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Reduced-Rank Regression: A Useful Determinant Identity


  • Peter Reinhard Hansen

    () (School of Economics and Management, University of Aarhus, Denmark and CREATES)


We derive an identity for the determinant of a product involving non-squared matrices. The identity can be used to derive the maximum likelihood estimator in reduced-rank regressions with Gaussian innovations. Furthermore, the identity sheds light on the structure of the estimation problem that arises when the reduced-rank parameters are subject to additional constraints.

Suggested Citation

  • Peter Reinhard Hansen, 2008. "Reduced-Rank Regression: A Useful Determinant Identity," CREATES Research Papers 2008-02, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2008-02

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    References listed on IDEAS

    1. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    2. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 114(2), pages 261-295, June.
    3. Velu, Raja P. & Reinsel, Gregory C., 1987. "Reduced rank regression with autoregressive errors," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 317-335, July.
    4. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    5. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    6. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    7. Anderson, T. W., 2002. "Reduced rank regression in cointegrated models," Journal of Econometrics, Elsevier, vol. 106(2), pages 203-216, February.
    8. Hansen, Peter Reinhard & Johansen, Soren, 1998. "Workbook on Cointegration," OUP Catalogue, Oxford University Press, number 9780198776079.
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    More about this item


    Determinant Identity; Reduced Rank Regression; Least Squares;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • 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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