By L. Bauwens
In their evaluate of the "Bayesian research of simultaneous equation systems", Dr~ze and Richard (1983) - hereafter DR - convey the next perspective in regards to the current country of improvement of the Bayesian complete info research of such sys tems i) the tactic permits "a versatile specification of the past density, together with good outlined noninformative earlier measures"; ii) it yields "exact finite pattern posterior and predictive densities". although, they demand extra advancements in order that those densities should be eval uated via 'numerical tools, utilizing an built-in software program packa~e. for this reason, they suggest using a Monte Carlo strategy, considering the fact that van Dijk and Kloek (1980) have validated that "the integrations could be performed and the way they're done". during this monograph, we clarify how we give a contribution to accomplish the advancements instructed by means of Dr~ze and Richard. A uncomplicated notion is to take advantage of recognized homes of the porterior density of the param eters of the structural shape to layout the significance capabilities, i. e. approximations of the posterior density, which are wanted for organizing the integrations.
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Additional info for Bayesian Full Information Analysis of Simultaneous Equation Models Using Integration by Monte Carlo
4 PTFC 140 sec. 6 PTDC 18867 sec. 08 999 sec. 14 Y2 I. 50 1• : e: O. O. 07 61 : II PTST-2 ROUND 2 1073 sec. 7 ROUND 2) CORRELATION MATRICES : II : a : YI I. 87 1- I. 60 I. 1. I : a YI e: 1. 61 62 Y2 : II : a I. 66 1. 39 I. 09 I. 55 I. 35 61 62 Y2 I 61 62 Y2 : e: : II : a 61 62 Y2 : mode ': a mode = expected value; a = standard deviation; YI = skewness coefficient; = estimated relative error bound of poste~ior expected value; - indicates a quantity that does not exist. 47 We adopt the formulation of VDK (1980) (except that we change the sign of 8 3 ) : wl =Ylx + Y2 X_ l + y 3 time + u a x=c+i+g p=x k = k_l + i where c is consumer expenditure i is net investment wl is the wage bill of the private sector x is net private production p is profits of the private sector k is the capital stock w is the total wage bill g is the government nonwage expenditure, including the net foreign balance t is business taxes w2 is the government wage bill.
F(6) = E... 1q,-:-)] • 'I' i=i 1. 1. -) as well as their integrating constants - which 1. 1. 15) has to be computed numerically. III how this can be organized efficiently for each drawing of 6 generated by the two step procedure described above. III suggest that the procedure is feasible in practice if the number of coefficients (t) is not too large. Whether it is worth- while is a question which we cannot answer in theory. , as was the case with PTFe, it cannot be 1. J proved that they are characterized by the correct form of dependence and variancecovariance structure.
16) p(/)=p(/)il/)r) p(/)r) and we can generate random drawings from p (/). ), for any value 1 this conditional density in the importance function. 17) where f(/) f (/)r) = p (/). :-) 1 f the conditional (/)-1' ) p(/)r) and select the index i of the equation for which we use 1 -1 poly-t density in the importance function. The problem of choice of an importance function for i) we can use is an importance function for p (/) r ). We mus t of course find a good approximation of p (/)r) /)-1" We define the latter by f (/)r) for the marginal density is similar to the original problem of choice of an importance function f(/) p(/).