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Title:Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery PDF Logo
Authors:Feicht, Robert
Stummer, Wolfgang
Issue Date:2010
Series/Report no.:IWQW discussion paper series 05/2010
Abstract:We consider a continuous-time neoclassical one-sector stochastic growth model of Ramsey-type with CRRA utility and Cobb-Douglas 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. short-term) time-horizon 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 non-equilibrium sample paths of the per capita effective capital stock kt = Kt / At Lt . Moreover, we also deduce explicitly the limiting long-term behaviour of kt expressed by the corresponding steady-state 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 realistic-size time-period.
Subjects:stochastic Ramsey-type growth
utility maximization
stochastic differential equations
explicit closed-form sample path dynamics
economic recovery
Monte Carlo simulations
steady-state
Document Type:Working Paper
Appears in Collections:IWQW Discussion Paper Series, FAU Erlangen-Nürnberg

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