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

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  • Durbin, James

Abstract

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.

Suggested Citation

  • Durbin, James, 1988. "Maximum Likelihood Estimation of the Parameters of a System of Simultaneous Regression Equations," Econometric Theory, Cambridge University Press, vol. 4(1), pages 159-170, April.
    • Handle: RePEc:cup:etheor:v:4:y:1988:i:01:p:159-170_01
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    Cited by:

    1. Mala Raghavan & George Athanasopoulos & Param Silvapulle, 2009. "VARMA models for Malaysian Monetary Policy Analysis," Monash Econometrics and Business Statistics Working Papers 6/09, Monash University, Department of Econometrics and Business Statistics.
    2. Kyriacou, Maria & Phillips, Peter C.B. & Rossi, Francesca, 2023. "Continuously Updated Indirect Inference In Heteroskedastic Spatial Models," Econometric Theory, Cambridge University Press, vol. 39(1), pages 107-145, February.
    3. Calzolari, Giorgio, 2012. "Econometric notes," MPRA Paper 36765, University Library of Munich, Germany.
    4. David F. Hendry & Peter C.B. Phillips, 2017. "John Denis Sargan at the London School of Economics," Cowles Foundation Discussion Papers 2082, Cowles Foundation for Research in Economics, Yale University.
    5. Oya, Kosuke & Morimune, Kimio, 1992. "The distribution of the full information maximum likelihood estimator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 33(5), pages 569-574.
    6. Richard Sweeney, 2014. "Equivalent valuations in cash flow and accounting models," Review of Quantitative Finance and Accounting, Springer, vol. 42(1), pages 29-49, January.
    7. Charles G. Renfro, 2009. "The Practice of Econometric Theory," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75571-5, July-Dece.

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