The I3E Model

I3E Model Logo

In response to the global climate crisis, the need to design adequate climate change policies in Ireland is becoming increasingly important. Moreover, Ireland is obliged to decrease its emissions under the EU Commission’s Climate and Energy Package. It is required to deliver a 20% reduction in greenhouse gas emissions not covered by the EU’s Emissions Trading Scheme (ETS) by 2020 relative to 2005 levels, increasing to 30% in 2030. Hence, designing appropriate energy policies to ensure a smooth and least-cost transition to a low-carbon economy is imperative. Research is needed to better understand the economic and environmental impacts of policies to advise the policy-making process. For this purpose, the Ireland Environment, Energy and Economy model (I3E) has been developed.

The I3E model is an intertemporal computable general equilibrium (CGE) model, which reproduces the structure of the economy in its entirety. It includes productive sectors, households, and the government, among others. In the model, the nature of all existing economic transactions among diverse economic agents is quantified. According to microeconomic behaviour, producers/consumers maximise their profits/utility given their budget constraints. In other words, a CGE model examines how inputs and outputs flow between production sectors of the economy and finally result in final goods consumed by households.

The explicit modelling of sectorial inter-linkages makes it possible to investigate the wider economic impacts of a specific shock or policy through the different transmission channels in the economy. Therefore, CGE models have become a standard tool of empirical analysis. They are widely used to analyse the welfare and distributional impacts of policies whose effects may be transmitted through multiple markets and channels in the economy. Because of its nature, CGE modelling is highly useful for policy design and evaluation, specifically when policy measures are expected to lead to indirect, as well as direct, effects, as in the case of energy-related policies. For example, the economic implications of an energy tax in the transport sector can be evaluated both for the transport sector and other sectors through inter-sectoral spill-overs.

Due to the level of detail, it is also possible to simulate specific policies, e.g. taxes on coal inputs, subsidies for renewable energies, etc. Hence the impacts of different types of energy policies that lead to the same mitigation goal can be investigated. Furthermore, CGE modelling presents the opportunity to evaluate distributive effects within the economy, and therefore identify winners and losers from certain policies, at the household level.

The I3E model includes energy flows and emissions in addition to the standard monetary flows. Each production sector produces an economic commodity using labour, capital, material inputs and energy inputs. The I3E model explicitly comprises a set of carbon commodities, including: peat, coal, natural gas, crude oil, fuel oil, LPG, gasoline, diesel, kerosene, and other petroleum products. Production activities produce commodities in the cheapest way possible by using the optimal set of capital, labour, energy and other intermediate inputs, based on both relative prices and substitution possibilities. When an energy policy is implemented (e.g. an increase in carbon tax) or in case of an external shock (e.g. an increase in international energy prices or ETS price), production sectors will, where possible, substitute energy inputs for other inputs and/or decrease the carbon content of their energy inputs by demanding cleaner energy. From the consumers’ perspective, higher prices of goods with higher carbon content will encourage them to consume less carbon-intensive products. The explicit inclusion of emissions makes it possible to evaluate the emissions reduction associated with a specific policy or to calculate the specific policies needed to reduce emissions to a certain target.

I3E is a dynamic model, which incorporates economic growth over the modelling horizon which runs from 2014 to 2050. Economic growth originates from three sources: the growth of employment driven by population growth, the growth in capital stock driven by investment, and the growth in total factor productivity or productivity of factors of production. It is assumed that the total population grows at a constant rate and the technology, i.e. the productivity of labour force, also grows at a constant rate. In the current version, the values of population growth and economic growth are retrieved from the medium-run estimates of the macroeconometric forecast model of the ESRI, namely COSMO (COre Structural MOdel for Ireland).

More details

The following subsections explain the characteristics of each agent and the assumptions driving the economic relationships among these agents in a non-technical manner to facilitate a better understanding of how the I3E model works. For the technical details of the model, see the technical report . The data sources and the construction process of the Irish energy social accounting matrix is also available at here .



The I3E model includes 39 commodities (or goods), 37 of which are domestically produced and imported, and two of which are not domestically produced but imported. The volume of export and domestic sales are determined by a revenue maximisation problem for the given levels of the elasticity of substitution, the share parameters, and the endogenously solved prices.

