# MaGE model and EconMap database

The MaGE model used to build MIRAGE-e baseline is an opensource long-term growth model (Jean Fouré, Agnès Bénassy-Quéré, Lionel Fontagné, 2013). These projections are based on a three-factor (capital, labor, energy) production function at national level, for 167 countries.

## MaGE basics

The three factors are gathered in a CES function of energy $E_{r,t}$ and a Cobb-Douglas aggregate of capital $K_{r,t}$ and labor $L_{r,t}$:

$$Y_{r,t} = \left[ \left(A_{r,t} K_{r,t}^\alpha L_{r,t}^{1-\alpha}\right)^\frac{\sigma-1}{\sigma} + \left( B_{r,t} E_{r,t}\right)^\frac{\sigma-1}{\sigma} \right]^\frac{\sigma}{\sigma-1}$$

were $A_{r,t}$ and $B_{r,t}$ respectively are the usual TFP – in our case the efficiency of labor and capital combined – and an energy-specific productivity. In line with the literature (N Gregory Mankiw, David Romer, David N Weil, 1992), $\alpha$ is set to $0.3$. In turn, the $\sigma=0.2$ parameter is calibrated, within the range estimated by (Edwin Van der Werf, 2008) but also considering that services are not included in these estimations; and the shape of energy productivity must not be reduced to an inverse function of energy price. In addition, GDP, $Y_{r,t}$, where appropriate, is considered net of oil rents to avoid a biased measure of productivity. Oil rents are added separately and are assumed to be pure rents: the volume of production is constant, but its real value (in terms of the GDP deflator) increases with the relative price of oil.

This model is fitted with UN population projections as well as econometric estimations for capital accumulation, education, female participation in the labor force, and two types of technical progresses. The energy consumption factor is not directly projected, it is recovered from the firms' optimization program.

In particular, capital accumulation follows a permanent inventory process, where the stock of capital increases each year with investment but also can be depleted. The depletion rate is set in accordance with the MIRAGE model at 6%, whereas investment-to-GDP ratios depend on savings rates through an error-correction Feldstein-Horioka-type relationship. This allows us to relax the common assumption of a closed economy. Savings rates are determined by both the demographic and economic situations in line with life-cycle theory.

The two productivity measures follow catch-up processes. While TFP growth is fueled by education levels, energy productivity growth is tempered by the levels of GDP per capita such that it mimics the impact of sectoral changes on energy productivity during a country's development process.

## Download MaGE and its projections

The MaGE model source code and results can be downloaded from CEPII's website:

- MaGE's projections: the EconMap database

## References

^{^}Jean Fouré, Agnès Bénassy-Quéré, Lionel Fontagné, 2013. Modelling the world economy at the 2050 horizon.

*Economics of Transition*, 21, pp.617–654, ISSN 1468-0351.

^{^}N Gregory Mankiw, David Romer, David N Weil, 1992. A contribution to the empirics of economic growth.

*The quarterly journal of economics*, 107, MIT Press, pp.407–437.

^{^}Edwin Van der Werf, 2008. Production functions for climate policy modeling: An empirical analysis.

*Energy economics*, 30, Elsevier, pp.2964–2979.