the terms 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 for crude oil, and 𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 for natural gas.52 5.4.2. Emissions We now present a detailed assessment of GHG emissions in the economy. In our analysis, we begin by categorizing emissions based on economic activity. In this regard, we distinguish emissions generated in the production process from those generated by household consumption. Afterwards, both sources of emissions (i.e., production and consumption-related emissions) are further classified into two types: i) Energy-Related Emissions (Direct Emissions), which are emissions caused by the use of energy sources, such as emissions resulting from burning fossil fuels like coal, oil, or natural gas; and ii) Other production related Emissions (Indirect Emissions), which are emissions associated with economic activities not directly caused by energy usage, e.g., emissions from waste management practices or methane emissions by livestock. Note that emissions originating from the aforementioned activities can take the form of specific gases. As mentioned in section 4.3.2, we include the following types of emissions: carbon dioxide (CO2), nitrous oxide (N2O), methane (CH4), sulfur hexafluoride (SF6), perfluorocarbons (PFC), and hydrofluorocarbons (HFC).53 These forms of emissions are later used to calculate the CO2equivalent measure.54 In what follows, it is helpful to understand the distinction between the sources of emissions (generated by 4 types of economic activity) and the forms they take (6 forms of GHG emissions as discussed above). In the following sections, we will first examine the direct and indirect emissions produced during the process of production. Afterward, we will address the direct and indirect emissions resulting from households’ consumption. A. Direct Energy-Related Emissions of domestic production Following the approach of Beck and Dahl (2020), we calculate emission coefficients linked to each energy type for each industry. To that end, we use a dataset linking emissions to the use of specific 52 As data on crude oil and natural gas reserves were inconsistent in 2006, 2014 and 2015, probably as a result of rounding errors, we have adjusted the data for 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 by + 1 m3 in 2006, +1 m3 in 2014, and by -1 m3 in 2015, thereby making the data consistent. For natural gas (𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 .), we +1 Nm3 in 1997, - 1 Nm3 in 2006, + 1 Nm3 in 2012. 53 SF6, PFC, and HFC are not emitted as a result of using energy, whereas they only occur for the category “unrelated to energy”. 54 The model can be extended to include additional emission types, Data from Denmark statistics allow us to include 15 types of emissions. 64 energy types for each industry. The emission coefficient in the case of direct emissions for each industry is calculated as follows: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑡𝑡 𝑢𝑢 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝑢𝑢 (equation 136a) where 𝑖𝑖 determines industry, 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼 determines the type of emissions (e.g. CO2, N20, and so on), and 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌 determines energy type (e.g. Crude oil, Oil products, and so on). To give an example, the energy coefficient relating the usage of oil products (OilP) to carbon dioxide emissions (CO2) in the agriculture industry is calculated as follows: 𝐶𝐶𝑃𝑃2𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐶𝐶𝑖𝑖𝑠𝑠𝑃𝑃,𝑉𝑉𝐺𝐺𝑃𝑃𝐼𝐼=𝐶𝐶𝑃𝑃2𝐶𝐶𝑖𝑖𝑠𝑠𝑃𝑃,𝑡𝑡 𝑉𝑉𝐺𝐺𝑃𝑃𝐼𝐼 𝑃𝑃𝑖𝑖𝑠𝑠𝑃𝑃𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝑉𝑉𝐺𝐺𝑃𝑃𝐼𝐼 (equation 136b) where 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼=𝐶𝐶𝑃𝑃2, 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌=𝑃𝑃𝑖𝑖𝑠𝑠𝑃𝑃, and 𝑖𝑖=𝑉𝑉𝐺𝐺𝑅𝑅𝐼𝐼. Since we have emissions related to each of the 21 energy types, we can take the sum across the energy types for each industry to calculate the total direct energy-related emissions for each individual industry. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝑢𝑢=�𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝑢𝑢∗𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢 21 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸=1 (equation 136c) Note that the available data used to estimate emission coefficient is available until 2017. Since, our sample extends to 2019, we assume the same emission coefficients from 2017-2019. B. Indirect emissions of domestic production To estimate indirect emissions related to production, we calculate emission coefficients using total production of a given industry.55 The calculation of emission coefficients in this case is given by: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑢𝑢=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝑢𝑢 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑢𝑢 (equation 137a) Again, using 𝑖𝑖 as the notation for industries, and 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼 as the notation for emission type. Using our calculated emission coefficient in equation 137a, the total indirect emission for each industry is given by: 55 This is similar to the methods used in the GreenREFORM model by the DREAM group. 65 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝑢𝑢=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑢𝑢∗𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑢𝑢 (equation 137b) By aggregating equation 136c and 137b, we can calculate the total emission (incl. direct and indirect) for each industry as follows: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡 𝑢𝑢=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝑢𝑢+𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝑢𝑢 (equation 138) C. Direct Energy-Related Emissions of households consumption To calculate direct energy-related emissions for the household sector, we follow the same procedure as was followed for industries. In this case, the emission coefficients linked to the use of each energy type is given by: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻𝐻𝐻=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑡𝑡 𝐻𝐻𝐻𝐻 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝐻𝐻𝐻𝐻 (equation 139a) The emission coefficients in equation 139a are used to calculate direct energy-related emissions for the household sector following the same approach as for industries in equation 136a. Again, we can take the sum across the energy types to calculate the total direct energy-related emission for the household sector as follows: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝐻𝐻=�𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝐻𝐻∗𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻 21 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸=1 (equation 139b) D. Indirect emissions of households consumption To estimate indirect emission for the household sector, we calculate emission coefficients using domestic consumption. The emission coefficients in this case are given by: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝐻𝐻=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝐻𝐻 𝑐𝑐𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 (equation 140a) The emissions coefficients from equation 140a are then used to estimate the indirect emissions associated with consumption: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝐻𝐻=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝐻𝐻∗𝑐𝑐𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 (equation 140b) By aggregating equation 139b and 140b, we can find the total emissions generated by households consumption as follows: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡 𝐻𝐻= 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝐻𝐻+𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝐻𝐻 (equation 141) 66 We can now find the total emission for each emission type in the entire economy by aggregating equation 138 and 141. That is, we add the total emissions from the 9 industries together with emissions from households: 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 +𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡 𝐻𝐻𝐻𝐻 (equation 142) As we now have total emissions for each of the 6 emission types, we can now convert each form of emission into CO2 equivalent using the commonly used GWP conversion rates. More specifically, for CO2, SF6, PFC, and HFC the conversion rate is 1 as they are already measured in CO2equivelants; for CH4 the conversion rate is 25, and for N2O the conversion rate is 298. We calculate the CO2-equivelant emissions (CO2E) first at an industry level: 𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑢𝑢=𝐶𝐶𝑃𝑃2𝑡𝑡𝑢𝑢+𝐶𝐶𝑃𝑃6𝑡𝑡𝑢𝑢+𝑃𝑃𝑃𝑃𝐶𝐶𝑡𝑡𝑢𝑢+𝐻𝐻𝑃𝑃𝐶𝐶𝑡𝑡𝑢𝑢+25 ∗𝐶𝐶𝐻𝐻4𝑡𝑡𝑢𝑢+298 ∗𝐼𝐼2𝑃𝑃𝑡𝑡𝑢𝑢 (equation 143a) And for the entire economy: 𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=𝐶𝐶𝑃𝑃2𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝐶𝐶𝑃𝑃6𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝑃𝑃𝑃𝑃𝐶𝐶𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝐻𝐻𝑃𝑃𝐶𝐶𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+25 ∗𝐶𝐶𝐻𝐻4𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+298 ∗𝐼𝐼2𝑃𝑃𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 (equation 143b) This completes the description of the environmental block of the model, where we have modelled the nexus between energy, emissions and economic activity. We now proceed to discussing an important policy variable, environmental taxes, that is recently receiving a lot of attention in the discussions related to climate targets. 5.4.3. Environmental taxes In section 5.1.2, we isolated environmental taxes from the rest of other production taxes (see equation 12). In equation 144a we assume environmental taxes to be dependent on CO2E emissions of the industry as follows:56 𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢=𝐶𝐶𝑃𝑃2𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑢𝑢∗𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑢𝑢 (equation 144a) We use an exogenously calculated tax rate for each industry 𝑖𝑖 (𝐶𝐶𝑃𝑃2𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑢𝑢), which is calculated outside the model using the following equation: 56 Equation 144a relates CO2-equivelent emissions directly to the environmental taxes paid by a given industry. In reality, most environmental taxes are paid using energy related taxes where a specific tax rate is put on energy usage. In this current version of the model, we rely on the simpler set-up of equation 144a whereas this should be modeled in more detail in future versions. 