Abstract
The purpose of this chapter is to review the fundamentals of ordinary least squares and generalized least squares in the context of linear regression analysis. The presentation here is somewhat condensed given our objective of focusing on more advanced topics in econometrics. The results presented, though brief in form, are important and are the foundation for much to come. In the next section we present the assumptions of the classical linear regression model. In the following section the Gauss-Markov theorem is proved and the optimality of the ordinary least squares estimator is established. In Section 2.4 we introduce the large sample concepts of convergence in probability and consistency. It is shown that convergence in quadratic mean is a sufficient condition for consistency and that the ordinary least squares estimator is consistent. In Section 2.5 the generalized least squares model is defined and the optimality of the generalized least squares estimator is established by Aitken’s theorem. In the next section we examine the properties of the ordinary least squares estimator when the appropriate model is the generalized least squares model. Finally, in Section 2.7 we summarize our discussion and briefly outline additional results and readings that are available.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aitken, A. C. (1935). On least squares and linear combinations of observations. Proceedings of the Royal Society, Edinburgh, 55, 42–48.
Dhrymes, P. (1971). Distributed Lags: Problems of Estimation and Formulation. San Francisco: Holden-Day.
Dhrymes, P. J. (1974). Econometrics: Statistical Foundations and Applications. New York: Springer-Verlag.
Gauss, K. F. (1821-23), Theoria Combinationis Observationum Erroribus Minimis Obnoxiae. French translation by J. Bertrand under title Methode des moindres corres. Paris: Mallet-Bachelier (1855).
Goldberger, A. (1964). Econometric Theory. New York: Wiley.
Johnston, J. (1972). Econometric Methods. New York: McGraw-Hill.
Maeshiro, A. (1980). Small sample properties of estimators of distributed lag models. International Economic Review, 21, 721–733.
Markov, A. A. (1900). Wahrscheinlichkeitsrechnung. Leipzig: Tuebner.
Ramsey, J. B. (1969). Tests for specification errors in classical linear least squares regression analysis. Journal of Royal Statistical Society, B,31, 350–371.
Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed. New York: Wiley.
Schmidt, P. (1976). Econometrics. New York: Marcel Dekker.
Theil, H. (1971). Principles of Econometrics. New York: Wiley.
Wilks, S. S. (1962). Mathematical Statistics. New York: Wiley.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fomby, T.B., Johnson, S.R., Hill, R.C. (1984). Review of Ordinary Least Squares and Generalized Least Squares. In: Advanced Econometric Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8746-4_2
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8746-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96868-1
Online ISBN: 978-1-4419-8746-4
eBook Packages: Springer Book Archive