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Computing 3SLS Solutions of Simultaneous Equation Models with Possible Singular Variance-Covariance Matrix


  • Erricos J. Kontoghiorghes

    () (Centre for Mathematical Trading and Finance and Centre for Insurance and Investment City University Business School, London)


In simultaneous equation models (SEMs) the assumption that the covariance matrix of the disturbances is non-singular cannot always be made. For example, allocation models and models with precise observations which may imply linear constraints on the parameters, have singular disturbance covariance matrix. The solution of such models can be obtained using the expensive computation of generalized inverse which can lead to loss of accuracy. The main motivation of this work is to provide computational strategies for solving an alternative formulation of the 3SLS estimation problem, where the disturbance covariance matrix is not required to be non- singular.

Suggested Citation

  • Erricos J. Kontoghiorghes, "undated". "Computing 3SLS Solutions of Simultaneous Equation Models with Possible Singular Variance-Covariance Matrix," Computing in Economics and Finance 1996 _032, Society for Computational Economics.
  • Handle: RePEc:sce:scecf6:_032

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    References listed on IDEAS

    1. Dent, Warren, 1976. "Information and computation in simultaneous equations estimation," Journal of Econometrics, Elsevier, vol. 4(1), pages 89-95, February.
    2. Kontoghiorghes, E. J. & Clarke, M. R. B., 1995. "An alternative approach for the numerical solution of seemingly unrelated regression equations models," Computational Statistics & Data Analysis, Elsevier, vol. 19(4), pages 369-377, April.
    3. Court, R H, 1974. "Three Stage Least Squares and Some Extensions where the Structural Disturbance Covariance Matrix May Be Singular," Econometrica, Econometric Society, vol. 42(3), pages 547-558, May.
    4. Belsley, David A, 1992. "Paring 3SLS Calculations Down to Manageable Proportions," Computer Science in Economics & Management, Kluwer;Society for Computational Economics, vol. 5(3), pages 157-169, August.
    5. Jennings, L. S., 1980. "Simultaneous equations estimation : Computational aspects," Journal of Econometrics, Elsevier, vol. 12(1), pages 23-39, January.
    6. Narayanan, R, 1969. "Computation of Zellner-Theil's Three Stage Least Squares Estimates," Econometrica, Econometric Society, vol. 37(2), pages 298-306, April.
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    Cited by:

    1. Foschi, Paolo & Belsley, David A. & Kontoghiorghes, Erricos J., 2003. "A comparative study of algorithms for solving seemingly unrelated regressions models," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 3-35, October.
    2. repec:kap:compec:v:50:y:2017:i:3:d:10.1007_s10614-016-9595-y is not listed on IDEAS
    3. Foschi, Paolo & Kontoghiorghes, Erricos J., 2003. "Estimating seemingly unrelated regression models with vector autoregressive disturbances," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 27-44, October.
    4. Gatu, Cristian & Kontoghiorghes, Erricos J. & Gilli, Manfred & Winker, Peter, 2008. "An efficient branch-and-bound strategy for subset vector autoregressive model selection," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1949-1963, June.

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