IDEAS home Printed from https://ideas.repec.org/p/usi/wpaper/815.html
   My bibliography  Save this paper

The usual robust control framework in discrete time: Some interesting results

Author

Listed:
  • Marco Paolo Tucci

Abstract

By applying robust control the decision maker wants to make good decisions when his model is only a good approximation of the true one. Such decisions are said to be robust to model misspecification. In this paper it is shown that the application of the usual robust control framework in discrete time problems is associated with some interesting, if not unexpected, results. Results that have far reaching consequences when robust control is applied sequentially, say every year in fiscal policy or every quarter (month) in monetary policy. This is true when unstructured uncertainty à la Hansen and Sargent is used, both in the case of a “probabilistically sophisticated” and a non-“probabilistically sophisticated” decision maker, or when uncertainty is related to unknown structural parameters of the model.

Suggested Citation

  • Marco Paolo Tucci, 2019. "The usual robust control framework in discrete time: Some interesting results," Department of Economics University of Siena 815, Department of Economics, University of Siena.
    • Handle: RePEc:usi:wpaper:815
    as

    Download full text from publisher

    File URL: http://repec.deps.unisi.it/quaderni/815.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Julio J. Rotemberg & Michael Woodford, 1998. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy: Expanded Version," NBER Technical Working Papers 0233, National Bureau of Economic Research, Inc.
    2. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    3. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    4. Ben S. Bernanke & Julio J. Rotemberg (ed.), 1997. "NBER Macroeconomics Annual 1997," MIT Press Books, The MIT Press, edition 1, volume 1, number 026252242x, December.
    5. Hansen, Lars Peter & Sargent, Thomas J., 2011. "Robustness and ambiguity in continuous time," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1195-1223, May.
    6. Marc P. Giannoni, 2007. "Robust optimal monetary policy in a forward-looking model with parameter and shock uncertainty," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(1), pages 179-213.
    7. Tetlow, Robert J. & von zur Muehlen, Peter, 2001. "Simplicity versus optimality: The choice of monetary policy rules when agents must learn," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 245-279, January.
    8. Christopher A. Sims, 2001. "Pitfalls of a Minimax Approach to Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 51-54, May.
    9. Ben S. Bernanke & Julio J. Rotemberg, 1997. "Editorial in "NBER Macroeconomics Annual 1997, Volume 12"," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 1-6, National Bureau of Economic Research, Inc.
    10. Lars P. Hansen & Thomas J. Sargent, 2016. "Sets of Models and Prices of Uncertainty," NBER Working Papers 22000, National Bureau of Economic Research, Inc.
    11. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    12. Barro, Robert J, 1979. "On the Determination of the Public Debt," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 940-971, October.
    13. Hansen, Lars-Peter & Sargent, Thomas-J, 2001. "Acknowledgement Misspecification in Macroeconomic Theory," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(S1), pages 213-227, February.
    14. Michael Woodford, 1999. "Optimal Monetary Policy Inertia," Manchester School, University of Manchester, vol. 67(s1), pages 1-35.
    15. J. Tetlow, Robert & von zur Muehlen, Peter, 2001. "Robust monetary policy with misspecified models: Does model uncertainty always call for attenuated policy?," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 911-949, June.
    16. Michael Woodford, 1999. "Optimal monetary policy inertia," Proceedings, Federal Reserve Bank of San Francisco.
    17. Hansen, Lars Peter & Sargent, Thomas J., 2003. "Robust control of forward-looking models," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 581-604, April.
    18. Campbell, John Y, 1987. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," Econometrica, Econometric Society, vol. 55(6), pages 1249-1273, November.
    19. Elizabeth Chase MacRae, 1972. "Linear Decision with Experimentation," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 4, pages 437-447, National Bureau of Economic Research, Inc.
    20. Bernhard, Pierre, 2002. "Survey Of Linear Quadratic Robust Control," Macroeconomic Dynamics, Cambridge University Press, vol. 6(1), pages 19-39, February.
    21. Giannoni, Marc P., 2002. "Does Model Uncertainty Justify Caution? Robust Optimal Monetary Policy In A Forward-Looking Model," Macroeconomic Dynamics, Cambridge University Press, vol. 6(1), pages 111-144, February.
    22. Hansen, Lars Peter & Sargent, Thomas J., 2007. "Recursive robust estimation and control without commitment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 1-27, September.
    23. Ben S. Bernanke & Julio J. Rotemberg, 1997. "NBER Macroeconomics Annual 1997, Volume 12," NBER Books, National Bureau of Economic Research, Inc, number bern97-1, March.
    24. Marco P. Tucci, 2009. "How Robust is Robust Control in the Time Domain?," Department of Economics University of Siena 569, Department of Economics, University of Siena.
