PACE (Policy Analysis based on Computable Equilibrium) is a multi-sector, multi-region computable general equilibrium (CGE) model of global production, consumption, trade and energy use. It is established in economic research and policy consulting.
PACE is implemented in MPSGE (Mathematical Programming System for General Equilibrium Analysis), a subsystem of GAMS (General Algebraic Modeling System) for solving the MCP (mixed complementarity problem). The model covers 23 regions and 36 sectors with a focus on energy-intensive industries. It runs until 2050 in five-year time steps and solves for a sequence of market equilibria. The model consists of a set of equations (i.e. market clearing, zero profit, and income balance conditions) that describe the world economy. For each year, the solution algorithm finds the set of prices and quantities that solves these equations.

Zero-profit conditions and market clearing conditions follow directly from the assumptions of profit maximization of firms, perfect competition among them, utility maximization of consumers, constant returns to scale in production, and homotheticity of consumer preferences. The latter class of conditions determines the price of each output good as the unit cost to produce this good. This cost equals the marginal and (given constant returns to scale) the average cost of production.

Each region consists of a representative consumer and representative producers (one for each production sector). The consumer chooses a bundle of consumption goods that maximizes her utility given her preferences and her budget. The budget is determined by her income received from selling the primary production factors (labour, capital and fossil-fuels) that she owns. The model also assumes that each region can obtain a certain amount of emission permits in each period. Final demand of the representative consumer is modelled as a constant elasticity of substitution (CES) composite good which combines an energy aggregate with a non-energy aggregate (analogue to the production structure described below). Substitution patterns within the non-energy aggregate are reflected by a Cobb-Douglas function. The energy aggregate consists of several energy goods combined with a constant elasticity of substitution.

The producers choose bundles of production goods that maximize their profits given their production possibilities. The production possibilities are determined by technologies, which efficiently transfer certain amounts of input goods and production factors into certain amounts of unique, sector specific output goods. Production factors entail labour, capital, (both perfectly mobile between sectors within a region) and sector specific resources for agriculture, oil and gas extraction, and coal and other mining. The labour supply is fixed for each region. There is full mobility among sectors and no unemployment. The production functions are nested CES functions with the following nesting structure: At the top level, non-energy inputs are employed with an aggregate of energy, capital and labour. At the second level, a CES function describes the substitution possibilities between the energy aggregate and the aggregate of labour and capital. At the third level, capital and labour (and if applicable: sector specific resources) are combined with a constant elasticity of substitution. Moreover, at the third level, the energy aggregate consists of electricity and a fossil fuel input. The latter input is further split into coal, gas and oil associated with different elasticities of substitution and with emission permits in fixed proportions (in the presence of a carbon pricing scheme). The CES specification allows producers to substitute fossil fuel inputs by other inputs as a reaction to an increasing carbon price. The extent of substitution, however, is limited by the choice of the cost minimizing input bundle given the elasticities of substitution.

Model improvements in R&D and human capital

Within the MONROE project, knowledge capital, which is gathered by investments in research and innovation, is introduced as an additional primary production factor. This enables the representation of endogenous technological progress in order to assess the impact of R&I policies.

The way we choose to introduce Endogenous Technological Change (ETC) in the PACE model is similar to the QUEST III model (Ratto et al., 2009), with the main difference that PACE is a static model instead of a fully intertemporal one. Innovation and increasing returns are modelled using the monopolistic competition framework with fixed costs. The sectoral output already in PACE is now considered as the aggregation of Nj product varieties. The production of one single variety requires the purchase of a patent to start production, which is purchased once as a fixed cost. Patents are produced in a separate R&D sector and are assumed to be sector-specific. This implies that there are as many R&D sectors as production sectors. This is obviously an assumption, which allows us to specify different cost structures for R&D activities in each sector. An example for this reasoning is the pharmaceutical industry where more capital is spent on R&D than in the services sector.

Patents, as a good, are produced by the R&D sector. Firms in this sector make positive profits from renting patents out to goods producers. The revenue source for these firms is the price of a patent. Monopolistic competitors instead earn a flow of positive profits. As a result, we have introduced a new production factor into the model, knowledge. However, knowledge is assumed to be nonexcludable, therefore nobody owns it.

In each sector, sectoral output is the aggregation of Nj product varieties supplied by monopolistically competitive firms. Each firm acquires monopoly rights in a niche market by purchasing a patented technology from an R&D sub-sector. The firm bears an initial fixed cost to acquire the patent necessary to produce each good. The R&D sub-sector's sector-specific patent-generating activity is a function of the R&D investment, the sectoral patent stock and the nationwide patent stock for a level of R&D investment.

The opportunity cost of R&D is in units of sectoral output: R&D activities compete with goods production to employ labour. Despite the assumption of sector-specific patents, the knowledge required to produce the single technology might well build on general knowledge. This property is captured by the spillovers from the national (average) knowledge stock.

Apart from the calibration to a benchmark year of the world economy, there are a set of assumptions concerning future growth patterns of regional GDP and sectoral energy use, in order to make multi-period analysis possible in order to compare the effects of endogenous R&D within the model. The GDP growth is introduced by increasing the production factors of each region by their corresponding rates. Assuming production and utility functions as in the base year, the model will endogenously balance trade imbalances caused by asymmetric growth of regions. However, the introduction of changes in energy intensity of economic activities is achieved by changing the production functions themselves, and in turn the model is endogenously rebalanced.