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Bayesian Inference in the Seemingly Unrelated Regressions Models

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  • Griffiths, W.E.

Abstract

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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Bibliographic Info

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

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References

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  1. 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.
  2. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Smith, M. & Kohn, R., 1998. "Nonparametric Seemingly Unrelated Regression," Monash Econometrics and Business Statistics Working Papers 7/98, Monash University, Department of Econometrics and Business Statistics.
  12. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
  13. 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.
  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. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  16. 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.
  17. 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.
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Citations

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Cited by:
  1. Tiberti, M., 2013. "Production costs of Soft Wheat in Italy," 2013 Second Congress, June 6-7, 2013, Parma, Italy 149898, Italian Association of Agricultural and Applied Economics (AIEAA).
  2. Corberán-Vallet, Ana & Bermúdez, José D. & Vercher, Enriqueta, 2011. "Forecasting correlated time series with exponential smoothing models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 252-265, April.
  3. Wolff, Hendrik & Heckelei, Thomas & Mittelhammer, Ronald C., 2004. "Imposing Monotonicity And Curvature On Flexible Functional Forms," 2004 Annual meeting, August 1-4, Denver, CO 20256, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
  4. Wang, Hao, 2010. "Sparse seemingly unrelated regression modelling: Applications in finance and econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2866-2877, November.
  5. Chiara Scotti, 2006. "A bivariate model of Fed and ECB main policy rates," International Finance Discussion Papers 875, Board of Governors of the Federal Reserve System (U.S.).
  6. Hendrik Wolff & Thomas Heckelei & Ron C. Mittelhammer, 2004. "Imposing Curvature and Monotonicity on Flexible Functional Forms: An Efficient Regional Approach," Econometric Society 2004 North American Summer Meetings 450, Econometric Society.
  7. Yiannis Kamarianakis, 2006. "Hierarchical Bayesian Modeling For Spatial Time Series: An Alternative Approach To Spatial Sur," Working Papers 0605, University of Crete, Department of Economics.

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