RDP 2012-08: Estimation and Solution of Models with Expectations and Structural Changes
Equation (21)
x
t
=
(
r
−
π
)
−
(
r
t
−
I
E
t
π
t
+
1
)
+
I
E
t
x
t
+
1
+
(
1
−
ω
)
(
1
−
ρ
a
)
a
t
MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBaaaleaacaWG0baabeaakiabg2da9iaabccacaGGOaGaamOCaiabgkHiTiabec8aWjaacMcacqGHsislcaGGOaGaamOCamaaBaaaleaacaWG0baabeaakiabgkHiTiaadMeacaWGfbWaaSbaaSqaaiaadshaaeqaaOGaeqiWda3aaSbaaSqaaiaadshacqGHRaWkcaaIXaaabeaakiaacMcacqGHRaWkcaWGjbGaamyramaaBaaaleaacaWG0baabeaakiaadIhadaWgaaWcbaGaamiDaiabgUcaRiaaigdaaeqaaOGaey4kaSIaaiikaiaaigdacqGHsislcqaHjpWDcaGGPaGaaiikaiaaigdacqGHsislcqaHbpGCdaWgaaWcbaGaamyyaaqabaGccaGGPaGaamyyamaaBaaaleaacaWG0baabeaaaaa@6076@
Equation (22)
π
t
=
π
+
β
(
I
E
t
π
t
+1
−
π
)
+
ψ
x
t
−
e
t
MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWda3aaS baaSqaaGqaciaa=rhaaeqaaOGaaeiiaiaab2dacaqGGaGaeqiWdaNa aeiiaiaabUcacqaHYoGycaaMc8UaaiikaiaadMeacaWGfbWaaSbaaS qaaiaa=rhaaeqaaOGaeqiWda3aaSbaaSqaaiaa=rhacaqGRaGaaeym aaqabaGccqGHsislcqaHapaCcaGGPaGaey4kaSIaeqiYdKNaamiEam aaBaaaleaacaWG0baabeaakiabgkHiTiaadwgadaWgaaWcbaGaamiD aaqabaaaaa@5411@
Equation (23)
r
t
=
r
+
ρ
r
(
r
t
−
1
−
r
)
+
ρ
π
(
π
t
−
π
)
+
ρ
g
(
g
t
−
g
)
+
ρ
x
x
t
+
ε
r
,
t
MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaBa aaleaacaWG0baabeaakiabg2da9iaabccacaWGYbGaey4kaSIaeqyW di3aaSbaaSqaaiaadkhaaeqaaOWaaeWaaeaacaWGYbWaaSbaaSqaai aadshacqGHsislcaaIXaaabeaakiabgkHiTiaadkhaaiaawIcacaGL PaaacqGHRaWkcqaHbpGCdaWgaaWcbaGaeqiWdahabeaakmaabmaaba GaeqiWda3aaSbaaSqaaiaadshaaeqaaOGaeyOeI0IaeqiWdahacaGL OaGaayzkaaGaey4kaSIaeqyWdi3aaSbaaSqaaiaadEgaaeqaaOWaae WaaeaacaWGNbWaaSbaaSqaaiaadshaaeqaaOGaeyOeI0Iaam4zaaGa ayjkaiaawMcaaiabgUcaRiabeg8aYnaaBaaaleaacaWG4baabeaaki aadIhadaWgaaWcbaGaamiDaaqabaGccqGHRaWkcqaH1oqzdaWgaaWc baGaamOCaiaacYcacaWG0baabeaaaaa@6611@
Equation (24)
x
t
=
y
^
t
−
ω
a
t
MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBaaaleaacaWG0baabeaakiabg2da9iaabccaceWG5bGbaKaadaWgaaWcbaGaamiDaaqabaGccqGHsislcqaHjpWDcaWGHbWaaSbaaSqaaiaadshaaeqaaaaa@40CB@
Equation (25)
g
t
=
g
+
y
^
t
−
y
^
t
−
1
+
ε
z
,
t
MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaaBaaaleaacaWG0baabeaakiabg2da9iaadEgacqGHRaWkcaqGGaGabmyEayaajaWaaSbaaSqaaiaadshaaeqaaOGaeyOeI0IabmyEayaajaWaaSbaaSqaaiaadshaaeqaaOWaaSbaaSqaaiabgkHiTiaaigdaaeqaaOGaey4kaSIaeqyTdu2aaSbaaSqaaiaadQhaaeqaaOWaaSbaaSqaaiaacYcaaeqaaOWaaSbaaSqaaiaadshaaeqaaaaa@4894@