[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v60y2015icp112-133.html
   My bibliography  Save this article

Using nonlinear model predictive control for dynamic decision problems in economics

Author

Listed:
  • Grüne, Lars
  • Semmler, Willi
  • Stieler, Marleen
Abstract
This paper presents a new approach to solve dynamic decision models in economics. The proposed procedure, called Nonlinear Model Predictive Control (NMPC), relies on the iterative solution of optimal control problems on finite time horizons and is well established in engineering applications for stabilization and tracking problems. Only quite recently, extensions to more general optimal control problems including those appearing in economic applications have been investigated. Like Dynamic Programming (DP), NMPC does not rely on linearization techniques but uses the full nonlinear model and in this sense provides a global solution to the problem. However, unlike DP, NMPC only computes one optimal trajectory at a time, thus avoids to grid the state space and for this reason the computational demand grows much more moderately with the space dimension than for DP. In this paper we explain the basic idea of NMPC, give a proof concerning the accuracy of NMPC for discounted optimal control problems, present implementational details, and demonstrate the ability of NMPC to solve dynamic decision problems in economics by solving low and high dimensional examples, including models with multiple equilibria, tracking and stochastic problems.

Suggested Citation

  • Grüne, Lars & Semmler, Willi & Stieler, Marleen, 2015. "Using nonlinear model predictive control for dynamic decision problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 112-133.
    • Handle: RePEc:eee:dyncon:v:60:y:2015:i:c:p:112-133
    DOI: 10.1016/j.jedc.2015.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016518891500158X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2015.08.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sims, Christopher A., 2005. "Rational inattention: a research agenda," Discussion Paper Series 1: Economic Studies 2005,34, Deutsche Bundesbank.
    2. Alexander J. Zaslavski, 2014. "Turnpike Phenomenon and Infinite Horizon Optimal Control," Springer Optimization and Its Applications, Springer, edition 127, number 978-3-319-08828-0, June.
    3. Parra-Alvarez, Juan Carlos, 2018. "A Comparison Of Numerical Methods For The Solution Of Continuous-Time Dsge Models," Macroeconomic Dynamics, Cambridge University Press, vol. 22(6), pages 1555-1583, September.
    4. Grune, Lars & Semmler, Willi, 2004. "Using dynamic programming with adaptive grid scheme for optimal control problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2427-2456, December.
    5. Roch, Francisco & Uhlig, Harald, 2018. "The dynamics of sovereign debt crises and bailouts," Journal of International Economics, Elsevier, vol. 114(C), pages 1-13.
    6. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    7. Barro, Robert J & Mankiw, N Gregory & Sala-i-Martin, Xavier, 1995. "Capital Mobility in Neoclassical Models of Growth," American Economic Review, American Economic Association, vol. 85(1), pages 103-115, March.
    8. Juillard, Michel & Villemot, Sébastien, 2011. "Multi-country real business cycle models: Accuracy tests and test bench," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 178-185, February.
    9. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    10. Brock, William A. & Scheinkman, JoseA., 1976. "Global asymptotic stability of optimal control systems with applications to the theory of economic growth," Journal of Economic Theory, Elsevier, vol. 12(1), pages 164-190, February.
    11. Semmler, Willi & Greiner, Alfred & Diallo, Bobo & Rezai, Armon & Rajaram, Anand, 2007. "Fiscal policy, public expenditure composition, and growth theory and empirics," Policy Research Working Paper Series 4405, The World Bank.
    12. Eo, Yunjong, 2008. "Bayesian Analysis of DSGE Models with Regime Switching," MPRA Paper 13910, University Library of Munich, Germany, revised 11 Feb 2009.
    13. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
    14. Mikhail Kaganovich, 1985. "Efficiency of Sliding Plans in a Linear Model with Time-Dependent Technology," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 691-702.
    15. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    16. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
    17. Greiner, Alfred & Semmler, Willi (ed.), 2008. "The Global Environment, Natural Resources, and Economic Growth," OUP Catalogue, Oxford University Press, number 9780195328233.
    18. Greiner, Alfred & Gruene, Lars & Semmler, Willi, 2014. "Economic growth and the transition from non-renewable to renewable energy," Environment and Development Economics, Cambridge University Press, vol. 19(4), pages 417-439, August.
    19. Costas Azariadis & Allan Drazen, 1990. "Threshold Externalities in Economic Development," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(2), pages 501-526.
    20. Gustav Feichtinger & Peter M. Kort & Richard F. Hartl & Franz Wirl, 2001. "The Dynamics of a Simple Relative Adjustment Cost Framework," German Economic Review, Verein für Socialpolitik, vol. 2(3), pages 255-268, August.
    21. Marco Gallegati & Mauro Gallegati & James Bernard Ramsey & Willi Semmler, 2011. "The US Wage Phillips Curve across Frequencies and over Time," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(4), pages 489-508, August.
