IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v21y2003i1p45-64.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 Zadrozny

Abstract

The paper obtains two principal results. First, using a new definition ofhigher-order (>2) matrix derivatives, the paper derives a recursion forcomputing any Gaussian multivariate moment. Second, the paper uses this resultin a perturbation method to derive equations for computing the 4th-orderTaylor-series approximation of the objective function of the linear-quadraticexponential Gaussian (LQEG) optimal control problem. Previously, Karp (1985)formulated the 4th multivariate Gaussian moment in terms of MacRae'sdefinition of a matrix derivative. His approach extends with difficulty to anyhigher (>4) multivariate Gaussian moment. The present recursionstraightforwardly computes any multivariate Gaussian moment. Karp used hisformulation of the Gaussian 4th moment to compute a 2nd-order approximationof the finite-horizon LQEG objective function. Using the simpler formulation,the present paper applies the perturbation method to derive equations forcomputing a 4th-order approximation of the infinite-horizon LQEG objectivefunction. By illustrating a convenient definition of matrix derivatives in thenumerical solution of the LQEG problem with the perturbation method, the papercontributes to the computational economist's toolbox for solving stochasticnonlinear dynamic optimization problems. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Baoline Chen & Peter 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), pages 45-64, February.
    • Handle: RePEc:kap:compec:v:21:y:2003:i:1:p:45-64
    DOI: 10.1023/A:1022270430175
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1022270430175
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1022270430175?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. 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.
    2. Evan W. Anderson & Lars Peter Hansen, "undated". "Perturbation Methods for Risk-Sensitive Economies," Computing in Economics and Finance 1996 _062, Society for Computational Economics.
    3. 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.
    4. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    5. 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.
    6. Peter A. Zadrozny & Baoline Chen, 1999. "Perturbation Solution of Nonlinear Rational Expectations Models," Computing in Economics and Finance 1999 334, 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. Yi Wen & Huabin Wu, 2011. "Dynamics of externalities: a second-order perspective," Review, Federal Reserve Bank of St. Louis, vol. 93(May), pages 187-206.
    2. Paul Castillo & Carlos Montoro & Vicente Tuesta, 2005. "Inflation Premium and Oil Price Volatility," Working Papers Central Bank of Chile 350, Central Bank of Chile.
    3. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    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. repec:hum:wpaper:sfb649dp2013-024 is not listed on IDEAS
    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. 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.
    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. De Paoli, Bianca & Scott, Alasdair & Weeken, Olaf, 2010. "Asset pricing implications of a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2056-2073, October.
    10. 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.
    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. 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.
    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. 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. Ajevskis, Viktors, 2019. "Nonlocal Solutions To Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2544-2571, September.
    18. Ajevskis, Viktors, 2014. "Global Solutions to DSGE Models as a Perturbation of a Deterministic Path," MPRA Paper 55145, University Library of Munich, Germany.
    19. Wieland, V. & Afanasyeva, E. & Kuete, M. & Yoo, J., 2016. "New Methods for Macro-Financial Model Comparison and Policy Analysis," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1241-1319, Elsevier.
    20. Castillo, Paul & Montoro, Carlos & Tuesta, Vicente, 2020. "Inflation, oil price volatility and monetary policy," Journal of Macroeconomics, Elsevier, vol. 66(C).
    21. 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.

    More about this item

    Keywords

    solving dynamic stochastic models;

    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:p:45-64. 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: 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. RePEc uses bibliographic data supplied by the respective publishers.