Illustrationsbillede indhold

General equilibrium model

The main model in GreenREFORM integrates the sub-models for transportation, agriculture, waste management and energy supply. The model is developed as a general equilibrium model, describing the total economic activity in Denmark.


The general equilibrium model is the central model in GreenREFORM, through which the sub-models for transportation, agriculture, waste management and energy supply are integrated. The model describes the combined economic activity in Denmark, transfers to and from the public sector, energy consumption and the associated emission of pollutants and greenhouse gasses for a large number of sectors and households.

The model is based on the National Accounts, the Environmental-Economic Accounts and the Air Emissions Accounts compiled by Statistics Denmark. The classification of sectors in the model and other definitions are based on these accounts.

Using a given baseline year, the model can forecast the information included in these accounts. This relies on a number of preconditions, but it is possible to examine how specific changes to these conditions affect the forecast, using sensitivity analysis.

In some areas, the model will have a lower level of detail than what is included in the accounts from Statistics Denmark. In other areas, the model will supplement these accounts with more detailed data, to ensure a satisfactory description of the relevant environmental and climate-related issues.

The model is a multi-sector model like REFORM. However, unlike REFORM, which is a static model, GreenREFORM is a dynamic model like MAKRO. That means that it provides an account for economic development for multiple years into the future. This presents a technical challenge, since the large number of sectors and the highly detailed description of for example energy consumption, increases the dimensionality of the model compared to MAKRO, which is already a relatively complex model. Another challenge comes from the fact that the model requires a higher level of detail than in the data that is currently available.

Methodologically and theoretically there are fewer challenges, since GreenREFORM is based on the model architecture that has been developed by the DREAM group for MAKRO and REFORM. The exceptions to this are the sectors and issues covered by GreenREFORM’s sub-models. These include energy, transportation, agriculture, waste management and the abatement of pollution through investment in new technologies across all sectors. The development of each sub-model is described on separate webpages.

Development of the model is based on the model structure and the technical framework, which has been developed by DREAM for MAKRO. However, the purpose of GreenREFORM is different than that of MAKRO, which will be reflected in the prioritization of the level of detail with which the two models describe different issues.

GreenREFORM will in some areas be simpler than MAKRO. This includes descriptions of the labor market and the social security system, since MAKRO, among other things, aims to explain the transition from the current state of the economy towards the structural equilibrium state and to describe the effect of changes to social security taxation over time. These states are exogenous in GreenREFORM, since the model is calibrated to match a baseline from MAKRO.

The model must be able to accurately describe the effect of environmental and climate policies over time. This requires that the model accounts for the gradual nature of investment transitions in specific sectors.

The development process described in the following text is based on the status as of October 1, 2019, with the ambition of having a finished model within two years. An early version of the general equilibrium model had already been developed by the beginning of October, 2019. This is a dynamic multi-sector model, where each sector produces a homogenous good, and where the material input for each sector is split into input of energy and other material input in production. The labor market in the model is calibrated against MAKRO and the description of household behavior as well as the public sector is relatively simple. The model describes economic development in Denmark every year until 2100.

Development of the general equilibrium model is currently focused on preparing it for integration with the first sub-models. Integration with the respective sub-models is described on separate webpages. Notice the paragraph on the energy sub-model webpage, where it is explained that the sub-model has been successfully and completely integrated with the general equilibrium model.

Sectors and Goods

As a starting point, production in sectors covered by GreenREFORM’s sub-models, i.e. the energy, agriculture and transportation sectors, are already described in the general equilibrium model, although using the same assumptions about firm behavior as in other sectors. However, by relying on data already integrated into the general equilibrium model, the sub-models can contribute with alternative descriptions of firm behavior in the respective sectors. This also has the advantage that sub-models can, in principal, be turned on and off as required. It does, however, require the availability and development of several datasets with more detailed divisions of sectors than are currently published by Statistics Denmark.

In general equilibrium models such as REFORM and MAKRO, each sector is assumed to produce a single homogenous aggregate good. In GreenREFORM, many sectors will produce more than one good as well as byproducts in the form of emissions and waste. Energy products will be described in physical units of energy content, and may be produced by several sectors simultaneously.

The choice of sectors and production structure in the model has not yet been finalized, but a paper presents the current choice of sectors and goods in GreenREFORM. The modelling of energy good markets in GreenREFORM and its challenges are presented in a paper. Both papers can be accessed by the following links.

Link to Excel spreadsheet with overview of sectors and energy types in GreenREFORM

Link to paper about the structure of sectors and goods in GreenREFORM (in Danish)

Link to paper about markets for energy goods in the CGE-model

Data framework

Development of internally consistent and sufficiently detailed data is a corner stone for the project. A collaboration with Statistics Denmark has been established with the purpose of developing a complete but preliminary dataset for the model by mid-2020.

