Transitional Dynamics and Endogenous Growth Revisited. The Case of Public Capital

Abstract

This paper explores some applications of the time elimination technique to models of endogenous growth that include two kinds of inputs (private and public capital). Two alternative specifications of the production function are considered: i.e. a CES and a Jones-Manuelli technology. Because of the homogeneity of degree one of both production functions on private and public capital considered together, these new models predict endogenous growth, but the main difference with the standard model (Barro, 1990) is that these new specifications allow for transitional dynamics towards the steady state. First, the steady state rate of growth of output is obtained for both models, by means of applying the traditional optimal control techniques. Next, the models are calibrated and simulated by applying the time elimination technique. This numerical method allows us to understand the transitional dynamics more deeply.

It also provides some insights about the speed of convergence of the model towards the steady state under each of the production function settings and for various values of the parameters. Basic results show that the speed of convergence is slower if we use a CES specification, whereas the transition is faster and less smooth if a Jones-Manuelli production function is assumed. Finally, the technique enables us to compare the results using different values of some parameters of the models.

JEL Classification: O 41, E 62, C 61