The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Reduced Rank Regression

  • Søren Johansen
Reference work entry


The reduced rank regression model is a multivariate regression model with a coefficient matrix with reduced rank. The reduced rank regression algorithm is an estimation procedure which estimates the reduced rank regression model. It is related to canonical correlations and involves calculating eigenvalues and eigenvectors. We give a number of different applications to regression and time series analysis, and show how the reduced rank regression estimator can be derived as a Gaussian maximum likelihood estimator. We briefly mention asymptotic results.


Instrumental variable estimation Limited information maximum likelihood Maximum likelihood Reduced rank regression 

JEL Classifications

C10 C13 
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  1. Anderson, T.W. 1951. Estimating linear restrictions on regression coefficients for multivariate normal distributions. Annals of Mathematical Statistics 22: 327–351.CrossRefGoogle Scholar
  2. Anderson, T.W., and H. Rubin. 1949. Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics 20: 46–63.CrossRefGoogle Scholar
  3. Bartlett, M.S. 1938. Further aspects of the theory of multiple regression. Proceedings of the Cambridge Philosophical Society 34: 33–40.CrossRefGoogle Scholar
  4. Box, G.E.P., and G.C. Tiao. 1977. A canonical analysis of multiple time series. Biometrika 64: 355–365.CrossRefGoogle Scholar
  5. Doornik, J.A., and R.J. O’Brien. 2002. Numerically stable cointegration analysis. Computational Statistics and Data Analysis 41: 185–193.CrossRefGoogle Scholar
  6. Engle, R.F., and C.W.J. Granger. 1987. Co-integration and error correction: Representation, estimation and testing. Econometrica 55: 251–276.CrossRefGoogle Scholar
  7. Engle, R.F., and S. Kozicki. 1993. Testing for common factors (with comments). Journal of Business Economics and Statistics 11: 369–378.Google Scholar
  8. Hotelling, H. 1936. Relations between two sets of variables. Biometrika 28: 321–377.CrossRefGoogle Scholar
  9. Johansen, S. 1996. Likelihood based inference on cointegration in the vector autoregressive model. Oxford: Oxford University Press.Google Scholar
  10. Reinsel, G.C., and R.P. Velu. 1998. Multivariate reduced rank regression. Lecture notes in statistics. New York: Springer.CrossRefGoogle Scholar
  11. Robinson, P.M. 1973. Generalized canonical analysis for time series. Journal of Multivariate Analysis 3: 141–160.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Søren Johansen
    • 1
  1. 1.