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Bayesian Inference in the Seemingly Unrelated Regressions Models

The objective of this chapter is to provide a practical guide to computer-aided Bayesian inference for a variety of problems that arise in applications of the SUR model. We describe examples of problems, models and algorithms that have been placed within a general framework in the chapter by Geweke et al (this volume); our chapter can be viewed as complimentary to that chapter. The model is described in Section II; the joint, conditional and marginal posterior density functions that result from a noninformative prior are derived. In Section III we describe how to use sample draws of parameters from their posterior densities to estimate posterior quantities of interest; two Gibbs sampling algorithms and a Metropolis-Hastings algorithm are given.

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Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 793.

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Length: 41 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:mlb:wpaper:793
Contact details of provider: Postal: Department of Economics, The University of Melbourne, 4th Floor, FBE Building, Level 4, 111 Barry Street. Victoria, 3010, Australia
Phone: +61 3 8344 5355
Fax: +61 3 8344 6899
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  1. Smith, Michael & Kohn, Robert, 2000. "Nonparametric seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 98(2), pages 257-281, October.
  2. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
  3. 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.
  4. William E Griffiths & Lisa S Newton & Christopher J O’Donnell, 2008. "Predictive Densities for Shire Level Wheat Yield in Western Australia," Department of Economics - Working Papers Series 1051, The University of Melbourne.
  5. 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.
  6. Geweke, John F. & Keane, Michael P. & Runkle, David E., 1997. "Statistical inference in the multinomial multiperiod probit model," Journal of Econometrics, Elsevier, vol. 80(1), pages 125-165, September.
  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. 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.
  9. 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 321-41, December.
  10. W. E. Griffiths, 1999. "Estimating consumer surplus comments on "using simulation methods for bayesian econometric models: inference development and communication"," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 75-87.
  11. Richard, J. -F. & Tompa, H., 1980. "On the evaluation of poly-t density functions," Journal of Econometrics, Elsevier, vol. 12(3), pages 335-351, April.
  12. 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.
  13. repec:cep:stiecm:/1997/328 is not listed on IDEAS
  14. Kai, Li, 1998. "Bayesian inference in a simultaneous equation model with limited dependent variables," Journal of Econometrics, Elsevier, vol. 85(2), pages 387-400, August.
  15. Denzil Fiebig & Jae Kim, 2000. "Estimation and inference in sur models when the number of equations is large," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 105-130.
  16. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  17. 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.
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