This data consists of national accounts input-output tables, expanded with similarly detailed energy accounts, emissions accounts, waste accounts, and accounts of the transport vehicle stock.

Separate divisions of the National Accounts’ input-output tables have already been made for the transportation, agricultural and waste management sectors, and these are currently being used in the development of the respective sub-models.

The separation of energy inputs according to purpose (heating, process etc.), as well as taxation and subsidy schemes, is crucial. First of all, it is important that the model is able to describe the nuances of taxation and subsidies in a detailed manner. Secondly, the technological abatement possibilities may differ significantly depending on the specific energy type and purpose. An established consistent dataset, describing the distribution of energy consumption and tax payments according to purpose and taxation scheme, does not exist. However, development of the necessary dataset is currently underway in cooperation with Statistics Denmark, and a preliminary dataset has already been delivered.

The following paper presents a description of the manufacturing industries’ consumption of energy for energy purposes based on this data.

Link to paper about manufacturing industries’ consumption of energy for energy purposes (in Danish)

Link to documentation for the expanded energy accounts used in the paper about the manufacturing industries’ consumption of energy for energy purposes (in Danish)

The following paper describes a method of cleaning for small values in the GreenREFORM IO-system, with the aim of reducing the computational requirements of the model.

Link to paper about RAS-adjustment (in Danish)

Firm Behavior

Firm behavior in the model is currently a slightly simplified version of MAKRO, but with the major difference that the use of material (goods and services) in production is separated into energy input and the input of other materials.

Link to paper about technology in the CGE-model

Household Behavior

The description of household behavior is relatively simple in the current version of the model. The final version of the model will also have a simpler description of households’ dynamic optimization (expectations) than MAKRO, in order to reduce the computational complexity.

Household behavior is not essential for the integration of the sub-models with the general equilibrium model and while modelling of it is underway, it is currently not a high priority. 

A new method of separating the consumption by international tourists in Denmark from private consumption has been developed for GreenREFORM. The method is described in the following paper.

Link to paper about modelling of consumption by international tourists in GreenREFORM (in Danish)

Public Sector

Modelling of the public sector in GreenREFORM will closely resemble MAKRO, but with a less detailed description in a number of other areas in favor of a more detailed description of environmental and energy-related taxes and subsidies.

The public sector is not essential for the integration of the sub-models with the general equilibrium model and while modelling of it is underway, it is currently not a high priority. 

A new method of separating the public sector’s production as a distinct sector in the IO-system of the model has been developed for GreenREFORM. The method is described in the following paper.

Link to paper about production by the public sector in GreenREFORM (in Danish)


GreenREFORM includes a detailed description of greenhouse gas emissions and a range of other air pollutants. Emissions of the following greenhouse gasses are included in the model:

  • CO2 (excluding and including biomass)
  • CH4
  • N2O
  • SF6
  • PFC
  • HFC

The following pollutants are also currently included in the model:

  • SO2
  • NOX
  • CO
  • NH3
  • Particulate pollution (PM10 and PM2.5)

The following paper describes GreenREFORM’s general approach to modelling emissions. With regard to waste and agriculture, however, this approach is replaced by a more detailed sector-specific approach.

Link to paper about emissions

International Trade

International trade is modelled using the classic Armington assumption. This implies that Danish goods are considered imperfect substitutes compared to similar imported goods. The model’s predictions about the effect of changes to competitiveness depend heavily on the choice of parameters. In one extreme, Danish firms are able to pass on the cost from higher taxes or wages to the output price without losing market share to imported alternatives or on the export market. In the other extreme, the level of competition is so high that the output price is fixed at the exogenous world price. Where the equilibrium state is located between these two extremes may differ significantly depending on the sector and the good in question. Many energy types and agricultural goods face an established world price, which it is assumed in the model that the Danish producers will closely follow.

Regulation of Danish greenhouse gas emissions can impact greenhouse gas emissions in other countries. This phenomenon is known as CO2-leakage. Tighter regulations on Danish emissions will in many cases lead to higher emissions outside of Denmark. The global effect on greenhouse gas emissions will therefore be smaller than the effect on emissions within Denmark.

GreenREFORM is a model of the Danish economy and the associated emissions in Denmark. The model therefore does not implicitly consider the degree of CO2-leakage nor the global effect of Danish environmental and climate policy. There is, however, significant interest in these issues. The plan is therefore to implement a simple model, which can calculate the long-term leakage effects of a simulation in GreenREFORM. This model will use external estimates of the leakage effect from different parts of the Danish economy. The report ‘Economy and Environment 2019’ by the Chairmanship of the Danish Economic Council could, for example, be used as the underlying dataset. 

The report "Economy and Environment 2019" (in Danish)

Trade and leakage are not essential for the integration of the sub-models with the general equilibrium model and while modelling of them is underway, it is therefore not currently a high priority.