Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery
AbstractWe 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. --
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Bibliographic InfoPaper provided by Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW) in its series IWQW Discussion Paper Series with number 05/2010.
Date of creation: 2010
Date of revision:
stochastic Ramsey-type growth; utility maximization; stochastic differential equations; explicit closed-form sample path dynamics; economic recovery; Monte Carlo simulations; steady-state;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-11-13 (All new papers)
- NEP-DGE-2010-11-13 (Dynamic General Equilibrium)
- NEP-FDG-2010-11-13 (Financial Development & Growth)
- NEP-ORE-2010-11-13 (Operations Research)
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