Unifying Time-to-Build Theory
Social Science Research Network
In this paper we investigate how the choice of continuous or discrete time may change the dynamics of a one sector growth model with time to build. A description of the procedure used to move from the original discrete time dynamical model to its continuous counterpart is provided and its economic implications fully explained. It is indeed shown that the structure of capital, characterized by a time to build parameter, J, can be preserved but induces a deeply different analytical structure in
... e continuous and discrete model as the latter consists of a finite, 2J dimensional system of difference equations, while the former reduces to a couple of first order mixed functional differential equations, having infinite dimension. Notwithstanding this structural diversity, the main difference in the qualitative dynamic behaviour of the economy emerges only for J sufficiently small when the local transitional dynamics is characterized by damping fluctuations in continuous time but monotonic behavior in discrete time. Moreover an Hopf bifurcation always exists in the continuous model for a critical value of J. Once the economy is calibrated, damping fluctuations in the optimal path of capital are found both in discrete and continuous time but are around 6% larger in the latter. Finally a computational tool to approximate the solution of infinite dimensioned system is also presented in details.