67 𝐶𝐶𝑃𝑃2𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑢𝑢=𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑝𝑝𝑑𝑑𝑠𝑠𝑠𝑠𝑢𝑢𝑡𝑡𝑖𝑖𝑑𝑑𝑢𝑢 𝑢𝑢 𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑢𝑢 (equation 144b) This completes the environmental aspects of the model and also the entire model description. We are now ready to evaluate the model, after which we will perform three simple scenarios. 6. Model evaluation To evaluate the model, we perform two standard checks. First, we numerically solve the model to establish a baseline, the results of which are compared with the observed data. Second, we analyse the response of the model to several shocks to analyse whether or not the model is capable of capturing the stylised facts. This step is also crucial for understanding the different transmission mechanisms embedded in the model. Figure 2 shows the prediction of the model for real production of domestic industries in domestic currency. The model decently captures the overall tendency and fluctuation within each of the nine industries. Figure 2: Total real production of domestic industries Figure 3 shows the development of real GDP (including its components) and employment. Again, we can see that the model captures the development of key macroeconomic variables. There are 68 some episodes of divergences between the model predictions and original data for employment, but the model performs fairly well in capturing both the long run tendency as well as cyclical movements. Figure 3: GDP components and employment We now present the model performance related to the environmental aspects of the model. Figure 4 shows the model prediction of total CO2 equivalent emissions associated with the 6 emission types. The prediction of the model for emissions is consistent with the original data; it decently captures both the trend and fluctuations. We can conclude that the model performs reasonably well in capturing the development in key variables related to the economy and environment. 69 Figure 4: Emissions To ensure that our model fulfils the properties of a stock-flow-consistent model, we need to ensure that each financial asset has a counterparty, and that each transaction has an origin and a destination. First, to ensure consistency in financial assets, we need to check that net holdings of financial stocks across the institutional sectors sum to zero, implying that the holding of every financial asset has a counterparty, or put differently, someone’s financial asset is someone’s financial liability. In principle, one can perform this check on each financial stock, but in practice, performing the check on the net holding of securities will suffice in our case. The reason is that transactions related to securities by the rest of the world (𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅) are not included as an equation in the model, as this is our redundant equation. All other financial stocks and their related transactions, through specific accounting identities, are tied across the sectors through explicit equations in the model. Therefore, if net holdings of securities across the sectors sum to zero, we can safely conclude that the model fulfils the requirement of stock consistency. Second, we need to ensure that the sum of net lendings (or financial balances) across sectors sum to zero, meaning that a sector’s deficit is financed by other sectors’ surplus. After carrying out the aforementioned-tests, we find that both conditions are fulfilled, and the model is stock-flow-consistent. 6.1. Introducing three simple scenarios We now analyse the response of the model to various types of shocks related to monetary and fiscal policy. First, we introduce a monetary policy shock, in which we permanently increase the interest rates on loans, deposits and bonds by 2 percentage points. Second, we introduce 2 types of fiscal policy shocks as follows: i) public spending shock, where we permanently increase government 70 consumption by 5% in the biggest industry (categorised as “other industries”), and ii) carbon tax shock, in which we permanently increase the carbon tax rate in the agricultural industry. The effects of the shocks are presented as deviations from the baseline. Note that these shocks are introduced independently of each other in the baseline in 2010. For instance, when we introduce a carbon tax shock to the model, we do not introduce any other shock in the same scenario. 6.1.1. A shock to interest rates The effects of a contractionary monetary policy shock on gross domestic product (GDP) components are visualised in Figure 5. Following a monetary policy shock, GDP contracts by about 0.8% relative to the baseline value; this development is mainly driven by a fall in consumption (which reduces by 2.1%). The main mechanism is that higher interest rates lower disposable income, which causes final consumption to fall. The overall contraction in the economy also has the effect of lowering investment and employment; trade balance slightly improves as imports contract sharply whereas exports remain unaffected. Figure 5: Change in GDP components In Figure 6, we show the effects of the shock on real production along with some of the key components for each industry. We can observe that an increase in interest rate has the effect of lowering real production across all industries. The main transmission channel is that the fall in final consumption lowers production, which in turn, reduces intermediate consumption. The reduction in intermediate consumption reinforces the reduction in total production. It is interesting to note that the effects of the shock on total production across the industries are heterogenous (i.e., financial 71 corporations experience a larger drop in real production compared to other industries), but the effects of the shock on final consumption are homogenous, i.e., the final consumption of the goods supplied by each industry falls with the same magnitude. The reason is that income shocks (in this case induced by higher interest rates) affect the final consumption proportionally. The heterogenous response of total production across the industries is partly driven by their sales of inputs to other industries (which in turn, depend on the production requirement of the industry) and partly by the difference in weights of the underlying components of total production. Figure 6: Changes in real production for industries We now proceed to discussing the effects of fiscal shocks in our model. 6.1.2. A shock to government spending We introduce a government spending shock, characterized by a 5% increase in government consumption of final goods supplied by industry no. 9 called “other industries”. In figure 7, we depict the effects of this shock on GDP, along with several key macroeconomic components. We can see that the shock triggers expansionary economic effects; specifically, we observe an increase in final consumption and real investments, reflecting the positive spillover effects of higher government demand on private sector activity. Moreover, we find the fiscal multiplier for this shock to be around 1.14. 78 While building the model structure, most of the model parameters were estimated using annual time series data from 1995 to 2019. To assess model validity, we performed two standard checks. First, we numerically solved the model to establish a baseline, the results of which were compared with the observed data. We found that the model decently captured the overall tendency and fluctuation in key variables related to economic activity and environment. Second, we analysed the response of the model to a variety of shocks related to monetary and fiscal policy. We found that the model effectively captures the stylized facts and that these shocks affect the economy through multiple channels, which are important in policy making. We believe, our model in this paper will serve as a foundation, which can be extended in a variety of ways. The model has the potential to offer a reasonable assessment of the climate policies to the relevant stakeholders. References Beck, U. R., & Dahl, G. E. (2020). Emissions in greenreform. Technical report, DREAM. Berg, M., Hartley, B., & Richters, O. (2015). A stock-flow consistent input–output model with applications to energy price shocks, interest rates, and heat emissions. New journal of physics, 17(1), 015011. Byrialsen, M. R., & Raza, H. (2022). Household debt and macroeconomic stability: An empirical stock‐flow consistent model for the Danish economy. Metroeconomica, 73(1), 144-197. Bhaduri, A., & Marglin, S. (1990). Unemployment and the real wage: the economic basis for contesting political ideologies. Cambridge journal of Economics, 14(4), 375-393. Danish Council on Climate Change (DCCC). (2024). Status outlook 2024. https://klimaraadet.dk/en/report/status-outlook-2024. Danish Council on Climate Change (DCCC). (2023.) Status outlook 2023. https://klimaraadet.dk/en/report/status-outlook-2023. Danish Energy Agency (DEA). (2023). Denmark's Climate Status and Outlook 2023 (CSO23). https://www.ens.dk. Denmark statistics (DST). (2021). Annual Sector Accounts Inventory. Denise T. L. Almeida, Bo P. Weidema, Antoine Godin. Beyond normative system boundaries in life cycle assessment: The environmental effect of income redistribution. Cleaner Environmental Systems, 2022, 4, pp.100072. ff10.1016/j.cesys.2022.100072ff. ffhal-03781880f Dunz, N., Naqvi, A., & Monasterolo, I. (2021). Climate sentiments, transition risk, and financial stability in a stock-flow consistent model. Journal of Financial Stability, 54, 100872. European Parliamentary Research Service. (2021). EU progress on climate action – How are the Member States doing? Climate action in Denmark (PE 679.106). European Union. Retrieved from https://climate.ec.europa.eu/eu-action/climate-strategies-targets/progress-climate-action_en. Feenstra, R. C., Luck, P., Obstfeld, M., & Russ, K. N. (2018). In search of the Armington elasticity. Review of Economics and Statistics, 100(1), 135-150. 