Numerical solution of dynamic equilibrium models under Poisson uncertainty

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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. Terms of use: Documents inJEL-Code: C630, E210, O410.

Resurrecting the New-Keynesian Model: (Un)Conventional Policy and the Taylor Rule

“…In this way, we can separate the solution in the time dimension from the solution in the policy space, which turns out to be computationally more robust and less expensive. 20 Following the idea in Posch and Trimborn (2013) we obtain the unknown derivatives starting from the solution of the deterministic system, then iteratively definec…”

Natural Disasters and Macroeconomic Performance

“…Kellenberg and Mobarak 2008;Hallegatte 2013, andPosch andTrimborn 2013). Ex ante mitigation in response to disaster risk exposure is certainly an important aspect for a proper quantitative assessment of the impact of disasters on GDP.…”

Stochastic Optimization for Multispecies Fisheries in the Barents Sea

“…To our knowledge, three species continuous time model with stochastic stock dynamics are very rare. The reasons for the lack of multispecies stochastic bioeconomic models are due to unavailability of analytical solutions (Kar & Chaudhuri, 2004;Posch & Trimborn, 2010) and computational difficulties particularly in solving nonlinear dynamic models in higher dimensions (Munos & Zidani, 2005;Singh, Weninger, & Doyle, 2006). In this study, we develop a multispecies model that not only considers the interactions among these species but also takes into account of the physical and biological or environmental system uncertainties by including stochasticity in the stock growth dynamics.…”