Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-26T21:19:00.739Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum Likelihood Estimation of the Parameters of a System of Simultaneous Regression Equations

Published online by Cambridge University Press:  18 October 2010

James Durbin
James Durbin
Affiliation:
London School of Economics and Political Science
Get access Rights & Permissions [Opens in a new window]

Extract

Procedures for computing the full information maximum likelihood (FIML) estimates of the parameters of a system of simultaneous regression equations have been described by Koopmans, Rubin, and Leipnik, Chernoff and Divinsky, Brown, and Eisenpress. However, all of these methods are rather complicated since they are based on estimating equations that are expressed in an inconvenient form. In this paper, a transformation of the maximum likelihood (ML) equations is developed which not only leads to simpler computations but which also simplifies the study of the properties of the estimates. The equations are obtained in a form which is capable of solution by a modified Newton-Raphson iterative procedure. The form obtained also shows up very clearly the relation between the maximum likelihood estimates and those obtained by the three-stage least squares method of Zellner and Theil.

Type
Special Article
Information
Econometric Theory , Volume 4 , Issue 1 , April 1988 , pp. 159 - 170
Copyright
Copyright © Cambridge University Press 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Brown, T.M.Simplified full information maximum likelihood and comparative structural estimates. Econometrica 27 (1959): 638–653.CrossRefGoogle Scholar
2.Chernoff, J. & Divinsky, N.. The computation of maximum likelihood estimates of linear structural equations. In Hood, W.C. & Koopmans, T.C. (eds.), Studies in Econometric Method, Chapter 10, New York: Wiley, 1953.Google Scholar
3.Crockett, J.B. & Chernoff, H.. Gradient methods of maximization. Pacific Journal of Mathematics 5 (1955).CrossRefGoogle Scholar
4.Eisenpress, H.Note on the computation of full information maximum likelihood estimates of coefficients of a simultaneous system. Econometrica 30 (1962): 343–348.CrossRefGoogle Scholar
5.Koopmans, T.C., Rubin, H., & Leipnik, R.B.. Measuring the equation systems of dynamic economics. In Koopmans, T.C. (éd.), Statistical Inference in Dynamic Economic Models, Chapter 2, New York: Wiley, 1950.Google Scholar
6.Madansky, A. On the efficiency of three-stage least squares estimation. RAND Corporation Memorandum RM-3557-PR, March (1963).Google Scholar
7.Rothenberg, T. & Leenders, T.C.. Efficient estimation of simultaneous equation systems. Econometrica, 32 (1964), 57–76.CrossRefGoogle Scholar
8.Sargan, J.D.Three-stage least squares and full maximum likelihood estimates. Econometrica, 32 (1964), 77–81..CrossRefGoogle Scholar
9.Zellner, A. & Theil, H.. Three-stage least squares: Simultaneous estimation of simultaneous equations. Econometrica 30 (1962): 54–78.CrossRefGoogle Scholar