Advanced Search
MyIDEAS: Login

A Technique for Solving Rational-Expectations Models

Contents:

Author Info

  • Jean-Louis Brillet

    ()
    (INSEE)

Registered author(s):

    Abstract

    I consider a method using loop variables that can limit the size of the of a rational-expectations model and hopefully speed up the process of solving it. We can generally write such a model using a "Blanchard-Kahn" specification f_t(y_t, y_{t-1}, y_{t+1}, x_t) = 0 , where y is endogenous, x is exogenous, t is time and y_0 and y_{T+1} are known. Two methods are generally considered for solving such a system: Fair-Taylor and Stacked-Time. Let us consider the model (without rational expectations) y_t = f_t(y(t), y(t-1), x(t)) . Considering a particular ordering of the equations, the loop variables are the ones used through their present value before they are computed. Computing the value of y associated through g to a starting value of y_b can be done using a Gauss-Seidel iteration. This allows computation, through finite differences, of the Jacobian of y_b = g(y_b) and the application of Newton-Raphson method to a problem with the size of the number of loop variables. This technique is easily applied to rational-expectations models. In the full model, the loop variables are actually the union of the original loop variables and the leads so that, if we consider computing (not solving) the whole set of equations in one pass, only loop variables and leads affect the result. Computing the Jacobian of the whole model will be limited, and to do the Newton-Raphson process, we need realize (at most) T x n_b + (T-1) x n_l + 1 iterations and invert a matrix of dimension T x n_b + (T-1) x n_l . To evaluate the efficiency (speed and convergence probability) of this method, we use a small macro economic model of the French economy. The initial version does not use rational expectations and contains three loop variables, associated with the Keynesian loop, the price-wage loop, and the exchange rate loop. In this version, we introduce rational expectations in the investment equation (where firms are supposed to know the next production level) and in the consumption equation (where households know in advance their future revenue). We produce simulations over 20 to 100 periods to compare our method with the above in terms of speed and convergence reliability.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://fmwww.bc.edu/cef99/papers/BrilletRE.pdf
    Our checks indicate that this address may not be valid because: 404 Not Found. If this is indeed the case, please notify (Christopher F. Baum)
    File Function: main text
    Download Restriction: no

    Bibliographic Info

    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1999 with number 333.

    as in new window
    Length:
    Date of creation: 01 Mar 1999
    Date of revision:
    Handle: RePEc:sce:scecf9:333

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

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

    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.:
    as in new window
    1. Michel Juillard & Douglas Laxton, 1996. "A Robust and Efficient Method for Solving Nonlinear Rational Expectations Models," IMF Working Papers 96/106, International Monetary Fund.
    2. Jean-Pierre LAFFARGUE, 1990. "Résolution d'un modèle macroéconomique avec anticipations rationnelles," Annales d'Economie et de Statistique, ENSAE, issue 17, pages 97-119.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

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

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:sce:scecf9:333. 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.