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]).
