IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2102.07431.html
   My bibliography  Save this paper

On the Basis of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics

Author

Listed:
  • Yuhki Hosoya

Abstract

We consider the classical Ramsey-Cass-Koopmans capital accumulation model and present three examples in which the Hamilton-Jacobi-Bellman (HJB) equation is neither necessary nor sufficient for a function to be the value function. Next, we present assumptions under which the HJB equation becomes a necessary and sufficient condition for a function to be the value function, and using this result, we propose a new method for solving the original problem using the solution to the HJB equation. Our assumptions are so mild that many macroeconomic growth models satisfy them. Therefore, our results ensure that the solution to the HJB equation is rigorously the value function in many macroeconomic models, and present a new solving method for these models.

Suggested Citation

  • Yuhki Hosoya, 2021. "On the Basis of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics," Papers 2102.07431, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:2102.07431
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2102.07431
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, December.
    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. Yuhki Hosoya, 2022. "On the Fragility of the Basis on the Hamilton-Jacobi-Bellman Equation in Economic Dynamics," Papers 2203.10595, arXiv.org, revised Jan 2024.
    2. Antony Millner & Daniel Heyen, 2021. "Prediction: The Long and the Short of It," American Economic Journal: Microeconomics, American Economic Association, vol. 13(1), pages 374-398, February.
    3. Fernando de Holanda Barbosa, 2017. "Hyperinflation: Inflation Tax and Economic Policy Regime," SpringerBriefs in Economics, in: Exploring the Mechanics of Chronic Inflation and Hyperinflation, chapter 0, pages 61-75, Springer.
    4. Stanley Fischer, 1991. "Growth, Macroeconomics, and Development," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 329-379, National Bureau of Economic Research, Inc.
    5. John Haltiwanger & Scott Schuh, 1999. "Gross job flows between plants and industries," New England Economic Review, Federal Reserve Bank of Boston, issue Mar, pages 41-64.
    6. Spiro E. Stefanou, 1987. "Technical Change, Uncertainty, and Investment," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 69(1), pages 158-165.
    7. Stefan Ried, 2009. "Putting Up a Good Fight: The Galí-Monacelli Model versus “The Six Major Puzzles in International Macroeconomicsâ€," SFB 649 Discussion Papers SFB649DP2009-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Fredrik Carlsson & Dinky Daruvala & Olof Johansson‐Stenman, 2005. "Are People Inequality‐Averse, or Just Risk‐Averse?," Economica, London School of Economics and Political Science, vol. 72(287), pages 375-396, August.
    9. Christian Groth & Karl-Josef Koch & Thomas Steger, 2006. "Rethinking the Concept of Long-Run Economic Growth," CESifo Working Paper Series 1701, CESifo.
    10. J.P.G. Reijnders, 2007. "Impulse or propagation? How the tides turned in Business Cycle Theory," Working Papers 07-07, Utrecht School of Economics.
    11. Menzio, Guido & Shi, Shouyong & Sun, Hongfei, 2013. "A monetary theory with non-degenerate distributions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2266-2312.
    12. Thomas Seegmuller, 2005. "Steady state analysis and endogenous fluctuations in a finance constrained model," Cahiers de la Maison des Sciences Economiques v05029, Université Panthéon-Sorbonne (Paris 1).
    13. Smulders, Sjak & Gradus, Raymond, 1996. "Pollution abatement and long-term growth," European Journal of Political Economy, Elsevier, vol. 12(3), pages 505-532, November.
    14. Andersen, Torben M., 2005. "Product market integration, wage dispersion and unemployment," Labour Economics, Elsevier, vol. 12(3), pages 379-406, June.
    15. Xavier Pautrel, 2015. "Abatement Technology and the Environment–Growth Nexus with Education," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 61(3), pages 297-318, July.
    16. McCallum, Bennett T, 2000. "Theoretical Analysis Regarding a Zero Lower Bound on Nominal Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(4), pages 870-904, November.
    17. Radwanski, Juliusz, 2020. "On the Purchasing Power of Money in an Exchange Economy," MPRA Paper 104244, University Library of Munich, Germany.
    18. repec:hal:wpspec:info:hdl:2441/2961 is not listed on IDEAS
    19. Loewy, Michael B., 1995. "Equilibrium policy with dynamically naive agents," Journal of Macroeconomics, Elsevier, vol. 17(2), pages 319-331.
    20. Etienne Gagnon & David López-Salido & Nicolas Vincent, 2013. "Individual Price Adjustment along the Extensive Margin," NBER Macroeconomics Annual, University of Chicago Press, vol. 27(1), pages 235-281.
    21. Picard, Pierre M. & Toulemonde, Eric, 2006. "Firms agglomeration and unions," European Economic Review, Elsevier, vol. 50(3), pages 669-694, April.

    More about this item

    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:arx:papers:2102.07431. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.