846 The Econometrics of Monetary Policy
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00 ρR 00 000
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0000 ρG 000
00000 ρZ 00
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⎥⎦.As a solution to (16.15), we obtain the following policy function:Z ̃t=T(θ)Z ̃t− 1 +R(θ) (^) t. (16.16)
To provide the mapping between the observable data and those computed as devi-
ations from the steady-state of the model, we set the following measurement
equations, as in DS:
lnxt=lnγ+ ̃xt+z ̃t (16.17)
lnPt=lnπ∗+ ̃πt (16.18)
lnRt= 4 [(lnR∗+lnπ∗)+R ̃t], (16.19)
which can also be cast into matrices as:
Yt=% 0 (θ)+% 1 (θ)Z ̃t+vt, (16.20)
whereYt =
(
lnxt,lnPt,lnRt
)′
,vt=0 and% 0 and% 1 are defined accord-
ingly. For completeness, we write the matricesT,R,% 0 and% 1 as a function of
the structural parameters in the model,θ=
(
lnγ,lnπ∗,lnr∗,κ,τ,ψ 1 ,ψ 2 ,ρR,ρg,
ρZ,σR,σg,σZ
)′
: such a formulation derives from the rational expectations solution.
The evolution of the variables of interest,Yt, is therefore determined by (16.15)
and (16.20), which impose a set of restrictions across the parameters of the MA
representation. Finally, the MA representation is approximated by a finite-order
VAR representation.
Notes
- The LSE approach was initiated by Denis Sargan but owes its diffusion to a number of
Sargan’s students and is extremely well described in the book by David Hendry (1995).