Working Paper: CEPR ID: DP5414
Authors: Fabrice Collard; Omar Licandro; Luis Puch
Abstract: 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.
Keywords: DDES; Delay; Shooting Method; Time-to-Build
JEL Codes: C63; E32; O40
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| delays (C41) | cycles in economic models (E32) |
| past capital (E22) | present production (E23) |
| optimal control theory with delays (C61) | advanced differential equation (ADE) (C22) |
| advanced differential equation (ADE) (C22) | alters dynamics of the system (C69) |
| increasing size of the delay (C41) | impacts model's internal dynamics (C69) |
| increasing size of the delay (C41) | oscillations in the convergence path (C62) |