79 Feyen, E. H., Utz, R. J., Zuccardi Huertas, I. E., Bogdan, O., & Moon, J. (2020). Macro-financial aspects of climate change. World Bank Policy Research working Paper, (9109). Godley, W., & Lavoie, M. (2006). Monetary economics: an integrated approach to credit, money, income, production and wealth. Springer. Imbs, J., & Mejean, I. (2009). Elasticity optimism (IMF Working Paper No. 2009/279). International Monetary Fund. Jackson, A., & Jackson, T. (2021). Modelling energy transition risk: The impact of declining energy return on investment (EROI). Ecological economics, 185, 107023. Kastrup, C. B., Vasi, T., & Vikkelsø, C. (2023). Estimating trade elasticities for Denmark (Working Paper No. 2023:1). DREAM. Published April 26, 2023 Kirk, J. S., Steward, L.B., Stephensen, P., Dalgaard, T. N., & Berg, A. K. (2024). Development of the GreenREFORM model - Sharing learnings from development of the climate and energyeconomic CGE-model GreenREFORM. Retrieved from Development of the GreenREFORM model | DREAM (dreamgroup.dk). Kirk, J. S., & Hansen, M. K. (2023, December 7). Elasticiteter og markedsvilkår i GrønREFORM. DREAM. https://dreamgruppen.dk/ Kronborg, A. F., Poulsen, K. A., & Kastrup, C. S. (2020). Estimering af udenrigshandelselasticiteter i MAKRO. DREAM. Retrieved from https://dreamgruppen.dk/ Lavoie, M., & Godley, W. (2001). Kaleckian models of growth in a coherent stock-flow monetary framework: a Kaldorian view. Journal of Post Keynesian Economics, 24(2), 277-311. Naqvi AA (2015) Modeling growth, distributions and the environment in a stock-flow consistent framework. WWWforEurope Policy Paper 18. Nikiforos, M., & Zezza, G. (2018). Stock‐flow consistent macroeconomic models: A survey. Analytical Political Economy, 63-102. Pollitt, H., Lewney, R., & Mercure, J. F. (2019). Conceptual differences between macroeconometric and CGE models. In 27th International Input-Output Association Conference [Internet]. Glasgow, Scotland. Svarer, M., Cordtz, J. F., Juhl, S., Kreiner, C. T., Sørensen, P. B., & Termansen, M. (2024). Grøn skattereform: Endelig afrapportering. Danish Government. https://skm.dk/aktuelt/publikationer/rapporter/groen-skattereform-endelig-afrapportering Temere, D. S. (2017). The Armington elasticity: From a micro-level data. Danmarks Statistik. Thomsen, S., Raza, H., & Byrialsen, M. (2024). Macroeconomic Aspects of Unemployment Benefits: Evaluating the Danish Policy. Review of Political Economy, 1-21. United Nations Framework Convention on Climate Change (UNFCCC). (2015). Paris Agreement. Retrieved from https://unfccc.int/documents/184656 Valdecantos, S. (2021), Grasping Argentina’s Green Transition: Insights from a Stock-Flow Consistent Input-Output Model, Macroeconomic Methodology, Theory and Economic Policy (MaMTEP) Working Paper Series No. 4, 2021. Available at: https://www.boeckler.de/pdf/v_2021_10_30_valdecantos.pdf 80 8. Appendix: 8.1. Industry statistics The industry level data imported from Statistics Denmark includes a total of 117 industries. In this paper, we aggregate these 117 industries to 9 to obtain a simpler representation of the economy. The 9 industries are presented below together with key environmental and economic statistics.59 Table A1: Industry statistics 8.2. Distribution of gross operating surplus and mixed income (B2) This appendix will provide a description on how we make the transition from industry to sectoral level in the model using gross operating surplus as the combining variable. The main reason that we need to make this transition is that not all entries below gross surplus in the TFM (table 4) are available at an industrial level. The most appropriate point for transitioning from industry to sectoral accounts is at the gross operating surplus and mixed income (B2), as this is the final entry reflected in the input-output tables (see Table 2). The objective is to ensure a consistent transition by aligning observed data for B2 at both the industry and sectoral levels. A common practice in the Stock-Flow-Consistent literature is to assume that the non-financial corporations sector collects the entire gross operating surplus, which is then distributed to the household, government, and financial corporation sectors 59 The “Other energy intensive” industry includes industries that are not part of the energy production and supply, but still regulated by the ETS program. 81 using exogenous shares. This method could be easily incorporated into the current model by summing the total gross operating surplus of mixed income across industries and then allocating it according to these sectoral shares. This approach assumes that all industries are equally linked to the four domestic sectors based on exogenous shares, which diminishes the value of including industrial aggregation in the model. For instance, consider the impact of a carbon tax on the agricultural industry, which reduces gross operating surplus. If we fail to account for the fact that this industry is predominantly "owned" by the household sector (67%) and instead use aggregate sectoral shares, where the household sector holds a weight of just 21%, we will underestimate the effect on the household balance sheet. To calculate these shares at the industry level, we rely on the industry by sector matrix provided by Statistics Denmark (DST 2021), which details the industrial contributions to sectoral accounts based on gross value added (GVA) in 2016. This matrix helps us estimate how gross operating surplus and mixed income should be allocated among the four domestic sectors across the nine industries. The process involves the following steps: 1. Within each industry we calculate the weight of NFCs, FCs, households, and the government for each row in the matrix of industry by sector. 2. As the matrix of industry by sector is disaggregated into more than 90 industries, we use gross operating surplus and mixed income for each industry to make a weighted average for the shares at the 9-industry level used in this paper.60 3. As these shares are calculated based on 2016 data, they have most likely changed since 1998, in which we start the simulation of the model. To take this into account, we include a trend calculated from the sectoral to total gross operating surplus and mixed income and apply this trend on the industry level shares calculated in step 2. 4. Lastly, we calculate an adjustment term to consider discrepancies between our estimated sectoral gross operating surplus and mixed income variables, based on the first 3 steps, and observed gross operating surplus and mixed income for each sector. These steps result in equation 57a-57d in which gross operating surplus and mixed income are calculated for the household, government, financial corporations, and non-financial corporations. In the table below, we show the estimated shares for 2016. Table A2: Sectoral weights by industry 60 In the current version of the model, we only use the 2016 values for B2 to make this aggregation. 82 To give an example, for gross operating surplus in the agricultural industry, 67% will be associated with the household sector, while 33% will be associated with the non-financial corporation sector. For the Mining industry, gross operating surplus will be associated only with the non-financial corporation sector. As no gross operating surplus should be lost while making this transition, all rows sum to 1. Lastly, in figure A1 we show the magnitude of the adjustment terms (calculated in step 4) relative to the observed value of gross operating surplus. The adjustment terms for the financial corporations and government sector are close to 0. The reason for the undershooting of gross operating surplus for the household sector (as the adjustment term is positive) and the overshooting of non-financial corporations gross operating surplus, are to be found in the matrix of industry by sectors.61 A majority of industries show that household contribute by 0.0% to total gross operating surplus within a specific industry. When this notation is used, it means that the actual value is between 0.0% and 0.05%.62 61 The level of adjustment in the household and non-financial corporation sector is almost equal in absolute values. 62 In cases where the true value is 0%, the entry is empty. 83 Figure A1: Adjustment terms relative to observed values 8.3. Calculation of financial flows In this appendix, we calculate three types of rates of returns:63 i) first, we calculate 3 different interest rates (related to deposits, securities, loans, and other accounts), which will determine the net interest income denoted by NINT, ii) second, we calculate the rate of return on equity holdings, which determines the flow associated with equities (mostly dividends) denoted by NDIV, and iii) third, we calculate the rate of return on other investment income (related to pension and insurances), which determines the flow called NOIR. Note that the income flow related to reinvested earnings on FDI expresses the operating surplus of the foreign direct investment corporations. This is not related to any of the financial assets in the TFM.64 Following standard accounting, we know that payment flows in the current period depends on the stock of last period and the rate of returns from the last period. This relationship, expressed in equation A1, is used to calculate our rates of returns: 63 We use unconsolidated data to calculate the rates of returns in the model. 64 Rent is defined as income received by the owner of a natural resource and is simply included as a flow without associating it to any type of rate of return. 