[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/ecb/ecbwps/2008850.html
   My bibliography  Save this paper

Statistical tests and estimators of the rank of a matrix and their applications in econometric modelling

Author

Listed:
  • Camba-Méndez, Gonzalo
  • Kapetanios, George
Abstract
Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics literature where such methods are required. Four different methods to test the true rank of a general matrix are described, as well as one method that can handle the case of a matrix subject to parameter constraints associated with defineteness structures. The technical requirements for the implementation of the tests of rank of a general matrix differ and hence there are merits to all of them that justify their use in applied work. Nonetheless, we review available evidence of their small sample properties in the context of different modelling scenarios where all, or some, are applicable. JEL Classification: C12, C15, C32

Suggested Citation

  • Camba-Méndez, Gonzalo & Kapetanios, George, 2008. "Statistical tests and estimators of the rank of a matrix and their applications in econometric modelling," Working Paper Series 850, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:2008850
    as

    Download full text from publisher

    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp850.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gonzalo Camba‐Mendez & George Kapetanios, 2005. "Estimating the Rank of the Spectral Density Matrix," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 37-48, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Arturas Juodis & Sarafidis, V., 2015. "A Simple Estimator for Short Panels with Common Factors," UvA-Econometrics Working Papers 15-03, Universiteit van Amsterdam, Dept. of Econometrics.
    2. Ignace De Vos & Gerdie Everaert & Vasilis Sarafidis, 2021. "A method for evaluating the rank condition for CCE estimators," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 21/1013, Ghent University, Faculty of Economics and Business Administration.
    3. Carriero, Andrea & Kapetanios, George & Marcellino, Massimiliano, 2016. "Structural analysis with Multivariate Autoregressive Index models," Journal of Econometrics, Elsevier, vol. 192(2), pages 332-348.
    4. Anyck Dauphin & Bernard Fortin & Guy Lacroix, 2018. "Is consumption efficiency within households falsifiable?," Review of Economics of the Household, Springer, vol. 16(3), pages 737-766, September.
    5. Ruli Xiao, 2016. "Nonparametric Identification of Dynamic Games with Multiple Equilibria and Unobserved Heterogeneity," CAEPR Working Papers 2016-002, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    6. Ruli Xiao, 2015. "Identification and Estimation of Incomplete Information Games with Multiple Equilibria," CAEPR Working Papers 2015-007, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    7. Al-Sadoon, Majid M., 2017. "A unifying theory of tests of rank," Journal of Econometrics, Elsevier, vol. 199(1), pages 49-62.
    8. Xiao, Ruli, 2018. "Identification and estimation of incomplete information games with multiple equilibria," Journal of Econometrics, Elsevier, vol. 203(2), pages 328-343.
    9. Erhao Xie, 2022. "Nonparametric Identification of Incomplete Information Discrete Games with Non-equilibrium Behaviors," Staff Working Papers 22-22, Bank of Canada.
    10. Elena Andreou & Patrick Gagliardini & Eric Ghysels & Mirco Rubin, 2016. "Is Industrial Production Still the Dominant Factor for the US Economy?," Swiss Finance Institute Research Paper Series 16-11, Swiss Finance Institute.
    11. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2015.
    12. Blake LeBaron, 2013. "Heterogeneous Agents and Long Horizon Features of Asset Prices," Working Papers 63, Brandeis University, Department of Economics and International Business School, revised Sep 2013.
    13. White, Halbert & Pettenuzzo, Davide, 2014. "Granger causality, exogeneity, cointegration, and economic policy analysis," Journal of Econometrics, Elsevier, vol. 178(P2), pages 316-330.
    14. Guay, Alain, 2021. "Identification of structural vector autoregressions through higher unconditional moments," Journal of Econometrics, Elsevier, vol. 225(1), pages 27-46.
    15. Luo, Yao & Xiao, Ping & Xiao, Ruli, 2022. "Identification of dynamic games with unobserved heterogeneity and multiple equilibria," Journal of Econometrics, Elsevier, vol. 226(2), pages 343-367.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2015.

    More about this item

    Keywords

    model specification; Multiple time series; tests of rank.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    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:ecb:ecbwps:2008850. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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: Official Publications (email available below). General contact details of provider: https://edirc.repec.org/data/emieude.html .

    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.