Annex A. Details on the modelling framework for Chapters 3 and 7 and its implementation

The GTAP V10A Power database has been aggregated to 14 regions and 27 sectors – the detailed aggregation mapping is available in Tables A.2 and A.3 below. Europe has been split into three regions: Lithuania (LTU), an aggregate of the other 10 Eastern European countries members of the European Union (E10), and an aggregate of the remaining 16 EU countries plus the countries that form EFTA and Great Britain (X16). The aggregation of sectors places great emphasis on the energy carriers: coal, gas, oil (crude and refined) and a disaggregated power sector (coal, gas, oil, nuclear, hydro, wind, solar and other renewables). Another area of emphasis is the ETS sectors such as wood and paper, chemicals, non-metallic minerals and metals.

The simulations have a reference year of 2014. The model is solved in annual steps through 2030, and five-year steps between 2030 and 2050.

The Envisage Model at its core is a recursive dynamic and global computable general equilibrium model (CGE) (van der Mensbrugghe, 2019[1]). It follows the circular flow of an economy paradigm. Firms purchase input factors (for example labour and capital) to produce goods and services. Households receive the factor income and in turn demand the goods and services produced by firms. And equality of supply and demand determine equilibrium prices for factors, goods and services. The model is solved as a sequence of comparative static equilibria where the factors of production are exogenous for each time period and linked between time periods with accumulation expressions.

Production is implemented as a series of nested constant-elasticity-of-substitution (CES) functions the aim of which is to capture the substitutability across all inputs. Three production archetypes are implemented. The first is for crops that reflects intensification of inputs versus land extensification. The second is for livestock that reflects range-fed versus ranch-fed production. The final, also referred to as the default, revolves largely around capital/labour substitutability. Some production activities highlight specific inputs (for example agricultural chemicals in crops and feed in livestock) and all activities include energy and its components as part of the cost minimisation paradigm. Production is also identified by vintage – divided into Old and New – with typically lower substitution possibilities associated with Old capital.

Each production activity is allowed to produce more than one commodity – for example the ethanol sector can produce ethanol and distiller's dried grains with solubles (DDGS). And commodities can be formed by the output of one or more activities (for example electricity). Envisage therefore uses a different classification of activities and commodities. One of the features of the model is that it integrates the GTAP power data base that disaggregates GTAP's electricity sector ('ely') into 11 different power sources plus electricity transmission and distribution (Chepeliev, 2020[2]). Though the database has both the supply and demand side for all 11 power sources, the aggregation facility permits the aggregation of electricity demand into a single commodity and the 'make' matrix specification combines the output from the different power activities into a single electricity commodity.

Income accrues from payments to factors of production and is allocated to households (after taxes). The government sector accrues all net tax payments and purchases goods and services. The standard preference function is based on the constant-differences-in-elasticity (CDE) utility function that is used in the core GTAP model (Hertel, 1997[3]; Corong et al., 2017[4]). Investment is savings driven and equal to domestic saving adjusted by net capital flows.

Trade is modelled using the so-called Armington specification that posits that demand for goods are differentiated by region of origin. The model allows for domestic/import sourcing at the aggregate level (after aggregating domestic absorption across all agents), or at the agent-level. In the standard specification, a second Armington nest allocates aggregate import demand across all exporting regions using a representative agent specification. Note that a newer, though minimally tested version, allows for sourcing imports by agent—also known as the MRIO specification. Exports are modelled in an analogous fashion using a nested constant-elasticity-of-transformation (CET) specification. The domestic supply of each commodity is supplied to the domestic market and an aggregate export bundle using a top-level CET function. The latter is allocated across regions of destination using a second-level CET function.1 Each bilateral trade node is associated with four prices: 1) the producer price; 2) the export border price, also referred to as the free-on-board (FOB) price; 3) the import border price, also referred to as the cost, insurance and freight (CIF) price; and 4) the end-user price that includes all applicable trade taxes (but before domestic sales or VAT taxes). The wedge between the producer price and the FOB price is represented by the export tax (or subsidy if negative) and the wedge between the CIF and end-user prices represents the import tariff (and perhaps other import related distortions). The wedge between the CIF and FOB prices represents the international trade and transport margins. These margins represent the use of real resources that are supplied by each region. The global international trade and transport sector purchases these services from each region so as to minimise the aggregate cost.

The model has two fundamental markets for goods and services. Domestically produced goods sold on the domestic market, and domestically produced goods sold by region of destination. All other goods and services are composite bundles of these goods. Two market equilibrium conditions are needed to clear these two markets.

