Growth and Convergence with a Normalized CES Production Function and Human Capital

Employing a neoclassical growth model with a constant elasticity of substitution production function, I examine the implications of assuming different values of the elasticity of substitution for the steady state growth path, growth threshold, and speed of convergence. Unlike earlier studies along these lines, I incorporate human capital, along with physical capital and raw labor, as a third input in the production function, thus eschewing the common assumption of ``perfect substitutability" between human capital and labor inputs. I find that a higher elasticity of substitution leads to a higher steady state level for physical capital and human capital per effective unit of labor. For a high enough level, the elasticity of substitution can lead to permanent growth. Similarly, for a low enough level, the elasticity of substitution can lead to permanent decline. Higher elasticity of substitution can lead to a higher speed of convergence when the baseline level of capital per effective unit of labor is greater than the steady state level. I estimate the normalized production function and find estimates for the elasticity of substitution that range between 0.7331--0.82.Models that employ the normalized aggregate production function have primarily focused on explaining the importance of the elasticity of substitution, between factors for production, for exogenous and constant savings decisions. The balance growth path for these models are invariant to the level of the elasticity of substitution. Thus, Relaxing the assumption of constant savings for capitals, I employ a neoclassical growth model with endogenous consumption and saving decisions to examine the effects of the level of the elasticity of substitution on the balance growth rate and speed of converge. I find that the effects of the elasticity of substitution on the aforementioned depend upon the initial levels of the factors of production