# **3.3 CGE Modeling**

We conduct a top-down analysis using a three-region, 14-sector recursive-dynamic CGE simulation of the world economy. Consumers in each region are modeled as a representative agent who owns the factors of production (labor and jelly capital) and rents them out to producers in exchange for income which is used to finance consumption of commodities. Producers in each region’s sectors are modeled as a representative firm which combines inputs of intermediate commodities and factors to produce a sector-specific good which is sold to the households, other sectors, the government, and other regions. The government is modeled as a passive entity which produces a government good from purchases of commodity inputs that are financed by revenue collected from taxes on production, imports and exports. Inter-regional trade in commodities is modeled using the Armington formulation in which a region’s uses of a given commodity are a constant elasticity of substitution (CES) composite of domestic and imported varieties, and the region’s aggregate imports of each commodity are a CES composite of quantities exported by its trade partners. The dimensions of this static general equilibrium structure are summarized in Figure 2.A. Following the complementarity format of equilibrium, the structure is posed algebraically as a square system of zero profit, market clearance and income balance conditions. The technical coefficients of the constituent cost and demand functions are numerically calibrated on the Global Trade Analysis Project (GTAP) version 8 database (Narayanan et al, 2012) using the MPSGE subsystem (Rutherford, 1999) for GAMS (Brooke et al, 1998), and the resulting numerical problem is expressed and solved as a mixed complementarity problem using the PATH solver (Dirkse and Ferris, 1995; Ferris and Munson, 2000).

The static sub-model described above is embedded within a dynamic process which updates economies’ savings/investment demands, and endowments of labor, capital and natural resources, over the 2015-2035 simulation horizon on a five-year time step. Regions’ labor endowments are assumed to increase exogenously with population, following projections in World Bank (2015). Regions’ representative agents are assumed to exhibit constant marginal propensity to save and invest out of factor income, and investment drives interperiod jelly capital accumulation according to the standard perpetual inventory formulation. The model’s dynamics are tuned to produce baseline trajectories of GDP and CO2 emissions are consistent with DOE/EIA (2014) projections. We do this by adjusting the growth rates of exogenous aggregate labor productivity and autonomous energy efficiency improvement (AEEI) parameters. Additional modeling details are given in an appendix to the paper.

Two challenges attend implementation of the general equilibrium model of section 2.4. The first is specifying the demand for technology-specific services in eq. (16). In technologyrich sectors (denoted by the index _j_<sup>_′_</sup> ) discrete technology options’ demand for fuel and capital ( _QFe,θ,j′_ and _QXθ,j′_ ) make up a portion of the total sectoral use of these inputs. From a modeling perspective, the key unknown is how precisely the services thus produced ( _QSθ,j′_ ) combine with the broader set of inputs to generate the sector’s output. Our approach is to specify a “technology services composite” which is a constant elasticity of substitution (CES) aggregation of the outputs of the technologies in that sector, and allow this bundle of services to substitute for capital, labor energy and materials. As shown in Figure 2.B, the practical consequence is to split the target sectors into technology and non-technology components (indicated by the dashed and dotted areas), where, starting at the top of the 14