The Human Development Index and an endogenous growth model

Most of the currently existing endogenous growth models were developed within and for industrial countries, i.e. for a well endowed world. Most developing countries, especially in Africa, however, have low capital endowments, low rates of capital accumulation and low technological capabilities. For developing countries, GDP, GDP growth or the per capita versions of both are not the only important issues. African countries --have large young populations, which can be considered as huge potential amounts of human capital. For this potential human capital to become productive human capital, the population needs to be well educated and healthy, both of which are major development concerns addressed by many development programmes for Africa. These aspects are captured for instance in the Millennium Development Goals or in the Human Development Reports. A growth model for developing countries should therefore put special emphasis on these non-monetary issues of development. The endogenous growth model developed in this paper explicitly considers health and education next to consumption in the utility function.The model is based on the Lucas-Uzawa model of human capital accumulation and models both (education and health) sectors individually. The constant intertemporal elasticity of substitution utility function includes consumption, education and health factors. Final output production is modelled with a usual Cobb-Douglas production function depending on physical capital and healthy human capital. Human capital accumulation is modelled analogous to the original Lucas model. The increase in the health level of the population depends on the number of specialisations in the health sector. The model is calibrated using parameters from the literature and both, the long run balanced growth path and the transition towards this growth path, are calculated.The long run equilibrium of the model can be solved numerically for a variety of parameter specifications. Central results are growth rate, labour shares in production, education and health sectors, propensity to consume or savings rate, return to capital and the health level, which is assumed to be constant in the long run equilibrium. Output, consumption, physical and human capital grow at the same rate. The growth rate is positively correlated with the share of the population working in the education sector, savings rate and the health level. Labour in final output production and health sectors are substitutes. A higher preference of the present over the future has a positive influence on the final output production and consumption and a negative influence on education and health. Higher productivity in either one of the health and education sector increases the labour share in the respective sector. Still, the largest impact on the labour shares is given by the relative contribution of consumption, education and health in the utility function. As the weights for education and health increase from values close to zero to one third (implying an equal preference for consumption, education and health), so do the labour shares. This shows the importance of the valuation of education and health for the economy. Preliminary calculations of the transitional dynamics show that for values of physical and human capital or the health level far below the long run equilibrium the economy only very slowly starts to converge to the balanced growth path. The transition accelerates over time, but then slows down again as it gets closer to the balanced growth paths. For starting values in the order of one half of the final values, the transition process starts off very fast and slows down over time.