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Gibbs Samplers for a Set of Seemingly Unrelated Regressions

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  • W.E. Griffiths
  • Ma. Rebecca Valenzuela

Abstract

Bayesian estimation of a collection of seemingly unrelated regressions, referred to as a ‘set of seemingly unrelated regressions’ is considered. The collection of seemingly unrelated regressions is linked by common coefficients and/or a common error covariance matrix. Gibbs samplers useful for estimating posterior quantities are described and applied to two examples – a set of linear expenditure functions and a cost function and share equations from production theory.

Suggested Citation

  • W.E. Griffiths & Ma. Rebecca Valenzuela, 2004. "Gibbs Samplers for a Set of Seemingly Unrelated Regressions," Department of Economics - Working Papers Series 912, The University of Melbourne.
  • Handle: RePEc:mlb:wpaper:912
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    File URL: http://www.economics.unimelb.edu.au/downloads/wpapers-04/912.pdf
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    References listed on IDEAS

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    1. Lluch, Constantino, 1973. "The extended linear expenditure system," European Economic Review, Elsevier, vol. 4(1), pages 21-32, April.
    2. Smith, Michael & Kohn, Robert, 2000. "Nonparametric seemingly unrelated regression," Journal of Econometrics, Elsevier, pages 257-281.
    3. Chotikapanich, D. & Griffiths, W.E. & Skeels, C.L., 2001. "Sample Size Requirements for Estimation in SUR Models," Department of Economics - Working Papers Series 794, The University of Melbourne.
    4. Badi Baltagi & Alain Pirotte, 2011. "Seemingly unrelated regressions with spatial error components," Empirical Economics, Springer, vol. 40(1), pages 5-49, February.
    5. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    6. Richard, J. -F. & Tompa, H., 1980. "On the evaluation of poly-t density functions," Journal of Econometrics, Elsevier, pages 335-351.
    7. Chib, Siddhartha & Greenberg, Edward, 1995. "Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models," Journal of Econometrics, Elsevier, vol. 68(2), pages 339-360, August.
    8. Griffiths, William E. & O'Donnell, Christopher J. & Cruz, Agustina Tan, 2000. "Imposing regularity conditions on a system of cost and factor share equations," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 44(1), March.
    9. Srivastava, V. K. & Dwivedi, T. D., 1979. "Estimation of seemingly unrelated regression equations : A brief survey," Journal of Econometrics, Elsevier, vol. 10(1), pages 15-32, April.
    10. Kakwani, Nanak C, 1977. "On the Estimation of Consumer Unit Scales," The Review of Economics and Statistics, MIT Press, vol. 59(4), pages 507-510, November.
    11. Griffiths, William E & Chotikapanich, Duangkamon, 1997. "Bayesian Methodology for Imposing Inequality Constraints on a Linear Expenditure System with Demographic Factors," Australian Economic Papers, Wiley Blackwell, vol. 36(69), pages 321-341, December.
    12. Richard, J. F. & Steel, M. F. J., 1988. "Bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 7-37.
    13. Bauwens, Luc & Richard, Jean-Francois, 1985. "A 1-1 poly-t random variable generator with application to Monte Carlo integration," Journal of Econometrics, Elsevier, pages 19-46.
    14. Griffiths, W.E. & Valenzuela, R., 2001. "Estimating Costs of Children from Micro-Unit Records: A New Procedure Applied to Australian Data," Department of Economics - Working Papers Series 795, The University of Melbourne.
    15. Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
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    Cited by:

    1. Hanneke Geerlings & Cees Glas & Wim Linden, 2011. "Modeling Rule-Based Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 337-359, April.

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