Fiscal Policy Rules in Practice

where P denotes the matrix of transition probabilities. This equation can be rearranged to

(I-P)p(S0|X) =0,

with I being a (k × k) identity matrix. We know that by construction the k probabilities in
the vector of p(S₀∣X) add up to one. Thus, with ι = (1,..., 1)' we may express this fact in vector
notation as

ιp(So∣X ) = 1.

In matrix notation (4.12) and (4.13) can be rewritten as

≡M

We premultiply this expression by (M'M) ¹M' and obtain for the initial probabilities

p(So∣X ) = (M 'M )^-1M '

4.1.4 Generating the Parameters

After having generated S , we are now able to formulate the conditional density of the parameters,
which is generally given by

p(λj∣S,λ-j,X) ∖ L(X∣S,λ) ∙p(S∣λ) ∙p(λj),                        (4.16)

where λ-j denotes the set of all parameters except for λj .

17

<<   15   16   17   18   19   20   21   >>

More intriguing information