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

The Blanchard And Kahn' S Conditions In Macro-Econometric Models With Perfect Foresight

Contents:

Author Info

  • Jean-Pierre Laffargue

    (CEPREMAP et TEAM-CED)

Registered author(s):

    Abstract

    Many recent large macro-econometric models assume perfect foresight (for instance the multinational models Multimod Mark 3 and Quest 2). This choice has been made possible by the development of simulation algorithms, which are powerful and easy to use (for example the command Stacks and Lkroot in Troll and the software Dynare which works under Gauss and Matlab - see Juillard). However, the existence and the uniqueness of a solution for these models are not warranted a priori. Blanchard and Kahn established local conditions for these properties, which are easy to check, in terms of eigenvalues computed at the steady state of the model. However, these conditions can be used only on linear models, with coefficients independent of time, and with exogenous variables taking constant values after some date. Unfortunately, macro-econometric models are non-linear, their linear approximation has coefficients which change over time, in the long run many variables grow at positive and different rates, and these models may present an hysteresis. This paper explains how to overcome these difficulties, and apply the Blanchard and Kahn's conditions on this kind of models.We start by imposing a homogeneity condition on the model, which implies that it has a balanced growth path solution. Afterward, we can compute a linear approximation of the model around this path, and require that the solution of the model tends toward the balanced growth path when time increases indefinitely. We call this last condition stability in the absolute difference. However, some coefficients of the linear approximation are geometrical functions of time, and it is impossible to use the results of Blanchard and Kahn in this kind of situation (although the eigenvalues, but not the eigenvectors, of the linear approximation are independent of time).We can overcome this difficulty if we make a change of variables and put all of them on a common trend (with the same growth rate). If this trend has a zero rate, we will say that we write the model in reduced variables and that we require its stability in the relative difference. If the common growth rate is the highest balanced growth rate among all the variables, , we will say that we write the model in expanded variables, and that we require its stability in the expanded difference. In these both situations the coefficients of the linear approximation of the model are constant and we can apply Blanchard and Kahn's results. The eigenvalues of the second linear approximation are equal to times those of the first. If the Blanchard and Kahn's conditions are satisfied for the model written in reduced variables and in the expanded variable, then the model has a unique solution stable in the absolute difference.Hysteresis can be easily identified by the existence of eigenvalues equal to 1 in the model written in reduced variables. In models of endogenous growth, hysteresis is relative to the indeterminacy of the output level in the steady state. In more traditional macro-econometric models, indeterminacy concerns the price level when monetary policy follows a kind of Taylor's rule, in conformity to an old idea of Wicksell.The first section of the paper presents the results of Blanchard and Kahn, with the extension to the case of hysteresis developed by Giavazzi and Wyplosz. In the second section we present a very simple example to investigate some of the difficulties met with large econometric models, which are not taken into account by Blanchard and Kahn. The third section uses a much richer example, the endogenous growth model by Lucas, which includes all the difficulties we want to deal with in this paper. Finally, in the last section, we give a general theoretical treatment of our problem.Our results can also be applied to the study of the stability of more traditional macro-econometric models, which assume adaptive expectations, and where the current state of the economy does not depend on the future states foreseen by the model.

    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/cef00/papers/paper225.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)
    Download Restriction: no

    Bibliographic Info

    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2000 with number 225.

    as in new window
    Length:
    Date of creation: 05 Jul 2000
    Date of revision:
    Handle: RePEc:sce:scecf0:225

    Contact details of provider:
    Postal: CEF 2000, Departament d'Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas, 25,27, 08005, Barcelona, Spain
    Fax: +34 93 542 17 46
    Email:
    Web page: http://enginy.upf.es/SCE/
    More information through EDIRC

    Related research

    Keywords:

    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. Delphine BÉRAUD, 1998. "Croissance et endettement dans un modèle à deux pays," Annales d'Economie et de Statistique, ENSAE, issue 51, pages 149-168.
    2. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
    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:scecf0:225. 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.