IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v21y2003i1_2p45-64.html
   My bibliography  Save this article

Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem

Author

Listed:
  • Baoline Chen
  • Peter A. Zadrozny

    (Bureau of Labor Statistics, 2 Massachusetts Ave., NE, Washington, DC 20212, U.S.A.)

Abstract

The paper obtains two principal results. First, using a new definition of higher-order (>2) matrix derivatives, the paper derives a recursion for computing any Gaussian multivariate moment. Second, the paper uses this result in a perturbation method to derive equations for computing the 4th-order Taylor-series approximation of the objective function of the linear-quadratic exponential Gaussian (LQEG) optimal control problem. Previously, Karp (1985) formulated the 4th multivariate Gaussian moment in terms of MacRae's definition of a matrix derivative. His approach extends with difficulty to any higher (>4) multivariate Gaussian moment. The present recursion straightforwardly computes any multivariate Gaussian moment. Karp used his formulation of the Gaussian 4th moment to compute a 2nd-order approximation of the finite-horizon LQEG objective function. Using the simpler formulation, the present paper applies the perturbation method to derive equations for computing a 4th-order approximation of the infinite-horizon LQEG objective function. By illustrating a convenient definition of matrix derivatives in the numerical solution of the LQEG problem with the perturbation method, the paper contributes to the computational economist's toolbox for solving stochastic nonlinear dynamic optimization problems.

Suggested Citation

  • Baoline Chen & Peter A. Zadrozny, 2003. "Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem," Computational Economics, Springer;Society for Computational Economics, vol. 21(1_2), pages 45-64, February.
  • Handle: RePEc:kap:compec:v:21:y:2003:i:1_2:p:45-64
    as

    Download full text from publisher

    File URL: http://journals.kluweronline.com/issn/0927-7099/contents
    Download Restriction: Access to the full text of the articles in this series is restricted.
    ---><---

    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. 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.
    2. Karp, Larry S., 1985. "Higher moments in the linear-quadratic-gaussian problem," Journal of Economic Dynamics and Control, Elsevier, vol. 9(1), pages 41-54, September.
    3. Peter A. Zadrozny & Baoline Chen, 1999. "Perturbation Solution of Nonlinear Rational Expectations Models," Computing in Economics and Finance 1999 334, Society for Computational Economics.
    4. Baoline Chen & A. Zadrozny, 2000. "Estimated U.S. Manufacturing Capital And Productivity Based On An Estimated Dynamic Economic Model," Computing in Economics and Finance 2000 133, Society for Computational Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    2. Andrew Binning, 2013. "Third-order approximation of dynamic models without the use of tensors," Working Paper 2013/13, Norges Bank.
    3. Baoline Chen & Peter A. Zadrozny, 2005. "Multi-Step Perturbation Solution of Nonlinear Rational Expectations Models," Computing in Economics and Finance 2005 254, Society for Computational Economics.
    4. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
    5. Chen, Baoline & Zadrozny, Peter A., 2009. "Multi-step perturbation solution of nonlinear differentiable equations applied to an econometric analysis of productivity," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2061-2074, April.
    6. Anderson, Evan W. & Hansen, Lars Peter & Sargent, Thomas J., 2012. "Small noise methods for risk-sensitive/robust economies," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 468-500.

    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. Rajeev Dhawan & Karsten Jeske & Pedro Silos, 2010. "Productivity, Energy Prices and the Great Moderation: A New Link," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 715-724, July.
    2. John Bound & Breno Braga & Joseph M. Golden & Gaurav Khanna, 2015. "Recruitment of Foreigners in the Market for Computer Scientists in the United States," Journal of Labor Economics, University of Chicago Press, vol. 33(S1), pages 187-223.
    3. Paul Castillo & Carlos Montoro & Vicente Tuesta, 2005. "Inflation Premium and Oil Price Volatility," Working Papers Central Bank of Chile 350, Central Bank of Chile.
    4. Ajevskis Viktors, 2017. "Semi-global solutions to DSGE models: perturbation around a deterministic path," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(2), pages 1-28, April.
    5. Lim, G.C. & McNelis, Paul D., 2008. "Computational Macroeconomics for the Open Economy," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262123061, February.
    6. Den Haan, Wouter J. & De Wind, Joris, 2012. "Nonlinear and stable perturbation-based approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1477-1497.
    7. Rahul Anand & Eswar S. Prasad, 2010. "Optimal Price Indices for Targeting Inflation Under Incomplete Markets," NBER Working Papers 16290, National Bureau of Economic Research, Inc.
    8. Viktors Ajevskis, 2019. "Generalised Impulse Response Function as a Perturbation of a Global Solution to DSGE Models," Working Papers 2019/04, Latvijas Banka.
    9. 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.
    10. Gelain, Paolo & Lansing, Kevin J., 2014. "House prices, expectations, and time-varying fundamentals," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 3-25.
    11. 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.
    12. Rajeev Dhawan & Karsten Jeske, 2008. "Energy Price Shocks and the Macroeconomy: The Role of Consumer Durables," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(7), pages 1357-1377, October.
    13. 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.
    14. Wieland, Volker & Cwik, Tobias & Müller, Gernot J. & Schmidt, Sebastian & Wolters, Maik, 2012. "A new comparative approach to macroeconomic modeling and policy analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 523-541.
    15. Kline, Patrick, 2008. "Understanding Sectoral Labor Market Dynamics: An Equilibrium Analysis of the Oil and Gas Field Services Industry," Working Papers 43, Yale University, Department of Economics.
    16. Guay C. Lim & Paul D. McNelis, 2005. "Real Exchange Rate and Current Account Dynamics with Sticky Prices and Distortionary Taxes," DNB Working Papers 056, Netherlands Central Bank, Research Department.
    17. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    18. 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.
    19. Adema, Y. & Bonenkamp, J. & Meijdam, A.C., 2011. "Retirement Flexibility and Portfolio Choice," Discussion Paper 2011-077, Tilburg University, Center for Economic Research.
    20. 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.

    More about this item

    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:kap:compec:v:21:y:2003:i:1_2:p:45-64. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.springer.com .

    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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.