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A Generalized Singular Value Decomposition Strategy for Estimating the Block Recursive Simultaneous Equations Model

Author

Listed:
  • Mircea I. Cosbuc

    (“Alexandru Ioan Cuza” University of Iasi)

  • Cristian Gatu

    (“Alexandru Ioan Cuza” University of Iasi)

  • Ana Colubi

    (University of Oviedo)

  • Erricos John Kontoghiorghes

    (Cyprus University of Technology
    Birkbeck University of London)

Abstract

A new strategy for deriving the three-stage least squares (3SLS) estimator of the simultaneous equations model (SEM) is proposed. The main numerical tool employed is the generalized singular value decomposition. This provides a numerical estimation procedure which can tackle efficiently the particular case when the variance-covariance matrix is singular. The proposed algorithm is further adapted to deal with the special case of the block-recursive SEM. The block diagonal structure of the variance-covariance matrix is exploited in order to reduce significantly the computational burden. Experimental results are presented to illustrate the computational efficiency of the new estimation strategy when compared with the equivalent method that ignores the block-recursive structure of the SEM.

Suggested Citation

  • Mircea I. Cosbuc & Cristian Gatu & Ana Colubi & Erricos John Kontoghiorghes, 2017. "A Generalized Singular Value Decomposition Strategy for Estimating the Block Recursive Simultaneous Equations Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(3), pages 503-515, October.
    • Handle: RePEc:kap:compec:v:50:y:2017:i:3:d:10.1007_s10614-016-9595-y
    DOI: 10.1007/s10614-016-9595-y
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    References listed on IDEAS

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    1. Lloyd, William P & Lee, Cheng F, 1976. "Block Recursive Systems in Asset Pricing Models," Journal of Finance, American Finance Association, vol. 31(4), pages 1101-1113, September.
    2. Kontoghiorghes, Erricos J & Dinenis, Elias, 1997. "Computing 3SLS Solutions of Simultaneous Equation Models with a Possible Singular Variance-Covariance Matrix," Computational Economics, Springer;Society for Computational Economics, vol. 10(3), pages 231-250, August.
    3. Srivastava, V K & Tiwari, Ramji, 1978. "Efficiency of Two-Stage and Three-Stage Least Squares Estimators," Econometrica, Econometric Society, vol. 46(6), pages 1495-1498, November.
    4. David A. Belsley, 1988. "Two or Three Stages of Least Squares?," Boston College Working Papers in Economics 184, Boston College Department of Economics.
    5. Jennings, L. S., 1980. "Simultaneous equations estimation : Computational aspects," Journal of Econometrics, Elsevier, vol. 12(1), pages 23-39, January.
    6. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    7. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448, Elsevier.
    8. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 499-527.
    9. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, September.
    10. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    11. Dent, Warren, 1976. "Information and computation in simultaneous equations estimation," Journal of Econometrics, Elsevier, vol. 4(1), pages 89-95, February.
    12. 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.
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