Abstract
In this paper we investigate the underlying structure of the Lucas (1988) endogenous growth model. We derive analytically, the restrictions on the parameter space that are necessary and sufficient for the existence of balanced growth paths and saddle-path stable local dynamics. We demonstrate that in contrast to the original model, with the addition of an external effect and depreciation in the human capital sector, the Lucas model can be made consistent with the high degrees of intertemporal elasticities of substitution increasingly estimated in the empirical literature—even if there is a significant degree of increasing returns to scale in the physical production sector of the economy. Finally we demonstrate that for a given baseline rate of steady state growth, with the inclusion of modest degrees of depreciation and external effects to the human capital production process, the model can accommodate the widest possible range of economies—including those characterized by low discount factors, high elasticities of intertemporal substitution, increasing returns in the final goods sector, and also both the high rates of population growth and steady state per-capita output growth we observe in many parts of the world today.
Highlights
Along with the growing body of empirical evidence pointing towards higher values for the intertemporal elasticity of substitution, this paper demonstrates that by adding a degree of sector-specific external effects and/or depreciation to the human capital sector, the two-sector model can be made consistent with high rates of intertemporal elasticity of substitution, as the well as high rates of population growth and high rates of output growth we commonly observe in many countries in Africa, Asia, and Central and South America
Fixing the baseline rate of steady state growth, we demonstrate that including modest degrees of depreciation and external effects to the human capital production process, enables us to calibrate the model for the widest possible range of economies—including those characterized by low discount factors, high elasticities of intertemporal substitution, increasing returns in the production sector, as well as the high rates of population growth found in much of Africa, Asia and Latin America
What emerges in each of the six panels is that given this high rate of intertemporal substitution, interior balanced growth paths only emerge if there is at least some curvature in human capital production at the private level
Summary
Attfield and Temple (2010) point out how sensitive the relationships between steady state ratios and growth are to the intertemporal elasticity of substitution With this in mind, along with the growing body of empirical evidence pointing towards higher values for the intertemporal elasticity of substitution, this paper demonstrates that by adding a degree of sector-specific external effects and/or depreciation to the human capital sector, the two-sector model can be made consistent with high rates of intertemporal elasticity of substitution, as the well as high rates of population growth and high rates of output growth we commonly observe in many countries in Africa, Asia, and Central and South America. Fixing the baseline rate of steady state growth, we demonstrate that including modest degrees of depreciation and external effects to the human capital production process, enables us to calibrate the model for the widest possible range of economies—including those characterized by low discount factors, high elasticities of intertemporal substitution, increasing returns in the production sector, as well as the high rates of population growth found in much of Africa, Asia and Latin America
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