84 𝑓𝑓𝑠𝑠𝑝𝑝𝑤𝑤𝑡𝑡=𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑡𝑡−1∗𝑠𝑠𝑡𝑡𝑝𝑝𝑐𝑐𝑘𝑘𝑡𝑡−1⟺𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑡𝑡−1=𝑓𝑓𝑠𝑠𝑝𝑝𝑤𝑤𝑡𝑡 𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑡𝑡−1 (equation A1) Focusing on interest rate calculations, first we calculate the interest rate on securities, assuming the rate of return on securities to be the same domestically and abroad. Therefore, we calculate the interest rate on securities (𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶) as the mean of the rate in Denmark and ECB as follows: 𝑝𝑝𝑡𝑡−1 𝐶𝐶𝐸𝐸𝐶𝐶= 0.5 ∗ 𝑖𝑖_𝑠𝑠𝑖𝑖𝑐𝑐𝑡𝑡−1 𝑃𝑃𝐷𝐷 + 0.5 ∗ 𝑖𝑖_𝑠𝑠𝑖𝑖𝑐𝑐𝑡𝑡−1 𝐸𝐸𝐶𝐶𝐸𝐸 (equation A2) By multiplying this rate of return with the stock of securities in the last period, we get the interest payment related to securities. The interest payment on securities is then subtracted from the overall interest payment, the resultant of which is used to calculate interest rate on deposits and loans. To calculate the interest rate on deposits (𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃𝐶𝐶) paid by the financial corporations, we take the total net interest paid by financial corporations, from which we subtract interest payments on securities issued by the financial corporations. The resultant is divided with the stock of deposits (representing a liability) for the financial corporations in the last period. This calculation can be expressed as follows: 𝑝𝑝𝑡𝑡−1 𝑃𝑃𝐸𝐸𝑃𝑃𝐶𝐶=𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑝𝑝𝑖𝑖𝑠𝑠𝑡𝑡 𝑝𝑝𝑎𝑎𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡−(𝑝𝑝𝑡𝑡−1 𝐶𝐶𝐸𝐸𝐶𝐶∗𝑠𝑠𝑖𝑖𝑐𝑐𝑠𝑠𝑡𝑡−1 𝑁𝑁𝐶𝐶,𝐿𝐿) 𝑝𝑝𝑖𝑖𝑝𝑝𝑝𝑝𝑠𝑠𝑖𝑖𝑡𝑡𝑠𝑠 𝑖𝑖𝑖𝑖 𝑃𝑃𝐶𝐶𝑡𝑡−1 (equation A3a) where 𝑝𝑝𝑡𝑡−1 𝐶𝐶𝐸𝐸𝐶𝐶∗𝑠𝑠𝑖𝑖𝑐𝑐𝑠𝑠𝑡𝑡−1 𝑁𝑁𝐶𝐶,𝐿𝐿is the interest payments of financial corporations on their issued securities. To calculate the interest rate on loans 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉, we use the same approach, i.e., we take the total net interest received by financial corporations, from which we subtract interest income received on securities owned by the financial corporations, which is then divided with the stock of loans (which represents an asset) issued by financial corporations in the last period. This is given by equation 8b as follows: 𝑝𝑝𝑡𝑡−1 𝐿𝐿𝐶𝐶𝑉𝑉=𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑝𝑝𝑖𝑖𝑠𝑠𝑡𝑡 𝑝𝑝𝑖𝑖𝑐𝑐𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡−(𝑝𝑝𝑡𝑡−1 𝐶𝐶𝐸𝐸𝐶𝐶∗𝑠𝑠𝑖𝑖𝑐𝑐𝑠𝑠𝑡𝑡−1 𝑁𝑁𝐶𝐶,𝑉𝑉) 𝐿𝐿𝑝𝑝𝑎𝑎𝑖𝑖 𝑃𝑃𝐶𝐶𝑡𝑡−1 (equation A3b) where 𝑝𝑝𝑡𝑡−1 𝐶𝐶𝐸𝐸𝐶𝐶∗𝑠𝑠𝑖𝑖𝑐𝑐𝑠𝑠𝑡𝑡−1 𝑁𝑁𝐶𝐶,𝑉𝑉 denotes interest payments received by financial corporations on holding securities as financial assets. Once interest rates on interest bearing stocks are computed, we can show that the net interest payments (NINT) of sector 𝑠𝑠 are given by the following equation: 85 𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝐶𝐶=𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐶𝐶)+𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐶𝐶+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉 ∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐶𝐶 (equation A4) Note that the rate of return on three financial stocks namely, net deposits (NDEPO), net derivatives (NDERV), and net trade credits (NTCRED), is the same as denoted by interest rate 𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃. The net stock of securities (NSEC) and net stock of loans (NLOA) are linked to their corresponding rate of returns denoted (𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶) and 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉, respectively. The return on equities (𝑝𝑝𝑡𝑡𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃) is also calculated using equation A1. This calculation is expressed in equation A5 as follows: 𝑝𝑝𝑡𝑡−1 𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃=𝑝𝑝𝑖𝑖𝑖𝑖𝑖𝑖𝑝𝑝𝑖𝑖𝑖𝑖𝑝𝑝𝑠𝑠 𝑝𝑝𝑎𝑎𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡 𝑖𝑖𝑒𝑒𝑠𝑠𝑖𝑖𝑡𝑡𝑖𝑖𝑖𝑖𝑠𝑠 𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡−1 (equation A5a) We can now determine net income received from dividend payments for sector 𝑠𝑠 as follows: 𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝐶𝐶= 𝑝𝑝𝑡𝑡𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐶𝐶 (equation A5b) where NEQ represents the net stock of equities. Similarly, the rate of return for insurance and pensions (𝑝𝑝𝑡𝑡𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼) is given by: 𝑝𝑝𝑡𝑡−1 𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼=𝑝𝑝𝑖𝑖𝑡𝑡𝑠𝑠𝑝𝑝𝑖𝑖 𝑝𝑝𝑎𝑎𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡 𝑖𝑖𝑖𝑖𝑠𝑠𝑠𝑠𝑝𝑝𝑎𝑎𝑖𝑖𝑐𝑐𝑖𝑖𝑠𝑠 𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡−1 (equation A6a) We can use the rate of return 𝑝𝑝𝑡𝑡𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼 to calculate the income associated with net insurance payments for sector 𝑠𝑠 as follows: 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝐶𝐶=𝑝𝑝𝑡𝑡𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝐶𝐶 (equation A6b) where NINSU represents the net stock of insurance and pensions. This concludes the presentation of industry and sectoral level variables used within the model. In the next section we instead focus on environmental data used in the model. 8.4. Substitution between consumption products In this appendix, we show the two substitution effects modelled for final consumption. The two effects are i) substitution between product types, ii) substitution between domestically and foreign produced products. 86 Substitution between product types To allow for substitution between product types, we endogenize the shares γ 𝑡𝑡 𝑐𝑐𝑝𝑝(used in equation 19) following a similar method as used in the GreenREFORM and ADAM models, which includes a nested structure. In our model, the first nest includes a choice between industry specific consumption products (𝑐𝑐𝑡𝑡𝑐𝑐𝑝𝑝𝑟𝑟𝑐𝑐) and food products (𝑐𝑐𝑡𝑡110+ 𝑐𝑐𝑡𝑡120+ 𝑐𝑐𝑡𝑡130+𝑐𝑐𝑡𝑡140+𝑐𝑐𝑡𝑡160+𝑐𝑐𝑡𝑡180). In the second nest, consumers choose between the six different food products. The nested structure can be modelled as follows:65 γ 𝑡𝑡𝑐𝑐𝑢𝑢𝑝𝑝𝑢𝑢𝑠𝑠 =𝜃𝜃𝑐𝑐𝑝𝑝𝑟𝑟𝑐𝑐∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑑𝑑𝑡𝑡ℎ,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equation A7. ) γ 𝑡𝑡𝑐𝑐110 =𝜃𝜃110∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡110,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equation A8. ) γ 𝑡𝑡𝑐𝑐120 =𝜃𝜃120∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡120,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equation A9. ) γ 𝑡𝑡𝑐𝑐130 =𝜃𝜃130∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡130,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equation A10. ) γ 𝑡𝑡𝑐𝑐140 =𝜃𝜃140∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡140,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equation A11.) γ 𝑡𝑡𝑐𝑐160 =𝜃𝜃160∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡160,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equation A12. ) γ 𝑡𝑡𝑐𝑐180 =𝜃𝜃180∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡180,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equation A13. ) Several parameters go into the equations above. Starting with 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡2 and 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡1 these represent the elasticity of substitution in the two nests. We set 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡2= 0.8 and 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡1= 0.2 which is slightly lower compared to the parameters used by GreenREFORM who use a different disaggregation of the consumer basket. Lastly, the parameters 𝜃𝜃𝑡𝑡𝑐𝑐𝑝𝑝𝑟𝑟𝑐𝑐,𝜃𝜃110,𝜃𝜃120,𝜃𝜃130,𝜃𝜃140,𝜃𝜃160, and 𝜃𝜃180 are calibrated to match the starting value of each corresponding share. Equation A.7-A.13 includes several price 65 To ensure consistency, we model the share γ 𝑡𝑡𝑐𝑐𝑢𝑢𝑝𝑝𝑢𝑢𝑠𝑠 as a residual, to ensure that the sum of the shares always sum to 1. 87 deflators, all of them adjusted for the tax rate.66 First, we define seven price deflators; one for each product type: 67 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐=⎝ ⎜ ⎛ 𝐶𝐶𝑡𝑡𝑝𝑝 ∑𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 9𝑢𝑢=1 + ∑𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 9𝑢𝑢=1 +𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢𝑢𝑢 𝑝𝑝 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢𝑢𝑢⎠ ⎟ ⎞ ∗�1 + 𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑝𝑝� (Equation A14. ) Thereby each of the 7 product types 𝑝𝑝 are a function of the producer price indexes for the 9 domestic industries (𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢) as well as the ten foreign price indexes (𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢,𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢𝑢𝑢). As the consumer is faced with the price after taxes, we multiply on the average tax-rate for a given product (𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑝𝑝). The average tax-rate is modelled as follows: 𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑝𝑝=�𝐶𝐶𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝+𝐶𝐶𝑠𝑠𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡 𝑝𝑝+𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑝𝑝� 𝐶𝐶𝑡𝑡𝑝𝑝 (Equation A15. ) Where 𝐶𝐶𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝 defines import duties, 𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑝𝑝 defines commodity taxes, and 𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑝𝑝 defines value added taxes all associated with consumption of product type 𝑝𝑝. Besides from the 7 price indexes for each of the 7 product types (𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐), we need two aggregate price indexes, one for the entire consumption (𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐), and one for consumption of food products (𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐). We follow the same approach as in equation (𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐) but aggregate across the relevant product types 𝑝𝑝. The same goes for the average tax rate. Thereby, we have the 9 price indexes for different consumption goods and baskets used in equation A7-A13. In the following we focus on the second substitution effect. Substitution between domestic and foreign products To allow substitution between domestic and foreign products, we need to calculate a domestic and foreign price index for each product type p. For each of the 7 product types in the consumption basket the price deflator is calculated as follows: 66 We can use this tax-adjusted deflator to go from nominal value plus taxes to real-values without taxes. 𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝∗𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐=𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝+𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑝𝑝+𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑝𝑝+𝐶𝐶𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝 67 We include these tax rates within the consumer price indexes, as these rates are included within the final price paid by the consumer. Also, this allows us to implement carbon taxes on the consumers for different product types for future analysis. 