    25. Hansen, Lars Peter & Sargent, Thomas J. & Wang, Neng E., 2002. "Robust Permanent Income And Pricing With Filtering," Macroeconomic Dynamics, Cambridge University Press, vol. 6(1), pages 40-84, February.
    26. S. Rao Aiyagari & Albert Marcet & Thomas J. Sargent & Juha Seppala, 2002. "Optimal Taxation without State-Contingent Debt," Journal of Political Economy, University of Chicago Press, vol. 110(6), pages 1220-1254, December.
    27. Peter Von zur Muehlen, 2001. "Activist vs. non-activist monetary policy: optimal rules under extreme uncertainty," Finance and Economics Discussion Series 2001-02, Board of Governors of the Federal Reserve System (U.S.).
    28. Onatski, Alexei & Stock, James H., 2002. "Robust Monetary Policy Under Model Uncertainty In A Small Model Of The U.S. Economy," Macroeconomic Dynamics, Cambridge University Press, vol. 6(1), pages 85-110, February.
    29. Lars Peter Hansen & Thomas J. Sargent, 2001. "Acknowledging Misspecification in Macroeconomic Theory," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 519-535, July.
    30. Heaton, John, 1993. "The Interaction between Time-Nonseparable Preferences and Time Aggregation," Econometrica, Econometric Society, vol. 61(2), pages 353-385, March.
    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. Marco P. Tucci, 2009. "How Robust is Robust Control in the Time Domain?," Department of Economics University of Siena 569, Department of Economics, University of Siena.
    2. Marco P. Tucci, 2021. "How Robust is Robust Control in Discrete Time?," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 279-309, August.
    3. Michael Paetz, 2007. "Robust Control and Persistence in the New Keynesian Economy," Quantitative Macroeconomics Working Papers 20711, Hamburg University, Department of Economics.
    4. André Marine Charlotte & Dai Meixing, 2018. "Learning, robust monetary policy and the merit of precaution," The B.E. Journal of Macroeconomics, De Gruyter, vol. 18(2), pages 1-20, June.
    5. Tetlow, Robert J. & von zur Muehlen, Peter, 2009. "Robustifying learnability," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 296-316, February.
    6. Kilponen, Juha, 2004. "Robust expectations and uncertain models: a robust contol approach with application to the new Keynesian economy," Bank of Finland Research Discussion Papers 5/2004, Bank of Finland.
    7. Levin, Andrew T. & Williams, John C., 2003. "Robust monetary policy with competing reference models," Journal of Monetary Economics, Elsevier, vol. 50(5), pages 945-975, July.
    8. Marine Charlotte André & Meixing Dai, 2018. "The limits to robust monetary policy in a small open economy with learning agents," Working Papers of BETA 2018-45, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    9. Marc P. Giannoni, 2007. "Robust optimal monetary policy in a forward-looking model with parameter and shock uncertainty," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(1), pages 179-213.
    10. Marc Giannoni & Michael Woodford, 2004. "Optimal Inflation-Targeting Rules," NBER Chapters, in: The Inflation-Targeting Debate, National Bureau of Economic Research, Inc.
    11. Olalla, Myriam García & Gómez, Alejandro Ruiz, 2011. "Robust control and central banking behaviour," Economic Modelling, Elsevier, vol. 28(3), pages 1265-1278, May.
    12. Marco Tucci, 2006. "Understanding the Difference Between Robust Control and Optimal Control in a Linear Discrete-Time System with Time-Varying Parameters," Computational Economics, Springer;Society for Computational Economics, vol. 27(4), pages 533-558, June.
    13. Dai, Meixing & Spyromitros, Eleftherios, 2012. "A Note On Monetary Policy, Asset Prices, And Model Uncertainty," Macroeconomic Dynamics, Cambridge University Press, vol. 16(5), pages 777-790, November.
    14. Giordani, Paolo & Soderlind, Paul, 2004. "Solution of macromodels with Hansen-Sargent robust policies: some extensions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2367-2397, December.
    15. Marc Giannoni, 2006. "Robust Optimal Policy in a Forward-Looking Model with Parameter and Shock Uncertainty," NBER Working Papers 11942, National Bureau of Economic Research, Inc.
    16. Steinsson, Jon, 2003. "Optimal monetary policy in an economy with inflation persistence," Journal of Monetary Economics, Elsevier, vol. 50(7), pages 1425-1456, October.
    17. William A. Brock & Steven N. Durlauf, 2004. "Elements of a Theory of Design Limits to Optimal Policy," Manchester School, University of Manchester, vol. 72(s1), pages 1-18, September.
    18. Nikolov, Kalin & Aoki, Kosuke, 2005. "Rule-Based Monetary Policy Under Central Banking Learning," CEPR Discussion Papers 5056, C.E.P.R. Discussion Papers.
    19. André Marine Charlotte & Medina Espidio Sebastián, 2022. "Optimal Robust Monetary Policy in a Small Open Economy," Working Papers 2022-17, Banco de México.
    20. A. Hakan Kara, 2002. "Robust Targeting Rules for Monetary Policy," Discussion Papers 0208, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.

    More about this item

    Keywords

    Linear quadratic tracking problem; optimal control; robust control; time-varying parameters;
    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
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

    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:usi:wpaper:815. 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: Fabrizio Becatti (email available below). General contact details of provider: https://edirc.repec.org/data/desieit.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.