Measurement equations
yt
πt
Rt
|
ɪ- π |
yt-1 - У |
r -, | ||
|
I-------------------------------------------------- '⅞l Ok Ok + I__________________________________________________ |
+ β(L) |
πt-1 - πP (t) Rt_1 — r — nʃ (t) — θ rt-1 - r - πp(t) |
+ |
ey,t |
rt = r + πp (t) + Yy (Et-iyt - y)+ γ∏ (Et-I∏t,4 - ΠT (t)) + ρ(rt-1 - r - πp (t)) + Êr,t,
• Transition equations
πT(t +1)
πP(t+1)
10
δγπ 1 - δγπ
πT (t)
πP(t)
d79-82 +
eτ,t
ep,t
• Structural shock identification
|
ey,t |
1 |
0 |
0 |
0 |
0 |
0 |
uD,t | ||
|
^π,t |
CDS |
1 |
0 |
0 |
0 |
0 |
us,t | ||
|
tR,t |
CDτ |
cSτ |
1 |
crτ |
0 |
0 |
uτ,t | ||
|
^r,t |
γy |
Yπ/4 |
0 |
1 |
0 |
0 |
ur,t | ||
|
eT,t |
0 |
cST |
0 |
0 |
1 |
0 |
uT,t | ||
|
- eP,t - |
0 |
0 |
0 |
-δ |
0 |
1 |
uP,t |
where Et-ιyt and Et-ι∏t (the latter enters through Et-1πt,4) are conditional expectations
formed from the output gap and inflation equations, and uD , uS, uτ , ur , uT ,and
uP are serially uncorrelated and mutually uncorrelated structural shocks to aggregate
demand, aggregate supply, the term premium, monetary policy (transitory), monetary
policy (permanent), and expectations. These structural shocks are assumed to be Normally
distributed with mean zero and variance σi2 for i = D, S, τ, r, T, P . The lag polynomial β(L)
allows for four lags. The inflation target of policy and the perceived target are unobserved
variables to be jointly estimated with the rest of the model. The model is estimated using
maximum likelihood with Kalman filters used to extract the time-varying paths of the
inflation target and the perceived inflation target. The target and perceived target are
initialized using a diffuse prior.
Coefficients of the matrix lag polynomial are assumed to be constant over the entire
sample. A consequence of this assumption is that any structural breaks will be mapped
15
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