Endogenous technological progress in a multi-sector growth model

Abstract

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.

Self-similar measures in multi-sector endogenous growth models

“…We consider first the simplest case, namely the Uzawa-Lucas (1988) two-sector model, and then an extended three-sector model, as in La Torre and Marsiglio (2010). Both the models exhibit two peculiar features: the log-CobbDouglas structure of preferences and production functions in each sector allows for a closed form solution of the Bellman equation, thus permitting to explicitly compute the optimal dynamics of the state variables; moreover, through simple log-transformations of the capital ratio variable dynamics we are able to show that the model economy converges to an invariant measure supported on some compact set which, under some restrictions on parameters, may exhibit a fractal nature (a generalized Cantor set in the case of the two-sector model, and a generalized Sierpinski gasket in the case of the three-sector model).…”

“…In Section 3 we consider the simplest form of multi-sector endogenous growth models, namely a Uzawa-Lucas (1988) model driven by human capital accumulation. In Section 4 we analyze an extended version of the model, that is a three-sector model, as in La Torre and Marsiglio (2010), in which human capital is endogenously allocated across three (physical, human and knowledge) sectors. For both the models, we derive the optimal dynamics and construct an affine IFS conjugate to the optimal dynamics of stationary variables (the physical to human capital, and, in the latter, also the knowledge to human capital ratios).…”

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AbstractWe analyze two types of stochastic discrete time multi-sector endogenous growth models, namely a basic Uzawa-Lucas (1965, 1988 model and an extended three-sector version as in La Torre and Marsiglio (2010). As in the case of sustained growth the optimal dynamics of the state variables are not stationary, we focus on the dynamics of the capital ratio variables, and we show that, through appropriate log-transformations, they can be converted into affine iterated function systems converging to an invariant distribution supported on some (possibly fractal) compact set.

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Endogenous Recombinant Growth Through Market Production of Knowledge and Intellectual Property Rights

“…25 They clearly indicate that the initial push deriving from starting above any turnpike, if on one hand entails sacrificing consumption in early times as shown by Figure 2(d), on the other hand it turns out to be sufficiently strong to 1) let the economy escape the stagnation trap otherwise forecasted by Table 1 for all active-policy regimes in which τ > 0, and 2) yield a social welfare that is strictly increasing in the τ parameter values, as it is apparent from the fifth column. Indeed, consistently with the first row in Table 1, when τ = 0 our economy happens to be born on the highest turnpikek 0 (A 0 ) and doomed to renounce growth in the long-run as the Skiba condition is not satisfied.…”

The Determinants of Long Run Economic Growth in Nigeria

“…Many variables have been considered as the key determinants of growth of modern economies. This increased the interest in identifying the underlying causes of such improvements, and different variables have been identified as possible sources of growth in the literature during the last fifty years: output, productivity, average human capital and knowledge were used in various models to capture economic growth (see, La Torre and Marsiglio (2010)). The neoclassical economists led by Solow (1956); Swan (1956); Cass (1965) and Koopmans (1965) identified the accumulation of physical capital as crucial in explaining growing economies in their exogenous growth models.…”