Document Actions
A Short Description of DART
The DART-Model of the Kiel Institute for World Economics (IfW) is a recursiv-dynamic computable general equilibrium (CGE) model of the world economy that is designed for the analysis of international climate policies. The first version of DART was developed in the late 90's ties and used to analyse the implementation of the Kyoto Protocol by unilateral action but also to assess the effects of international capital mobility. In addition, DART was coupled to a ozean-atmosphere model, to estimate the economic costs of climate change. Today, new data allow e.g. to disaggregate the European Union into its individual member states. Besides, new topics require to continuously develop the original model, for example in order to analyse international emissions trading regimes, technology transfer, or the impacts of the extended use of biofuel. In the following we shortly present the current DART model. For a more detailed description see Klepper et al. (2003).
The Static Model
DART stands for "Dynamic Applied Regional Trade". The static part of DART is a multi-regional, multi-sectoral computable general equilibrium model of the world economy. It is written in the mathematical programming language GAMS/MPSGE and is based on the GTAP5-E(nergy) data set of the Global Trade Projects. The 57 sectors and 113 regions of GTAP7 can be aggregated to the question at hand. The common aggregations are found here. The economic structure of DART is fully specified for each region and covers production, investment and final demand. Primary factors are labour, capital and land.
Production
Producer behaviour is characterized by cost minimization for a given output. All industry sectors are assumed to operate at constant returns to scale. For the non fossil fuel industries, a multi-level nested separable constant elasticity of substitution (CES) function describes the technological possibilities in domestic production between intermediate inputs on the one side and a capital-labour-energy (KLE) aggregate on the other side. The intermediate inputs are combined of non-energy domestic and imported inputs that have fixed input coefficients. The KLE-aggregat is a CES function of an energy aggregate and the primary factors that are linked by a Cobb-Douglas function. Inside the energy aggregate, substitution is possible between electricity and fossil fuels. The fossil fuels gas, coal and crude oil are each produced of specific, fixed resources and a macro aggregate of all other intermediate inputs and primary factors. Furthermore, an investment good is produced in each region using fixed shares of the different intermediate inputs. Investment is not sector specific and does not use primary factors.
Producer goods are directly demanded by final consumers (comprising regional households and governments), the investment sector, other industries and the export sector.
Consumption
The representative household, that comprises private households and the government sector, receives all income generated by providing primary factors to the production process. After deducting taxes and savings, the disposable income is used for maximizing utility by purchasing goods. The final consumer decides between different primary energy input and non-energy inputs depending on their relative price in order to receive its consumption (utility) with the lowest expenditures. First, consumption covers a subsistence share, which is determined by the income elasticities for the demand of the various goods. The expenditure function for the remaining consumption is a Cobb-Douglas function of energy and non energy inputs. In each period, a fixed share of income is saved.
Factor Markets
Factor markets are perfectly competitive and full employment of all factors is assumed. Labour is assumed to be a homogenous good, mobile across industries within regions but internationally immobile. In the basic version of the DART model capital is also inter-sectorally but not internationally mobile. Regional Capital stocks are given at the beginning of each time period and results from the capital accumulation equation. In every time period they earn a correspondent amount of income measured as physical units in terms of capital services.
Foreign Trade
The world is divided into economic regions, which are linked by bilateral trade flows. All goods are traded among regions, except for the investment good. Following the proposition of Armington (1969), domestic and foreign goods are imperfect substitutes, and distinguished by country of origin. Import demand is derived from a three stage, nested, separable CES cost of expenditure function respectively and distinguishes between imported and domestically produced goods as well as between the country of origin. On the first level domestic goods substitute with imports. On the second level the imports of different regions are aggregated. The imports of one region r are equivalent to the exports of all other regions into that region r including transport. Transport costs, distinguished by commodity and bilateral flow, apply to international trade but not to domestic sales. The exports are connected to transport costs by a Leontief function on the third level. International transports are treated as a world-wide activity which is financed by domestic production proportional to the trade flows of each commodity. There is no special sector for transports related to international trade.
On the export side, the Armington assumption applies to final output of the industry sectors destined for domestic and international markets. Here, produced commodities for the domestic and for the international market are no perfect substitutes. Exports are not differentiated by country of destination.
CO2 Emissions
The use of energy in production and consumption leads depending on the energy source to different amounts of carbon emission. CO2 emissions with high quantities of emissions and a long life time in the atmosphere play the main role in the greenhouse gas effect. Other greenhouse gases and sinks are not accounted for in DART.
