The WTMBT model

Short overview

The World Trade Model with Bilateral Trades (WTMBT in the following) is a meso-economic linear optimization model based on the comparative advantage principle. Considering m world regions with n industries each, the WTMBT enables to endogenously determine the production yields and trades patterns required to satisfy an exogenously specified final demand yield in each region, minimizing the use of factors of production (labor and capital) by complying with regional factors endowments (e.g. availability of natural resources, land, workforce, etc.). The choice of developing a model which includes the cost of bilateral trades (i.e. WTMBT), is driven by the relevance of transport in determining the arrangement of production and trades and by its non-negligible impact on carbon emissions. The economic and environmental implications of national and international transport of products are included in the model and weighed depending on transport distances. With respect to General Equilibrium Models (CGE), the WTMBT requires less exogenous data since it considers households and government final demand as constant and perfectly rigid with respect to endogenous change in prices of goods and services. Therefore, instead of maximizing social utility, the WTMBT establishes that the highest-cost producers set the products prices, and each region chooses to produce or to import by minimizing the overall costs complying with their own production factors availability (i.e. factor endowments). In the WTMBT, production technologies, factors use coefficients and final demand for each country are derived from Multi-Regional Input-Output tables (MRIO). Other exogenous inputs like factor endowments, weights of transported goods and regional distances are derived from other databases (e.g. World Bank, International Energy Agency), depending on the scope of the adopted MRIO and on the type of analysis to be carried out.

Key features of the WTMBT model

Linear optimization in an input-output formulation of an economy.

Comparative static.

The model is asked to provide the minimization of factor cost of economic activities while meeting, for every economy, the final demand of consumers, the intermediate demand of industries and export demand (with its demand of transport services) of each sector by means of production or import.

Every economic production implies the consumption of factors (natural resources, capital and labour) and the emission of CO2 and other polluters.

In this formulation of the model, the electricity sector generates an output which can be produced by several different technologies: the model will chose between the alternatives on the basis of the solely principle of comparative advantage, which regulates all the model decisions.

Climate module & emissions granularity

The model considers CO2 emissions as a direct consequence of the endogenous production of the sectors and regions considered in the model. These emissions are expressed with respect to the sector, region and type of pollutant or greenhouse gas. Thanks to the input-output structure of the model, it is possible to consider various mechanisms for assigning responsibility for emissions (e.g. Production-Based Approach, Consumption-Based Approach).

Socioeconomic dimensions

The socio-economic dimension is considered in the objective function of the model, which foresees a minimisation of the global use of productive factors net of scarcity rents that may emerge when one or more resources become scarce. In fact, these resources are bound not to exceed a maximum level of availability, called factor endowments (e.g. maximum number of high-skilled workers for a given sector in a given region).

Mitigation/adaptation measures and technologies

The existing technology is determined by the multiregional input-output database adopted as input to the optimization model. Sectoral interrelationships, characterizing the technology mix of each region, are exogenously determined. An exception is made for the electricity sector where it is possible to choose between several technologies to meet the needs of both industries and households for electricity. Also in this choice, the model is guided by the principle of comparative advantage that will produce the least expensive technology until one or more resources are exhausted.In this sense, mitigation and adaptation scenarios can be simulated by introducing additional constraints (which model the introduction of a policy) that disrupt either the cost of a technology, the availability of one or more resources or other types of constraints (e.g. impose exogenously a new final demand).

Economic rationale and model solution

The model minimizes the global cost, in terms of the use of productive factors, like labour and capital, of satisfying an exogenously determined quantity of goods and services. The primary formulation of this linear model provides for the satisfaction of the final demand for each region, taking into account the resulting need for intermediate demand due to the sectoral interrelationships of each region, the possibility to import from another region, the possibility to export one's own product net of transport costs and resource limits. This formulation is underpinned by a dual formulation of the same problem that provides for a maximization of final demand net of scarcity rents that may emerge when the limits of a resource are reached. Price indices will take into account transport costs and relative price differences that may arise. In this way it will be possible to assess the impact in terms of price indices, linked to each solution found by the model, under the assumption that there is no influence of the mechanisms of balance between supply and demand.

