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.
A full online documentation of the model can be accessed here: http://doc.witchmodel.org
- Countries included within the model are grouped into macro regions (13 regions by default, but adjustable to the scope of the analysis) clustered on the basis of geography, income and the structure of energy demand. Regional disaggregation can be easily performed subject to the issue being tackled.
The world economy in WITCH is described by a Ramsey-type neo-classical optimal growth model.
- For each of the regions a forward-looking central planner maximizes the present value of (the log of) per capita consumption (with 5-year time intervals);
- These central planners maximize these intervals simultaneously over the whole optimization period of 100 years. This optimization is made subject to strategic consideration of the choices of the other decision makers (strategic interaction);
- When choosing optimal investments, agents are forward-looking (take into account future events, including future policies) and behave strategically (take into account present and future policy measures in the other regions);
- The model yields the optimal strategy for the energy sector in terms of investments in power generation technologies and the direct consumption of fuels.
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:
- Exhaustible resource use (with prices dependent on aggregate demand);
- CO2 emissions (via the climate damage feedback);
- Technology spillovers (in terms of both Learning-by-Doing and R&D);
- Global CO2 permit market (when emission caps are imposed).
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.
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:
- electric and non-electric energy use;
- 6 fuels;
- 13 technologies for electricity generation.
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.
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:
- Learning-by-Doing via experience curves that decrease power plants investment costs with accumulated installed capacity;
- Energy R&D aimed at increasing energy efficiency;
- R&D directed at reducing the cost of cellulosic biofuels.
See the Technical Report for a detailed description of the model.