1. Local and global dynamics of Ramsey model: From continuous to discrete time
- Author
-
Elisabetta Michetti and Małgorzata Guzowska
- Subjects
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie ,Steady state ,Discretization ,Applied Mathematics ,Numerical analysis ,05 social sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Monotonic function ,Fixed point ,01 natural sciences ,010305 fluids & plasmas ,Discrete time and continuous time ,0502 economics and business ,0103 physical sciences ,Convergence (routing) ,State space ,Applied mathematics ,050207 economics ,Mathematical Physics ,Mathematics - Abstract
The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.
- Published
- 2018