# Economic activity - IMACLIM

Model Documentation - IMACLIM | |
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Corresponding documentation | |

Model information | |

Institution | Centre international de recherche sur l'environnement et le développement (CIRED), Societe de Mathematiques Appliquees et de Sciences Humaines (SMASH) |

Concept | Hybrid: general equilibrium with technology explicit modules. Recursive dynamics: each year the equilibrium is solved (system of non-linear equations), in between two years parameters to the equilibrium evolve according to specified functions. |

Solution method | Imaclim-R is implemented in Scilab, and uses the fonction fsolve from a shared C++ library to solve the static equilibrium system of non-linear equations. |

Anticipation | Recursive dynamics: each year the equilibrium is solved (system of non-linear equations), in between two years parameters to the equilibrium evolve according to specified functions. |

## Modelling economic growth

### An exogenous growth engine composed of demography and labour productivity growth

The IMACLIM-R model growth engine is composed of exogenous demographic trends (See section on Population) and exogenous trends in labor productivity, as proposed in Solow's neoclassical model of economic growth (Solow 1956)1. To build these labor productivity trends we draw on stylized facts from the literature, in particular the convergence assumption (Barro and Sala-i-Martin 1992)2 and two empirical analyses on economic convergence, one investigating past trends by Maddison (1995)3, and another by Martins and al. (2005)4 looking at future trends. In the default parameterization of the model, we retain a 'leader', the US, whose labor productivity growth trend lies between 2% in the short run and 1.65% in the long run. The trends in labor productivity of the other regions catch up with that of the leader over time, i.e. their growth in labor productivity is higher the further their level of absolute labor productivity is from the leader's. All sectors within one region exhibit the same growth in labor productivity, while the respective initial levels are sector and region specific

The two sets of assumptions on demography and labor productivity growth describe natural growth (Phelps, 1961)5, i.e. the growth rate that an aggregated one-sector economy would follow under full employment of factors of production.

### Realized GDP growth is endogenous

In this multi-sectoral framework of Imaclim-R, with partial use of factors of production, the effective economic growth rate may depart from the exogenous natural growth rate trend. The structure and rate of realized growth are endogenously determined by: (i) the allocation of labor force across sectors, which is itself governed by the final demand of these sectors, and (ii) the evolution in unemployment rates, which also result from the final demand of these sectors and the constraints of installed productive capacities and their technical characteristics.

First, the twelve production sectors have different productivities, captured by unitary labor requirements for a unit of production. Therefore the effective labor productivity of the economy depends on the allocation of the labor force among production sectors. For instance, the overall productivity of labor increases through structural changes that favour the reallocation of labor towards highly productive sectors. In that case, realized economic growth can be higher than the natural growth rate. Second, exogenous labor productivity gains may not be transformed into actual growth if unemployment increases due to demand shortage or constraints on installed productive capacities.

## References

- ^ ↑ Robert M Solow (1956). A contribution to the theory of economic growth.
*The quarterly journal of economics, ()*, 65-94. - ^ ↑ Robert J Barro, Xavier Sala-i-Martin (1992). Convergence.
*Journal of political Economy, ()*, 223-251. - ^ ↑ Angus Maddison (1995). Monitoring the world economy: 1820-1992. '
**.** - ^ ↑ Joaquim Oliveira Martins, Frédéric Gonand, Pablo Antolin, Christine De la Maisonneuve, Kwang-Yeol Yoo (2005). The impact of ageing on demand, factor markets and growth. '
**.** - ^ ↑ Edmund S Phelps (1961). The golden rule of accumulation: a fable for growthmen.
*The American Economic Review, 51 (4)*, 638-643.