DP5414 The Short-Run Dynamics of Optimal Growth Models with Delays

Author(s): Fabrice Collard, Omar Licandro, Luis Puch
Publication Date: December 2005
Keyword(s): DDEs, delay, shooting method, time-to-build
JEL(s): C63, E32, O40
Programme Areas: International Macroeconomics
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=5414

Differential equations with advanced and delayed time arguments may arise in the optimality conditions of simple growth models with delays. Models with delayed adoption of new technologies, habit formation or learning-by-using lie in this category. In this paper we present new insight on the role of advanced time arguments to mitigate the echo effects induced by lag structures. In so doing we use optimal control theory with delays, and we propose a shooting method to deal with leads and lags in the Euler system associated to dynamic general equilibrium models in continuous time. We implement these methods to solve for the short run dynamics of a neoclassical growth model with a simple time-to-build lag.