Parameter identification, population and economic growth in an extended Lucas and Uzawa-type two sector model

The aim of this paper is twofold. First of all we re-examine the long-run relationship between population and economic growth. To do this we extend the Lucas-Uzawa model along two different directions: we introduce the growth of the physical capital stock into the human capital supply equation and include in the intertemporal maximization problem of the representative household a preference parameter controlling for the degree of agents’ altruism towards future generations. These two extensions allow us to capture eventual complementarity/substitutability links between physical and human capital in the production of new human capital and to study how such links, along with agents’ altruism, may impact on the interplay between economic and demographic growth along the balanced growth path equilibrium. In the second part of this paper we develop the inverse problem for this extended Lucas-Uzawa model. The method we are going to use is based on fractals and has been developed by two of the authors in recent papers. Through the solution of the inverse problem one can get the estimation of some key-parameters such as the total factor productivity, the productivity of human capital in the production of new skills, the physical capital share in total income, the inverse of the intertemporal elasticity of substitution in consumption, the depreciation rate of (physical and human) capital and the parameter controlling for the degree of altruism towards future generation