# Population - WITCH

Model Documentation - WITCH | |
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Corresponding documentation | |

Model information | |

Institution | Fondazione Eni Enrico Mattei (FEEM), Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC) |

Concept | Hybrid: Economic optimal growth model, including a bottom-up energy sector and a simple climate model, embedded in a `game theory` framework. |

Solution method | Regional growth models solved by non-linear optimization and game theoretic setup solved by tatonnement algorithm (cooperative solution: Negishi welfare aggregation, non-cooperative solution: Nash equilibrium) |

Anticipation | Perfect foresight |

## Population

An important driver for the emissions of greenhouse gases is the rate at which population grows. In the WITCH model, population growth is exogenous. The model base year is 2005, and use the most recent estimates of population growth. The annual estimates and projections produced by the UN Population Division are used for the first 50 years. For the period 2050 to 2100, the updated data are not available, and less recent long-term projections, also produced by the UNPopulation Division (UN, 2004) are adopted instead. The differences in the two datasets are smoothed by extrapolating population levels at 5-year periods for 2050-2100, using average 2050-2100 growth rates. Similar techniques are used to project population trends beyond 2100.

## Economic growth

The GDP data for the new base year are from the World Bank Development Indicators 2007, and are reported in 2005 US$. We maintain the use of market exchange rates (MER). World GDP in 2005 equals to 44.2 Trillions US$.

Although part of the GDP dynamics is endogenously determined in the WITCH model, it is possible to calibrate growth of different countries by adjusting the growth rate of total factor productivity, the main engine of macroeconomic growth.

Economic growth rates and the level of convergence are strong determinants of energy demand and, therefore, GHG emissions. In the model, we depart from existing IPCC scenarios, and base our projections for regional GDP growths on assumptions regarding labour productivity convergence.

OECD countries are assumed to reach a rather constant growth rate while the catch-up of non-OECD is driven by labour productivity which should bring most developing countries closer to the level of OECD countries by the end of the century. The convergence is nonetheless slow in per capita terms given the higher population growth of developing countries. Sub-Saharan Africa, in particular, experiences delays in catch-up. Eastern Europe shows the highest convergence rate. The model is therefore dynamically calibrated to match a growth path consistent with these underlying assumptions on convergence and growth.