Numerical solution of dynamic equilibrium models under Poisson uncertainty

Arbeitspapier

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: CESifo Working Paper ; No. 3431

Classification and Topics

• Classification: Wirtschaft ; Computational Techniques; Simulation Modeling ; Macroeconomics: Consumption; Saving; Wealth ; One, Two, and Multisector Growth Models
• Subject: continuous-time DSGE ; Poisson uncertainty ; waveform relaxation ; Dynamisches Gleichgewicht ; Kontrolltheorie ; Stochastischer Prozess ; Algorithmus ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Posch, Olaf ; Trimborn, Timo
• Event: Veröffentlichung
• (who): Center for Economic Studies and ifo Institute (CESifo)
• (where): Munich
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/46280
• Last update: 10.03.2025, 11:43 AM CET