"The time-elimination technique in practice: an application to models of endogenous growth with public capital", Seventh Viennese Workshop on optimal control, dynamic games and nonlinear dynamics, Vienna , May 24-26, 2000

This paper analyzes and compares the transitional dynamics of two models of endogenous growth with private and public capital. The basic difference between the models refers to the production function assumed in each case: i.e., a CES and a Jones – Manuelli (JM) specification.

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 that provide the correspondent systems of non-linear differential equations with boundary conditions. Next, the paper accomplishes the numerical study of the dynamics towards the steady state by employing the time elimination technique (designed by Mulligan and Sala-i-Martin, 1991). The calibration and simulation of the models along the lines of the time elimination procedure allows us to understand the transitional dynamics more deeply.

The main results may be summarized as follows:

1. Both models predict endogenous growth at positive rates in the steady state and display the convergence property. However, their transitions towards the steady state are slightly different: it is faster and more uneven in the JM case, and more gradual for the CES function.
2. The sensitivity analysis gives some interesting insights for policymakers in order to speed up the transition towards the equilibrium, and also suggests that, in the case of the JM specification, the privatization of part of the public capital stock may be more efficient for the economy.
3. Finally, the time elimination technique is found to be an effective procedure in order to get some insight of the performance of complex dynamic systems.

Key words: endogenous growth models, public capital, Time Elimination.

JEL codes: O 5, C 6.