94 𝑀𝑀𝑖𝑖𝑢𝑢𝑣𝑣𝑟𝑟𝑢𝑢𝑡𝑡,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =�𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 + 𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 (M.21) 𝑀𝑀𝑎𝑎𝑑𝑑𝑣𝑣 𝑡𝑡𝑑𝑑𝑡𝑡 =�𝐺𝐺𝑃𝑃𝑉𝑉𝑖𝑖𝑑𝑑 𝑢𝑢 9 𝑢𝑢=1 +𝐺𝐺𝑃𝑃𝑉𝑉𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 (M.22) 𝑀𝑀𝑐𝑐𝑡𝑡𝑑𝑑𝑡𝑡=�𝑋𝑋𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 + 𝑋𝑋𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 (M.23) Final demand components lnΔ(𝑐𝑐 𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡)= 0.37∗∗ 𝑠𝑠𝑖𝑖Δ𝑦𝑦𝑝𝑝 𝑡𝑡 𝐻𝐻−0.30∗∗∗ 𝑠𝑠𝑖𝑖 𝑐𝑐 𝑡𝑡−1 𝑡𝑡𝑑𝑑𝑡𝑡+ 0.29∗∗∗ln 𝑦𝑦𝑝𝑝 𝑡𝑡−1 𝐻𝐻+ 0.01 ln 𝑓𝑓𝑖𝑖𝑤𝑤𝑡𝑡−1 𝐻𝐻−0.002∗∗ 𝑉𝑉𝑝𝑝𝑖𝑖𝑖𝑖𝑝𝑝 (M.24) 𝑐𝑐𝑡𝑡 𝑝𝑝 = γ 𝑡𝑡 𝑐𝑐𝑝𝑝 ∗𝑐𝑐𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (M.25) γ 𝑡𝑡𝑐𝑐𝑢𝑢𝑝𝑝𝑢𝑢𝑠𝑠 =𝜃𝜃𝑑𝑑𝑡𝑡ℎ∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑑𝑑𝑡𝑡ℎ,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (M.26) γ 𝑡𝑡𝑐𝑐110 =𝜃𝜃110∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡110,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2 ∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (M.27) γ 𝑡𝑡𝑐𝑐120 =𝜃𝜃120∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡120,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2 ∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 � 𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (M.28) γ 𝑡𝑡𝑐𝑐130 =𝜃𝜃130∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡130,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (M.29) γ 𝑡𝑡𝑐𝑐140 =𝜃𝜃140∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡140,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2 ∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (M.30) γ 𝑡𝑡𝑐𝑐160 =𝜃𝜃160∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡160,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2 ∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (M.31) γ 𝑡𝑡𝑐𝑐180 =𝜃𝜃180∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡180,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2 ∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎 𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (M.32) 𝑐𝑐 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝= (1 −𝜙𝜙 𝑐𝑐,𝑡𝑡 𝑝𝑝)∗𝑐𝑐 𝑡𝑡 𝑝𝑝 (M.33) 𝑐𝑐 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝= (𝜙𝜙 𝑐𝑐,𝑡𝑡 𝑝𝑝)∗𝑐𝑐 𝑡𝑡 𝑝𝑝 (M.34) ln(𝜙𝜙𝑐𝑐,𝑡𝑡 𝑝𝑝 ) = 𝛽𝛽0 𝑐𝑐𝑝𝑝 +𝛽𝛽1 𝑐𝑐𝑝𝑝 ∗ln (𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡 𝑝𝑝 ) + 𝑎𝑎𝑝𝑝𝑗𝑗𝜙𝜙,𝑡𝑡 𝑝𝑝 (M.35) 𝑐𝑐 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝=𝜆𝜆 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝∗𝑐𝑐 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝 (M.36) 95 𝑐𝑐 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝=𝜆𝜆 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝∗𝑐𝑐 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝 (M.37) 𝑐𝑐 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝=𝛾𝛾 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝∗𝑐𝑐 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝 (M.38) 𝐶𝐶 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝=𝑐𝑐 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝∗𝑝𝑝𝑦𝑦 𝑡𝑡 𝑢𝑢 (M.39) 𝐶𝐶 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝=𝑐𝑐 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝∗𝑝𝑝𝑚𝑚 𝑡𝑡 𝑢𝑢 (M.40) 𝐶𝐶 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝=𝑐𝑐 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝∗𝑝𝑝𝑚𝑚 𝑡𝑡 𝑢𝑢𝑢𝑢 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝=�𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 9 𝑢𝑢=1 (M.41) 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝=�𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 9 𝑢𝑢=1 +𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢𝑢𝑢 𝑝𝑝 (M.42) 𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝=�𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 9 𝑢𝑢=1 (M.43) 𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝=�𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 9 𝑢𝑢=1 +𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢𝑢𝑢 𝑝𝑝 (M.44) 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢=�𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 (M.45) 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢=�𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 (M.46) 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢𝑢𝑢=�𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 (M.47) 𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢=�𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 (M.48) 𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢=�𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 (M.49) 𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢𝑢𝑢=�𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢𝑢𝑢 𝑝𝑝 7 𝑝𝑝=1 (M.50) 𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 (M.51) 96 𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 (M.52) 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 (M.53) 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 (M.54) 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 (M.55) 𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡= 1.8∗∗∗Δln � 𝑦𝑦 𝑡𝑡−1 𝑘𝑘𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶�−0.09∗∗∗ln(𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡−1 𝑡𝑡𝑑𝑑𝑡𝑡)+ 1.42∗∗∗ 𝑝𝑝𝑠𝑠𝑡𝑡−1 (M.56) 𝑖𝑖𝑖𝑖𝑖𝑖 𝑡𝑡 𝑢𝑢=𝜆𝜆 𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢∗𝑖𝑖𝑖𝑖𝑖𝑖 𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (M.57) 𝑖𝑖𝑖𝑖𝑖𝑖 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 =𝛾𝛾 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 ∗𝑖𝑖𝑖𝑖𝑖𝑖 𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 =�1−𝜙𝜙𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢 �∗𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡 𝑢𝑢 (M.58) 𝑖𝑖𝑖𝑖𝑖𝑖 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢=�𝜙𝜙 𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢�∗𝑖𝑖𝑖𝑖𝑖𝑖 𝑡𝑡 𝑢𝑢 (M.59) 𝐼𝐼𝐼𝐼𝑉𝑉 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑖𝑖𝑖𝑖𝑖𝑖 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦 𝑡𝑡 𝑢𝑢 (M.60) 𝐼𝐼𝐼𝐼𝑉𝑉 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑖𝑖𝑖𝑖𝑖𝑖 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑚𝑚 𝑡𝑡 𝑢𝑢 (M.61) 𝐼𝐼𝐼𝐼𝑉𝑉 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 =𝑖𝑖𝑖𝑖𝑖𝑖 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝∗𝑝𝑝𝑚𝑚 𝑡𝑡 𝑢𝑢𝑢𝑢 (M.62) 𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.63) 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.64) 𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.65) 𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.66) ln � 𝑥𝑥 𝑡𝑡 𝑢𝑢 𝑚𝑚𝑡𝑡𝑢𝑢∗�= α 0 𝑢𝑢+ α 1𝑢𝑢∗ln(𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡−1 𝑢𝑢)+𝑎𝑎𝑝𝑝𝑗𝑗𝑐𝑐,𝑡𝑡 𝑢𝑢 (M.67) 𝑥𝑥 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=�1−𝜙𝜙 𝑐𝑐,𝑡𝑡 𝑢𝑢�∗𝑥𝑥 𝑡𝑡 𝑢𝑢 (M.68) 𝑥𝑥 𝑑𝑑,𝑡𝑡 𝑢𝑢=�𝜙𝜙 𝑐𝑐,𝑡𝑡 𝑢𝑢�∗𝑥𝑥 𝑡𝑡 𝑢𝑢 (M.69) 97 𝑋𝑋 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑥𝑥 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑦𝑦 𝑡𝑡 𝑢𝑢 (M.70) 𝑋𝑋 𝑑𝑑,𝑡𝑡 𝑢𝑢=𝑥𝑥 𝑑𝑑,𝑡𝑡 𝑢𝑢∗𝑝𝑝𝑚𝑚 𝑡𝑡 𝑢𝑢 (M.71) 𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.72) 𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.73) 𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.74) 𝑋𝑋𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡= �𝑋𝑋𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.75) Labor market and prices 𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 = (1 + 𝜇𝜇𝑡𝑡𝑢𝑢)∗ 𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 (M.76) 𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑢𝑢=𝑥𝑥𝑝𝑝𝑡𝑡∗ 𝑝𝑝𝑦𝑦 𝑡𝑡 𝑢𝑢 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (M.77) 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐=⎝ ⎜ ⎛ 𝐶𝐶𝑡𝑡𝑝𝑝 ∑𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 9𝑢𝑢=1 + ∑𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 9𝑢𝑢=1 +𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢𝑢𝑢 𝑝𝑝 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢𝑢𝑢⎠ ⎟ ⎞ ∗�1 + 𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑝𝑝� (M.78) 𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑝𝑝=�𝐶𝐶𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡 𝑝𝑝 +𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑝𝑝 +𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑝𝑝 � 𝐶𝐶𝑡𝑡𝑝𝑝 (M.79) 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝=⎝ ⎜ ⎛ 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝 ∑𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 9𝑢𝑢=1 ⎠ ⎟ ⎞ (M.80) 𝑝𝑝𝑚𝑚𝑡𝑡𝑝𝑝=⎝ ⎜ ⎛ 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝 ∑𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 9𝑢𝑢=1 ⎠ ⎟ ⎞ (M.81) 𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑝𝑝=𝑥𝑥𝑝𝑝𝑡𝑡∗ 𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖 𝑡𝑡 𝑝𝑝 𝑝𝑝𝑚𝑚𝑡𝑡𝑝𝑝 (M.82) 98 𝑉𝑉𝑀𝑀𝑃𝑃𝑡𝑡𝑢𝑢= 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑡𝑡 𝑢𝑢 𝑎𝑎𝑡𝑡𝑢𝑢 (M.83) 𝑈𝑈𝐼𝐼𝑉𝑉𝑀𝑀𝑃𝑃𝑡𝑡=𝐿𝐿𝑃𝑃𝑡𝑡− �𝑉𝑉𝑀𝑀𝑃𝑃𝑡𝑡𝑢𝑢 9 𝑢𝑢=1 (M.84) 𝑈𝑈𝑅𝑅𝑡𝑡= 𝑈𝑈𝐼𝐼𝑉𝑉𝑀𝑀𝑃𝑃 𝑡𝑡 𝐿𝐿𝑃𝑃𝑡𝑡 (M.85) 𝑊𝑊 𝑡𝑡 𝑢𝑢=𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖 𝑡𝑡 𝑢𝑢∗𝑉𝑉𝑀𝑀𝑃𝑃 𝑡𝑡 𝑢𝑢 (M.86) 𝑠𝑠𝑖𝑖Δ�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖 𝑡𝑡 𝑎𝑎𝑟𝑟𝑢𝑢� = 0.24∗∗∗+ 0.78∗∗∗𝑠𝑠𝑖𝑖Δ�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−2 𝑎𝑎𝑟𝑟𝑢𝑢� + 0.08∗∗𝑠𝑠𝑖𝑖Δ�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−2 𝑎𝑎𝑟𝑟𝑢𝑢,𝑉𝑉�−0.15∗∗ln�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−1 𝑎𝑎𝑟𝑟𝑢𝑢� + 0.09∗ln�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−2 𝑎𝑎𝑟𝑟𝑢𝑢,𝑉𝑉�+ 0.28∗∗∗ln(𝑎𝑎𝑡𝑡−1) (M.87) 𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡 𝑎𝑎𝑟𝑟𝑢𝑢,𝑉𝑉 =𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−1 𝑎𝑎𝑟𝑟𝑢𝑢 ∗ ( 1 + 𝜋𝜋𝑡𝑡−1 ) (M.88) ln (𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖 𝑡𝑡 𝑢𝑢) = ω 0 + ω 1 ln (𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖 𝑡𝑡 𝑎𝑎𝑟𝑟𝑢𝑢) (M.89) II.) Sectoral level equations Non-financial corporations 