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

Author

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  • 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
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    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp850.pdf
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    References listed on IDEAS

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    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.
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    Citations

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    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. Carriero, Andrea & Kapetanios, George & Marcellino, Massimiliano, 2016. "Structural analysis with Multivariate Autoregressive Index models," Journal of Econometrics, Elsevier, vol. 192(2), pages 332-348.
    3. Al-Sadoon, Majid M., 2017. "A unifying theory of tests of rank," Journal of Econometrics, Elsevier, vol. 199(1), pages 49-62.
    4. Xiao, Ruli, 2018. "Identification and estimation of incomplete information games with multiple equilibria," Journal of Econometrics, Elsevier, vol. 203(2), pages 328-343.
    5. Erhao Xie, 2022. "Nonparametric Identification of Incomplete Information Discrete Games with Non-equilibrium Behaviors," Staff Working Papers 22-22, Bank of Canada.
    6. 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.
    7. Guay, Alain, 2021. "Identification of structural vector autoregressions through higher unconditional moments," Journal of Econometrics, Elsevier, vol. 225(1), pages 27-46.
    8. White, Halbert & Pettenuzzo, Davide, 2014. "Granger causality, exogeneity, cointegration, and economic policy analysis," Journal of Econometrics, Elsevier, vol. 178(P2), pages 316-330.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    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.

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    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

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