The dynamic and strategic features of the model, the energy sector specification and the representation of technological change make WITCH a specially designed tool well suited to explicitly analyze the consequences of climate change. WITCH incorporates a hybrid top-down optimization structure with a detailed energy sector breakdown and a game theoretic setup. Further details are noted below.



The world economy in WITCH is described by a Ramsey-type neo-classical optimal growth model.

In WITCH, strategies implemented in one region of the world affect what goes on in all the other regions. This is achieved by means of a non-cooperative Nash game among regions with the following sources of interaction:

The non-cooperative Nash game is solved numerically as follows: at each iteration the social planner of every region takes the behavior of other players as given (based on the previous iteration) and sets the optimal value of all choice variables. These computed variables are then stored and fed into the next round of optimizations. The process is repeated until each region’s behavior converges. Convergence is achieved when each region’s choice is the best response to all of the other regions’ responses subject to the prevailing behavior.

Energy sector

In WITCH, the energy sector is represented by a downward expansion of the energy input within the economy.

The energy sector is represented within the economy (“hard link”) as shown in the diagrammatic description in the figure below. The energy detail – though still simplified with respect to large scale energy system models – is a novelty for macro-growth models and enables to a reasonable portray of future energy and technological scenarios. Energy (EN in the figure) is decomposed as follows:

The parameters governing the production function take into account the technical features of each power generation technology. The cost of electricity is endogenously derived in accordance to each region’s interest rate to ensure capital market equilibrium, as well as incorporating fuel costs which have been set to reflect exhaustibility.

Climate system

The climate system in WITCH is described by a climate module which feeds back into the economic system via a damage function.

As shown in the figure below, a three-box climate module converts carbon dioxide emissions produced by the economy into atmospheric concentration, radiative forcing and eventually temperature increases above pre-industrial levels. Increases in global temperature ultimately affect each region’s output via a climate damage function that translates the global warming effects into monetary losses or gains in each region.

Innovation in the energy sector

In WITCH, both Research and Development and Learning-by-Doing in energy use and energy technologies account for Endogenous Technical Change. Technical change in WITCH is endogenous and can be induced by climate policy, international spillovers and other economic effects. The hybrid nature of WITCH allows the portrayal of endogenous technological change both in its bottom-up and top-down dimensions.

Endogenous technological change takes the form of accumulated experience and direct R&D investment with the following specific features:

See the Technical Report for a detailed description of the model.


"The WITCH 2016 Model - Documentation and Implementation of the Shared Socioeconomic Pathways'" by Emmerling, J., L. Drouet, L. A. Reis, M. Bevione, L. Berger, V. Bosetti, S. Carrara, E. De Cian, G. De Maere D'Aertrycke, T. Longden, M. Malpede, G. Marangoni, F. Sferra, M. Tavoni, J. Witajewski-Baltvilks and P. Havlik. FEEM Note di Lavoro 42.2016

"Documentation on the development of damage functions and adaptation in the WITCH model" by Francesco Bosello and Enrica De Cian, CMCC Research Paper RP0228

"The 2008 WITCH Model: New Model Features and Baseline" by Valentina Bosetti, Massimo Tavoni, Enrica De Cian and Alessandra Sgobbi. FEEM Working Paper 2009.085

"The WITCH Model. Structure, Baseline, Solutions" by Valentina Bosetti, Emanuele Massetti and Massimo Tavoni FEEM Working Paper 2007.010