2.1 General Framework

WITCH (World Induced Technical Change Hybrid) is an integrated assessment model designed to assess climate change mitigation and adaptation policies. WITCH is maintained and developed at the RFF-CMCC European Institute on Economics and the Environment (EIEE). It was originally co-developed by Fondazione Eni Enrico Mattei and the Centro Euro-Mediterraneo sui Cambiamenti Climatici. For descriptions of previous model version, please refer to (Bosetti et al. 2006), (Bosetti, Massetti, and Tavoni 2007) and (Bosetti et al. 2009).

WITCH consists of a dynamic global model that integrates in a unified framework the most important elements of climate change. The economy is modelled through an inter-temporal optimal growth model which captures the long term economic growth dynamics. A compact representation of the energy sector is fully integrated (hard linked) with the rest of the economy so that energy investments and resources are chosen optimally, together with the other macroeconomic variables. Land use mitigation options are available through a soft link with a land use and forestry model (GLOBIOM). A climate model (MAGICC) is used to compute the future climate. Climate change impacts the economic output through a damage function, depending also on the rate of investments in adaptation. This allows accounting for the complete dynamic of climate change mitigation and adaptation.

2.1.1 Methodology and features

WITCH represents the world in a set of representative native regions (or coalitions of regions); for each it generates optimal mitigation and adaptation strategies for the long term (from 2005 to 2100) as a response to either climate damage or some external constrain on emissions, concentrations or temperature. These strategies consist of investment profiles resulting from a maximization process in which the welfare of each region (or coalition of regions) is chosen strategically and simultaneously accordingly to other regions. This makes it possible to capture regional free-riding behaviours and strategic interaction induced by the presence of global externalities. The non-cooperative, simultaneous, open membership game with full information, is implemented through an iterative algorithm which yields the open-loop Nash equilibrium. In this game-theoretic set-up, regional strategic actions interrelate through GHG emissions, dependence on exhaustible natural resources, trade of oil and carbon permits, and technological R&D spillovers.

The endogenous representation of R&D diffusion and innovation processes constitute a distinguishing feature of WITCH, allowing to describe how R&D investments in energy efficiency and carbon free technologies integrate the currently available mitigation options. The model features multiple externalities, both on the climate and the innovation side. The technology externalities are modelled via international spillovers of knowledge and experience across countries and time. In each country, the productivity of low carbon mitigation technologies and of energy depend on the region stock of energy R&D and by the global cumulative installed capacity, two proxies for knowledge and experience respectively. The R&D stock depends on domestic investments, domestic knowledge stock, and foreign knowledge stock through international spillovers. The spillover term depends on the interaction between the countries’ absorptive capacity, and the distance of each region from the technology frontier. This formulation of technical change affects both decarbonization as well as energy savings.

2.1.2 Policy Applications

A distinctive feature of WITCH is the ability to assess the optimal response to climate policies with all degrees of cooperation (from non-cooperative to fully cooperative), by appropriately defining the coalition structure. In the cooperative solution all externalities are internalized and therefore it can be interpreted as a first-best solution. The Nash equilibrium instead can be seen as a second-best solution.

The model can also perform both cost effective analysis, as well as cost benefit analysis, depending on whether exogenous constraints are placed on the climate (e.g. emissions caps or carbon taxes) and whether the climate feedback on the economy is activated. By definition the non-cooperative setting cannot handle global constraints; global constraints can be implemented via a recursive procedure in which regional policies (e.g. cap and trade or carbon taxes) are adjusted till the global cap is met.

The model is calibrated on a set of predefined policies. They are used as benchmark or as a starting point for further policy assessments. Below is an illustrative set of these predefined policies:

  • Business as usual (BAU);

  • Damage Induced Mitigation (BAU with Climate Damage Feedback);

  • Concentration target of 450 ppm;

  • Radiative forcing target at 2.8 W/m2 in 2100;

  • Global temperature increase limits at 2 degree Celsius.


Bosetti, Valentina, Carlo Carraro, Marzio Galeotti, Emanuele Massetti, and Massimo Tavoni. 2006. “A World Induced Technical Change Hybrid Model.” The Energy Journal SI2006 (01). https://doi.org/10.5547/ISSN0195-6574-EJ-VolSI2006-NoSI2-2.

Bosetti, Valentina, Emanuele Massetti, and Massimo Tavoni. 2007. “The Witch Model: Structure, Baseline, Solutions.” 2007.010. FEEM Working Paper.

Bosetti, Valentina, Massimo Tavoni, Enrica De Cian, and Alessandra Sgobbi. 2009. “The 2008 Witch Model: New Model Features and Baseline.” 2009.085. FEEM Working Paper.