Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery
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.
Year of publication: |
2010
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Authors: | Feicht, Robert ; Stummer, Wolfgang |
Publisher: |
Nürnberg : Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW) |
Subject: | Stochastisches Wachstumsmodell | Schock | Wirtschaftliche Anpassung | Soziale Wohlfahrtsfunktion | Dynamisches Gleichgewicht | Monte-Carlo-Methode | Theorie | stochastic Ramsey-type growth | utility maximization | stochastic differential equations | explicit closed-form sample path dynamics | economic recovery | Monte Carlo simulations | steady-state |
Saved in:
freely available
Series: | IWQW Discussion Papers ; 05/2010 |
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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: |
Persistent link: https://www.econbiz.de/10010302618