Two practical algorithms for solving rational expectations models
This paper describes the E-Newton and E-QNewton algorithms for solving rational expectations (RE) models. Both algorithms treat a model's RE terms as exogenous variables whose values are iteratively updated until they (hopefully) satisfy the RE requirement. In E-Newton, the updates are based on Newton's method; E-QNewton uses an efficient form of Broyden's quasi-Newton method. The paper shows that the algorithms are reliable, fast enough for practical use on a mid-range PC, and simple enough that their implementation does not require highly specialized software. The evaluation of the algorithms is based on experiments with three well-known macro models--the Smets-Wouters (SW) model, EDO, and FRB/US--using code written in EViews, a general-purpose, easy-to-use software package. The models are either linear (SW and EDO) or mildly nonlinear (FRB/US). A test of the robustness of the algorithms in the presence of substantial nonlinearity is based on modified versions of each model that include a smoothed form of the constraint that the short-term rate of interest cannot fall below zero. In two single-simulation experiments with the standard and modified versions of the models, E-QNewton is found to be faster than E-Newton, except for solutions of small-to-medium sized linear models. In a multi-simulation experiment using the standard versions of the models, E-Newton dominates E-QNewton.
|Date of creation:||2011|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.federalreserve.gov/
More information through EDIRC
|Order Information:||Web: http://www.federalreserve.gov/pubs/feds/fedsorder.html|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
- Fisher, P. G. & Hallett, A. J. Hughes, 1988. "Efficient solution techniques for linear and non-linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 12(4), pages 635-657, November.
- Juillard, Michel, 1996. "Dynare : a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm," CEPREMAP Working Papers (Couverture Orange) 9602, CEPREMAP.
When requesting a correction, please mention this item's handle: RePEc:fip:fedgfe:2011-44. 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: (Kris Vajs)
If references are entirely missing, you can add them using this form.