African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Full Length Research Paper

A note on indirect least squares and matrix partitioning

  Isaac D.  Essi1*, N. M. Nafo2 and E. H. Amadi2
    1Centre for Econometric and Allied Research, University of Ibadan, Ibadan, Nigeria. 2Department of Mathematics/Computer Science, Rivers State University of Science and Technology, Port Harcourt, Nigeria.  
Email: [email protected]

  •  Accepted: 26 August 2010
  •  Published: 30 November 2010




At times, it is discovered that in using OLS in estimating an equation, inconsistent estimates are obtained because of correlation between the independent variable and the stochastic disturbance term. In such a circumstance, it is likely that the equation so estimated belongs to a wider family of equations related to the practical situation under consideration. Inevitably, a model describing the joint dependence of variables, called simultaneous – equation model evolves. In order to obtain consistent estimator, one may resort to indirect least squares (ILS) or two – stage least squares (2SLS). For an over-identified system, ILS through unguided coefficient technique (UCT) produces non-unique estimates for a just identified equation. Unique estimates can only be possible if ILS is approached through matrix partition techniques (MPT). The authors’ objective in this paper is to prove the proposition stated above. The definitions of UCT and MPT are also given in the paper.  


Key words: Least squares, matrix partitioning, unguided coefficient technique, matrix partition technique, simultaneous equation model.