Bayesian Inference in the Seemingly Unrelated Regressions Model

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39 Richard, J.-F., Tompa, H., 1980. On the evaluation of poly-t density functions. Journal of Econometrics 12, 335-351. 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 38, 7-37. Smith, M., Kohn, R., 2000. Nonparametric seemingly unrelated regression. Journal of Econometrics 98, 257-282. Srivastava, V.K., Dwivedi, T.D., 1979. Estimation of seemingly unrelated regression equations: a brief survey. Journal of Econometrics 10, 15-32. Srivastava, V.K., Giles, D.E.A., 1987. Seemingly Unrelated Regression Equations Models: Estimation and Inference. Marcel Dekker, New York. Steel, M.F.J., 1992. Posterior analysis of restricted seemingly unrelated regression equation models: a recursive analytical approach. Econometric Reviews 11, 129-142. Supat, K., 1996. Seemingly Unrelated Regression with Missing Observations on Dependent Variables. B.Ec. Honours dissertation, University of New England, Armidale. Tanner, M.A., 1996. Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, third ed. Springer, New York. Tierney, L., 1994. Markov chains for exploring posterior distributions (with discussion and rejoinder). Annals of Statistics 22, 1701-1762.
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Page 1 and 2: Bayesian Inference in the Seemingly
Page 3 and 4: 2 The objective of this chapter is
Page 5 and 6: 4 A Y X B ′ Y X B = ( − * )(
Page 7 and 8: 6 E( β| y, Σ ) =β= ˆ [ X′ (
Page 9 and 10: 8 Collecting all these results, sub
Page 11 and 12: 10 N ( $ ) ( $ ) ( $ ) ( $ ) ( 1
Page 13 and 14: 12 N N 1 ˆ( ) 1 1( ) 1 1( ) ˆ( |
Page 15 and 16: 14 1. Draw ( ) β $ from ( −1) f(
Page 17 and 18: 16 G. A Metropolis-Hastings Algorit
Page 19 and 20: 18 algorithms that we described are
Page 21 and 22: 20 Suppose a set of J linear restri
Page 23 and 24: 22 The conditional posterior pdf fo
Page 25 and 26: 24 Although Griffiths et al (2001)
Page 27 and 28: 26 σ ij = β i ij S S j + 1 i ≠
Page 29 and 30: 28 m x ∑ m k k k 0 = x − ∑k
Page 31 and 32: 30 −1 f( y* | β, y) ∝ ⎡1 ( y
Page 33 and 34: 32 ⎛ U U U y ⎞ ⎛ () t X ⎞
Page 35 and 36: 34 B. Multivariate t Distribution C
Page 37 and 38: 36 REFERENCES Albert, J.H., Chib, S
Page 39: 38 Handbook of Applied Econometrics

Bayesian Inference in the Seemingly Unrelated Regressions Model

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