# MaGE model and EconMap database

The MaGE model used to build MIRAGE-e baseline is an open-source long-term growth model (Fouré, Bénassy-Quéré, and Fontagné 2013). These projections are based on a three-factor (capital, labor, energy) production function at the 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 \(L_{r,t}\): \[Y_{r,t} = \left[ \left(A_{r,t} K_{r,t}^\alpha L_{r,t}^{1-\alpha}\right)^\frac{\sigma-1}{\sigma} + \left( B_{r,t} E_{r,t}\right)^\frac{\sigma-1}{\sigma} \right]^\frac{\sigma}{\sigma-1},\] where \(A_{r,t}\) 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 (Mankiw, Romer, and Weil May, 1992), \(\alpha\) is set to \(0.3\). In turn, the \(\sigma=0.2\) parameter is calibrated, within the range estimated by 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 production volume 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 progress. 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 Source code
- MaGE’s projections: the EconMap database

## References

*Economics of Transition*21 (4): 617–54. https://doi.org/10.1111/ecot.12023.

*The Quarterly Journal of Economics*107 (2): 407–37. http://www.jstor.org/stable/2118477.

*Energy Economics*30 (6): 2964–79. https://doi.org/10.1016/j.eneco.2008.05.008.