The supply of domestically sold commodities comes from imported commodities and domestically produced commodities, which are imperfect substitutes of each other. Total domestic demand comes from five sources: intermediate input demands of activities, private demand of households, government demand, investment demand, and trade and transportation margins. The level of intermediate input demand stems from the activities' cost minimisation problem, while the level of consumption demand stems from the household's utility maximisation problem. The government demand per commodity is a fixed fraction of the total government consumption. The investment per commodity, i.e. the investment by origin, is a fixed fraction of the total investment expenditures of the activities.

Production sectors (Activities)

The production side of the model comprises 32 representative firms (or industries) that produce multiple products, where these firms are referred to as activities or sectors. Examples of industries are agriculture, textiles, chemical producers, construction. Allowing activities to produce multiple products is an important feature of I3E since activities can change their production composition, to some extent, in reaction to changes in tax rates, international prices, demand-side conditions, etc.

The activities are assumed to produce a product using value added (factors of production), business energy, and other inputs. Value added is an aggregate of capital and labour, i.e. the factors of production, while the composite commodity of other inputs comprises all intermediate inputs besides the above-mentioned energy commodities and electricity. The composite commodity of business energy is an aggregate of other model-defined composite commodities, namely business heating and fuel, which are also aggregates of the aforementioned energy commodities. The substitution elasticities across energy commodities within the composite commodity of business energy differ across activities, to reflect the distinct energy needs of the various production processes. For instance, the business energy of the water transportation sector is a Leontief aggregate (i.e. the elasticity of substitution is zero) of the energy commodities as diesel constitutes more than 90% of the total energy demand of the activity.

Another important characteristic of the I3E model is that the determination of investment for the majority of activities (27 out of 32), i.e. the investment by destination, is an endogenous decision based on a dividend maximisation problem. Dividend maximising activities are introduced to better represent the economic dynamics. If the investment decision is not made by activities endogenously, all model dynamics would rely on the consumers' consumption smoothing. Firms maximise the present discounted value of the firm, i.e. the dividend stream, subject to the law of motion of capital. The sectoral dividend is equal to net-of-corporate tax sectoral profit minus total investment expenditure, which includes the cost of new investment equipment and the adjustment costs. Adjustment costs are an increasing and convex function of investment; for a given level of sectoral capital stock, the cost of installing new capital equipment will be greater. In this structure, firms choose the level of physical investment, capital stock, and labour demand.

The Emission Trading System (ETS) is the European Union’s (EU) key policy tool to reduce industrial emissions. In the current phase of the system, Phase-III that covers the period 2013–2020, each installation (i.e. a production unit) receives an amount of free allowances. If the installation’s total emissions exceed its free allowances, the installation will need to purchase additional allowances at the ETS price determined in the EU-wide ETS market. If the installation emits less than its free allowances, it can sell its unused allowances to other installations at the EU-ETS price. In other words, the system generates a cost (revenue) for those installations which emit more (less) than their allowances. An installation may generate more revenue from the ETS system by reducing its emissions as it invests more on cleaner production technologies. The coverage of sectoral emissions by the ETS is 100% for the energy production sectors; energy production installations do not receive any free allowances and need to purchase allowances to cover all their emissions. Petroleum refining, mineral, and aviation sectors’ emissions are also fully covered by the ETS, but installations operating in these industries receive some free allowances. On the contrary, land transportation (road or railway), agriculture, waste, and residential sectors are exempted from the ETS. For the other sectors, the ETS coverage varies based on the average size of production units regarding the combustion capacity, production capacity, etc. In the I3E model, economic activities directly internalise the cost of ETS in their cost minimisation problems. Each activity pays the same purchaser, i.e. retail, price to buy an energy commodity but the perceived cost of unit demand is a function of the activity’s emissions covered by the EU-ETS, the level of its free allowances, and the EU-ETS price which is an exogenous variable.


Households are represented through ten Ramsey-type representative household groups (RHGs). The household sector is firstly divided into two major groups based on the area of residence of households: urban RHGs and rural RHGs. Subsequently, each of these major groups is further disaggregated into five RHGs according to household disposable income. The RHG level parameters are calibrated by using the Household Budget Survey (HBS) that provides household level data on the sources of disposable income and the composition of private consumption by commodities. To this end, each household in the HBS is uniquely assigned to an I3E RHG, and then the RHG-level variables are calculated.

