Model Documentation - WITCH

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Model Documentation - WITCH

Corresponding documentation
Previous versions
Model information
Model link
Institution European Institute on Economics and the Environment (RFF-CMCC EIEE), Italy,
Solution concept General equilibrium (closed economy)
Solution method Optimization

WITCH (World Induced Technical Change Hybrid) is an optimal growth model of the world economy that integrates into a unified framework the sources and the consequences of climate change. A climate module links GHG emissions produced by economic activities to their accumulation in the atmosphere and the oceans. The effect of these GHG concentrations on the global mean temperature is derived. A damage function explicitly accounts for the consequences of temperature increases on the economic system.

Regions interact with each other because of the presence of economic (technology, exhaustible natural resources) and global environmental externalities. For each region, a forward-looking agent maximises its inter-temporal social welfare function, strategically and simultaneously to other regions. The inter-temporal equilibrium is calculated as an open-loop Nash equilibrium, or, a cooperative solution can also be solved by aggregating the welfare of each region. More precisely, the Nash equilibrium is the outcome of a non-cooperative, simultaneous, open membership game with full information. Through the optimisation process, regions choose the optimal dynamic path of a set of control variables, namely investments in the main economic variables.

WITCH is a hard-link hybrid model because the energy sector is fully integrated with the rest of the economy and therefore investments and the quantity of resources for energy generation are chosen optimally, together with the other macroeconomic variables. The model can be defined hybrid because the energy sector features a bottom-up characterization. A broad range of different fuels and technologies can be used in the generation of energy. The energy sector endogenously accounts for technological change, with considerations for the positive externalities stemming from Learning-By-Doing and Learning-By-Researching. Overall, the economy of each region consists of eight sectors: one final good, which can be used for consumption or investments, and seven energy sectors (or technologies): coal, oil, gas, wind & solar, nuclear, electricity, and bio-fuels.

The official model documentation is available at [1]