New PDF release: Posterior and Predictive Densities for Simultaneous Equation

By Dr. Jean-François Richard (auth.)

ISBN-10: 3540065253

ISBN-13: 9783540065258

ISBN-10: 3642657494

ISBN-13: 9783642657498

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Extra info for Posterior and Predictive Densities for Simultaneous Equation Models

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44) 1121 1122 = 1 1-S1S2 Consequently, given Band H, the 1I'S are jointly normally distributed. Their conditional distribution is singular so long as either i1 or i3 is non zero. This does not imply that their joint posterior marginal density is singular. Anyw ay · we s h a 11 not t ry t 0 f1nd that d ' (1) ens1ty . ,1nstead, we . 1nvest1gate how to compute some of the corresponding moments. 3. (1)As soon as zero restrictions on the y's are built into the model, there are no longer any general formulae to apply, since we have to identifY one-to-one transformations from the structural parameter space to the reduced form parameter space (eventually completed) and to compute their Jacobians.

25) through the transformation: 0 .. = [h .. (o .. Jp) 1 11 ni - 1 32 For adequate f03(P) (1) , we could also derive some marginal moments of cr .. 30) The analytical derivations that lead to such a decomposition are somewhat tedious, although simple in principle. Since they are not essential for the understanding of our method, we just sketch them. ) 2 For example, we would find: s? -1 1 1 (\l+v-1) (\l+v-2) 4 ( \1-1 )( v-1) v-1 33 auxiliary definitions may be found in Appendix III.

As far as points b and c are concerned, the approach we develop in the next section is more flexible. This will enable us to investigate the importance of the limitations b and c. 14) f*(6) ex IIBIIT+a 1(6-6*)M*(6-6*)' + s*1 2 where f;(01 102) is a conditional t-density and f*(02) is a product of three quadratic forms in 02 raised to certain powers ( ~ 0, see Appendix II). Details and comments about those derivations may be found in Dreze and Morales [8] . 14) calls succesively for: 27 - analytical integration of the elements of Y,.

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Posterior and Predictive Densities for Simultaneous Equation Models by Dr. Jean-François Richard (auth.)

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