Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery

Robert Feicht and Wolfgang Stummer

No 05/2010, FAU Discussion Papers in Economics from Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics

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.

Keywords: stochastic Ramsey-type growth; utility maximization; stochastic differential equations; explicit closed-form sample path dynamics; economic recovery; Monte Carlo simulations; steady-state (search for similar items in EconPapers)
Date: 2010
New Economics Papers: this item is included in nep-dge, nep-fdg and nep-ore
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:iwqwdp:052010

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