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From simple growth to numerical simulations: a primer in dynamic programming

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  • Gianluca Femminis

    () (DISCE, Università Cattolica)

Abstract

These notes provide an intuitive introduction to dynamic programming. The first two Sections present the standard deterministic Ramsey model using the Lagrangian approach. These can be skipped by whom is already acquainted with this framework. Section 3 shows how to solve the well understood Ramsey model by means of a Bellman equation, while Section 4 shows how to "guess" the solution (when this is possible). Section 5 is devoted to applications of the envelope theorem. Section 6 provides a "paper and pencil" introduction to the numerical techniques used in dynamic programming, and can be skipped by the uninterested reader. Sections 7 to 9 are devoted to stochastic modelling, and to stochastic Bellman equations. Section 10 extends the discussion of numerical techniques. An Appendix provides details about the Matlab routines used to solve the examples.

Suggested Citation

  • Gianluca Femminis, 2007. "From simple growth to numerical simulations: a primer in dynamic programming," DISCE - Quaderni dell'Istituto di Teoria Economica e Metodi Quantitativi itemq0745, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
  • Handle: RePEc:ctc:serie6:itemq0745
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    File URL: http://www.unicatt.it/Istituti/TeoriaEconomica/Quaderni/itemq0745.pdf
    File Function: First version, 2007
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    References listed on IDEAS

    as
    1. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    2. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    3. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
    4. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    5. Albert Marcet & Guido Lorenzoni, 1998. "Parameterized expectations approach; Some practical issues," Economics Working Papers 296, Department of Economics and Business, Universitat Pompeu Fabra.
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    Cited by:

    1. Enrico Bellino, 2012. "Pasinetti on Ricardo," DISCE - Quaderni dell'Istituto di Teoria Economica e Metodi Quantitativi itemq1258, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
    2. Elena Cottini & Paolo Ghinetti, 2017. "Is it the way you live or the job you have? Health effects of lifestyles and working conditions," DISCE - Working Papers del Dipartimento di Economia e Finanza def056, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
    3. Michele Tettamanzi, 2017. "E Many Pluribus Unum: A Behavioural Macro-Economic Agent Based Model," DISCE - Working Papers del Dipartimento di Economia e Finanza def062, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).

    More about this item

    Keywords

    Dynamic programming; Bellman equation; Optimal growth; Numerical techniques.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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