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On automatic derivation of first order conditions in dynamic stochastic optimisation problems

Author

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  • Klima, Grzegorz
  • Retkiewicz-Wijtiwiak, Kaja

Abstract

This note presents an algorithm for deriving first order conditions applicable to the most common optimisation problems encountered in dynamic stochastic models automatically. Given a symbolic library or a computer algebra system one can efficiently derive first order conditions which can then be used for solving models numerically (steady state, linearisation).

Suggested Citation

  • Klima, Grzegorz & Retkiewicz-Wijtiwiak, Kaja, 2014. "On automatic derivation of first order conditions in dynamic stochastic optimisation problems," MPRA Paper 55612, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:55612
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    File URL: https://mpra.ub.uni-muenchen.de/55612/1/MPRA_paper_55612.pdf
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    References listed on IDEAS

    as
    1. Adjemian, Stéphane & Bastani, Houtan & Juillard, Michel & Karamé, Fréderic & Maih, Junior & Mihoubi, Ferhat & Mutschler, Willi & Perendia, George & Pfeifer, Johannes & Ratto, Marco & Villemot, Sébasti, 2011. "Dynare: Reference Manual Version 4," Dynare Working Papers 1, CEPREMAP, revised Mar 2021.
    2. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
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    Cited by:

    1. Janusz Jabłonowski, 2018. "Implications of Transitory and Permanent Changes in Tax Rates for Poland," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 2, pages 73-97.
    2. Einian, Majid & Nili, Masoud, 2016. "Elasticity of Intertemporal Substitution: An Investigation in Iran," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 11(2), pages 207-223, April.
    3. Klima, Grzegorz & Podemski, Karol & Retkiewicz-Wijtiwiak, Kaja & Sowińska, Anna E., 2015. "Smets-Wouters '03 model revisited - an implementation in gEcon," MPRA Paper 64440, University Library of Munich, Germany.

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    More about this item

    Keywords

    DSGE; stochastic optimisation; first order conditions; symbolic computations;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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