Endogenous technological progress in a multi-sector growth model

This paper presents an endogenous growth model driven by human capital, where human capital can be allocated across three sectors: the production of the final consumption good, the educational sector and the production of technological capital (in the form of knowledge or ideas). In our model, which also includes public expenditure and population growth, labor augmenting technical progress is endogenous and this enriches the transitional dynamics of the economy. With respect to ideas-based growth models, we assume knowledge is produced according to a neoclassical technology, combining ideas and human capital. Such an assumption is motivated by empirical works showing the existence of significant decreasing returns in the creation of ideas at the aggregate level (as Kortum, 1993; and Pessoa, 2005) and of the weak relationship between some inputs of the knowledge production process (as the number of researchers) and the total factor productivity growth rate (as Jones, 2002). Under some general conditions, this economy exhibits the existence of a steady state equilibrium and an unstable multidimensional manifold. Numerical examples are provided to show the existence of stable arms.