The model incorporates four types of production factors: 1) labour (of which there can be up to 5 types); 2) capital; 3) land; and 4) a sector specific natural resource (such as fossil fuel reserves). The model allows for regime switching between full and partial wage flexibility. Capital is allocated across sectors so as to equalise rates of returns. If all sectors are expanding, Old capital is assumed to receive the economy-wide rate of return. In contracting sectors, Old capital is sold on secondary markets using an upward sloping supply curve. This implies that capital is only partially mobile across sectors. Aggregate land supply is specified using an asymptotic supply curve, with an upward bound that provides the maximum expansion. Land is allocated across activities using a nested CET specification. Natural resources are supplied to each sector using an iso-elastic supply function with the possibility of differentiated elasticities depending on market conditions.

Envisage incorporates the main greenhouse gases – carbon, methane, nitrous oxides and fluorinated gases – as well as an additional set of 10 emissions, such as particulate matter and black carbon. Emissions are generated by consumption of commodities (such as fuels), factor use (for example land in rice production and herds in livestock production) and there are also processed base emissions such as methane from landfills.2 A number of carbon control regimes are available in the model. Carbon taxes can be imposed exogenously—potentially differentiated across regions. The incidence of the carbon tax allows for partial or full exemption by commodity and end-user. For example, households can be exempted from the carbon tax on natural gas consumption. The model allows for emission caps in a flexible manner – where regions can be segmented into coalitions on a multi-regional or global basis. The model allows for countries/regions to be in multiple trading systems simultaneously—such as Europe's Emission Trading System (ETS). In addition to the standard cap system, a cap-and-trade system can be defined where each region within a coalition is assigned an initial emission quota.

Dynamics involves three elements. Labour supply (by skill level) grows at an exogenously determined rate. The aggregate capital supply evolves according to the standard stock/flow motion equation, i.e. the capital stock at the beginning of each period is equal to the previous period's capital stock, less depreciation, plus the previous period's level of investment. The third element is technological change. The standard version of the model assumes labour augmenting technical change—calibrated to given assumptions about GDP growth and inter-sectoral productivity differences. In policy simulations, technology is typically assumed to be fixed at the calibrated levels. Detailed documentation of the ENVISAGE model is provided in (van der Mensbrugghe, 2019[1]).

Macro assumptions

The demographic projections are provided by the UN Population Division’s 2015 Revision. Labour force growth is equated with the growth of the standard working age population (those aged between 15 and 64). Growth across labour skills (unskilled and skilled) is assumed to be uniform. The chart below shows the UN’s 2015 assumptions for Lithuania with a steadily declining rate of population at around 0.5% per annum and declining labour force growth (under our assumptions)..This would see Lithuania’s population decline to 2.4 million in 2050 from a 2014 reference year level of 2.9 million.

The GDP projections are sourced from the WEO Fall 2021 forecast, which provide the consistent global coverage. The WEO forecast has observed or estimated GDP trends between 2014 and 2021 and projections for the period 2022-2026. Post-2026 GDP growth rates converge to the Shared Socioeconomic Pathways (SSP) middle of the road (SSP2) scenario. For the case of Lithuania, 2020-2030 growth rates constructed in this way are very close to the provided OECD LT projections (the cumulative difference in 2030 is less than one percent). Corresponding projections can be refined when the simulated period would be extended post-2030.

The chart below reports GDP trend for the reference scenarios for Lithuania (in terms of per capita GDP at USD 2014 market exchange rates. Under this projection, Lithuania’s per capita GDP would rise from around USD 21 000 in 2021 to over USD 50 000 by 2050 (in constant $2014 at market exchange rates).

Capital accumulation is generated by the standard neo-classical growth expression: current capital is equal to last year’s depreciated capital plus last year’s investments. The annual depreciation rate is set at 5%. Investment is savings-driven: private, public and foreign. The latter two are fixed at base year levels. Private savings in the reference scenario adjusts to smooth out changes to the aggregate rate of return to capital.

Productivity assumptions

The key productivity assumptions are divided into 3: (1) agricultural productivity is assumed to improve at a rate of 1% per annum (this is measured as output per hectare or yield), (2) energy efficiency is assumed to improve at a rate of 1.5% per annum; and (3) labour productivity is targeted in the reference to match the GDP growth projections. Labour productivity is held fixed in policy scenarios. Assumptions regarding agricultural productivity and energy efficiency changes under the reference scenario are driven by the historically observed trends and can be refined upon additional data availability.

Policy assumptions

In the reference scenario, we include an interpretation of the Nationally Determined Contributions (NDCs) across countries. The latter are constructed as emission reductions relative to no-mitigation (lower-ambition mitigation) case in 2030. To reach the NDC targets, it is assumed that all countries, excluding EU and China, implement carbon prices both in ETS and non-ETS sectors. Carbon prices in the non-ETS sectors could be interpreted as an explicit representation of the costs of mitigation in the corresponding activities. Two exceptions are EU and China, where carbon prices are imposed on ETS sectors only based on the current practices. For the case of Canada, which is included to the Rest of OECD (XOE) region, a carbon price trajectory is imposed exogenously based on the available projections that carbon prices would reach 170 CAD per ton of CO2 in 2030.3 Corresponding carbon price trajectories for Canada are emission-weighted with other countries in the XOE region. The table below provides an overview of the carbon prices imposed under NDC scenario in 2030 across regions.

