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== Introduction ==
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 [http://doc.witchmodel.org]
== Table of contents ==
=== [[Model scope and methods - WITCH|Model scope and methods]] ===
* '''[[Model concept, solver and details - WITCH |Model concept, solver and details]]'''
* '''[[Temporal dimension - WITCH |Temporal dimension]]'''
* '''[[Spatial dimension - WITCH|Spatial dimension]]'''
* '''[[Policy - WITCH|Policy]]'''
=== [[Socio-economic drivers - WITCH|Socio-economic drivers]] ===
* '''[[Population - WITCH|Population]]'''
* '''[[Economic activity - WITCH|Economic activity]]'''
=== [[Macro-economy - WITCH|Macro-economy]] ===
* '''[[Production system and representation of economic sectors - WITCH|Production system and representation of economic sectors]]'''
* '''[[Capital and labour markets - WITCH|Capital and labour markets]]'''
* '''[[Monetary instruments - WITCH|Monetary instruments]]'''
* '''[[Trade - WITCH|Trade]]'''
* '''[[Technological change - WITCH|Technological change]]'''
=== [[Energy - WITCH|Energy]] ===
* '''[[Energy resource endowments - WITCH|Energy resource endowments]]'''
** [[Fossil energy resources - WITCH|Fossil energy resources]]
** [[Uranium and other fissile resources - WITCH|Uranium and other fissile resources]]
** [[Bioenergy - WITCH|Bioenergy]]
** [[Non-biomass renewables - WITCH|Non-biomass renewables]]
* '''[[Energy conversion - WITCH|Energy conversion]]'''
** [[Electricity - WITCH|Electricity]]
** [[Heat - WITCH|Heat]]
** [[Gaseous fuels - WITCH|Gaseous fuels]]
** [[Liquid fuels - WITCH|Liquid fuels]]
** [[Solid fuels - WITCH|Solid fuels]]
** [[Grid, pipelines and other infrastructure - WITCH|Grid, pipelines and other infrastructure]]
** [[Energy end-use - WITCH|Energy end-use]]
** [[Transport - WITCH|Transport]]
** [[Residential and commercial sectors - WITCH|Residential and commercial sectors]]
** [[Industrial sector - WITCH|Industrial sector]]
** [[Other end-use - WITCH|Other end-use]]
* '''[[Energy demand - WITCH|Energy demand]]'''
* '''[[Technological change in energy - WITCH|Technological change in energy]]'''
=== [[Land-use - WITCH|Land-use]] ===
* '''[[Agriculture - WITCH|Agriculture]]'''
* '''[[Forestry - WITCH|Forestry]]'''
* '''[[Land-use change - WITCH|Land-use change]]'''
* '''[[Bioenergy land-use - WITCH|Bioenergy land-use]]'''
* '''[[Other land-use - WITCH|Other land-use]]'''
* '''[[Agricultural demand - WITCH|Agricultural demand]]'''
* '''[[Technological change in land-use - WITCH|Technological change in land-use]]'''
=== [[Emissions - WITCH|Emissions]] ===
* '''[[GHGs - WITCH|GHGs]]'''
* '''[[Pollutants and non-GHG forcing agents - WITCH|Pollutants and non-GHG forcing agents]]'''
* '''[[Carbon dioxide removal (CDR) options - WITCH|Carbon dioxide removal (CDR) options]]'''
=== [[Climate - WITCH|Climate]] ===
* '''[[Modelling of climate indicators - WITCH|Modelling of climate indicators ]]'''
* '''[[Climate damages, temperature changes - WITCH|Climate damages, temperature changes ]]'''
=== [[Non-climate sustainability dimension - WITCH|Non-climate sustainability dimension]] ===
* '''[[Air pollution and health - WITCH|Air pollution and health]]'''
* '''[[Water - WITCH|Water]]'''
* '''[[Other materials - WITCH|Other materials]]'''
* '''[[Other sustainability dimensions - WITCH|Other sustainability dimensions]]'''
=== [[Appendices - WITCH|Appendices]] ===
* '''[[Mathematical model description - WITCH|Mathematical model description]]'''
* '''[[Data - WITCH|Data]]'''
=== [[References - WITCH|References]] ===

Latest revision as of 11:52, 22 July 2025

Model Documentation - WITCH

    Corresponding documentation
    Previous versions
    Model information
    Model link
    Institution European Institute on Economics and the Environment (RFF-CMCC EIEE), Italy, http://www.eiee.org.
    Solution concept General equilibrium (closed economy)
    Solution method Optimization
    Anticipation

    Introduction

    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]

    Table of contents

    Model scope and methods

    Socio-economic drivers

    Macro-economy

    Energy

    Land-use

    Emissions

    Climate

    Non-climate sustainability dimension

    Appendices

    References

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