Advanced Search
MyIDEAS: Login to save this paper or follow this series

Perturbation Solution of Nonlinear Rational Expectations Models


Author Info

  • Peter A. Zadrozny

    (Bureau of Labor Statistics)

  • Baoline Chen

    (Rutgers University)


The paper derives and illustrates a convenient implementation of a perturbation method for computing an approximate perfect foresight solution of a nonlinear rational-expectations model. The solution space is the set of finite Taylor-series approximations. In discussing this setting, Gaspar and Judd (1997) wrote the higher-order Taylor terms in an algebraically unstructured form. Choosing an algebraic structure for the Taylor terms imparts a related structure to the solution equations, which facilitates understanding and design of a computer program. This paper contributes by providing such a structure. By generalizing a "good definition" of matrix derivatives (Magnus and Neudecker, 1988) to higher-order arrays, the paper shows how to derive structured solution equations for any model and any order of Taylor approximation in terms of conventional linear algebraic operations on vectors and matrices. The computations involve three major steps: (i) solve a nonlinear vector equation to obtain the constant term of the solution; (ii) solve a matrix polynomial equation to obtain the linear term of the solution; (iii) solve K-2 systems of linear equations to obtain remaining higher-order terms of a K -term solution. The computations are illustrated with a reduction of Taylor's (1993) G7-country macroeconomic model. Step (ii) is implemented with an eigenvalue method for solving a matrix polynomial equation (Zadrozny, 1998).

Download Info

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1999 with number 334.

as in new window
Date of creation: 01 Mar 1999
Date of revision:
Handle: RePEc:sce:scecf9:334

Contact details of provider:
Postal: CEF99, Boston College, Department of Economics, Chestnut Hill MA 02467 USA
Fax: +1-617-552-2308
Web page:
More information through EDIRC

Related research



No references listed on IDEAS
You can help add them by filling out this form.


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

Cited by:
  1. Baoline Chen & Peter A. Zadrozny, 2003. "Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem," Computational Economics, Society for Computational Economics, vol. 21(1_2), pages 45-64, 02.
  2. 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.
  3. Hans M. Amman & David A. Kendrick, 2003. "A Classification System for Economic Stochastic Control Models," Computing in Economics and Finance 2003 114, Society for Computational Economics.


This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:sce:scecf9:334. 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: (Christopher F. Baum).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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