𝐵𝐵2𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎=�𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢 9 𝑢𝑢=1 (M.90) 𝐵𝐵2𝑁𝑁𝑁𝑁𝐶𝐶=𝐵𝐵2 𝑡𝑡 𝑎𝑎𝑎𝑎𝑎𝑎−(𝐵𝐵2𝐻𝐻+𝐵𝐵2𝑁𝑁𝐶𝐶+𝐵𝐵2𝐺𝐺) (M.91) 𝐼𝐼𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 =𝐼𝐼𝑡𝑡 𝑎𝑎𝑎𝑎𝑎𝑎 − ( 𝐼𝐼𝑡𝑡 𝐻𝐻 +𝐼𝐼𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑡𝑡 𝐺𝐺) (M.92) 𝑌𝑌 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌 𝑡𝑡 −(𝐵𝐵2 𝑡𝑡 𝑎𝑎𝑎𝑎𝑎𝑎−𝐵𝐵2 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶)−�𝐼𝐼𝑉𝑉𝑎𝑎𝑥𝑥 𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑,𝑡𝑡 + 𝑃𝑃𝑃𝑃𝑉𝑉 𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡�−𝑊𝑊 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 +𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (M.93) 𝑌𝑌𝑃𝑃 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.94) 𝐶𝐶 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌𝑃𝑃 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.95) 𝐼𝐼𝐿𝐿 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐶𝐶 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑃𝑃 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶−𝐶𝐶𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.96) 𝑃𝑃𝐼𝐼𝐿𝐿 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.97) 𝑃𝑃𝐼𝐼𝑊𝑊 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (M.98) � 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 𝐾𝐾𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 �= 0.26∗∗∗+ 0.28∗∗� 𝐼𝐼 𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶 𝐶𝐶𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶�−2.11∗∗∗𝑝𝑝𝑡𝑡−1 𝐿𝐿𝐶𝐶𝑉𝑉 (M.99) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.100) 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.101) 99 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.102) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.103) 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.104) 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=−�𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (M.105) 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.106) 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐿𝐿 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿 𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 −(𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶) (M.107) 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡−1 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.108) 𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝑝𝑝 𝑡𝑡 𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶) +𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (M.109) 𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶= 𝑝𝑝 𝑡𝑡 𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.110) 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶=𝑝𝑝 𝑡𝑡 𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.111) Households 𝐵𝐵2𝑡𝑡𝐻𝐻=�𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢∗𝐶𝐶𝐻𝐻,𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 + adjtH (M.112) 𝐼𝐼𝑡𝑡𝐻𝐻=�𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎∗𝐶𝐶𝐻𝐻,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 9 𝑢𝑢=1 (M.113) 𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=�𝑊𝑊𝑡𝑡𝑢𝑢 9 𝑢𝑢=1 (M.114) 𝑊𝑊 𝑡𝑡 𝐻𝐻= 𝑊𝑊 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶−𝑊𝑊 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.115) 𝑌𝑌 𝑡𝑡 𝐻𝐻=𝐵𝐵2 𝑡𝑡 𝐻𝐻+𝑊𝑊 𝑡𝑡 𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉 𝑡𝑡 𝐻𝐻+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉 𝑡𝑡 𝐻𝐻+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅 𝑡𝑡 𝐻𝐻+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼 𝑡𝑡 𝐻𝐻 −𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡 𝐻𝐻+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻 (M.116) 𝑌𝑌𝑃𝑃 𝑡𝑡 𝐻𝐻=𝑌𝑌 𝑡𝑡 𝐻𝐻−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝐻𝐻 (M.117) 𝐶𝐶𝑡𝑡𝐻𝐻=𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻−𝐶𝐶𝑡𝑡 𝑎𝑎𝑎𝑎𝑎𝑎 +𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡 𝑎𝑎𝑑𝑑𝑗𝑗 (M.118) 𝐼𝐼𝐿𝐿 𝑡𝑡 𝐻𝐻=𝐶𝐶 𝑡𝑡 𝐻𝐻−𝐼𝐼 𝑡𝑡 𝐻𝐻−𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉 𝑡𝑡 𝐻𝐻−𝐼𝐼𝑃𝑃 𝑡𝑡 𝐻𝐻−𝐶𝐶𝑉𝑉 𝑡𝑡 𝐻𝐻 (M.119) 𝑃𝑃𝐼𝐼𝐿𝐿 𝑡𝑡 𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝐻𝐻 (M.120) 𝑃𝑃𝐼𝐼𝑊𝑊 𝑡𝑡 𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝐻𝐻 +𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐻𝐻 (M.121) 𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻=� 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝐻𝐻−𝐼𝐼𝑉𝑉𝑄𝑄 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡−1 𝐻𝐻� (M.122) 100 Δ𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻= 0.33∗Δ𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1 𝐻𝐻+ 0.060Δ�𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡−1 𝐻𝐻 +𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡−1 𝐻𝐻 � 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−2 𝐻𝐻 −0.18𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1 𝐻𝐻+ 0.10∗�𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡−2 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡−2 𝐻𝐻� 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−3 𝐻𝐻 (M.123) 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝐻𝐻=𝑉𝑉𝑄𝑄 𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻∗𝑃𝑃𝐼𝐼𝑊𝑊 𝑡𝑡−1 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (M.124) 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻=Δ𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝐻𝐻−𝐼𝐼𝑉𝑉𝑄𝑄 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (M.125) 𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻=�− 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝐻𝐻 𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻� (M.126) 𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻= 0.91∗∗∗𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1+ 2.28∗∗∗� 𝐼𝐼 𝑡𝑡 𝐻𝐻 𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻�−0.31𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉 −0.37∗∗∗𝑃𝑃2016 (M.127) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝐻𝐻=−𝐿𝐿𝑃𝑃𝑉𝑉 𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡 𝐻𝐻∗𝑌𝑌𝑃𝑃 𝑡𝑡 𝐻𝐻 (M.128) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻=Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝐻𝐻−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (M.129) 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻=𝐼𝐼𝐿𝐿 𝑡𝑡 𝐻𝐻+𝐼𝐼𝐿𝐿 𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝐻𝐻−(𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻 +𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻) (M.130) 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (M.131) 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝐻𝐻=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (M.132) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝐻𝐻=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (M.133) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (M.134) 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝐻𝐻=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡−1 𝐻𝐻+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐻𝐻 (M.135) 𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉 𝑡𝑡 𝐻𝐻=𝑝𝑝 𝑡𝑡 𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝐻𝐻)+𝑝𝑝 𝑡𝑡 𝐶𝐶𝐸𝐸𝐶𝐶 ∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐻𝐻+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻 (M.136) 𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉 𝑡𝑡 𝐻𝐻= 𝑝𝑝 𝑡𝑡 𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝐻𝐻 (M.137) 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅 𝑡𝑡 𝐻𝐻=𝑝𝑝 𝑡𝑡 𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝐻𝐻 (M.138) Financial corporations 𝐵𝐵2𝑡𝑡𝑁𝑁𝐶𝐶=�𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢∗𝐶𝐶𝑁𝑁𝐶𝐶,𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 + adjtFC (M.135) (M.139) 𝐼𝐼𝑡𝑡𝑁𝑁𝐶𝐶=�𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎∗𝐶𝐶𝑁𝑁𝐶𝐶,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 9 𝑢𝑢=1 (M.140) 𝑌𝑌 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐵𝐵2 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼 𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶−𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶 (M.141) 𝑌𝑌𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶=𝑌𝑌 𝑡𝑡 𝑁𝑁𝐶𝐶−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑁𝑁𝐶𝐶 (M.142) 101 𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶=𝑌𝑌𝑃𝑃𝑁𝑁𝐶𝐶−𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡 𝑎𝑎𝑑𝑑𝑗𝑗 (M.143) 𝐼𝐼𝐿𝐿 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐶𝐶 𝑡𝑡 𝑁𝑁𝐶𝐶−𝐼𝐼 𝑡𝑡 𝑁𝑁𝐶𝐶−𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶−𝐼𝐼𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶−𝐶𝐶𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶 (M.144) 𝑃𝑃𝐼𝐼𝐿𝐿 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 (M.145) 𝑃𝑃𝐼𝐼𝑊𝑊 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶 (M.146) 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (M.147) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 � (M.148) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (M.149) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (M.150) 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (M.151) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (M.152) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (M.153) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (M.154) 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 =𝐼𝐼𝐿𝐿 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿 𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝑁𝑁𝐶𝐶 −(𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶) (M.155) 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (M.156) 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (M.157) 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡−1 𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑁𝑁𝐶𝐶 (M.158) 𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶=𝑝𝑝 𝑡𝑡 𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝑁𝑁𝐶𝐶)+𝑝𝑝 𝑡𝑡 𝐶𝐶𝐸𝐸𝐶𝐶 ∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶 (M.159) 𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉 𝑡𝑡 𝑁𝑁𝐶𝐶= 𝑝𝑝 𝑡𝑡 𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝑁𝑁𝐶𝐶 (M.160) 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅 𝑡𝑡 𝑁𝑁𝐶𝐶=𝑝𝑝 𝑡𝑡 𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝑁𝑁𝐶𝐶 (M.161) Government 