# Energy and GHG Emissions

The value of energy aggregate in sector $j$ in country $r$, $ETOT_{j,r,t}$, is subject to productivity improvements, $EE_{j,r,t}$ based on the growth model. These productivity improvements are introduced at the capital–energy bundle level, $KE_{j,r,t}$.

$$ETOT_{j,r,t} = a_E EE_{j,r,t} KE_{j,r,t} \left( \frac{PKE_{j,r,t}}{PE_{j,r,t}}\right)^{\sigma_{KE}}$$

Using CES functional forms with variables in monetary units leads to inconsistencies when trying to retrieve physical quantities. In our case, this matters for energy consumption, production, and trade, and their consequences for CO2 emissions1). Therefore, in addition to accounting relations in constant dollars, MIRAGE-e integrates a parallel accounting in energy physical quantities (in million tons of oil equivalent, Mtoe) allowing CO2 emissions to be computed (in million tons of carbon dioxide, MtCO2). Since the CES architecture does not maintain coherence in physical quantities, MIRAGE-e introduces energy- and country-specific adjustment coefficients. These two aggregation coefficients allow our basic energy accounting relationships to remain valid. This means that the quantity produced by one country $EY_{e,r,t}$ must equal the demand in this country both local, $ED_{e,r,t}$ and from abroad, $EDEM_{e,r,s,t}$ ; and energy consumption (by households, $EC_{e,s,t}$ and firms, $EEIC_{e,j,s,t}$) in one country must equal its local and foreign demand.

$$EY_{e,r,t} = ED_{e,r,t} + \sum_{s} EDEM_{e,r,s,t}$$ $$EC_{e,s,t} + \sum_j EEIC_{e,j,s,t} = ED_{e,s,t} + \sum_r EDEM_{e,r,s,t}$$

The corresponding adjustment coefficient, $AgDem_{e,r,t}$ (resp. $AgCons_{e,r,t}$) rescales the country's demand (resp. consumption) such that it matches the physical quantities produced (resp. demanded). In turn, only energy quantity produced is proportional to the volume production $Y$ due to its being above rather than inside the CES. The epsilons below are constant conversion coefficients calibrated from the energy quantity data; they allow us to link energy quantities with corresponding volumes of demand for local good, $D_{e,r,t}$, bilateral demand, $DEM_{e,r,t}$, local final consumption, $C_{e,s,t}$ and local intermediate consumption, $EIC_{e,j,s,t}$.

$$EY_{e,r,t} = \epsilon_{e,r}^{Y} Y_{e,r,t}$$ $$ED_{e,r,t} = \epsilon_{e,r}^{D} AgDem_{e,r,t} D_{e,r,t}$$ $$EDEM_{e,r,s,t} = \epsilon_{e,r,s}^{DEM} AgDem_{e,r,t} DEM_{e,r,s,t}$$ $$EC_{e,s,t} = \epsilon_{e,s}^{C} AgCons_{e,s,t} C_{e,s,t}$$ $$EEIC_{e,j,s,t} = \epsilon_{e,j,s}^{EIC} AgCons_{e,s,t} EIC_{e,j,s,t}$$

Emissions occur at three different levels :

• Final consumption of energy goods (only CO2)
• Intermediate consumption of energy goods (only CO2)
• Emissions related to production process (non-CO2 gases)

Therefore, CO2 emissions are dealt with in a different way as other gases:

• CO2 emissions are recovered as proportional to the energy quantities consumed, using energy-, sector- and country-specific factors determined by the data. This means that the accounting correction coefficient applies to these emissions.
• Other GHG emissions enter the production function directly and are left as-is.

1) Preliminary simulations of MIRAGE-e showed that there could be a gap of more than 20% between a country’s energy consumption and energy demanded if proportionality was assumed between monetary and physical values.