IDEAS home Printed from https://ideas.repec.org/p/crb/wpaper/2017-10.html
   My bibliography  Save this paper

Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter

Author

Listed:
  • Pierre Bernhard

    (Université Côte d'Azur, INRIA)

  • Marc Deschamps

    (Université de Bourgogne Franche-Comté, CRESE)

Abstract

Rudolf Emil Kalman (R.E.K.) passed away on July, 2nd, 2016. Among contemporary economists Kalman is mainly remembered for his filter, an algorithm that allows recursive estimation of unobserved time varying variables in a system. However, he has also a key part on the whole of recursive macroeconomic theory as is notably expressed by Lars Ljungqvist's and Thomas Sargent's book [Ljunqvist and Sargent, 2012]. Our paper is a contribution to show the links between Kalman's works on filtering, linear quadratic optimal control, and system theory. We also provide a model on cooperative advertising to show that Kalman's works on dynamics and control can be useful in macroeconomics as in microeconomics, a domain where his contributions seem to be unfortunately less used.

Suggested Citation

  • Pierre Bernhard & Marc Deschamps, 2017. "Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter," Working Papers 2017-10, CRESE.
    • Handle: RePEc:crb:wpaper:2017-10
    as

    Download full text from publisher

    File URL: https://crese.univ-fcomte.fr/uploads/wp/WP-2017-10.pdf
    File Function: First version, 2017
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Weber, Thomas A., 2011. "Optimal Control Theory with Applications in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015730, December.
    2. Jørgensen, Steffen & Zaccour, Georges, 2014. "A survey of game-theoretic models of cooperative advertising," European Journal of Operational Research, Elsevier, vol. 237(1), pages 1-14.
    3. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    4. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, December.
    5. Petit,Maria Luisa, 2009. "Control Theory and Dynamic Games in Economic Policy Analysis," Cambridge Books, Cambridge University Press, number 9780521127158, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Acocella, Nicola & Di Bartolomeo, Giovanni, 2007. "Towards a new theory of economic policy: Continuity and innovation," MPRA Paper 4419, University Library of Munich, Germany.
    2. Nicola acocella & Giovanni Di Bartolomeo & Andrew Hughes Hallett, "undated". "The theory of economic policy: from a theory of control to a theory of conflict (resolutions)," Working Papers 91/11, Sapienza University of Rome, Metodi e Modelli per l'Economia, il Territorio e la Finanza MEMOTEF.
    3. D’Erasmo, P. & Mendoza, E.G. & Zhang, J., 2016. "What is a Sustainable Public Debt?," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 2493-2597, Elsevier.
    4. Voelkel, Michael A. & Sachs, Anna-Lena & Thonemann, Ulrich W., 2020. "An aggregation-based approximate dynamic programming approach for the periodic review model with random yield," European Journal of Operational Research, Elsevier, vol. 281(2), pages 286-298.
    5. Sergeyev, Dmitriy & Iovino, Luigi, 2018. "Central Bank Balance Sheet Policies Without Rational Expectations," CEPR Discussion Papers 13100, C.E.P.R. Discussion Papers.
    6. Reinhard Neck & Dmitri Blueschke, 2014. "“Haircuts” for the EMU periphery: virtue or vice?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(2), pages 153-175, May.
    7. Karray, Salma & Martín-Herrán, Guiomar & Zaccour, Georges, 2017. "Assessing the profitability of cooperative advertising programs in competing channels," International Journal of Production Economics, Elsevier, vol. 187(C), pages 142-158.
    8. Kazuya Kamiya & So Kubota & Kayuna Nakajima, 2017. "Real Indeterminacy of Stationary Monetary Equilibria in Centralized Economies," The Japanese Economic Review, Japanese Economic Association, vol. 68(4), pages 497-520, December.
    9. Tan, Madeleine Sui-Lay, 2016. "Policy coordination among the ASEAN-5: A global VAR analysis," Journal of Asian Economics, Elsevier, vol. 44(C), pages 20-40.
    10. Auster, Sarah & Kettering, Jeremy & Kochov, Asen, 2024. "Sequential trading with coarse contingencies," Journal of Economic Theory, Elsevier, vol. 220(C).
    11. Toshihiko Mukoyama, 2019. "Heterogeneous Jobs and the Aggregate Labour Market," The Japanese Economic Review, Springer, vol. 70(1), pages 30-50, March.
    12. D. W. K. Yeung, 2008. "Dynamically Consistent Solution For A Pollution Management Game In Collaborative Abatement With Uncertain Future Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 517-538.
    13. Ramani, Vinay & De Giovanni, Pietro, 2017. "A two-period model of product cannibalization in an atypical Closed-loop Supply Chain with endogenous returns: The case of DellReconnect," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1009-1027.
    14. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    15. Chatelain, Jean-Bernard & Ralf, Kirsten, 2021. "Hopf Bifurcation From New-Keynesian Taylor Rule To Ramsey Optimal Policy," Macroeconomic Dynamics, Cambridge University Press, vol. 25(8), pages 2204-2236, December.
    16. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    17. Pierre‐Richard Agénor & Timothy Jackson & Enisse Kharroubi & Leonardo Gambacorta & Giovanni Lombardo & Luiz A. Pereira Da Silva, 2021. "Assessing the Gains from International Macroprudential Policy Cooperation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(7), pages 1819-1866, October.
    18. Mark Egan & Tomas Philipson, 2016. "Health Care Adherence and Personalized Medicine," Working Papers 2016-H01, Becker Friedman Institute for Research In Economics.
    19. Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economics Research Papers 2015-005, Friedrich-Schiller-University Jena.
    20. Changming Ji & Chuangang Li & Boquan Wang & Minghao Liu & Liping Wang, 2017. "Multi-Stage Dynamic Programming Method for Short-Term Cascade Reservoirs Optimal Operation with Flow Attenuation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(14), pages 4571-4586, November.

    More about this item

    Keywords

    Dynamic Programming; System Theory; Linear Quadratic Optimal Control; Kalman Filter; Riccati Equation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crb:wpaper:2017-10. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Laurent Kondratuk (email available below). General contact details of provider: https://edirc.repec.org/data/crufcfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.