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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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    More about this item

    Keywords

    Business cycle models with poisson shocks; RBC models in continuous time; Delay differential equations;
    All these keywords.

    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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