Each household has a Constant Relative Risk Aversion (CRRA) type utility function which ensures that the household smooths her consumption over time. The households maximise their present discounted value of utility subject to their budget constraint by choosing the optimal path of composite consumption. The difference between disposable income and consumption expenditure is private savings. Once the households determine their optimal path of composite consumption, they disaggregate it into consumption across the various commodities for the given parameters and prices endogenously solved within the model.

The disposable income of the households is equal to net wage income (net of wage income tax and social security premiums) from labour accounts, capital income in the form of dividends from the enterprise account, unilateral and unconditional welfare transfers and pension income from the government, and net factor income receipts from the rest of the world account.

Labour Types

There are three types of labour in the I3E model: low-skilled, medium-skilled, and high-skilled. In order to introduce the composition of household wage income regarding the labour types, the Survey on Income and Living Conditions (SILC) is utilised, as the HBS does not provide individual-level information. In the SILC, all households are uniquely assigned to an I3E RHG and the compositions of wage income by RHGs are retrieved by considering the level of educational attainment of all working members of households. For the production activities’ labour demand by types of labour, the Labour Force Survey (LFS) is utilised.


The model includes an “enterprises” account, where a representative enterprise is assumed to be the owner of all firms. This specification helps to simplify some details of the model and also solves the issue of a lack of sector-specific data such as corporate tax payments. The enterprise account collects all gross sectoral profits and receives transfers from the government, which are fixed in nominal terms, and pays corporate tax to the government. The remaining amount is either saved by the enterprise account (fixed fraction of net-of-tax profit receipts) or paid to households as dividend payments.


The I3E model has an explicit representation of the government sector. The government collects direct taxes on labour incomes and sectoral profits (corporate tax), indirect taxes on sales of commodities, the carbon tax on energy commodities, the export tax on exported commodities, the production tax on production activities, and half of the cost of ETS due to the EU legislation. The carbon tax, which is exogenously determined by the government, is implemented as a fixed price of per-tonne equivalent of carbon and collected on the domestic consumption of energy-commodities.

The government allocates its total revenues to the consumption of commodities, welfare transfers and pension payments to households (fixed in real terms - indexed to the average wage), transfers to enterprises (fixed in nominal terms), and interest payments over the outstanding foreign debt stock.

The total government consumption on commodities has an autonomous part which is fixed in nominal terms and an induced part which is a positive function of the current period’s nominal gross domestic product. This structure indicates that the Irish fiscal policy is pro-cyclical, and is consistent with the previous findings of the ESRI. The difference between total revenues and expenditures of the government is public saving which drives changes in the foreign debt stock, i.e. as public saving increases (decreases), the government debt stock becomes lower (higher).

Rest of the world

As in the case of all single-country CGE models, all countries except Ireland are assumed to be a single unit called “rest of the world”. All monetary flows between the rest of the world and Ireland are traced within the rest of the world (RoW) account. Since all transactions related to this account are assumed to be denominated in a foreign currency, an exchange rate adjustment takes place. In the case of Ireland, although there is no exchange rate discrepancy for the transactions within the European Union, almost two-thirds of the value of foreign trade consists of trade flows between Ireland and the United States and Ireland and the United Kingdom. As there is no distinction between these trade partners within the I3E model, the exchange rate movements also play an important role.

The sources of the foreign exchange supply are exports of commodities and the net factor income of the households. As the rest of the world is not introduced in the model explicitly, i.e. there are no foreign agents with maximisation behaviour, it is assumed that all exports of Ireland are absorbed by the rest of the world. The volume of exports is a function of exogenous international commodity prices and the elasticity of substitution between sales in the domestic market and export. The sources of foreign exchange demand are imports of commodities, the interest payments of the government over the outstanding foreign debt stock, and half of the cost of ETS due to the EU legislation. The difference between the totals of foreign exchange supply and demand is covered by foreign savings, i.e. the current account balance. The foreign market closure rule implies that for the given level of foreign savings, the equilibrium in the rest of the world account is ensured by the exchange rate adjustment. In other words, the I3E model is a price-adjustment model.

The money flows between agents within the model are represented in the figure below.


I3E Money Flow


The development of the I3E model has been funded by the Department of Communication, Climate Action and Environment. The Department of Finance has also provided funding to include household distinctions in the model.