Gas and coal each have a fixed carbon content. To calculate the associated carbon dioxide emissions one simply has to multiply the physical quantity of gas and coal used in either domestic production or domestic consumption (which is given in the GTAP data) and multiply it by its emission coefficient. DART uses the recommendations from the IPCC (1996) which are 0.0258 kgC/MJ for coal and 0.0153 kgC/MJ for gas.
For oil emissions the calculation is more complicated. In order to determinate the CO2 emissions which originate from the use of crude oil in the different production and consumption processes one needs to know at which point in the value-added chain this fossil fuel is actually burned, i.e. leads to emissions. In the current model crude oil only enters the production of refined oil products where it is not burned. Only refined oil products are burned as inputs in production or as final consumption goods. One cannot use the domestic use of crude oil for determining CO2 emissions since some of these oil products are exported and some are imported, hence there is no one-to-one correspondence between crude oil consumption and emissions.
Since crude oil is the emission relevant input in refined oil production, only the crude oil share can be used for determining CO2 emissions. The emission coefficient for crude oil is set to (IPCC, 1996) 0.02 KgC/MJ. The emission of each region are calculated by multiplying imports and domestic refined oil products by its specific crude oil share and the emission factor. The calculation also takes into account that a share of petrol products used in the chemical industry are used as an intermediate input without being burned.
The supply elasticities of fossil fuels are chosen in such a way that the carbon emission in 2030 resulting from the model in the business as usual scenario meet the newest projections of the IEA (2010).
Dynamics
The DART model is recursive-dynamic, meaning that it solves for a sequence of static one period equilibria for future time periods connected through capital accumulation and changes in labour supply. The dynamics of the DART model are defined by equations which describe how the endowments of the primary factors capital and labour evolve over time. The major driving exogenous factors of the labour dynamic are population change, the rate of labour productivity growth and the change in human capital. The driving forces for capital accumulation are the savings rate and the gross rate of return on capital, and thus the endogenous rate of capital accumulation. The DART model is recursive in the sense that it is solved stepwise in time without any ability to anticipate possible future changes relative prices or constraints.
Labour Supply
The main factors influencing the develoopment of labour supply are population and productivity growth and human capital accumulation. Labour is thus measured in efficiency units, L(r,t). It evolves exogenously over time. Hence, labour supply for each region r at the beginning of time period t+1 is given by:
L(r,t+1) = L(r,t) *(1+gp(r,t) +ga(r) + gh(r))
An increase of effective labour implies either growth of the human capital accumulated per physical unit of labour, gh(r), population growth gp(r) or total factor productivity ga(r), or the sum of all. DART assumes constant, but regionally different labour productivity improvement rates ga(r) and declining population growth rates over time, gp(r,t), according to the World Bank population growth projections. Because of the lack of data for the evolution of the labour participation rate in the future the growth rate of population instead of the labour force is used implying that the labour participation rate is constant over time. The human growth rates of human capital gh(r) are also assumed to be constant over time and regionally different. The 1990 levels of human capital endowments are taken from Hall and Jones (1999). For the future development of the endowments, we assume that the maximum endowment of 12 years of schooling will be reached in 2050 and that this process starts at the computed 1990 levels and continues in a linear fashion. This approach can be be criticized as being rather ad-hoc. Since we could not identify a reasonable indicator for the future development of human capital endowments, we simply assumed optimistically that there is complete convergence in human capital intensities in the long run.
Capital Formation
Current period's investment augments the capital stock in the next period. The aggregated regional capital stock, Kst at period t is updated by an accumulation function equating the next-period capital stock, Kst at t+1 to the sum of the depreciated capital stock of the current period and the current period's physical quantity of investment, Iq(r,t). The equation of motion for capital stock Kst(r,t+1) in region r is given by:
Kst(r,t+1) = (1-d)*Kst(r,t) + Iq(r,t)
where d denotes the exogenously given constant depreciation rate. According to the GTAP data set d = 0.04, and we use the same value for all time periods. The allocation of capital among sectors follows from the intra-period optimization of the firms. The savings behaviour of regional households is characterized by a constant savings rate over time. This rather ad-hoc assumption seems consistent with empirical observable, regional different, but nearly constant savings rates of economies, which adjust according to income developments over very long time periods. Additionally, a wide range of empirical evidence in macro economic literature neglect the theoretically elegant permanent income hypothesis and shows that a huge fraction of the consumption decisions are based entirely on current after tax income.
References
Hall, R E and Jones, C I (1999). Why do some countries produce so much more output per worker than others? The Quarterly Journal of Economics 114(1):83-116.
IEA (2010). International Energy Outlook 2010.