Statistical tests and estimators of the rank of a matrix and their applications in econometric modelling
AbstractTesting 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
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Date of creation: Jan 2008
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Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-02-09 (All new papers)
- NEP-ECM-2008-02-09 (Econometrics)
- NEP-ETS-2008-02-09 (Econometric Time Series)
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.:
- 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, 01.
- Davide Pettenuzzo & Halbert White, 2010.
"Granger Causality, Exogeneity, Cointegration, and Economic Policy Analysis,"
Working Papers, Brandeis University, Department of Economics and International Businesss School
36, Brandeis University, Department of Economics and International Businesss School.
- White, Halbert & Pettenuzzo, Davide, 2014. "Granger causality, exogeneity, cointegration, and economic policy analysis," Journal of Econometrics, Elsevier, Elsevier, vol. 178(P2), pages 316-330.
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