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Analytical and Numerical Solution of a Poisson RBC model

  • Schlegel, Christoph
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    This paper analyses a RBC model in continuous time featuring deterministic incremental development of technology and stochastic fundamental inventions arriving according to a Poisson process. Other than in standard RBC models, shocks are uncorrelated, irregular and rather seldom. In two special cases analytical solutions are presented. In the general case a delay differential equation (DDE) has to be solved. Standard numerical solution methods fail, because the steady state is path dependent. A new solution based on a modified method of steps for DDEs provides not only approximations but also upper and lower bounds for optimal consumption path and steady state.

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    File URL: http://econstor.eu/bitstream/10419/22709/1/ddpe200405.pdf
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    Paper provided by Dresden University of Technology, Faculty of Business and Economics, Department of Economics in its series Dresden Discussion Paper Series in Economics with number 05/04.

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    Date of creation: 2004
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    Handle: RePEc:zbw:tuddps:0504
    Contact details of provider: Postal: 01062 Dresden
    Phone: ++49 351 463 2196
    Fax: ++49 351 463 7739
    Web page: http://www.tu-dresden.de/wiwi/
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    1. Robert J. Barro & N. Gregory Mankiw & Xavier Sala-i-Martin, 1992. "Capital Mobility in Neoclassical Models of Growth," NBER Working Papers 4206, National Bureau of Economic Research, Inc.
    2. Boucekkine, Raouf & del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1999007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    3. Stephen Redding, 2002. "Path Dependence, Endogenous Innovation, and Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1215-1248, November.
    4. George W. Stadler, 1994. "Real Business Cycles," Journal of Economic Literature, American Economic Association, vol. 32(4), pages 1750-1783, December.
    5. Raouf Boucekkine & Omar Licandro & Christopher Paul, . "Differential-Difference Equations in Economics: On the Numerical Solution of Vintage Capital Growth Models," Computing in Economics and Finance 1996 _036, Society for Computational Economics.
    6. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
    7. Benhabib, Jess & Rustichini, Aldo, 1994. "A note on a new class of solutions to dynamic programming problems arising in economic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 18(3-4), pages 807-813.
    8. Walde, Klaus, 1999. "Optimal Saving under Poisson Uncertainty," Journal of Economic Theory, Elsevier, vol. 87(1), pages 194-217, July.
    9. Walde, Klaus, 2002. "The economic determinants of technology shocks in a real business cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 1-28, November.
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