Excise taxes across fuels and uses are held fixed at the base year level (in ad valorem equivalent). A comparison of the petroleum excise taxes for the 2014 and currently observed 2022 gasoline prices shows that for the case of EU-average for both years excise tax rates equal to around 25%.

Figures below provide comparison of the excise tax carbon rate equivalents as observed in GTAP and estimated in the OECD databases. It should be noted that provided estimates (GTAP vs OECD) represent different reference years (2014 vs 2021) and thus are not directly comparable since correspond to different energy price levels addition, production subsidies in fossil fuel mining and transportation sectors in EU are removed, by setting production taxes to 3% (consistent with average production taxes observed in other activities across EU, in particular, in manufacturing sectors).

Energy technologies/preferences

These are broadly in three categories. The first is an autonomous electrification trend. This assumption is driven by the historically observed trends, including an increasing share of electric vehicles, transitioning from gas-based cooking to electric stoves, etc. The share of electricity is assumed to double across the economy, while for the case of households and air transport it is assumed to increase three times. Note that in the reference year the share of electricity is relatively low in most activities, including air transportation. In the latter case the share is below 1% of the total energy consumption and the increase in electricity use could be interpreted as an increase in electricity use for related service activities, such as airport-related passenger and cargo transport. In land transport and water transport, we assume a four-fold increase of the share of electricity (but the shares are capped at 30% and 10% respectively for the 2050 target). The shift in the electricity share is independent of changes in relative prices. Should electricity prices fall relative to other sources of energy, the increase in its share would be accelerated. The second is a downward trend in the price of renewable electricity technologies – continuing trends seen over the last decade or two.4 The third is an autonomous non-price shift towards renewable power technologies. In the case of Europe, we assume that renewable share in 2050 would be 45% in the absence of a change in relative prices. A drop in renewable prices would accelerate these trends. Changes in these shares in the rest of the world are variegated across the modelled regions. In the case of Lithuania, assumptions regarding solar and wind power generation volumes till 2030 are based on the data provided by Lithuanian Energy Agency. Energy mix till 2030 is also broadly calibrated to the Lithuania’s Energy Agency projections.

The discussed reference scenario is broadly consistent with the first EU’s NDC commitment of 40% emissions reduction target. It is assumed that most of the technological and efficiency changes would be occurring without any specific policy measures. For instance, as older cars retire and new cars enter the market, an overall efficiency of passenger cars would increase, even without any additional measures. Even considering all these changes, observed emission trends are less ambitious than the Fit for 55 target and thus additional mitigation efforts are needed, as further discussed below.


[2] Chepeliev, M. (2020), “GTAP- Power Database: Version 10”, Journal of Global Economic Analysis, Vol. 5/2, pp. 110-137,

[4] Corong, E. et al. (2017), “The Standard GTAP Model, version 7”, Journal of Global Economic Analysis, Vol. 2/1, pp. 1-119,

[3] Hertel, T. (1997), Global Trade Analysis: Modeling and Applications, United Nations, New York: Cambridge University Press.

[7] IEA (2020), Extended world energy balances (database),

[5] OECD (2019), Taxing Energy Use 2019: Using Taxes for Climate Action, OECD Publishing, Paris,

[6] OECD (2016), Effective Carbon Rates: Pricing CO2 through Taxes and Emissions Trading Systems, OECD Publishing, Paris,

[1] van der Mensbrugghe, D. (2019), The Environmental Impact and Sustainability Applied General Equilibrium (ENVISAGE) Model. Version 10.01, Center for Global Trade Analysis, Purdue University,


← 1. The model allows for perfect transformation, which is the standard specification in the GTAP model.

← 2. The current version of the model is not tracking carbon emissions linked to changes in the land use and forestry activities.

← 3.

← 4. The cost reduction is implemented using a hyperbola specification with a cost asymptote. The curve is calibrated to three parameters – the asymptote (relative to current costs), a targeted reduction and the year the target is reached. For wind and solar, the asymptote is 50% of 2014's price and the costs are dropping by 40% between 2014 and 2050. For other renewables, the asymptote is 90% and the costs are dropping by 10% between 2014 and 2050. For the case of Lithuania, for wind and solar, the asymptote is 40% of 2014's price and the costs are dropping by 50% between 2014 and 2050. It should be noted that between 2014 and 2019.

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