Key parameters

The fundamental exogenous parameters for the model concern:

  • final demand by sector and region
  • technology (i.e. input-output coefficients)
  • maximum availability of resources outside the economy (e.g. availability of fossil fuels, availability of labour)

The endogenous parameters provided by the model concern:

  • sectoral production (which determines the sectoral GDP and related CO2 emissions)
  • import-export (allowing trade between regions and consequent choice of make-or-buy)

Policy questions and SDGs

Key policies that can be addressed

One of WTMBT uses is to explore the implications of different future policies. There are a number of types of policies that can be easily modelled in GCAM:

Emissions-related policies Through this model it is possible to model emission constraints as a maximum level of emissions for a given group of regions and sectors (e.g. Emission Trading System) or by imposing an emission cost level (e.g. Carbon Tax). These two different types of constraints will disrupt minimization by either affecting external constraints or directly affecting exogenous coefficients (i.e. a tax per ton of GHG in a certain sector and/or region).

Energy production policies It may be possible to include a constraint requiring the model to provide, as an aggregate or regional value, a minimum quantity of production from one or more energy sources. Through the possibility of choice, both in terms of regional production and technology used to supply electricity, the model will be able to choose different ways, moving towards the one that minimizes global costs.

Behavioural policies In principle it is possible to assess the impact of changes in behaviour, translated as a change in consumption preferences of the final demand category of households (e.g. impact of teleworking).

Implications for other SDGs

The WTMBT does not independently assess the impact on SDGs but it is possible to derive indicators that may partially indicate an impact on some of the dimensions of several SDGs.

Model presentation



Download slides in pdf

Recent use cases

Paper DOI Paper Title Key findings Restricting water withdrawals of the thermal power sector: An input-output analysis for the northeast of the United States Based on an annual analysis, it is conclude that Northen East USA can satisfy its electric power requirements while fully complying with legislated water restrictions at moderate cost by compensating the curtailment of output from some plants by otherwise unutilized capacities of other plants in the region. The global economic costs of substituting dietary protein from fish with meat, grains and legumes, and dairy The WTM is used to analyze alternative scenarios about protein content and sources in global diets. It is found that the substitution of fish by meat or dairy entails several trillion US dollars of additional costs annually, corrsiponding to increased use of pastureland, cropland, water and other factor of production. Fighting carbon leakage through consumption-based carbon emissions policies: Empirical analysis based on the World Trade Model with Bilateral Trades The WTMBT is adopted to evaluate two different approaches in limiting carbon emission within EU. Production-based approach and Consumption-based approach are simulated in the modelling framework and their impacts in terms of global emission and increase in the use of factor of production is evaluated.
Recent publications using the EnergyPLAN model


Duchin, F., S.H. Levine, and A.H. Stromman, 2016. Combining Multiregional Input-Output Analysis with a World Trade Model for Evaluating Scenarios for Sustainable Use of Global Resources, Part I: Conceptual Framework, Journal of Industrial Ecology, 20(4): 775-782.

Duchin, F. and Levine, S.H., 2016. Combining multiregional input‐output analysis with a world trade model for evaluating scenarios for sustainable use of global resources, Part II: Implementation. Journal of Industrial Ecology, 20(4): 783-791.

Duchin, F., 2016. A global case‐study framework applied to water supply and sanitation. Journal of Industrial Ecology, 20(3): 387-395.

Duchin, F. 2017. “Resources for Sustainable Economic Development: A Framework for Evaluating Infrastructure System Alternatives,” Sustainability, 9(11), 2105,

Duchin, F. and S. Levine, 2019. The Recovery of Products and Materials for Reuse: A Global Context for Resource Management, Resources, Conservation and Recycling (Special Issue on Economy-wide Prospects for Material Recovery and Waste Recycling: Advances in Integrating Input-Output Economics and Industrial Ecology).