IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v50y2017i3d10.1007_s10614-016-9595-y.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-016-9595-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-016-9595-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. David A. Belsley, 1988. "Two or Three Stages of Least Squares?," Boston College Working Papers in Economics 184, Boston College Department of Economics.
    3. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, September.
    4. 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.
    5. Dent, Warren, 1976. "Information and computation in simultaneous equations estimation," Journal of Econometrics, Elsevier, vol. 4(1), pages 89-95, February.
    6. 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.
    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. 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.
    10. 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.
    11. 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.
    12. Jennings, L. S., 1980. "Simultaneous equations estimation : Computational aspects," Journal of Econometrics, Elsevier, vol. 12(1), pages 23-39, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    2. George Halkos & Kyriaki Tsilika, 2015. "Programming Identification Criteria in Simultaneous Equation Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 157-170, June.
    3. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    4. C. Lanier Benkard & Steven Berry, 2006. "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on Brown (1983) and Roehrig (1988)," Econometrica, Econometric Society, vol. 74(5), pages 1429-1440, September.
    5. 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.
    6. Kirill S. Evdokimov & Andrei Zeleneev, 2023. "Simple Estimation of Semiparametric Models with Measurement Errors," Papers 2306.14311, arXiv.org, revised Mar 2024.
    7. Guido W. Imbens, 2020. "Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics," Journal of Economic Literature, American Economic Association, vol. 58(4), pages 1129-1179, December.
    8. Karim Chalak & Halbert White, 2011. "Viewpoint: An extended class of instrumental variables for the estimation of causal effects," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 44(1), pages 1-51, February.
    9. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers 60/17, Institute for Fiscal Studies.
    10. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    11. Kasy, Maximilian, "undated". "Instrumental variables with unrestricted heterogeneity and continuous treatment - DON'T CITE! SEE ERRATUM BELOW," Working Paper 33257, Harvard University OpenScholar.
    12. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    13. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.
    14. Lee, Sokbae, 2007. "Endogeneity in quantile regression models: A control function approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 1131-1158, December.
    15. Wang, Ao, 2020. "Identifying the Distribution of Random Coefficients in BLP Demand Models Using One Single Variation in Product Characteristics," The Warwick Economics Research Paper Series (TWERPS) 1304, University of Warwick, Department of Economics.
    16. Blundell, Richard & Kristensen, Dennis & Matzkin, Rosa, 2014. "Bounding quantile demand functions using revealed preference inequalities," Journal of Econometrics, Elsevier, vol. 179(2), pages 112-127.
    17. George Planiteros, 2022. "Reverse matching for ex-ante policy evaluation," DEOS Working Papers 2206, Athens University of Economics and Business.
    18. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    19. Joshua D. Angrist, 2022. "Empirical Strategies in Economics: Illuminating the Path From Cause to Effect," Econometrica, Econometric Society, vol. 90(6), pages 2509-2539, November.
    20. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:50:y:2017:i:3:d:10.1007_s10614-016-9595-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.