    22. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    23. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448, Elsevier.
    24. R. F. Hartl & P. M. Kort & G. Feichtinger & F. Wirl, 2004. "Multiple Equilibria and Thresholds Due to Relative Investment Costs," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 49-82, October.
    25. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
    26. Simon Gilchrist & Egon Zakrajsek, 2012. "Credit Spreads and Business Cycle Fluctuations," American Economic Review, American Economic Association, vol. 102(4), pages 1692-1720, June.
    27. J. v. Neumann, 1945. "A Model of General Economic Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 13(1), pages 1-9.
    28. Thierry Bréchet & Carmen Camacho & Vladimir M. Veliov, 2012. "Adaptive Model-Predictive Climate Policies in a Multi-Country Setting," Documents de travail du Centre d'Economie de la Sorbonne 12029, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    29. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2009. "Understanding Markov-switching rational expectations models," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1849-1867, September.
    30. Manuel S. Santos & Jesus Vigo, 1995. "Accuracy estimates for a numerical approach to stochastic growth models," Discussion Paper / Institute for Empirical Macroeconomics 107, Federal Reserve Bank of Minneapolis.
    31. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, April.
    32. Haunschmied, Josef L. & Kort, Peter M. & Hartl, Richard F. & Feichtinger, Gustav, 2003. "A DNS-curve in a two-state capital accumulation model: a numerical analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 701-716, February.
    33. Geoffrey Heal, 2009. "The Economics of Renewable Energy," NBER Working Papers 15081, National Bureau of Economic Research, Inc.
    34. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    35. Christopher A. Sims, 2006. "Rational Inattention: Beyond the Linear-Quadratic Case," American Economic Review, American Economic Association, vol. 96(2), pages 158-163, May.
    36. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
    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. Grune, Lars & Semmler, Willi, 2004. "Using dynamic programming with adaptive grid scheme for optimal control problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2427-2456, December.
    2. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    3. Viktors Ajevskis, 2019. "Generalised Impulse Response Function as a Perturbation of a Global Solution to DSGE Models," Working Papers 2019/04, Latvijas Banka.
    4. Stephanie Becker & Lars Grüne & Willi Semmler, 2007. "Comparing accuracy of second-order approximation and dynamic programming," Computational Economics, Springer;Society for Computational Economics, vol. 30(1), pages 65-91, August.
    5. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    6. Lars Grüne & Willi Semmler, 2007. "Asset pricing with dynamic programming," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 233-265, May.
    7. Lars Grüne & Christopher M. Kellett & Steven R. Weller, 2017. "On the Relation Between Turnpike Properties for Finite and Infinite Horizon Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 727-745, June.
    8. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    9. Evans, Martin D.D. & Hnatkovska, Viktoria, 2012. "A method for solving general equilibrium models with incomplete markets and many financial assets," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1909-1930.
    10. Martin D. D. Evans & Viktoria Hnatkovska, 2005. "Solving General Equilibrium Models with Incomplete Markets and Many Assets," NBER Technical Working Papers 0318, National Bureau of Economic Research, Inc.
    11. Ernst, Ekkehard & Semmler, Willi & Haider, Alexander, 2017. "Debt-deflation, financial market stress and regime change – Evidence from Europe using MRVAR," Journal of Economic Dynamics and Control, Elsevier, vol. 81(C), pages 115-139.
    12. Fernández-Villaverde, Jesús & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Estimating dynamic equilibrium models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 216-229.
    13. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    14. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    15. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    16. José Cao-Alvira, 2010. "Finite Elements in the Presence of Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 35(4), pages 355-370, April.
    17. Özer Karagedikli & Troy Matheson & Christie Smith & Shaun P. Vahey, 2010. "RBCs AND DSGEs: THE COMPUTATIONAL APPROACH TO BUSINESS CYCLE THEORY AND EVIDENCE," Journal of Economic Surveys, Wiley Blackwell, vol. 24(1), pages 113-136, February.
    18. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    19. Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Solving DSGE models with perturbation methods and a change of variables," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2509-2531, December.
    20. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.

    More about this item

    Keywords

    Complex decision models; Long and short horizon models; Dynamic optimization; Multiple equilibria; Regime changes; NMPC;
    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

    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:eee:dyncon:v:60:y:2015:i:c:p:112-133. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.