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Reduced-Rank Regression: A Useful Determinant Identity

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Author Info
Peter Reinhard Hansen () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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Abstract

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 regres- sions 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.

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Publisher Info
Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-02.

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Length: 13
Date of creation: 15 Jan 2008
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Handle: RePEc:aah:create:2008-02

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Web page: http://www.econ.au.dk/afn/

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Related research
Keywords: Determinant Identity; Reduced Rank Regression; Least Squares;

Find related papers by 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

This paper has been announced in the following NEP Reports:

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  1. 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. [Downloadable!] (restricted)
  2. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 114(2), pages 261-295, June. [Downloadable!] (restricted)
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  3. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June. [Downloadable!] (restricted)
  6. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
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