Complete closedform solution to a stochastic growth model and corresponding speed of economic recovery
We consider a continuoustime neoclassical onesector stochastic growth model of Ramseytype with CRRA utility and CobbDouglas technology, where each of the following components are exposed to exogeneous uncertainties (shocks): capital stock K, effectiveness of labor A, and labor force L; the corresponding dynamics is modelled by a system of three interrelated stochastic differential equations. For this framework, we solve completely explicitly the problem of a social planner who seeks to maximize expected lifetime utility of consumption. In particular, for any (e.g. shortterm) timehorizon t > 0 we obtain in closed form the sample paths of the economy values Kt,At, Lt and the optimal consumption copt(Kt,At, Lt) as well as the nonequilibrium sample paths of the per capita effective capital stock kt = Kt / At Lt . Moreover, we also deduce explicitly the limiting longterm behaviour of kt expressed by the corresponding steadystate equilibrium distribution. As illustration, we present some Monte Carlo simulations where the abovementioned economy is considerably disturbed (out of equilibrium) by a sudden crash but recovers well within a realisticsize timeperiod.
Year of publication: 
2010


Authors:  Feicht, Robert ; Stummer, Wolfgang 
Publisher: 
Erlangen : FriedrichAlexanderUniversität ErlangenNürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW) 
Subject:  Stochastisches Wachstumsmodell  Schock  Wirtschaftliche Anpassung  Soziale Wohlfahrtsfunktion  Dynamisches Gleichgewicht  MonteCarloMethode  Theorie  stochastic Ramseytype growth  utility maximization  stochastic differential equations  explicit closedform sample path dynamics  economic recovery  Monte Carlo simulations  steadystate 
Series:  IWQW Discussion Papers ; 05/2010 

Type of publication:  Book / Working Paper 
Type of publication (narrower categories):  Working Paper 
Language:  English 
Other identifiers:  63745314X [GVK] hdl:10419/41470 [Handle] RePEc:zbw:iwqwdp:052010 [RePEc] 
Source: 