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Analytical and Numerical Solution of a Poisson RBC model

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  • Schlegel, Christoph

Abstract

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.

Suggested Citation

  • Schlegel, Christoph, 2004. "Analytical and Numerical Solution of a Poisson RBC model," Dresden Discussion Paper Series in Economics 05/04, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
  • Handle: RePEc:zbw:tuddps:0504
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    References listed on IDEAS

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    1. George W. Stadler, 1994. "Real Business Cycles," Journal of Economic Literature, American Economic Association, vol. 32(4), pages 1750-1783, December.
    2. 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.
    3. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
    4. Barro, Robert J & Mankiw, N Gregory & Sala-i-Martin, Xavier, 1995. "Capital Mobility in Neoclassical Models of Growth," American Economic Review, American Economic Association, vol. 85(1), pages 103-115, March.
    5. Boucekkine, Raouf & del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Journal of Economic Theory, Elsevier, vol. 88(1), pages 161-187, September.
    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. 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.
    8. 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.
    9. Walde, Klaus, 1999. "Optimal Saving under Poisson Uncertainty," Journal of Economic Theory, Elsevier, vol. 87(1), pages 194-217, July.
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    More about this item

    Keywords

    Business cycle models with poisson shocks; RBC models in continuous time; Delay differential equations;

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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