IDEAS home Printed from https://ideas.repec.org/a/kap/jeczfn/v84y2005i1p71-94.html
   My bibliography  Save this article

A New Matrix Theorem: Interpretation in Terms of Internal Trade Structure and Implications for Dynamic Systems

Author

Listed:
  • Albert E. Steenge
  • Mark J. P. M. Thissen

Abstract

Economic systems often are described in matrix form as x=Mx. We present a new theorem for systems of this type where M is square, nonnegative and indecomposable. The theorem discloses the existence of additional economic relations that have not been discussed in the literature up to now, and gives further insight in the economic processes described by these systems. As examples of the relevance of the theorem we focus on static and dynamic closed Input-Output (I-O) models. We show that the theorem is directly relevant for I-O models formulated in terms of difference or differential equations. In the special case of the dynamic Leontief model the system’s behavior is shown to depend on the properties of matrix M=A + C where A and C are the matrices of intermediate and capital coefficients, respectively. In this case, C is small relative to A and a perturbation result can be employed which leads directly to a statement on the system’s eigenvalues. This immediately suggests a solution to the well-known problem of the instability of the dynamic Leontief model. Copyright Springer-Verlag Wien 2005

Suggested Citation

  • Albert E. Steenge & Mark J. P. M. Thissen, 2005. "A New Matrix Theorem: Interpretation in Terms of Internal Trade Structure and Implications for Dynamic Systems," Journal of Economics, Springer, vol. 84(1), pages 71-94, February.
    • Handle: RePEc:kap:jeczfn:v:84:y:2005:i:1:p:71-94
    DOI: 10.1007/s00712-004-0094-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00712-004-0094-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00712-004-0094-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Theodore Mariolis & Lefteris Tsoulfidis, 2012. "On Brody’S Conjecture: Facts And Figures From The Us Economy," Discussion Paper Series 2012_06, Department of Economics, University of Macedonia, revised May 2012.
    2. Theodore Mariolis, 2015. "Norm Bounds and A Homographic Approximation for the Wage–Profit Curve," Metroeconomica, Wiley Blackwell, vol. 66(2), pages 263-283, May.
    3. Schilirò, Daniele, 2007. "Theories and models of structural dynamics: an ‘ideal’ general framework ?," MPRA Paper 38256, University Library of Munich, Germany.
    4. Daniele SCHILIR, 2012. "Structural Change And Models Of Structural Analysis Theories Principles And Methods," Journal of Advanced Research in Law and Economics, ASERS Publishing, vol. 3(2), pages 31-49.
    5. Schilirò, Daniele, 2009. "Structural models and structural change: analytical principles and methodological issues," MPRA Paper 24480, University Library of Munich, Germany.
    6. Iliadi, Fotoula & Mariolis, Theodore & Soklis, George & Tsoulfidis, Lefteris, 2012. "Bienenfeld’s approximation of production prices and eigenvalue distribution: some more evidence from five European economies," MPRA Paper 36282, University Library of Munich, Germany.
    7. Mariolis, Theodore & Tsoulfidis, Lefteris, 2010. "Eigenvalue distribution and the production price-profit rate relationship in linear single-product systems: theory and empirical evidence," MPRA Paper 43716, University Library of Munich, Germany.

    More about this item

    Keywords

    leverage matrix; stability analysis; input-output analysis; dynamic input-output models; C62; C67; D57;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • D57 - Microeconomics - - General Equilibrium and Disequilibrium - - - Input-Output Tables and Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jeczfn:v:84:y:2005:i:1:p:71-94. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.