𝐵𝐵2𝑡𝑡𝐺𝐺=�𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢∗𝐶𝐶𝐺𝐺,𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢 9 𝑢𝑢=1 + adjtG (M.162) 𝐼𝐼𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉=�𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎∗𝐶𝐶𝐺𝐺𝐶𝐶𝑉𝑉,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 9 𝑢𝑢=1 (M.163) 102 𝐶𝐶𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢 9 𝑢𝑢=1 +𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐺𝐺𝑃𝑃𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡+𝐼𝐼𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝑋𝑋𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (M.164) 𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢 9 𝑢𝑢=1 +𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐺𝐺𝑃𝑃𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝑋𝑋𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (M.165) 𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑃𝑃𝑉𝑉𝑃𝑃𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 (M.166) 𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 =�𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡 𝑢𝑢 9 𝑢𝑢=1 +𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡 𝐶𝐶+𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉 +𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡 𝐼𝐼𝑁𝑁𝑉𝑉 +𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡 𝑋𝑋 (M.167) 𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑 =𝐶𝐶𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 (M.168) 𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋 𝑝𝑝,𝑡𝑡 =𝑀𝑀 𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 +𝑃𝑃𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋 𝑝𝑝 (M.169) 𝐼𝐼𝐼𝐼𝑀𝑀𝑉𝑉𝑎𝑎𝑥𝑥 𝑡𝑡 =𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋 𝑝𝑝 −𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋 𝑝𝑝 (M.170) 𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝐻𝐻= 0.36 ∗𝑌𝑌 𝑡𝑡 𝐻𝐻 (M.171) 𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶= 0.12 ∗𝑌𝑌 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 (M.172) 𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑁𝑁𝐶𝐶= 0.08 ∗𝑌𝑌 𝑡𝑡 𝑁𝑁𝐶𝐶 (M.173) 𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡=𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝐻𝐻+𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.174) 𝑌𝑌𝑃𝑃𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉 =𝐵𝐵2𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉 +𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑 + 𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑 +𝐼𝐼𝐼𝐼𝑀𝑀𝑉𝑉𝑎𝑎𝑥𝑥𝑡𝑡 +𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉,𝑝𝑝+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉 +𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉−𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉 (M.175) 𝐶𝐶𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉 =𝑌𝑌𝑃𝑃𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉 −𝐺𝐺𝑡𝑡 𝑎𝑎𝑎𝑎𝑎𝑎 (M.176) 𝐼𝐼𝐿𝐿 𝑡𝑡 𝐺𝐺=𝐶𝐶 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉−𝐼𝐼 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉−𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉−𝐼𝐼𝑃𝑃 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉−𝐶𝐶𝑉𝑉 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉 (M.177) 𝑃𝑃𝐼𝐼𝐿𝐿 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐺𝐺𝐶𝐶𝑉𝑉 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝 𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝐺𝐺𝐶𝐶𝑉𝑉 (M.178) 𝑃𝑃𝐼𝐼𝑊𝑊 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝐺𝐺𝐶𝐶𝑉𝑉 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉 (M.179) 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺=𝐼𝐼𝐿𝐿 𝑡𝑡 𝐺𝐺+𝐼𝐼𝐿𝐿 𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡 𝐺𝐺−(𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡,𝑡𝑡𝑝𝑝 𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺 + 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺) (M.180) 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝐺𝐺=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡−1 𝐺𝐺+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐺𝐺 (M.181) 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝐺𝐺=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡−1 𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐺𝐺 (M.182) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝐺𝐺=𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡−1 𝐺𝐺+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐺𝐺 (M.183) 103 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝐺𝐺=𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡−1 𝐺𝐺+ 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+𝐼𝐼𝑉𝑉𝑄𝑄 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐺𝐺 (M.184) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝐺𝐺=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡−1 𝐺𝐺+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐺𝐺 (M.185) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝐺𝐺=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡−1 𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐺𝐺 (M.186) 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡 𝐺𝐺=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡−1 𝐺𝐺+ 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐺𝐺 (M.187) 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝐺𝐺=𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡−1 𝐺𝐺+ 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝐺𝐺 (M.188) 𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉 𝑡𝑡 𝐺𝐺=𝑝𝑝 𝑡𝑡 𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝐺𝐺+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝐺𝐺+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝐺𝐺)+𝑝𝑝 𝑡𝑡 𝐶𝐶𝐸𝐸𝐶𝐶 ∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐺𝐺+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐺𝐺 (M.189) 𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉 𝑡𝑡 𝐺𝐺= 𝑝𝑝 𝑡𝑡 𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝐺𝐺 (M.190) 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅 𝑡𝑡 𝐺𝐺=𝑝𝑝 𝑡𝑡 𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝐺𝐺 (M.191) Rest of the world 𝑌𝑌𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝑀𝑀 𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡−𝑋𝑋 𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡+𝑊𝑊 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅−(𝐼𝐼𝐼𝐼𝑀𝑀𝑉𝑉𝑎𝑎𝑥𝑥 𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅) +𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 +𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅−𝐼𝐼𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 +𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 (M.192) 𝐼𝐼𝐿𝐿 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝑌𝑌𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅−𝐶𝐶𝑉𝑉 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅−𝐼𝐼𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.193) 𝑃𝑃𝐼𝐼𝐿𝐿 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡,𝑡𝑡𝑝𝑝 𝑃𝑃𝐶𝐶𝑅𝑅 +𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡,𝑡𝑡𝑝𝑝 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝 𝑃𝑃𝐶𝐶𝑅𝑅 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝 𝑃𝑃𝐶𝐶𝑅𝑅 (M.194) 𝑃𝑃𝐼𝐼𝑊𝑊 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 +𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 (M.195) 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=−�𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (M.196) 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 =−�𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑁𝑁𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐻𝐻 + 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝐺𝐺 + 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅� (M.197) 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡−1 𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.198) 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡−1 𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.199) 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡−1 𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑉𝑉𝑄𝑄 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.200) 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡−1 𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.201) 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡−1 𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.202) 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡−1 𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑡𝑡𝑝𝑝,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃 𝑝𝑝𝑣𝑣,𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.203) 𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅=𝑝𝑝 𝑡𝑡 𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅) +𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 (M.204) 𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅= 𝑝𝑝 𝑡𝑡 𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄 𝑡𝑡 𝑃𝑃𝐶𝐶𝑅𝑅 (M.205) 110 Total net production taxes 𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋 𝑡𝑡𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑 Total net other production taxes 𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑 Total net import taxes 𝐼𝐼𝐼𝐼𝑀𝑀𝑉𝑉𝑎𝑎𝑥𝑥𝑡𝑡 Import taxes received by Denmark 𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋𝑝𝑝,𝑡𝑡 Import taxes paid by Denmark 𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋𝑝𝑝,𝑡𝑡 Other net import taxes paid by Denmark. 𝑃𝑃𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋𝑝𝑝,𝑡𝑡 Interest rate on securities 𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶 Interest rate on deposits 𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃𝐶𝐶 Interest rate on loans 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉 Interest rate on dividends 𝑝𝑝𝑡𝑡𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃 Interest rate on pensions and insurance 𝑝𝑝𝑡𝑡𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼 Sectoral real capital stock 𝑘𝑘𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶,𝑘𝑘𝑡𝑡𝐻𝐻,𝑘𝑘𝑡𝑡𝑁𝑁𝐶𝐶,𝑘𝑘𝑡𝑡𝐺𝐺 Sectoral nominal capital stock 𝐾𝐾𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶,𝐾𝐾𝑡𝑡𝐻𝐻,𝐾𝐾𝑡𝑡𝑁𝑁𝐶𝐶,𝐾𝐾𝑡𝑡𝐺𝐺 capacity utilization rate 𝑠𝑠𝑡𝑡 Environmental variables notation Energy supply in industry n. 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡 𝑢𝑢 Energy supply imported. 