By L. Bauwens
Of their evaluate of the "Bayesian research of simultaneous equation systems", Dr~ze and Richard (1983) - hereafter DR - convey the next point of view concerning the current country of improvement of the Bayesian complete details research of such sys tems i) the tactic permits "a versatile specification of the earlier density, together with good outlined noninformative past measures"; ii) it yields "exact finite pattern posterior and predictive densities". besides the fact that, they demand additional advancements in order that those densities might be eval uated via 'numerical equipment, utilizing an built-in software program packa~e. hence, they suggest using a Monte Carlo procedure, because van Dijk and Kloek (1980) have verified that "the integrations should be performed and the way they're done". during this monograph, we clarify how we give a contribution to accomplish the advancements steered via Dr~ze and Richard. A uncomplicated thought is to take advantage of recognized houses of the porterior density of the param eters of the structural shape to layout the significance features, i. e. approximations of the posterior density, which are wanted for organizing the integrations.
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Additional resources for Bayesian Full Information Analysis of Simultaneous Equation Models Using Integration by Monte Carlo (Lecture Notes in Economics and Mathematical Systems)
Secondly, this approach is less adapted to the computation of expected values of functions of y and S, and even of y only. 18), it is clear that E (y I S, r) and V (y Is, E) integrated analytically wi th respect to S, but not wi th respect to E. can be The latter marginalization should be performed by Monte Carlo, using random drawings of r, but even this is not feasible, since the kernel of the rnarp,inal density of E is not known. As a consequence, these moments must be marp,inalized by Monte Carlo with respect to Sand E.
1. 24 I I I I I I 1. 79 1. 08 1. 38 I I 1. 67 I I I I 1. 40 I. : See the comments after Table 2 for a detailed description of the contents of this table and of Table 7-b. F. 8 : e: 3725 sec. 03 : a 17059 sec. 50 : \l = expected value; e: = estimated a = standard deviation; Y1 = skewness coefficient; relative error bound of posterior expected value. F. (truncated) STUD 2 a 3 al I. 53 I. 14 I I. 19 I. 32 I. 51 PTST-2 al I. 35 I. 61 l I. 34 I. I. I. 08 I I. 37 1. 17 I. 34 l I. 33 I. POSTERIOR a l l .
Table 2 reports the main characteristics of the importance functions and of the posterior density. Figures 1 to 4, re~rouped in Appendix C, show the marginal impor- tance functions and posterior density of each structural coefficient, and the corresponding posterior distribution function. 1. In particular, even PTFC essentially satisfies the second crit- erion, since the posterior correlations10 between the coefficients of the 2 equations are all rather small. 2) However, the graphs of figures I to 4 show that the marginal importance functions based on I-I poly-t densities are better approximations of the marginal posterior densities than those based on the Student density.