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

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  • 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

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File URL: http://hdl.handle.net/10.1023/A:1022270430175
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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 21 (2003)
Issue (Month): 1 (February)
Pages: 45-64

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Handle: RePEc:kap:compec:v:21:y:2003:i:1:p:45-64

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Web page: http://www.springerlink.com/link.asp?id=100248
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Keywords: solving dynamic stochastic models;

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References

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  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. 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.
  3. 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.
  4. Peter A. Zadrozny & Baoline Chen, 1999. "Perturbation Solution of Nonlinear Rational Expectations Models," Computing in Economics and Finance 1999 334, Society for Computational Economics.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  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.

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