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡 𝐸𝐸 Energy supply in the form of waste. 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡 𝑅𝑅𝑎𝑎𝑐𝑐𝑡𝑡𝑟𝑟 Energy supply in the form of renewable energy. 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡 𝑃𝑃𝐸𝐸 Total energy supply 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡 𝑡𝑡𝑑𝑑𝑡𝑡 Energy usage in industry n. 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝑢𝑢 Energy exported for usage outside Denmark 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝑋𝑋 Distribution losses related to energy usage. 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝑃𝑃𝐿𝐿 Energy usage by households. 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝐻𝐻𝐻𝐻 Change in inventories for energy types. 𝐼𝐼𝑖𝑖𝑖𝑖𝑃𝑃𝑟𝑟𝑠𝑠𝑡𝑡𝑎𝑎,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸 Inventory stock of energy. 𝐼𝐼𝑖𝑖𝑖𝑖𝑡𝑡𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸 New discoveries of crude oil reserves. 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠 𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 Stock of crude oil reserve. 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠 𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡 𝑎𝑎𝑗𝑗 New discoveries of natural gas for extraction reserves. 𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠 𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1 𝑎𝑎𝑗𝑗 Stock of natural gas for extraction reserve. 𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠 𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡 𝑎𝑎𝑗𝑗 Emissions Emission for industry n directly related to energy. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝑢𝑢 Emission for industry n unrelated to energy. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝑢𝑢 Total emissions for industry n (both direct and indirect) 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡 𝑢𝑢 Emissions for households directly related to energy. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝐻𝐻𝐻𝐻 Emissions for households unrelated to energy. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡 𝐻𝐻𝐻𝐻 Total emissions for households. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡 𝐻𝐻𝐻𝐻 Total emissions in the Danish economy 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 CO2-equivelant emissions for each industry n. 𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑢𝑢 Total CO2-equivelant emissions in the Danish economy. 𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 Note: The notation for energy (𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌) covers the 21 types of energy (Coil (crude oil), Oilp: Oil products), RefG (Refinery gas), GasT (Gasoline for transportation), FGas (jet fuel), FGasBunk (Jet fuel bunkered), DieT (Diesel for transportation), DietTBunk (Diesel for transportation - bunkered), NGasExt (Natural gas extraction), NGasCons (Natural gas consumption – incl. city gas), CC (coal and smoke), Waste (Waste), RE (Renewable energy), Straw (Straw), FW (Firewood and wood chips), WP (wood pellets), BioG (Bio gas), BBB (Biodiesel, bioethanol and bio oil), El (electricity), DHeat (District heat).). 111 The notation for emissions (𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼) covers the 6 types of emissions (CO2 (carbon dioxide), N2O (nitrous oxide), CH4 (methane), SF6 (sulfur hexafluoride), PFC (perfluorocarbons), and HFC (Hydrofluorocarbons)) The notation for industries (n) covers the following industries: Agricultural, Forestry, Fishery, Mining, Manufacturing of food, Energy supply and refineries, Other energy intensive industries, Financial corporations, Other industries. Parameters Notation Economic parameters Technical coefficient relating output for industry n to inputs bought by industry n in industry i. 𝑎𝑎 𝑡𝑡 𝑖𝑖 𝑢𝑢 Import share for industry n. 𝜙𝜙𝑧𝑧,𝑡𝑡 𝑖𝑖 𝑢𝑢 Import share of investment products for industry n. 𝜙𝜙𝐼𝐼𝑁𝑁𝑉𝑉,𝑡𝑡 𝑢𝑢 Import share of exports for industry n. 𝜙𝜙𝑋𝑋,𝑡𝑡 𝑢𝑢 Intercept in the equation for import shares for product type p in final consumption. 𝛽𝛽0 𝑐𝑐𝑝𝑝 Intercept in the equation for import shares for product type p for industries. 𝛽𝛽0𝑧𝑧 𝑖𝑖 𝑖𝑖 Import elasticity for final consumption in product type p. 𝛽𝛽1𝑐𝑐𝑝𝑝 Import elasticity for inputs produced by industry n. 𝛽𝛽1𝑧𝑧𝑖𝑖 Wage premium for industry n. ω 0 𝑢𝑢 Wage bargaining parameter for industry n. ω 1𝑢𝑢 Share of product p supplied by domestic industry n for final consumption 𝜆𝜆 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 Share of product p supplied by foreign industry n for final consumption 𝜆𝜆 𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 𝑝𝑝 Share of investment products bought from industry n. 𝜆𝜆𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡 𝑢𝑢 Share of unspecified imports to total production in industry n. 𝛾𝛾 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑢𝑢 Share of unspecified imports to total production for final good p. 𝛾𝛾 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑝𝑝 Share of unspecified imports to total investments. 𝛾𝛾 𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 Parameter set to match first observation in consumption share γ 𝒕𝒕 𝒄𝒄𝒑𝒑 . 𝜃𝜃𝑝𝑝 Rate of substitution for consumption in nest 1. 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡1 Rate of substitution for consumption in nest 2 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡2 Intercept in export equation. Set to match starting value of 𝒙𝒙𝒕𝒕𝒏𝒏 𝒅𝒅𝒕𝒕 𝒏𝒏∗ for industry n. α 0 𝑢𝑢 Export elasticity of industry n. α 1𝑢𝑢 Interest rate on deposits 𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃 Interest rate on securities 𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶 Interest rate on loans 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉 Interest rate on dividends 𝑝𝑝𝑡𝑡𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃 Interest rate on insurance, pension, and standardized guarantee schemes. 𝑝𝑝 𝑡𝑡 𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼 Price index for import in industry n. 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 Price index for unspecified imports. 𝑝𝑝𝑚𝑚𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡 Mark-up rate for industry n. 𝜇𝜇𝑡𝑡𝑢𝑢 Share of industry n gross operating surplus and mixed income associated with the household sector. 𝐶𝐶𝐻𝐻,𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢 112 Share of industry n gross operating surplus and mixed income associated with the financial corporation sector. 𝐶𝐶𝑁𝑁𝐶𝐶,𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢 Share of industry n gross operating surplus and mixed income associated with the government sector. 𝐶𝐶𝐺𝐺,𝑡𝑡 𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢 Share distributing total investments to the household sector. 𝐶𝐶 𝐻𝐻,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 Share distributing total investments to the financial corporation sector. 𝐶𝐶𝑁𝑁𝐶𝐶,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 Share distributing total investments to the government sector. 𝐶𝐶 𝐺𝐺,𝑡𝑡 𝑖𝑖𝑢𝑢𝑣𝑣 Adjustment term used in import equation for industries 𝑎𝑎𝑝𝑝𝑗𝑗𝜙𝜙,𝑡𝑡 𝑢𝑢 Adjustment term used for import equation for final consumption products. 𝑎𝑎𝑝𝑝𝑗𝑗 𝜙𝜙,𝑡𝑡 𝑝𝑝 Adjustment term used in export equation for industries. 𝑎𝑎𝑝𝑝𝑗𝑗𝑐𝑐,𝑡𝑡 𝑢𝑢 Adjustment term used in the transition of profits from industry to sectoral level. adj t H Adjustment term used in the transition of profits from industry to sectoral level adj t FC Adjustment term used in the transition of profits from industry to sectoral level adj t G Environmental parameters Energy supply coefficient for industry n. 𝑃𝑃𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢 Energy usage coefficient for industry n. 𝑃𝑃𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢 Energy usage coefficient for households. 𝑃𝑃 𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻𝐻𝐻 Emission coefficient for emissions directly from energy usage in industry n. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼 𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢 Emission coefficient for emissions not directly from energy usage in industry n. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼 𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑢𝑢 Emission coefficient for emissions directly from energy usage by households. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼 𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻𝐻𝐻 Emission coefficient for emissions not directly from energy usage by the households. 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼 𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡 𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝐻𝐻𝐻𝐻 CO2-equivelant tax rate for each industry n. 𝐶𝐶𝑃𝑃2𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 𝑢𝑢 Note: The notation for energy (𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌) covers the 21 types of energy (Coil (crude oil), Oilp: Oil products), RefG (Refinery gas), GasT (Gasoline for transportation), FGas (jet fuel), FGasBunk (Jet fuel bunkered), DieT (Diesel for transportation), DietTBunk (Diesel for transportation - bunkered), NGasExt (Natural gas extraction), NGasCons (Natural gas consumption – incl. city gas), CC (coal and smoke), Waste (Waste), RE (Renewable energy), Straw (Straw), FW (Firewood and wood chips), WP (wood pellets), BioG (Bio gas), BBB (Biodiesel, bioethanol and bio oil), El (electricity), DHeat (District heat).). The notation for emissions (𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼) covers the 6 types of emissions (CO2 (carbon dioxide), N2O (nitrous oxide), CH4 (methane), SF6 (sulfur hexafluoride), PFC (perfluorocarbons), and HFC (Hydrofluorocarbons)) The notation for industries (n) covers the following industries: Agricultural, Forestry, Fishery, Mining, Manufacturing of food, Energy supply and refineries, Other energy intensive industries, Financial corporations, Other industries. The notation for product types (p) covers the following products: bread (𝑐𝑐𝑡𝑡110), meat (𝑐𝑐𝑡𝑡120), fish (𝑐𝑐𝑡𝑡130), dairy (𝑐𝑐𝑡𝑡140), fruits and vegetables (𝑐𝑐𝑡𝑡160), other food products (𝑐𝑐𝑡𝑡180), and finally industry specific products (𝑐𝑐𝑡𝑡𝑐𝑐𝑝𝑝𝑟𝑟𝑐𝑐). 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